Stereo Vision by lJt41jZz

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									Computer Vision



    Stereo Vision
Pinhole Camera




Bahadir K. Gunturk   2
Perspective Projection




                     x' y' f '
                        
                     x  y  z




Bahadir K. Gunturk               3
Stereo Vision

    Two cameras.
    Known camera positions.
    Recover depth.

                                         scene point



                                 p                     p’
                                      image plane

                     optical center


Bahadir K. Gunturk                                          4
Correspondences


       p             p’




Bahadir K. Gunturk        5
Matrix form of cross product
               a=axi+ayj+azk
                                         a×b=|a||b|sin(η)u
               b=bxi+byj+bzk


                   a y bz  az by   0         az    a2 
                                                        
          a  b   az bx  ax bz    az        0    ax  b     a  b
                   ax by  a y bz   a y      ax     0 
                                                        

                               a  (a  b)  0
                               b  (a  b)  0



Bahadir K. Gunturk                                                            6
The Essential Matrix




       pT Ep '  0

 Essential matrix     p  (u, v,1)T
                     p '  (u ', v ',1)T
Bahadir K. Gunturk                         7
     Stereo Constraints
                                             M
                            Image plane             Epipolar Line



                     Y1            p
                                                    p’
                                                              Y2
                                                                    X2
                    O1
Z1                            X1

                                                         O2         Z2
                          Focal plane
                                          Epipole


     Bahadir K. Gunturk                                             8
   A Simple Stereo System

              LEFT CAMERA                     RIGHT CAMERA
                            baseline



          Left image:                              Right image:
          reference                                target
                                       disparity

                                 Depth Z


                               Elevation Zw
Zw=0 K. Gunturk
  Bahadir                                                         9
  Stereo View




       Left View                 Right View




Bahadir K. Gunturk   Disparity                10
 Stereo Disparity
    The separation between two matching objects
     is called the stereo disparity.




Bahadir K. Gunturk                                 11
Parallel Cameras
                          P
                                         T x x T
                                              r
                                                      l


                                           Z f   Z
                         Z                               T
         xl                     xr
                                                  Z f
                                                       x x
f              pl              pr
                                                              l       r




          Ol                        Or
                     T
                                          Disparity:       d  x x
                                                                  l        r



    T is the stereo baseline


Bahadir K. Gunturk                                                    12
Finding Correspondences




Bahadir K. Gunturk        13
                               Correlation
      LEFT IMAGE               Approach
                                   (x , y )
                                         l   l




   For Each point (xl, yl) in the left image, define a window
    centered at the point
Bahadir K. Gunturk                                               14
                              Correlation
      RIGHT IMAGE             Approach
                                  (x , y )
                                       l   l




   … search its corresponding point within a search region in
    the right image
Bahadir K. Gunturk                                          15
                                  Correlation
      RIGHT IMAGE      (xr, yr)   Approach
                                   dx (x , y )
                                        l   l




   … the disparity (dx, dy) is the displacement when the
    correlation is maximum
Bahadir K. Gunturk                                          16
                         ?
Comparing Windows        =
                     f         g




                     Most
                     popular




Bahadir K. Gunturk                 17
Comparing Windows

   Minimize          Sum of Squared
                     Differences

   Maximize          Cross correlation




Bahadir K. Gunturk                 18
Correspondence Difficulties
    Why is the correspondence problem difficult?
           Some points in each image will have no
            corresponding points in the other image.
           (1) the cameras might have different fields of view.
           (2) due to occlusion.
    A stereo system must be able to determine
     the image parts that should not be matched.




Bahadir K. Gunturk                                                19
     Structured Light
   Structured lighting
        Feature-based methods are not applicable when the
         objects have smooth surfaces (i.e., sparse disparity
         maps make surface reconstruction difficult).
        Patterns of light are projected onto the surface of
         objects, creating interesting points even in regions
         which would be otherwise smooth.
        Finding and matching such
         points is simplified by
         knowing the geometry of the
         projected patterns.


Bahadir K. Gunturk                                              20
   Stereo results
          Data from University of Tsukuba




                Scene                        Ground truth

Bahadir K. Gunturk
                               (Seitz)                      21
   Results with window correlation




    Estimated depth of field             Ground truth
     (a fixed-size window)
                               (Seitz)
Bahadir K. Gunturk                                      22
    Results with better method




           A state of the art method                                  Ground truth
Boykov et al., Fast Approximate Energy Minimization via Graph Cuts,
   International Conference on Computer Vision, September 1999.

    Bahadir K. Gunturk                              (Seitz)                          23

								
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