SelfIntersected Boundary Detection and Prevention Methods Joachim Stahl
Self-Intersected Boundary Detection and Prevention Methods Joachim Stahl 4/26/2004
Introduction Image segmentation and most salient boundary detection. Why? • • Simulate human vision system. Object detection within an image. 2
Wang, Kubota, Siskind Method l 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. 3
WKS Method in a nutshell 4
Self-intersection problem #1 l First case of self-intersection. Two segments of the boundary intersect themselves. • It is a closed boundary though. Shape of eight or infinity. 5
Self-intersection problem #1 l (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. 6
Self-intersection problem #1 l (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. Original W = 5. 5 W=7 W=8 W = 7. 6 W = 10 W=9 7
Self-intersection problem #1 l (cont) Sample result of applying the branching method. 8
Self-intersection problem #2 l Second case. Given two edges, the stochasticcompletion-fields gap -filling method returns a selfintersecting segment. 9
Self-intersection problem #2 l (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). 10
Self-intersection problem #2 l (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. 11
Self-intersection problem #2 • • (cont) Given the four points as p = [p 1, p 2, p 3, p 4]. We have vector u = [1 u u 2 u 3]. We can calculate the a point in the approximation by doing: p(u) = u. MB. p. T where MB is the Bezier matrix 1 -3 MB = 3 -1 0 3 -6 3 0 0 3 -3 0 0 0 1 Note: Approximation done to a recursion depth of 10. Balance between fast and smooth. 12
Self-intersection problem #2 l (cont) Proposed solution implementation. • • Extend the given tangents and find intersection between them. Use the intersection point for both tangent points of Bezier approximation. 13
Self-intersection problem #2 l (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. 14
Self-intersection problem #2 l l (cont) The special case of parallel tangents needs to be addressed separately. In general, they are discarded. 15
Conclusion l l l 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. 16
Final Remarks l l This is a part of this research project. Other topics include: • Dealing with open boundaries. • Multiple boundaries. • To be presented by Jun Wang. 17
The End l Questions? 18
- Slides: 18