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Skeleton Extrac tion from Binary Images Kalman Palagyi University of Szeged, Hungary

Skeleton Extrac tion from Binary Images Kalman Palagyi University of Szeged, Hungary. The generic model of a modular machine vision system. Feature extraction. Shape representation. to describe the boundary that surrounds an object; to describe the region that is occupied by an object.

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Skeleton Extrac tion from Binary Images Kalman Palagyi University of Szeged, Hungary

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  1. Skeleton Extraction from Binary ImagesKalman PalagyiUniversity of Szeged,Hungary

  2. The generic model of a modular machine vision system

  3. Feature extraction

  4. Shape representation • to describe the boundary that surrounds an object; • to describe the region that is occupied by an object.

  5. Skeleton • result of the Medial Axis Transform: object points having at least two nearest boundary points; • praire-fire analogy: the boundary is set on fire and skeleton is formed by the loci where the fire fronts meet and quench each other; • the locus of the centers of all the maximal inscribed hyper-spheres.

  6. Nearest boundary pointsand inscribed hyper-spheres

  7. Skeleton of a 3D solid box The skeleton in 3D generally contains surface patches (2D segments).

  8. Properties: • It represents • the general form of an object, • the topological structure of an object, and • local object symmetries. • It is invariant to • translation, • rotation, and • (uniform) scale change. • It is thin.

  9. Uniqueness The same skeleton may belong to different elongated objects.

  10. Stability

  11. Representing local object symmetries and the topological structure

  12. Skeletonization techniques • distance transform, • Voronoi diagram, and • thinning.

  13. Distance transform Input: Binary array A containing feature elements (1’s) and non-feature elements (0’s). Output: Non-binary array B containing the distance to the nearest feature element.

  14. Example: distance map (non-binary image) input (binary image)

  15. M.C. Escher: Reptiles

  16. Distance transform using city-block (or 4) distance

  17. Distance transform using chess-board (or 8) distance

  18. Chamfer distance transform in linear time (G. Borgefors, 1984)

  19. forward scan backward scan

  20. Chamfer masks in 2D

  21. Chamfer masks in 3D

  22. original binary image initialization backward scan forward scan

  23. Skeletonization based on distance transform

  24. Positions marked boldface numbers belong to the skeleton.

  25. Voronoi diagram

  26. Incremental construction

  27. Delauney triangulation/tessalation

  28. Voronoi & Delauney

  29. Duality 0

  30. Skeletal elements of a Voronoi diagram

  31. A 3D example original Voronoi diagram regularization M. Näf (ETH, Zürich)

  32. ‘Thinning’ before after

  33. Thinning It is an iterative object reduction technique in a topology preserving way.

  34. Topology preservation in 2D(a counter example)

  35. HoleIt is a new concept in 3D  ”A topologist is a man who does not know the difference between a coffee cup and a doughnut.”

  36. Shape preservation

  37. End-points in 3D thinning medial surface original topological kernel medial lines

  38. Types of voxels in 3D medial lines

  39. A 2D thinning algorithm using 8 subiterations

  40. A 3D thinning algorithm using 6 subiterations

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