Stability Analysis of Medial Axis Transform under Relative Hausdorff Distance

Medial axis transform (MAT) is a basic tool for shape analysis. But, 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 "pruning" 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 "smoothed out" 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 "essent...

• Type: Conference
• Year: 2000
• Where: ICPR
• Authors: Sung Woo Choi, Seong-Whan Lee
• Keywords: Computer Vision, ICPR 2000, Medial Axis, Precise Error Estimation, Relative Hausdorff Distance