Linear onesided stability of MAT for weakly injective 3D domain
Proceedings of the seventh ACM symposium on Solid modeling and applications
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Medial axis transform (MAT) is a basic tool for shape analysis. However, in spite of its usefulness, it has some drawbacks, one of which is its instability under the boundary perturbation. To handle this problem in practical situations, various 驴pruning驴 methods have been proposed, which are usually heuristic in their nature and without sufficient error analyses. In this paper, we show that, although medial axis transform is unstable with respect to standard measures such as the Hausdorff distance, it is stable in a measure called relative Hausdorff distance for some 驴smoothed out驴 domains called injective domains. In fact, we obtain an upper bound of the relative Hausdorff distance of the MAT of an injective domain with respect to the MAT of an arbitrary domain, which is in small Hausdorff distance from the original injective domain. One consequence of the above result is that, by approximating a given domain with injective domains, we can extract the most 驴essential part驴 of the MAT within the prescribed error bound in Hausdorff distance. This introduces a new pruning strategy with precise error estimation. We illustrate our results with an example.