Self-Intersected Boundary Detection and Prevention Methods

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Self-Intersected Boundary Detection and
Prevention Methods

• Joachim Stahl
• 4/26/2004

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Introduction

• Image segmentation and most salient boundary
  detection. Why?
• Simulate human vision system.
• Object detection within an image.

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Wang, Kubota, Siskind Method

• Advantages of WKS method
• Global Optimal.
• Not biased towards boundaries with fewer
  fragments.
• Reference
• S. Wang, J. Wang, T. Kubota. From Fragments to
  Salient Closed Boundaries An In-Depth Study, to
  appear in IEEE Conference on Computer Vision and
  Pattern Recognition (CVPR), Washington, DC, 2004.

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WKS Method in a nutshell
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Self-intersection problem 1

• First case of self-intersection. Two segments of
  the boundary intersect themselves.
• It is a closed boundary though. Shape of eight or
  infinity.

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Self-intersection problem 1 (cont)

• Proposed solution Branch Bound
• First checks if an intersection occurred.
• If yes, branch execution. In each branch run the
  same set again, but ignore one of the segments.
• Repeat until you get non-intersected results.
• Pick the one with the least weight.

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Self-intersection problem 1 (cont)

• Additionally
• Establish a threshold. If the total weight of a
  boundary in a branch goes over it, reject.
• Do not go a level down if there is already a
  candidate with less weight in same level.

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Self-intersection problem 1 (cont)

• Sample result of applying the branching method.

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Self-intersection problem 2

• Second case. Given two edges, the
  stochastic-completion-fields gap-filling method
  returns a self-intersecting segment.

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Self-intersection problem 2 (cont)

• Proposed solution Use instead a Bezier
  approximation.
• First check that the set of points satisfy
  minimum requirements.
• Then calculate the Bezier approximation.
• Else, return an artificial infinite long segment.
  (i.e. discard the segment).

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Self-intersection problem 2 (cont)

• Bezier approximation works by calculating the
  middle points of segments.
• It needs four points, two for the origins and two
  to determine tangents at those points.

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Self-intersection problem 2 (cont)

• Given the four points as p p1, p2, p3, p4. We
  have vector u 1 u u2 u3.
• We can calculate the a point in the approximation
  by doing
• p(u) u.MB.pT where MB is the Bezier matrix

1 0 0 0
-3 3 0 0
3 -6 3 0
-1 3 -3 1
Note Approximation done to a recursion depth of
10. Balance between fast and smooth.
MB
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Self-intersection problem 2 (cont)

• Proposed solution implementation.
• Extend the given tangents and find intersection
  between them.
• Use the intersection point for both tangent
  points of Bezier approximation.

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Self-intersection problem 2 (cont)

• Cases where Bezier approximation does not work.
• But it is a case that is not desirable anyway.
• Can be detected easily, and return an infinite
  gap.

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Self-intersection problem 2 (cont)

• The special case of parallel tangents needs to be
  addressed separately.
• In general, they are discarded.

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Conclusion

• Both cases of self-intersecting boundaries can be
  overcome by implementing the proposed solutions.
• In the first case, the problem can be detect and
  corrected.
• In the second it is avoided.

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Final Remarks

• This is a part of this research project.
• Other topics include
• Dealing with open boundaries.
• Multiple boundaries.
• To be presented by Jun Wang.

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The End

• Questions?