1. Skeleton Extraction from Binary Images Kalman Palagyi University 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 points and 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

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

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

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

20. forward scan
backward scan

21. Chamfer masks in 2D

22. Chamfer masks in 3D

23. original binary image
initialization
forward scan
backward scan

24. Skeletonization based on distance transform

25. Positions marked boldface numbers belong to the skeleton.

26. Voronoi diagram

31. Incremental construction

32. Delauney triangulation/tessalation

33. Voronoi & Delauney

34. Duality

35. Skeletal elements of a Voronoi diagram

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

37. ‘Thinning’
before
after

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

40. Topology preservation in 2D (a counter example)

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

42. Shape preservation

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

45. Types of voxels in 3D medial lines

46. A 2D thinning algorithm using 8 subiterations

49. A 3D thinning algorithm using 6 subiterations

54. Blood vessel (infra-renal aortic aneurysms)

55. Airway (trachealstenosis)

56. Calculating cross sectional profiles and estimating diameter

57. Colon (cadaveric phantom)

59. Airway (intrathoracic airway tree)

60. Example
Centerlines
Segmented tree
Labeled tree
Formal tree

61. Requirements
Geometrical: The skeleton must be in the middle of the original object and must be invariant to translation, rotation, and scale change.
Topological: The skeleton must retain the topology of the original object.

62. Comparison