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Thinning & Distance Field

Thinning & Distance Field. Advisor ： Ku-Yaw Chang Speaker ： Jhen -Yu Yang. Outline. Introduction Method Method 1 Method 2 Reference. Introduction. Thinning To produce a skeleton Iteratively removing voxels from the boundary. Introduction. Distance field Find ridge points

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Thinning & Distance Field

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

  2. Outline • Introduction • Method • Method 1 • Method 2 • Reference

  3. Introduction • Thinning • To produce a skeleton • Iteratively removing voxels from the boundary

  4. Introduction • Distance field • Find ridge points • Connect them Polyp

  5. Outline • Introduction • Method • Method 1 • Method 2 • Reference

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

  7. Method 1 • 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’

  8. Method 1 • Use the Templates (or masks) • To test each boundary voxel • Remove the simple point Tested voxels

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

  10. Method 1 ( 1 ) • Voxel xisU-deletable • With a C-neighbor β(x) ( 2 ) ( 3 ) C-component = { a, b, c, β(x) }; x can be deleted

  11. Method 1 • Voxels are partitioned into two subfields • Two directly adjacent voxels • In different subfields • Two diagonally adjacent voxels • In same subfield Diagonally adjacent Directly adjacent

  12. Method 1 • Branches A tree structure object and its skeleton. A letter ‘A’ and its skeleton.

  13. Outline • Introduction • Method • Method 1 • Method 2 • Reference

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

  15. Method 2 • Compute the distance • Each inside voxel to the boundary • Recorded at each voxel (1)

  16. Method 2 • Another DT case Source Result

  17. Method 2 • Compute gradient vector • For each voxel position • Requires reading of neighboring voxels (2) Vector and its arrow

  18. Method 2 • Six classes of regions • Flag non-uniformgradient vectors • Directions are non-uniform (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 (4)

  20. Method 2 • Results Lobster and its skeleton. Aorta and its skeleton.

  21. Outline • Introduction • Method • Method 1 • Method 2 • Reference

  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

  23. The endThanks.

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