2D%20Skeleton%20Shape%20Representation%20using%20Shock%20Graphs

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2D Skeleton Shape Representation using Shock
Graphs

• Chung, In Young
• Lee, Kang Eui
• 12. 12. 2005

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Outline

• Motivation
• Suggestion
• Algorithm
• ltStep.1 Step3gt
• Results Conclusion

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Problem with previous methods?

• Blums techniques
• high computational complexity
• Voronoi techniques
• remove important edges
• (not preserve topology)

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Suggestion and key idea

• Suggestion
• Methods based on Euclidean distance functions
• Key idea
• is to measure the net outward flux of a vector
  field per unit area, and to apply thinning process

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Step 1. Result of Computed Vector Field
Original Image
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Step 2. Result of Computed Flux
Original Image
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Step 3.Thinning

• Thinning Algorithm

• Removable Point
• 8 neighbors make a tree or its Euler (V-E)
  is 1.
• End point
• Only one neighbor or
• Two neighbors if they are 4-adjacent to one
  another.

FOR each border point P IF (P is removable)
Insert(P,Heap) with Flux(P) END For WHILE
(Heap.sizegt0) PMaxHeapExtract(Heap) IF (P
is removable) IF P is not an end point
Flux(P)gtT remove(P, Heap) FOR
each neighbor, Q of P IF (Q is
removable) Insert(Q, Heap)
END FOR ELSE Mark P as a Skeletal
Point END WHILE
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Step 3.Result of Thinning
Original Image
Thinned Image
Thresholded Image (Threshold -0.3)
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Result Conclusion

• A novel algorithm form computing subpixel
  skeletal graphs
• Robust, accurate, computationally efficient,
  topology preserving
• Essential idea
• a divergence computation on the gradient vector
  filed
• a thining process that preserves toplogy