Self-Intersected Boundary Detection and Prevention Methods Joachim Stahl 4/26/2004.
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Transcript of Self-Intersected Boundary Detection and Prevention Methods Joachim Stahl 4/26/2004.
![Page 1: Self-Intersected Boundary Detection and Prevention Methods Joachim Stahl 4/26/2004.](https://reader030.fdocuments.us/reader030/viewer/2022033104/56649d555503460f94a32ff1/html5/thumbnails/1.jpg)
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.
OriginalW = 5.5
W = 7 W = 7.6
W = 8 W = 10 W = 9 W = 9
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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
MB = Note: Approximation doneto a recursion depth of 10.Balance between fast andsmooth.
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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?