1. Thinning & Distance Field Advisor ： Ku-Yaw Chang Speaker ： Jhen-Yu Yang

2. Outline  Introduction  Method  Method 1  Method 2  Reference 22011/12/29

3. Introduction  Thinning  To produce a skeleton  Iteratively removing voxels from the boundary 32011/12/29

4. Introduction  Distance field  Find ridge points  Connect them Polyp 42011/12/29

5. Outline  Introduction  Method  Method 1  Method 2  Reference 52011/12/29

6. Method 1  Use two-subfield thinning algorithm  Extracting medial curves on 3D images  Source： [C.-M. Ma et al., 2002] 62011/12/29 An original object and its skeleton.

7.  In a 3D binary image  Voxels are partitioned into two subsets  C (object voxel)  Marked by  C’ (background voxel)  Marked by  A voxel marked  Don’t care  Can match either C or C’ Method 1 72011/12/29

8. Method 1  Use the Templates (or masks)  To test each boundary voxel  Remove the simple point 82011/12/29 Tested voxels

9.  Let x be a C-voxel  Simple point  Only one C-component in N*(x)  x is adjacent to only one C-component Method 1 92011/12/29 C-component = { a1, d1, b1, e1, δ(x) };

10.  Voxel x is U-deletable  With a C-neighbor β(x) Method 1 102011/12/29 x can be deleted ( 1 ) ( 2 ) ( 3 ) C-component = { a, b, c, β(x) };

11. Method 1 112011/12/29  Voxels are partitioned into two subfields  Two directly adjacent voxels  In different subfields  Two diagonally adjacent voxels  In same subfield Directly adjacent Diagonally adjacent

12.  Branches Method 1 122011/12/29 A tree structure object and its skeleton. A letter ‘A’ and its skeleton.

13. Outline  Introduction  Method  Method 1  Method 2  Reference 132011/12/29

14. Method 2  Using a distance field  Compute an object’s centerline  Source：[ I. Bitter et al., 2001] 142011/12/29 Colon and its skeleton.Dinosaur and its skeleton.

15. Method 2  Compute the distance  Each inside voxel to the boundary  Recorded at each voxel 152011/12/29 (1)

16. Method 2 2011/12/2916  Another DT case SourceResult

17.  Compute gradient vector  For each voxel position  Requires reading of neighboring voxels Method 2 172011/12/29 Vector and its arrow (2)

18.  Six classes of regions  Flag non-uniform gradient vectors  Directions are non-uniform Method 2 182011/12/29 (3) GVF: Gradient Vector Field

19. Method 2  Connect flagged voxels  Pick a flagged voxel and flag the corresponding voxel  Start and traverse  Stop when another flagged voxel is reached 192011/12/29 (4)

20. Method 2 2011/12/2920  Results Lobster and its skeleton.Aorta and its skeleton.

21. Outline  Introduction  Method  Method 1  Method 2  Reference 212011/12/29

22. Reference  Cherng-Min Ma, Shu-Yen Wan. A medial-surface oriented 3-d two-subfield thinning algorithm. Pattern Recognition Letters 22 (2001) 1439-1446  Cherng-Min Ma, Shu-Yen Wan, Her-Kun Chang. Extracting medial curves on 3D images. Pattern Recognition Letters 23 (2002) 895-904  Ingmar Bitter, Arie E. Kaufman, Mie Sato.Penalized-Distance Volumetric Skeleton Algorithm.IEEE Transaction On Visualization And Computer Graphics, Vol. 7, No. 3, July- September 2001 222011/12/29

23. The end Thanks. 232011/12/29