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Conference Paper

One-sided stability of MAT and its applications

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Choi,  Sung Woo
Computer Graphics, MPI for Informatics, Max Planck Society;

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Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

Choi, S. W., & Seidel, H.-P. (2001). One-sided stability of MAT and its applications. In T. Ertl, B. Girod, G. Greiner, H. Niemann, & H.-P. Seidel (Eds.), Vision, Modeling and Visualization 2001 (VMV-2001) (pp. 291-298). Berlin, Germany: Akademische Verlagsgesellschaft Aka.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-32B4-E
Abstract
Although useful in many applications, the medial axis transform (MAT) has a few fit-falls, one of which is its extreme sensitivity to the boundary perturbation. In this paper, we first summarizes the previous attempts to get around this by bounding the one-sided Hausdorff distance of the MAT with respect to the boundary perturbation. We illustrate these results and their optimality with various examples. Finally, we suggest an application of them in pruning. In particular, we discuss the advantage of the results for the domains which are not weakly injective, over those for the weakly injective ones.