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					        Importance-Driven
        Focus of Attention

Ivan Viola1,3, Miquel Feixas2, Mateu Sbert2
      and Meister Eduard Gröller1
        1   Vienna University of Technology, Austria
                    2   University of Girona, Spain
                3   University of Bergen, Norway
Goal

    Input: known and classified volumetric data
    High level request: show me object X
    Output: guided navigation to object X




Ivan Viola                1
Focusing Considerations

    Characteristic view
    Emphasis of focus object
    Guided navigation between characteristic
    views




Ivan Viola               2
Framework
                                                                                                             object-space distance weight                          visibility estimation
                                                                                                                                                                                v2                                         image-space weight
                                        object-space distance weight                                                    visibility estimation
                                                                                                                                            v                                                           v3
                                                                                                                                     v2                               1
                                                                                                                                                                                                                     image-space weight




                                                                       characteristic viewpoint estimation
                                                                                                                                   o2                                                        o2
                                                                                                                        o1
                                                                                                                              v1                                          v3
                                                                                                                                                                           o   1
                                                                                                                              o3                                                            o3
  characteristic viewpoint estimation



                                                                                                                                              v
                                                        o2                                                                                                  o2
                                                 o1                                                                                         o1
                                                       o3                                                                                        3      o
                                                                                                                                   information-theoretic framework for optimal viewpoint estimation
                                                                   v                                                                    p(v1)     p(o1|v1) ...




                                                                                                                                        ...


                                                                                                                                                  ...
                                                                                                                                                                           m

                                                                                                                                                                          Σ p(o |v ) log
                                                                                                                                                                                                        p(oj|vi)
                                                                                                                                                            I(vi,O) =                   j    i
                                                                                                                                                                                                         p(oj)
                                                                                                                                                                           j




                                                                                                                                                                                                                     ...
                                                                                                                                    p(vn)                                                                      ...   p(om|vn)

                                                            information-theoretic framework for optimal viewpoint estimation
                                                                                                                  p(o )                            p(o1)     ...                                                               m




                                                             p(v1)     p(o1|v1) ...
                                                             ...


                                                                       ...




                                                                                                                                                                   importance distribution

                                                                                                                                m                                                                                      up-vector information

                                                                                                                                   Σ
                                                                                                               object selection by user                    p(oj|vi)
                                                                                                               I(vi,O) =                      p(oj|vi) log p(oj)                                                                          o2
                                                                                                                             o2         j
                                                                                                                                                                      o1           o2            o3                                o1
                                                                                                                   o1




                                                                                                                                                                                                             ...
                                                                                                                         o3                                                                                                              o3
                                                                       interactive focus of attention




                                                             p(vn)                                                                                                                                ...        p(om|vn)
                                                                               p(o1)                             ...                                                                                          p(om)
                                                                                                                                                                                                                               viewpoint transformation

                                                                                                                                                        cut-away and level of ghosting

                                                                                                               focus discrimination
                                                                                                                                                                                                                           v
                                                                                                                          o                                                         o2
                                                                                                                        importance distribution
                                                                                                                              2

                                                                                                                                          o                                1                                                        o1        o2
                                                                                                                   o1                                                              o3
                                                                                                                         o3                                                                                                              o3
                                                                                                                                                                                                  v
                                                                                                                                                                                                               up-vector information
                                          object selection by user
Ivan Viola                                                                                                                                                                         3
                                                                                                                                                                                                                                               o2
Characteristic Views
                                                                                            object-space distance weight                        visibility estimation
                                                                                                                                                             v2                                        image-space weight
                                                                                                                                                  v1                                v3




                                                      characteristic viewpoint estimation
                                                                                                                  o2                                                       o2
                                                                                                       o1                                                   o1
                                                                                                              o3                                                          o3
                                                                                                                             v




    Overview                                                                                                       information-theoretic framework for optimal viewpoint estimation

                                                                                                                       p(v1)     p(o1|v1) ...




                                                                                                                       ...


                                                                                                                                 ...
                                                                                                                                                        m

                                                                                                                                                       Σ p(o |v ) log
                                                                                                                                                                                    p(oj|vi)
                                                                                                                                         I(vi,O) =                    j    i
                                                                                                                                                                                     p(oj)
                                                                                                                                                        j




                                                                                                                                                                                                 ...
                                                                                                                    p(vn)                                                                  ...   p(om|vn)
                                                                                                                                  p(o1)   ...                                                     p(om)




             All objects are visible
                                                                                                                                                importance distribution

                                                                                                                                                                                                   up-vector information
                                                                                              object selection by user

                                                                                                            o2                                                                                                        o2
                                                                                                                                                   o1            o2            o3                              o1
                                                                                                  o1                                                                                                                 o3
                                                                                                        o3




                                                      interactive focus of attention
                                                                                                                                                                                                           viewpoint transformation




             Visibility of objects is balanced
                                                                                                                                       cut-away and level of ghosting

                                                                                              focus discrimination
                                                                                                                                                                                                       v
                                                                                                             o2                                                   o2
                                                                                                                                                     o1                                                         o1        o2
                                                                                                  o1                                                             o3
                                                                                                        o3                                                                                                           o3
                                                                                                                                                                                v




    Characteristic view of focus object
             High visibility for focus object
             If possible other objects also visible




Ivan Viola                         4
Characteristic View Estimation
                                        object-space distance weight                visibility estimation
                                                                                                       v2                                image-space weight
                                                                                        v1                            v3
  characteristic viewpoint estimation



                                                         o2                                                 o2
                                                  o1                                              o1
                                                       o3                                                  o3
                                                                  v


                                                                                                                                                         view rating
                                                            information-theoretic framework for optimal viewpoint estimation

                                                              p(v 1)   p(o 1|v 1) ...

                                                              ...      ...                   m
                                                                              I(vi,O) =      ∑ p(o |v )
                                                                                              j
                                                                                                       j    i   log
                                                                                                                      p(o j|vi)
                                                                                                                       p(o j)


                                                              p(v n)                                                                   ...
                                                                                                                                  ... p(o m|vn)

                                                                        p(o 1)    ...                                                 p(o m)




                                                                                    importance distribution
                            characteristic viewpoint estimation
                                                                                                                                       up-vector information
                                          object selection by user
Ivan Viola                                                                                                                 5
                                                                                                                                                    o2
View rating
                                                                                           object-space distance weight                        visibility estimation
                                                                                                                                                            v2                                        image-space weight
                                                                                                                                                 v1                                v3




                                                     characteristic viewpoint estimation
                                                                                                                 o2                                                       o2
                                                                                                      o1                                                   o1




    For every view
                                                                                                             o3                                                          o3
                                                                                                                            v




                                                                                                                  information-theoretic framework for optimal viewpoint estimation

                                                                                                                      p(v1)     p(o1|v1) ...




                                                                                                                      ...


                                                                                                                                ...
                                                                                                                                                       m

                                                                                                                                                      Σ p(o |v ) log
                                                                                                                                                                                   p(oj|vi)
                                                                                                                                        I(vi,O) =                    j    i
                                                                                                                                                                                    p(oj)
                                                                                                                                                       j




                                                                                                                                                                                                ...
                                                                                                                   p(vn)                                                                  ...   p(om|vn)




             For every object
                                                                                                                                 p(o1)   ...                                                     p(om)




                                                                                                                                               importance distribution

                                                                                                                                                                                                  up-vector information
                                                                                             object selection by user

                                                                                                           o2                                                                                                        o2
                                                                                                                                                  o1            o2            o3                              o1
                                                                                                 o1                                                                                                                 o3
                                                                                                       o3




                                                     interactive focus of attention
                                                                                                                                                                                                          viewpoint transformation

                                                                                                                                      cut-away and level of ghosting




                             v2
                                                                                             focus discrimination
                                                                                                                                                                                                      v
                                                                                                            o2                                                   o2
                                                                                                                                                    o1                                                         o1        o2
                                                                                                 o1                                                             o3
                                                                                                       o3                                                                                                           o3
                                                                                                                                                                               v




                   v1                      v3


                                  o2
              v8        o1                      v4
                              o3

                   v7                      v5
                             v6
Ivan Viola                             6
View Rating
                                                                                object-space distance weight                        visibility estimation
                                                                                                                                                 v2                                        image-space weight
                                                                                                                                      v1                                v3




                                          characteristic viewpoint estimation
                                                                                                      o2                                                       o2
                                                                                           o1                                                   o1




    Visibility
                                                                                                  o3                                                          o3
                                                                                                                 v




                                                                                                       information-theoretic framework for optimal viewpoint estimation

                                                                                                           p(v1)     p(o1|v1) ...




                                                                                                           ...


                                                                                                                     ...
                                                                                                                                            m

                                                                                                                                           Σ p(o |v ) log
                                                                                                                                                                        p(oj|vi)
                                                                                                                             I(vi,O) =                    j    i
                                                                                                                                                                         p(oj)
                                                                                                                                            j




                                                                                                                                                                                     ...
                                                                                                        p(vn)                                                                  ...   p(om|vn)




             High
                                                                                                                      p(o1)   ...                                                     p(om)




                                                                                                                                    importance distribution

                                                                                                                                                                                       up-vector information
                                                                                  object selection by user

                                                                                                o2                                                                                                        o2
                                                                                                                                       o1            o2            o3                              o1
                                                                                      o1                                                                                                                 o3
                                                                                            o3




                                          interactive focus of attention
             Low                                                                  focus discrimination



                                                                                      o1
                                                                                            o3
                                                                                                 o2
                                                                                                                           cut-away and level of ghosting




                                                                                                                                         o1
                                                                                                                                                      o2

                                                                                                                                                     o3
                                                                                                                                                                                           v
                                                                                                                                                                                               viewpoint transformation




                                                                                                                                                                                                    o1
                                                                                                                                                                                                         o3
                                                                                                                                                                                                              o2


                                                                                                                                                                    v




    Location in image
             In image center
             Outside center
    Distance to the viewer
             Object close to the viewer
             Far from the viewer

Ivan Viola                       7
  Visibility Computation
                                                                                                   object-space distance weight                        visibility estimation
                                                                                                                                                                    v2                                        image-space weight
                                                                                                                                                         v1                                v3




                                                             characteristic viewpoint estimation
                                                                                                                         o2                                                       o2
                                                                                                              o1                                                   o1
                                                                                                                     o3                                                          o3




 o0 = object 0
                                                                                                                                    v




                                                                                                                          information-theoretic framework for optimal viewpoint estimation

                                                                                                                              p(v1)     p(o1|v1) ...




                                                                                                                              ...


                                                                                                                                        ...
                                                                                                                                                               m




 o1 = object 1
                                                                                                                                                              Σ p(o |v ) log
                                                                                                                                                                                           p(oj|vi)
                                                                                                                                                I(vi,O) =                    j    i
                                                                                                                                                                                            p(oj)
                                                                                                                                                               j




                                                                                                                                                                                                        ...
                                                                                                                           p(vn)                                                                  ...   p(om|vn)
                                                                                                                                         p(o1)   ...                                                     p(om)




 r = ray
                                                                                                                                                       importance distribution

                                                                                                                                                                                                          up-vector information
                                                                                                     object selection by user




                                         α(o1,r1)
                                                                                                                   o2                                                                                                        o2
                                                                                                                                                          o1            o2            o3                              o1
                                                                                                         o1                                                                                                                 o3
                                                                                                               o3




                                                             interactive focus of attention
 r0 = sub-ray 0                                                                                      focus discrimination

                                                                                                                    o2
                                                                                                                                              cut-away and level of ghosting



                                                                                                                                                                         o2
                                                                                                                                                                                                              v
                                                                                                                                                                                                                  viewpoint transformation




                                                                                                                                                                                                                                 o2
                                                                                                                                                            o1                                                         o1




 r1 = sub-ray 1
                                                                                                         o1                                                             o3
                                                                                                               o3                                                                                                           o3
                                                                                                                                                                                       v




 r2 = sub-ray 2
                     αr
  v(o1 , r )  (1   (o0 , r0 )) . (o1 , r1 )
  v(o0 , r )   (o0 , r0 )
                                       α(o0,r2)
                (1  ( (o0 , r0,r  v(o1 , r ))) . (o0 , r2 )
                            α(o ) )
                                0   0


Ivan Viola                          8
Visibility Computation
                                                                            object-space distance weight                        visibility estimation
                                                                                                                                             v2                                        image-space weight
                                                                                                                                  v1                                v3




                                      characteristic viewpoint estimation
                                                                                                  o2                                                       o2
                                                                                       o1                                                   o1
                                                                                              o3                                                          o3
                                                                                                             v




                                                                                                   information-theoretic framework for optimal viewpoint estimation

                                                                                                       p(v1)     p(o1|v1) ...




                                                                                                       ...


                                                                                                                 ...
                                                                                                                                        m

                                                                                                                                       Σ p(o |v ) log
                                                                                                                                                                    p(oj|vi)
                                                                                                                         I(vi,O) =                    j    i
                                                                                                                                                                     p(oj)
                                                                                                                                        j




                                                                                                                                                                                 ...
                                                                                                    p(vn)                                                                  ...   p(om|vn)
                                                                                                                  p(o1)   ...                                                     p(om)




                                                                                                                                importance distribution

                                                                                                                                                                                   up-vector information
                                                                              object selection by user

                                                                                            o2                                                                                                        o2
                                                                                                                                   o1            o2            o3                              o1
                                                                                  o1                                                                                                                 o3
                                                                                        o3




                                      interactive focus of attention
                                                                                                                                                                                           viewpoint transformation

                                                                                                                       cut-away and level of ghosting

                                                                              focus discrimination
                                                                                                                                                                                       v
                                                                                             o2                                                   o2
                                                                                                                                     o1                                                         o1        o2
                                                                                  o1                                                             o3
                                                                                        o3                                                                                                           o3
                                                                                                                                                                v




             v(o1 )   v(o1 , rx )
                       x


Ivan Viola                 9
  View Rating Weights
                                                                                             object-space distance weight                        visibility estimation
                                                                                                                                                              v2                                        image-space weight
                                                                                                                                                   v1                                v3




                                                       characteristic viewpoint estimation
                                                                                                                   o2                                                       o2
                                                                                                        o1                                                   o1
                                                                                                               o3                                                          o3
                                                                                                                              v




                                                                                                                    information-theoretic framework for optimal viewpoint estimation

                                                                                                                        p(v1)     p(o1|v1) ...




                                                                                                                        ...


                                                                                                                                  ...
                                                                                                                                                         m

                                                                                                                                                        Σ p(o |v ) log
                                                                                                                                                                                     p(oj|vi)
                                                                                                                                          I(vi,O) =                    j    i
                                                                                                                                                                                      p(oj)
                                                                                                                                                         j




                                                                                                                                                                                                  ...
                                                                                                                     p(vn)                                                                  ...   p(om|vn)
                                                                                                                                   p(o1)   ...                                                     p(om)




                        object-space distance weight                                           object selection by user
                                                                                                                                                 importance distribution

                                                                                                                                                                                                    up-vector information


                                                                                                             o2                                                                                                        o2
                                                                                                                                                    o1            o2            o3                              o1
                                                                                                   o1                                                                                                                 o3
                                                                                                         o3




                                                       interactive focus of attention
                                                                                                                                                                                                            viewpoint transformation

                                                                                                                                        cut-away and level of ghosting

                                                                                               focus discrimination
                                                                                                                                                                                                        v
                                                                                                              o2                                                   o2
                                                                                                                                                      o1                                                         o1        o2
                                                                                                   o1                                                             o3
                                                                                                         o3                                                                                                           o3
                                                                                                                                                                                 v




                             image-space weight




Ivan Viola              10
Characteristic Viewpoint Estimation
                                        object-space distance weight                visibility estimation
                                                                                                       v2                                image-space weight
                                                                                        v1                            v3
  characteristic viewpoint estimation



                                                         o2                                                 o2
                                                  o1                                              o1
                                                       o3                                                  o3
                                                                  v


                                                                                                                                                         view rating
                                                            information-theoretic framework for optimal viewpoint estimation

                                                              p(v 1)   p(o 1|v 1) ...

                                                              ...      ...                   m
                                                                              I(vi,O) =      ∑ p(o |v )
                                                                                              j
                                                                                                       j    i   log
                                                                                                                      p(o j|vi)
                                                                                                                       p(o j)


                                                              p(v n)                                                                   ...
                                                                                                                                  ... p(o m|vn)

                                                                        p(o 1)    ...                                                 p(o m)


                                                                                                                                        characteristic views
                                                                                    importance distribution
                            characteristic viewpoint estimation
                                                                                                                                       up-vector information
                                          object selection by user
Ivan Viola                                                                                                                 11
                                                                                                                                                    o2
Characteristic Views
                                                                                             object-space distance weight                        visibility estimation
                                                                                                                                                              v2                                        image-space weight
                                                                                                                                                   v1                                v3




                                                       characteristic viewpoint estimation
                                                                                                                   o2                                                       o2
                                                                                                        o1                                                   o1
                                                                                                               o3                                                          o3
                                                                                                                              v




    Overview                                                                                                        information-theoretic framework for optimal viewpoint estimation

                                                                                                                        p(v1)     p(o1|v1) ...




                                                                                                                        ...


                                                                                                                                  ...
                                                                                                                                                         m

                                                                                                                                                        Σ p(o |v ) log
                                                                                                                                                                                     p(oj|vi)
                                                                                                                                          I(vi,O) =                    j    i
                                                                                                                                                                                      p(oj)
                                                                                                                                                         j




                                                                                                                                                                                                  ...
                                                                                                                     p(vn)                                                                  ...   p(om|vn)
                                                                                                                                   p(o1)   ...                                                     p(om)




             All objects are visible
                                                                                                                                                 importance distribution

                                                                                                                                                                                                    up-vector information
                                                                                               object selection by user

                                                                                                             o2                                                                                                        o2
                                                                                                                                                    o1            o2            o3                              o1
                                                                                                   o1                                                                                                                 o3
                                                                                                         o3




                                                       interactive focus of attention
                                                                                                                                                                                                            viewpoint transformation




             Visibility of objects is balanced
                                                                                                                                        cut-away and level of ghosting

                                                                                               focus discrimination
                                                                                                                                                                                                        v
                                                                                                              o2                                                   o2
                                                                                                                                                      o1                                                         o1        o2
                                                                                                   o1                                                             o3
                                                                                                         o3                                                                                                           o3
                                                                                                                                                                                 v




    Characteristic view of focus object
             High view rating (visibility) for focus object
             If possible other objects also visible




Ivan Viola                         12
Obtaining Characteristic Views
                                                                                      object-space distance weight                        visibility estimation
                                                                                                                                                       v2                                        image-space weight
                                                                                                                                            v1                                v3




                                                characteristic viewpoint estimation
                                                                                                            o2                                                       o2
                                                                                                 o1                                                   o1
                                                                                                        o3                                                          o3
                                                                                                                       v




    Sets of views and objects are random                                                                     information-theoretic framework for optimal viewpoint estimation

                                                                                                                 p(v1)     p(o1|v1) ...




                                                                                                                 ...


                                                                                                                           ...
                                                                                                                                                  m

                                                                                                                                                 Σ p(o |v ) log
                                                                                                                                                                              p(oj|vi)
                                                                                                                                   I(vi,O) =                    j    i
                                                                                                                                                                               p(oj)
                                                                                                                                                  j




                                                                                                                                                                                           ...
                                                                                                              p(vn)                                                                  ...   p(om|vn)




    variables
                                                                                                                            p(o1)   ...                                                     p(om)




                                                                                                                                          importance distribution

                                                                                                                                                                                             up-vector information
                                                                                        object selection by user

                                                                                                      o2                                                                                                        o2
                                                                                                                                             o1            o2            o3                              o1
                                                                                            o1                                                                                                                 o3
                                                                                                  o3




                                                interactive focus of attention
             Views V=(v1, v2, v3, ... , vn)                                             focus discrimination



                                                                                            o1
                                                                                                  o3
                                                                                                       o2
                                                                                                                                 cut-away and level of ghosting




                                                                                                                                               o1
                                                                                                                                                            o2

                                                                                                                                                           o3

                                                                                                                                                                          v
                                                                                                                                                                                                 v
                                                                                                                                                                                                     viewpoint transformation




                                                                                                                                                                                                          o1
                                                                                                                                                                                                               o3
                                                                                                                                                                                                                    o2




             Objects O=(o1, o2, o3, ... , om)
    View rating (visibility, weights)
             Information channel between V→O
             Conditional probability p(oj|vi)
    Mutual information between V and O
    expresses degree of dependance

Ivan Viola                        13
Obtaining Characteristic Views
                                                                                     object-space distance weight                        visibility estimation
                                                                                                                                                      v2                                        image-space weight
                                                                                                                                           v1                                v3




                                               characteristic viewpoint estimation
                                                                                                           o2                                                       o2
                                                                                                o1                                                   o1
                                                                                                       o3                                                          o3
                                                                                                                      v




    Viewpoint mutual information is dependance                                                              information-theoretic framework for optimal viewpoint estimation

                                                                                                                p(v1)     p(o1|v1) ...




                                                                                                                ...


                                                                                                                          ...
                                                                                                                                                 m

                                                                                                                                                Σ p(o |v ) log
                                                                                                                                                                             p(oj|vi)
                                                                                                                                  I(vi,O) =                    j    i
                                                                                                                                                                              p(oj)
                                                                                                                                                 j




                                                                                                                                                                                          ...
                                                                                                             p(vn)                                                                  ...   p(om|vn)




    between vi and O
                                                                                                                           p(o1)   ...                                                     p(om)




                                                                                                                                         importance distribution

                                                                                                                                                                                            up-vector information
                                                                                       object selection by user

                                                                                                     o2                                                                                                        o2
                                                                                                                                            o1            o2            o3                              o1
                                                                                           o1                                                                                                                 o3
                                                                                                 o3




                                               interactive focus of attention
             High values = high dependance                                             focus discrimination



                                                                                           o1
                                                                                                 o3
                                                                                                      o2
                                                                                                                                cut-away and level of ghosting




                                                                                                                                              o1
                                                                                                                                                           o2

                                                                                                                                                          o3

                                                                                                                                                                         v
                                                                                                                                                                                                v
                                                                                                                                                                                                    viewpoint transformation




                                                                                                                                                                                                         o1
                                                                                                                                                                                                              o3
                                                                                                                                                                                                                   o2




               Small number of objects
               Low average visibility
             Low values = low dependance
               Maximum objects visible
               Object visibility is balanced
    Minimal VMI determines the best view

Ivan Viola                        14
Probability Transition Matrix
                                                                                                               object-space distance weight                        visibility estimation
                                                                                                                                                                                v2                                        image-space weight
                                                                                                                                                                     v1                                v3




                                                                         characteristic viewpoint estimation
                                                                                                                                     o2                                                       o2
                                                                                                                          o1                                                   o1
                                                                                                                                 o3                                                          o3
                                                                                                                                                v




                                                                                                                                      information-theoretic framework for optimal viewpoint estimation

                                                                                                                                          p(v1)     p(o1|v1) ...




                                                                                                                                          ...


                                                                                                                                                    ...
                                                                                                                                                                           m

                                                                                                                                                                          Σ p(o |v ) log
                                                                                                                                                                                                       p(oj|vi)
                                                                                                                                                            I(vi,O) =                    j    i
                                                                                                                                                                                                        p(oj)
                                                                                                                                                                           j




                                                                                                                                                                                                                    ...
                                                                                                                                       p(vn)                                                                  ...   p(om|vn)
                                                                                                                                                     p(o1)   ...                                                     p(om)




                                                                                                                                                                   importance distribution

                                                                                                                                                                                                                      up-vector information
                                                                                                                 object selection by user

                                                                                                                               o2                                                                                                        o2




                   view rating of object
             probability of the viewpoint oj from viewpoint vi
                                                                                                                                                                      o1            o2            o3                              o1
                                                                                                                     o1                                                                                                                 o3
                                                                                                                           o3




                                                                         interactive focus of attention
                                                                                                                                                                                                                              viewpoint transformation

                                                                                                                                                          cut-away and level of ghosting

                                                                                                                 focus discrimination
                                                                                                                                                                                                                          v
                                                                                                                                o2                                                   o2
                                                                                                                                                                        o1                                                         o1        o2
                                                                                                                     o1                                                             o3
                                                                                                                           o3                                                                                                           o3
                                                                                                                                                                                                   v




              p(v1)   p(o1|v1) p(o2|v1)     ...              p(om|v1)

              p(v2)   p(o1|v2)
              p(v3)
                       ...
              ...




                                                               ...
                                 marginal probability of the object

              p(vn)   p(o1|vn)                         ...    p(om|vn)

                       p(o1)       p(o2)    p(o3)      ...     p(om)


Ivan Viola                                        15
Viewpoint Mutual Information
                                                                                                                       object-space distance weight                        visibility estimation
                                                                                                                                                                                        v2                                        image-space weight
                                                                                                                                                                             v1                                v3




                                                                                 characteristic viewpoint estimation
    Degree of correlation vj↔O
                                                                                                                                             o2                                                       o2
                                                                                                                                  o1                                                   o1
                                                                                                                                         o3                                                          o3
                                                                                                                                                        v




                                                                                                                                              information-theoretic framework for optimal viewpoint estimation

                                                                                                                                                  p(v1)     p(o1|v1) ...




                                                                                                                                                  ...


                                                                                                                                                            ...
                                                                                                                                                                                   m

                                                                                                                                                                                  Σ p(o |v ) log
                                                                                                                                                                                                               p(oj|vi)
                                                                                                                                                                    I(vi,O) =                    j    i
                                                                                                                                                                                                                p(oj)
                                                                                                                                                                                   j




                                                                                                                                                                                                                            ...
                                                                                                                                               p(vn)                                                                  ...   p(om|vn)
                                                                                                                                                             p(o1)   ...                                                     p(om)




                                                                                                                                                                           importance distribution

                                                                                                                                                                                                                              up-vector information
                                                                                                                         object selection by user

                                                                                                                                       o2                                                                                                        o2
                                                                                                                                                                              o1            o2            o3                              o1
                                                                                                                             o1                                                                                                                 o3
                                                                                                                                   o3




                                                                                 interactive focus of attention
                                                                  p(o j | vi )
       I (vi , O)   p(o j | vi ) log
                                                                                                                                                                                                                                      viewpoint transformation

                                                                                                                                                                  cut-away and level of ghosting

                                                                                                                         focus discrimination
                                                                                                                                                                                                                                  v
                                                                                                                                        o2                                                   o2
                                                                                                                                                                                o1                                                         o1        o2
                                                                                                                             o1                                                             o3
                                                                                                                                   o3                                                                                                           o3
                                                                                                                                                                                                           v




                                j                                     p (o j )

             p(v1)   p(o1|v1)       p(o2|v1)   ...                p(om|v1)

             p(v2)   p(o1|v2)
                        ...




             p(v3)
               ...




             p(vn)   p(o1|vn)                               ...       ...
                                                                  p(om|vn)

                      p(o1)          p(o2)     p(o3)        ...    p(om)

Ivan Viola                                             16
Characteristic Views
                                                                                            object-space distance weight                        visibility estimation
                                                                                                                                                             v2                                        image-space weight
                                                                                                                                                  v1                                v3




                                                      characteristic viewpoint estimation
                                                                                                                  o2                                                       o2
                                                                                                       o1                                                   o1
                                                                                                              o3                                                          o3
                                                                                                                             v




    Overview                                                                                                       information-theoretic framework for optimal viewpoint estimation

                                                                                                                       p(v1)     p(o1|v1) ...




                                                                                                                       ...


                                                                                                                                 ...
                                                                                                                                                        m

                                                                                                                                                       Σ p(o |v ) log
                                                                                                                                                                                    p(oj|vi)
                                                                                                                                         I(vi,O) =                    j    i
                                                                                                                                                                                     p(oj)
                                                                                                                                                        j




                                                                                                                                                                                                 ...
                                                                                                                    p(vn)                                                                  ...   p(om|vn)
                                                                                                                                  p(o1)   ...                                                     p(om)




             All objects are visible
                                                                                                                                                importance distribution

                                                                                                                                                                                                   up-vector information
                                                                                              object selection by user

                                                                                                            o2                                                                                                        o2
                                                                                                                                                   o1            o2            o3                              o1
                                                                                                  o1                                                                                                                 o3
                                                                                                        o3




                                                      interactive focus of attention
                                                                                                                                                                                                           viewpoint transformation




             Visibility of objects is balanced
                                                                                                                                       cut-away and level of ghosting

                                                                                              focus discrimination
                                                                                                                                                                                                       v
                                                                                                             o2                                                   o2
                                                                                                                                                     o1                                                         o1        o2
                                                                                                  o1                                                             o3
                                                                                                        o3                                                                                                           o3
                                                                                                                                                                                v




    Characteristic view at focus object
             High view rating for focus object
             If possible other objects also visible




Ivan Viola                        17
Incorporating Importance
                                                                                          object-space distance weight                        visibility estimation
                                                                                                                                                           v2                                        image-space weight
                                                                                                                                                v1                                v3




                                                    characteristic viewpoint estimation
                                                                                                                o2                                                       o2
                                                                                                     o1                                                   o1
                                                                                                            o3                                                          o3
                                                                                                                           v




  importance distribution                                                                                        information-theoretic framework for optimal viewpoint estimation

                                                                                                                     p(v1)     p(o1|v1) ...




                                                                                                                     ...


                                                                                                                               ...
                                                                                                                                                      m

                                                                                                                                                     Σ p(o |v ) log
                                                                                                                                                                                  p(oj|vi)
                                                                                                                                       I(vi,O) =                    j    i
                                                                                                                                                                                   p(oj)
                                                                                                                                                      j




                                                                                                                                                                                               ...
                                                                                                                  p(vn)                                                                  ...   p(om|vn)
                                                                                                                                p(o1)   ...                                                     p(om)




                                                                                                                                              importance distribution

                                                                                                                                                                                                 up-vector information
                                                                                            object selection by user

                                                                                                          o2                                                                                                        o2
                                                                                                                                                 o1            o2            o3                              o1
                                                                                                o1                                                                                                                 o3
                                                                                                      o3




                                                    interactive focus of attention
                                                                                                                                                                                                         viewpoint transformation

                                                                                                                                     cut-away and level of ghosting

                                                                                            focus discrimination
                                                                                                                                                                                                     v
                                                                                                           o2                                                   o2
                                                                                                                                                   o1                                                         o1        o2
                                                                                                o1                                                             o3
                                                                                                      o3                                                                                                           o3
                                                                                                                                                                              v




             o1 o2 o3


                                      p(op(oij)| vi )
                                           j |v
      I (vi , O)   p(o j | vi ) log
                   j
                                        p (o )
                                       p(o jj ) im (o j )
                                       p(ok )im(ok )
                                       k


Ivan Viola                     18
Resulting Characteristic Viewpoints
                                                                            object-space distance weight                        visibility estimation
                                                                                                                                            v2                                         image-space weight
                                                                                                                                  v1                                v3




                                      characteristic viewpoint estimation
                                                                                                  o2                                                       o2
                                                                                       o1                                                   o1
                                                                                              o3                                                          o3
                                                                                                             v




                                                                                                   information-theoretic framework for optimal viewpoint estimation

                                                                                                       p(v1)     p(o1|v1) ...




                                                                                                       ...


                                                                                                                 ...
                                                                                                                                       m

                                                                                                                                       Σ p(o |v ) log
                                                                                                                                                                    p(oj|vi)
                                                                                                                         I(vi,O) =                    j    i
                                                                                                                                                                     p(oj)
                                                                                                                                        j




                                                                                                                                                                                 ...
                                                                                                    p(vn)                                                                  ...   p(om|vn)
                                                                                                                  p(o1)   ...                                                     p(om)




                                                                                                                                importance distribution

                                                                                                                                                                                   up-vector information
                                                                              object selection by user

                                                                                            o2                                                                                                        o2
                                                                                                                                  o1             o2            o3                              o1
                                                                                  o1                                                                                                                 o3
                                                                                        o3




                                      interactive focus of attention
                                                                                                                                                                                           viewpoint transformation

                                                                                                                       cut-away and level of ghosting

                                                                              focus discrimination
                                                                                                                                                                                       v
                                                                                             o2                                                   o2
                                                                                                                                     o1                                                         o1        o2
                                                                                  o1                                                             o3
                                                                                        o3                                                                                                           o3
                                                                                                                                                                v




Ivan Viola           19
   characteristic viewpoint estimation characteri
Interactive Focus of Attention
                                                                                                                                                                                                                                  object-space distance weight                        visibility estimation
                                                                                                                                                                                                                                                                                                   v2                                        image-space weight
                                                                                                                                                                                                                                                                                        v1                                v3




                                                                                                                                                                                            characteristic viewpoint estimation
                                                                                                                                                                                                                                                        o2                                                       o2
                                                                                                                                                                                                                                             o1                                                   o1
                                                                                                                                                                                                                                                    o3                                                          o3
                                                                                                                                                                                                                                                                   v



                                                    object-space distance weight                    visibility estimation
                                                                                                   importance 2 vdistribution                                 image-space weight                                                                         information-theoretic framework for optimal viewpoint estimation

                                                                                                                                                                                                                                                             p(v1)     p(o1|v1) ...




                                                                                                                                                                                                                                                             ...


                                                                                                                                                                                                                                                                       ...
                                          characteristic viewpoint estimation
                                                                                                                                                                                                                                                                                              m

                                                                                                                                                                                                                                                                                             Σ p(o |v ) log
                                                                                                                                                                                                                                                                                                                          p(oj|vi)
                                                                                                                                                                                                                                                                               I(vi,O) =                    j    i




                                                                                                      v1                 v3                                                                                                                                                                   j
                                                                                                                                                                                                                                                                                                                           p(oj)




                                                                                                                                                                                                                                                                                                                                       ...
                                                                                                                                                                                                                                                          p(vn)                                                                  ...   p(om|vn)
                                                                                                                                                                                                                                                                        p(o1)   ...                                                     p(om)



                                                                                                                                                            up-vector information
                                                      object selection by user
                                                                     o2
                                                                                                                                                                                                                                                                                      importance distribution



                                                                                                                                 o2                                                                                                 object selection by user

                                                                                                                                                                                                                                                  o2
                                                                                                                                                                                                                                                                                                                                         up-vector information

                                                                                                                                                                                                                                                                                                                                                            o2
                                                                                                                                                                                                                                                                                         o1            o2            o3                              o1
                                                                                                                                                                                                                                        o1                                                                                                                 o3
                                                                                                                                                                                                                                              o3




                                                                                                                                                                                            interactive focus of attention
                                                               o1                                                 o1                                                        o2
                                                                    o2o3                                                        o3
                                                                                                         o1            o2            o3                              o1                                                                                                      cut-away and level of ghosting
                                                                                                                                                                                                                                                                                                                                                 viewpoint transformation




                                                         o1                                                                                                                o3
                                                                                                                                                                                                                                    focus discrimination
                                                                                                                                                                                                                                                                                                                                             v


                                                                                v
  interactive focus of attention




                                                                o3                                                                                                                                                                                 o2                                                   o2
                                                                                                                                                                                                                                                                                           o1                                                         o1        o2
                                                                                                                                                                                                                                        o1                                                             o3
                                                                                                                                                                                                                                              o3                                                                                                           o3
                                                                                                                                                                                                                                                                                                                      v




                                                                           information-theoretic framework for optimal viewpoint estimation

                                                                            p(v 1)   p(o 1|v1) ...                                                               viewpoint transformation

                                                                            ...      ... cut-away and level of ghosting
                                                                                                              m
                                                                                           I(v ,O) = ∑ p(o |v ) log
                                                                                                                    p(o |v )               j       i
                                                      focus discrimination                     i                            j    i
                                                                                                              j
                                                                                                                     p(o )                     j

                                                                                                                                                             v
                                                                     o2                                                 o2
                                                                            p(v n)
                                                                                                         o1
                                                                                                                                                            ...
                                                                                                                                                       ... p(o m|v n)
                                                                                                                                                                      o1        o2
                                                          o1                                                           o3
                                                                o3                    p(o 1)       ...                                                     p(o m)          o3
                                                                                                                                      v



                                                                                                   importance distribution
                                         characteristic viewpoint estimation
                                         interactive focus of attention
                                                                                                                                                            up-vector information
                                                      object selection by user
Ivan Viola                                                                                                                                20
                                                                                                                                                                            o2
         Emphasis of Focus Object
                                                                                             object-space distance weight                        visibility estimation
                                                                                                                                                             v2                                         image-space weight
                                                                                                                                                   v1                                v3




                                                       characteristic viewpoint estimation
                                                                                                                   o2                                                       o2
                                                                                                        o1                                                   o1
                                                                                                               o3                                                          o3
                                                                                                                              v




    Levels of sparseness                                                                                            information-theoretic framework for optimal viewpoint estimation

                                                                                                                        p(v1)     p(o1|v1) ...




                                                                                                                        ...


                                                                                                                                  ...
                                                                                                                                                        m

                                                                                                                                                        Σ p(o |v ) log
                                                                                                                                                                                     p(oj|vi)
                                                                                                                                          I(vi,O) =                    j    i
                                                                                                                                                                                      p(oj)
                                                                                                                                                         j




                                                                                                                                                                                                  ...
                                                                                                                     p(vn)                                                                  ...   p(om|vn)
                                                                                                                                   p(o1)   ...                                                     p(om)




                                                                                                                                                 importance distribution

                                                                                                                                                                                                    up-vector information
                                                                                               object selection by user

                                                                                                             o2                                                                                                        o2
                                                                                                                                                   o1             o2            o3                              o1
                                                                                                   o1




                       dense
                                                                                                         o3                                                                                                           o3




                                                       interactive focus of attention
                                                                                                                                                                                                            viewpoint transformation

                                                                                                                                        cut-away and level of ghosting

                                                                                               focus discrimination
                                                                                                                                                                                                        v
                                                                                                              o2                                                   o2
                                                                                                                                                      o1                                                         o1        o2
                                                                                                   o1                                                             o3
                                                                                                         o3                                                                                                           o3
                                                                                                                                                                                 v
  representation




                   0
Ivan Viola                     importance   21   max
    Emphasis of Focus Object
                                                                                  object-space distance weight                        visibility estimation
                                                                                                                                                   v2                                        image-space weight
                                                                                                                                        v1                                v3




                                            characteristic viewpoint estimation
                                                                                                        o2                                                       o2
                                                                                             o1                                                   o1
                                                                                                    o3                                                          o3
                                                                                                                   v




    Cut-aways to unveil internal features                                                                information-theoretic framework for optimal viewpoint estimation

                                                                                                             p(v1)     p(o1|v1) ...




                                                                                                             ...


                                                                                                                       ...
                                                                                                                                              m

                                                                                                                                             Σ p(o |v ) log
                                                                                                                                                                          p(oj|vi)
                                                                                                                               I(vi,O) =                    j    i
                                                                                                                                                                           p(oj)
                                                                                                                                              j




                                                                                                                                                                                       ...
                                                                                                          p(vn)                                                                  ...   p(om|vn)
                                                                                                                        p(o1)   ...                                                     p(om)




    Labeling to add textual information
                                                                                                                                      importance distribution

                                                                                                                                                                                         up-vector information
                                                                                    object selection by user

                                                                                                  o2                                                                                                        o2
                                                                                                                                         o1            o2            o3                              o1
                                                                                        o1                                                                                                                 o3
                                                                                              o3




                                            interactive focus of attention
                                                                                                                                                                                                 viewpoint transformation

                                                                                                                             cut-away and level of ghosting

                                                                                    focus discrimination
                                                                                                                                                                                             v
                                                                                                   o2                                                   o2
                                                                                                                                           o1                                                         o1        o2
                                                                                        o1                                                             o3
                                                                                              o3                                                                                                           o3
                                                                                                                                                                      v




                                                                                                                                                        vessels




             kidneys           intestine



Ivan Viola                22
Guided Navigation Between Objects
                                                                                        object-space distance weight                        visibility estimation
                                                                                                                                                         v2                                        image-space weight
                                                                                                                                              v1                                v3




                                                  characteristic viewpoint estimation
                                                                                                              o2                                                       o2
                                                                                                   o1                                                   o1
                                                                                                          o3                                                          o3
                                                                                                                         v




    Decreasing importance of Object X                                                                          information-theoretic framework for optimal viewpoint estimation

                                                                                                                   p(v1)     p(o1|v1) ...




                                                                                                                   ...


                                                                                                                             ...
                                                                                                                                                    m

                                                                                                                                                   Σ p(o |v ) log
                                                                                                                                                                                p(oj|vi)
                                                                                                                                     I(vi,O) =                    j    i
                                                                                                                                                                                 p(oj)
                                                                                                                                                    j




                                                                                                                                                                                             ...
                                                                                                                p(vn)                                                                  ...   p(om|vn)
                                                                                                                              p(o1)   ...                                                     p(om)




             De-emphasis of Object X
                                                                                                                                            importance distribution

                                                                                                                                                                                               up-vector information
                                                                                          object selection by user

                                                                                                        o2                                                                                                        o2
                                                                                                                                               o1            o2            o3                              o1
                                                                                              o1                                                                                                                 o3
                                                                                                    o3




                                                  interactive focus of attention
                                                                                                                                                                                                       viewpoint transformation




             Change to overview
                                                                                                                                   cut-away and level of ghosting

                                                                                          focus discrimination
                                                                                                                                                                                                   v
                                                                                                         o2                                                   o2
                                                                                                                                                 o1                                                         o1        o2
                                                                                              o1                                                             o3
                                                                                                    o3                                                                                                           o3
                                                                                                                                                                            v




    Increasing importance of Object Y
             Emphasis of Object Y
             Change to characteristic view of Y




Ivan Viola                       23
Refocusing
                                                                                          object-space distance weight                        visibility estimation
                                                                                                                                                           v2                                        image-space weight
                                                                                                                                                v1                                v3




                                                    characteristic viewpoint estimation
                                                                                                                o2                                                       o2




                        Overview   vc
                                                                                                     o1
                                                                                                            o3

                                                                                                                           v
                                                                                                                                                          o1
                                                                                                                                                                        o3




                                                                                                                 information-theoretic framework for optimal viewpoint estimation

                                                                                                                     p(v1)     p(o1|v1) ...




                                                                                                                     ...


                                                                                                                               ...
                                                                                                                                                      m

                                                                                                                                                     Σ p(o |v ) log
                                                                                                                                                                                  p(oj|vi)
                                                                                                                                       I(vi,O) =                    j    i
                                                                                                                                                                                   p(oj)
                                                                                                                                                      j




                                                                                                                                                                                               ...
                                                                                                                  p(vn)                                                                  ...   p(om|vn)
                                                                                                                                p(o1)   ...                                                     p(om)




                                                                                                                                              importance distribution

                                                                                                                                                                                                 up-vector information
                                                                                            object selection by user

                                                                                                          o2                                                                                                        o2
                                                                                                                                                 o1            o2            o3                              o1
                                                                                                o1                                                                                                                 o3
                                                                                                      o3




                                                    interactive focus of attention
                                                                                                                                                                                                         viewpoint transformation

                                                                                                                                     cut-away and level of ghosting

                                                                                            focus discrimination
                                                                                                                                                                                                     v
                                                                                                           o2                                                   o2
                                                                                                                                                   o1                                                         o1        o2
                                                                                                o1                                                             o3
                                                                                                      o3                                                                                                           o3
                                                                                                                                                                              v




                              o1        o2
                                   o3
  Characteristic                             v2
  view 1
                   v1                             Characteristic
                                                  view 2




Ivan Viola                         24
Example - Stagbeetle
                                                                                     object-space distance weight                        visibility estimation
                                                                                                                                                     v2                                         image-space weight
                                                                                                                                           v1                                v3




                                               characteristic viewpoint estimation
                                                                                                           o2                                                       o2
                                                                                                o1                                                   o1
                                                                                                       o3                                                          o3
                                                                                                                      v




                                                                                                            information-theoretic framework for optimal viewpoint estimation

                                                                                                                p(v1)     p(o1|v1) ...




                                                                                                                ...


                                                                                                                          ...
                                                                                                                                                m

                                                                                                                                                Σ p(o |v ) log
                                                                                                                                                                             p(oj|vi)
                                                                                                                                  I(vi,O) =                    j    i
                                                                                                                                                                              p(oj)
                                                                                                                                                 j




                                                                                                                                                                                          ...
                                                                                                             p(vn)                                                                  ...   p(om|vn)
                                                                                                                           p(o1)   ...                                                     p(om)




                                                                                                                                         importance distribution

                                                                                                                                                                                            up-vector information
                                                                                       object selection by user

                                                                                                     o2                                                                                                        o2
                                                                                                                                           o1             o2            o3                              o1
                                                                                           o1                                                                                                                 o3
                                                                                                 o3




                                               interactive focus of attention
                                                                                                                                                                                                    viewpoint transformation

                                                                                                                                cut-away and level of ghosting

                                                                                       focus discrimination
                                                                                                                                                                                                v
                                                                                                      o2                                                   o2
                                                                                                                                              o1                                                         o1        o2
                                                                                           o1                                                             o3
                                                                                                 o3                                                                                                           o3
                                                                                                                                                                         v




                        Focus view 1




             Overview                       Focus view 2
Ivan Viola                             25
Smooth Transition to Focus View
                                                                        object-space distance weight                        visibility estimation
                                                                                                                                         v2                                        image-space weight
                                                                                                                              v1                                v3




                                  characteristic viewpoint estimation
                                                                                              o2                                                       o2
                                                                                   o1                                                   o1
                                                                                          o3                                                          o3
                                                                                                         v




                                                                                               information-theoretic framework for optimal viewpoint estimation

                                                                                                   p(v1)     p(o1|v1) ...




                                                                                                   ...


                                                                                                             ...
                                                                                                                                    m

                                                                                                                                   Σ p(o |v ) log
                                                                                                                                                                p(oj|vi)
                                                                                                                     I(vi,O) =                    j    i
                                                                                                                                                                 p(oj)
                                                                                                                                    j




                                                                                                                                                                             ...
                                                                                                p(vn)                                                                  ...   p(om|vn)
                                                                                                              p(o1)   ...                                                     p(om)




                                                                                                                            importance distribution

                                                                                                                                                                               up-vector information
                                                                          object selection by user

                                                                                        o2                                                                                                        o2
                                                                                                                               o1            o2            o3                              o1
                                                                              o1                                                                                                                 o3
                                                                                    o3




                                  interactive focus of attention
                                                                                                                                                                                       viewpoint transformation

                                                                                                                   cut-away and level of ghosting

                                                                          focus discrimination
                                                                                                                                                                                   v
                                                                                         o2                                                   o2
                                                                                                                                 o1                                                         o1        o2
                                                                              o1                                                             o3
                                                                                    o3                                                                                                           o3
                                                                                                                                                            v




              o1        o2
                   o3




Ivan Viola              26
Example - Human Hand
                                                                    object-space distance weight                        visibility estimation
                                                                                                                                     v2                                        image-space weight
                                                                                                                          v1                                v3




                              characteristic viewpoint estimation
                                                                                          o2                                                       o2
                                                                               o1                                                   o1
                                                                                      o3                                                          o3
                                                                                                     v




                                                                                           information-theoretic framework for optimal viewpoint estimation

                                                                                               p(v1)     p(o1|v1) ...




                                                                                               ...


                                                                                                         ...
                                                                                                                                m

                                                                                                                               Σ p(o |v ) log
                                                                                                                                                            p(oj|vi)
                                                                                                                 I(vi,O) =                    j    i
                                                                                                                                                             p(oj)
                                                                                                                                j




                                                                                                                                                                         ...
                                                                                            p(vn)                                                                  ...   p(om|vn)
                                                                                                          p(o1)   ...                                                     p(om)




                                                                                                                        importance distribution

                                                                                                                                                                           up-vector information




             Any Questions?
                                                                      object selection by user

                                                                                    o2                                                                                                        o2
                                                                                                                           o1            o2            o3                              o1
                                                                          o1                                                                                                                 o3
                                                                                o3




                              interactive focus of attention
                                                                                                                                                                                   viewpoint transformation

                                                                                                               cut-away and level of ghosting

                                                                      focus discrimination
                                                                                                                                                                               v
                                                                                     o2                                                   o2
                                                                                                                             o1                                                         o1        o2
                                                                          o1                                                             o3
                                                                                o3                                                                                                           o3
                                                                                                                                                        v




Ivan Viola              27
Conclusions
     Focus of attention framework
             Characteristic view estimation
             Guided navigation
             Steered by changes in importance distribution
     Future Work
             Zooming to the focus
             Other smart visibility techniques
             Available soon as plugin in volumeshop.org




Ivan Viola                      28
    Thank you!




             The End

                            viola@cg.tuwien.ac.at


Ivan Viola             29
Comparison to Viewpoint Entropy
                                                                                    object-space distance weight                        visibility estimation
                                                                                                                                                     v2                                        image-space weight
                                                                                                                                          v1                                v3




                                              characteristic viewpoint estimation
                                                                                                          o2                                                       o2
                                                                                               o1                                                   o1




    Viewpoint Entropy [Bordoloi et al. '05]
                                                                                                      o3                                                          o3
                                                                                                                     v




                                                                                                           information-theoretic framework for optimal viewpoint estimation

                                                                                                               p(v1)     p(o1|v1) ...




                                                                                                               ...


                                                                                                                         ...
                                                                                                                                                m

                                                                                                                                               Σ p(o |v ) log
                                                                                                                                                                            p(oj|vi)
                                                                                                                                 I(vi,O) =                    j    i
                                                                                                                                                                             p(oj)
                                                                                                                                                j




                                                                                                                                                                                         ...
                                                                                                            p(vn)                                                                  ...   p(om|vn)
                                                                                                                          p(o1)   ...                                                     p(om)




                                                                                                                                        importance distribution

                                                                                                                                                                                           up-vector information
                                                                                      object selection by user

                                                                                                    o2                                                                                                        o2
                                                                                                                                           o1            o2            o3                              o1
                                                                                          o1                                                                                                                 o3
                                                                                                o3




                                              interactive focus of attention
                                                                                                                                                                                                   viewpoint transformation

                                                                                                                               cut-away and level of ghosting

                                                                                      focus discrimination
                                                                                                                                                                                               v
                                                                                                     o2                                                   o2
                                                                                                                                             o1                                                         o1        o2
                                                                                          o1                                                             o3
                                                                                                o3                                                                                                           o3
                                                                                                                                                                        v




    Viewpoint Mutual Information




Ivan Viola                30
Visibility Computation
                                                                                                          object-space distance weight                        visibility estimation
                                                                                                                                                                           v2                                        image-space weight
                                                                                                                                                                v1                                v3




                                                                    characteristic viewpoint estimation
                                                                                                                                o2                                                       o2
                                                                                                                     o1                                                   o1




    For overview and all focus objects
                                                                                                                            o3                                                          o3
                                                                                                                                           v




                                                                                                                                 information-theoretic framework for optimal viewpoint estimation

                                                                                                                                     p(v1)     p(o1|v1) ...




                                                                                                                                     ...


                                                                                                                                               ...
                                                                                                                                                                      m

                                                                                                                                                                     Σ p(o |v ) log
                                                                                                                                                                                                  p(oj|vi)
                                                                                                                                                       I(vi,O) =                    j    i
                                                                                                                                                                                                   p(oj)
                                                                                                                                                                      j




                                                                                                                                                                                                               ...
                                                                                                                                  p(vn)                                                                  ...   p(om|vn)




             For every viewpoint
                                                                                                                                                p(o1)   ...                                                     p(om)




                                                                                                                                                              importance distribution

                                                                                                                                                                                                                 up-vector information
                                                                                                            object selection by user

                                                                                                                          o2                                                                                                        o2
                                                                                                                                                                 o1            o2            o3                              o1
                                                                                                                o1                                                                                                                 o3
                                                                                                                      o3




                                                                    interactive focus of attention
                 For every object + background                                                              focus discrimination



                                                                                                                o1
                                                                                                                           o2
                                                                                                                                                     cut-away and level of ghosting




                                                                                                                                                                   o1
                                                                                                                                                                                o2

                                                                                                                                                                               o3
                                                                                                                                                                                                                     v
                                                                                                                                                                                                                         viewpoint transformation




                                                                                                                                                                                                                              o1        o2
                                                                                                                      o3                                                                                                           o3
                                                                                                                                                                                              v




                                                v2
                                 v1                       v3
 importance distribution

                                                     o2
                            v8             o1                  v4
                                                 o3
             o1 o2 o3

                                 v7                       v5
Ivan Viola                            31
                                                v6
  Visibility Computation for Focus Object
                                                                                   object-space distance weight                        visibility estimation
                                                                                                                                                    v2                                        image-space weight
                                                                                                                                         v1                                v3




                                             characteristic viewpoint estimation
                                                                                                         o2                                                       o2
                                                                                              o1                                                   o1
                                                                                                     o3                                                          o3




 o0 = object 0
                                                                                                                    v




                                                                                                          information-theoretic framework for optimal viewpoint estimation

                                                                                                              p(v1)     p(o1|v1) ...




                                                                                                              ...


                                                                                                                        ...
                                                                                                                                               m




 o1 = object 1
                                                                                                                                              Σ p(o |v ) log
                                                                                                                                                                           p(oj|vi)
                                                                                                                                I(vi,O) =                    j    i
                                                                                                                                                                            p(oj)
                                                                                                                                               j




                                                                                                                                                                                        ...
                                                                                                           p(vn)                                                                  ...   p(om|vn)
                                                                                                                         p(o1)   ...                                                     p(om)




 r = ray
                                                                                                                                       importance distribution

                                                                                                                                                                                          up-vector information
                                                                                     object selection by user




                                  α(o1,r1)
                                                                                                   o2                                                                                                        o2




                                  α(o
                                                                                                                                          o1            o2            o3                              o1
                                                                                         o1                                                                                                                 o3
                                                                                               o3




                                             interactive focus of attention
 r0 = sub-ray 0                                                                      focus discrimination

                                                                                                    o2
                                                                                                                              cut-away and level of ghosting



                                                                                                                                                         o2
                                                                                                                                                                                              v
                                                                                                                                                                                                  viewpoint transformation




                                                                                                                                                                                                                 o2
                                                                                                                                            o1                                                         o1




 r1 = sub-ray 1
                                                                                         o1                                                             o3
                                                                                               o3                                                                                                           o3
                                                                                                                                                                       v




 r2 = sub-ray 2
                  αr



                                  α(o0,r2)
                                  α(o
                       α(o0,r0)

Ivan Viola                  32
  Visibility Computation
                                                                                            object-space distance weight                        visibility estimation
                                                                                                                                                             v2                                        image-space weight
                                                                                                                                                  v1                                v3




                                                      characteristic viewpoint estimation
                                                                                                                  o2                                                       o2
                                                                                                       o1                                                   o1
                                                                                                              o3                                                          o3




 o0 = object 0
                                                                                                                             v




                                           α(o1,r1)                                                                information-theoretic framework for optimal viewpoint estimation

                                                                                                                       p(v1)     p(o1|v1) ...




                                                                                                                       ...


                                                                                                                                 ...
                                                                                                                                                        m




 o1 = object 1
                                                                                                                                                       Σ p(o |v ) log
                                                                                                                                                                                    p(oj|vi)
                                                                                                                                         I(vi,O) =                    j    i
                                                                                                                                                                                     p(oj)
                                                                                                                                                        j




                                                                                                                                                                                                 ...
                                                                                                                    p(vn)                                                                  ...   p(om|vn)
                                                                                                                                  p(o1)   ...                                                     p(om)




 r = ray
                                                                                                                                                importance distribution




                          αr
                                                                                                                                                                                                   up-vector information
                                                                                              object selection by user

                                                                                                            o2                                                                                                        o2
                                                                                                                                                   o1            o2            o3                              o1
                                                                                                  o1                                                                                                                 o3
                                                                                                        o3




                                                      interactive focus of attention
 r0 = sub-ray 0                                                                               focus discrimination

                                                                                                             o2
                                                                                                                                       cut-away and level of ghosting



                                                                                                                                                                  o2
                                                                                                                                                                                                       v
                                                                                                                                                                                                           viewpoint transformation




                                                                                                                                                                                                                          o2
                                                                                                                                                     o1                                                         o1




 r1 = sub-ray 1
                                                                                                  o1                                                             o3
                                                                                                        o3                                                                                                           o3
                                                                                                                                                                                v




                                           α(o0,r2)
 r2 = sub-ray 2                α(o0,r0)




  v(o1 , r )   (o1 , r1 )
  v(o0 , r )  (1  v(o1 , r )) . (o0 , r2 )


Ivan Viola                            33
Probability Transition Matrix
                                                                                                               object-space distance weight                        visibility estimation
                                                                                                                                                                                v2                                        image-space weight
                                                                                                                                                                     v1                                v3




                                                                         characteristic viewpoint estimation
                                                                                                                                     o2                                                       o2
                                                                                                                          o1                                                   o1
                                                                                                                                 o3                                                          o3
                                                                                                                                                v




                                                                                                                                      information-theoretic framework for optimal viewpoint estimation

                                                                                                                                          p(v1)     p(o1|v1) ...




                                                                                                                                          ...


                                                                                                                                                    ...
                                                                                                                                                                           m

                                                                                                                                                                          Σ p(o |v ) log
                                                                                                                                                                                                       p(oj|vi)
                                                                                                                                                            I(vi,O) =                    j    i
                                                                                                                                                                                                        p(oj)
                                                                                                                                                                           j




                                                                                                                                                                                                                    ...
                                                                                                                                       p(vn)                                                                  ...   p(om|vn)
                                                                                                                                                     p(o1)   ...                                                     p(om)




                                                                                                                                                                   importance distribution

                                                                                                                                                                                                                      up-vector information
                                                                                                                 object selection by user

                                                                                                                               o2                                                                                                        o2
                                                                                                                                                                      o1            o2            o3                              o1
                                                                                                                     o1                                                                                                                 o3
                                                                                                                           o3




                                                                         interactive focus of attention
                                                                                                                                                                                                                              viewpoint transformation




             p(v1) p(o1|v1)p(o2|v1) ...
                                                                                                                                                          cut-away and level of ghosting




                                                      p(om|v1)                                                   focus discrimination

                                                                                                                                o2
                                                                                                                                                                        o1
                                                                                                                                                                                     o2
                                                                                                                                                                                                                          v

                                                                                                                                                                                                                                   o1        o2




               p(v1) p(o1|v1)p(o2|v1) ...
                                                                                                                     o1                                                             o3
                                                                                                                           o3                                                                                                           o3




                                                        p(om|v1)
                                                                                                                                                                                                   v




             p(v2p(v1) 1p(o1|v1)p(o2|v1) ...
                 ) p(o |v2)                               p(om|v1)
               p(v2p(v1) 1p(o1|v1)p(o2|v1) ...
                   ) p(o |v2)                               p(om|v1)
                           ...

                 ) ) p(o |v2)
             p(v3p(v2p(v1) 1p(o1|v1)p(o2|v1) ...              p(om|v1)
                         ...

                   )
               p(v3p(v2) p(o1|v2)




                                                              ...
                       ...


                      ...

                      )
                 p(v3p(v2) p(o1|v2)




                                                            ...
                     ...


                   ...

                   p(v3)




                                                          ...
                  ...




                                               ... p(om|vn)
                 ...

                      p(v3)
             p(vn) p(o1|vn)




                                                        ...
               ...




               p(vn) p(o1|vn)                    ... p(om|vn)




                                                      ...
             ...




                 p(vp(o1) 1|vn) 2) p(o3)
                     n) p(o p(o                ... ... p(op(om|vn)
                                                          m)
active om               n) p(o p(o
                   p(vp(o1) 1|vn) 2) p(o3)       ... ... p(op(om|vn)
                                                            m)
                      p(vp(o1) 1|vn) 2) p(o3)
                          n) p(o p(o               ... ... p(op(om|vn)
                                                               m)
                            p(o1) p(o2) p(o3)        ... p(om)
      active o1               p(o1) p(o2) p(o3)        ... p(om)
          inactive


Ivan Viola                               34

				
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