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grayskeleton_smi2008_talk

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									             Segmentation-free
        Skeletonization of Grayscale
      Volumes for Shape Understanding




Sasakthi Abeysinghe   Washington University in St. Louis
Matthew Baker         Baylor College of Medicine
Wah Chiu              Baylor College of Medicine
Tao Ju                Washington University in St. Louis
                                                                 3D Biomedical Images

                                     MRI
                                     CT
                                     EM



                                                                          CT scan of a blood vessel



                                                         Plate                                          -Sheet


                                                         Rod                                            -Helix




              Cryo-EM scan of a protein                           Actual structure of the protein
Segmentation-free Skeletonization of Grayscale Volumes                                              2
                              Skeletons for Shape Understanding




  Cryo-EM scan of a protein                              Skeleton   Actual structure




Segmentation-free Skeletonization of Grayscale Volumes                         3
                          Previous Work: Segmentation Based

                                     “Ideal” threshold is not always present




       Original scan                              Iso-surface from threshold   Skeleton




Segmentation-free Skeletonization of Grayscale Volumes                                    4
                               Previous Work: Segmentation-free
                                     Ridge/Valley detection [Lopez 2000]
                                        Lacks curve / surface structure


                                     Use 2nd order tensor field [Yu 2006]
                                        Lacks branching information
                                        Requires domain knowledge
                                                    Min/Max thickness of a helix/sheet




Segmentation-free Skeletonization of Grayscale Volumes                                    5
                                                                             Observations

                                                    A shape component is captured at some
                                         1
                                                    segmentation




               Scan of a hand                            Fingers captured     Palm captured
                                                         at high threshold    at low threshold


Segmentation-free Skeletonization of Grayscale Volumes                                      6
                                                                         Observations

                                                    A shape component is captured at some
                                         1
                                                    segmentation


                                         2          The centers of the shape components lie
                                                    along the low gradient variations

                                                         Rod?
                                                         Plate?




Segmentation-free Skeletonization of Grayscale Volumes                              7
                                                                       Our Approach



                                     Compute skeletons at every gray level
                                                                                         1
                                        Centers of all possible shape features



                                     Identify skeletal elements aligned with
                                          the low-gradient direction                     2
                                             Centers of the likely shape features




Segmentation-free Skeletonization of Grayscale Volumes                               8
                                                                                              Overview
                                     Process each shape feature separately




                                                                             2

                                       1
                                                  Centers of all possible             Centers of likely plate
                                                     plate features                         features



                                     1
                                                                             2


                                                  Centers of all possible             Centers of likely rod
                                Thinning              rod features          Pruning        features
Segmentation-free Skeletonization of Grayscale Volumes                                                  9
                                                                                        Overview
                                     Process each shape feature separately




                                                                            2

                                       1
                                                  Centers of all possible       Centers of likely plate
                                                     plate features                   features



                                     1
                                                                            2


                                                  Centers of all possible       Centers of likely rod
                                Thinning              rod features                   features
Segmentation-free Skeletonization of Grayscale Volumes                                           10
                                             Thinning: Single Segmentation




               Scan of a hand                            A segmentation   Skeleton at that
                                                         /iso-contour     segmentation


Segmentation-free Skeletonization of Grayscale Volumes                                 11
                                                     Thinning: All Segmentations
                                     Accumulate skeletons (top down)
                                                    Skeleton from last
                                                    iteration




           Scan of a hand                                Current segmentation/   Accumulated skeleton
Segmentation-free Skeletonization of Grayscale Volumes
                                                         iso-contour             thus far          12
                                                     Thinning: All Segmentations
                                     Superset of all possible surface features




                                                                Centers of all possible
                                                                   plate features

Segmentation-free Skeletonization of Grayscale Volumes                                    13
                                                                                              Overview
                                     Process each shape feature separately




                                                                             2

                                       1
                                                  Centers of all possible             Centers of likely plate
                                                     plate features                         features



                                     1
                                                                             2


                                                  Centers of all possible             Centers of likely rod
                                                      rod features          Pruning        features
Segmentation-free Skeletonization of Grayscale Volumes                                                 14
                                                          Pruning: Structure Tensor

                                     Directions of principal gradient variation
                                          at any given point
                            x   x  Ix 2         Ix Iy 
                                         T
                            I       I
                     Tp'                         2 
                            I       I       I
                            y   y   x Iy         Iy 
                                                     v1
          Iy

           Ix
                                                  v2


                      Eigen analysis
                      on structure
                      tensor




                     2-dimensional
Segmentation-free Skeletonization of Grayscale Volumes                       15
                                                             Pruning: Structure Tensor

                                     Directions of principal gradient variation
                                          at any given point
                                                                               x   x  Ix 2                     Ix Iz 
                                                                                             T
                                                                               I        I                  Ix Iy
                          x   x  Ix                Ix Iy 
                                            T            2
                          I       I                                                                   2              
                     T       
                       '
                       p                                         2 
                                                                        Tp'   y   y    x Iy
                                                                               I        I         I        Iy            Iy Iz 
                          I       I       I
                          y   y   x Iy              Iy             z   z   x Iz
                                                                               I        I
                                                                                        I        Iy Iz         Iz 
                                                                                                                            2
                                                                                                                               
                                                     v1
          Iy

           Ix
                                                  v2
                                                               

                      Eigen analysis
                      on structure
                      tensor




                     2-dimensional                                               3-dimensional
Segmentation-free Skeletonization of Grayscale Volumes                                                              16
                                                          Pruning: Surface Scoring

                                     Compare surface area of least gradient
                                          direction with actual area




                                     Score = Area of least gradient direction
                                                 Area of skeletal direction




                                            High scoring surfaces   Low scoring surfaces


Segmentation-free Skeletonization of Grayscale Volumes                                     17
                                                              Pruning: Curve Scoring

                                     Compare curve length of least gradient
                                          direction with actual length




                                     Score = Length of least gradient direction
                                                 Length of skeletal direction




                                             High scoring curves    Low scoring curves


Segmentation-free Skeletonization of Grayscale Volumes                                   18
                                                         Pruning: Feature Extraction

                                     Threshold based on score
                                     Erosion + dilation to remove small branches [Ju2006]




                                       Scored rod features
                                     Scored plate features                              plate
                                                                      Centers of likely rod
                                                                            features
                                                                           features



Segmentation-free Skeletonization of Grayscale Volumes                                    19
                                                                                              Overview


                                                                            Surface
                                                                            Pruning
                              Surface
                              Thinning                                        2

                                       1
                                                  Centers of all possible             Centers of likely plate
                                                     plate features                         features



                                     1
                               Curve
                              Thinning                                        2
                                                                             Curve
                                                                            Pruning
                                                  Centers of all possible             Centers of likely rod
                                                      rod features                         features
Segmentation-free Skeletonization of Grayscale Volumes                                                 20
                                                         Results: Vessel (CT Scan)




         CT scan                            After thinning   After scoring   After pruning




Segmentation-free Skeletonization of Grayscale Volumes                             21
                                                         Results: Foot (CT Scan)




Segmentation-free Skeletonization of Grayscale Volumes                    22
                                                                                Results: Proteins




             CryoEM scan                                 Result of our method        Ground truth

Segmentation-free Skeletonization of Grayscale Volumes                                          23
                                                                                                      Performance
                                              Thinning time complexity= O(n g)
                                                 n - No of voxels in volume
                                                 g - No of distinct gray levels


                                              Pruning time complexity = O(s e)
                                                 s - No of features points before pruning
                                                 e - Size of the smallest shape feature
                 160
                 140
Time (seconds)




                 120
                 100
                 80
                 60
                 40
                 20
                  0
                            Hand       Protein 2ITG   Protein 1TIM    Protein 1BTV       CT vessel     MRI vessel       Bones
                       (129x129x129)   (64x64x64)      (96x96x96)    (128x128x128)     (121x71x66)   (101x82x111)   (150x128x128)

                                                                         Data set
                              Surface thinning         Surface pruning              Curve thinning        Curve pruning

   Segmentation-free Skeletonization of Grayscale Volumes                                                                 24
                                                         Limitations & Future Work

                                     Improving performance
                                        Bottom up thinning instead of top down



                                     Extending to general data sets
                                        Handling cases where the observations are
                                         not true




Segmentation-free Skeletonization of Grayscale Volumes                        25
                                                         Limitations & Future Work

                                     Noise removal
                                                    Removing noisy branches
                                                    Correcting connectivity
                                             An interactive approach




Segmentation-free Skeletonization of Grayscale Volumes                         26
                                                                          Conclusion

                                     A skeletonization technique of
                                          grayscale volumes:

                                             Aggregate thinning at all iso-contours


                                             Structure tensor based scoring function
                                                for pruning

                                             Segmentation free!




Segmentation-free Skeletonization of Grayscale Volumes                           27

								
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