TY - JOUR
T1 - Stability analysis of medial axis transform under relative hausdorff distance
AU - Choi, Sung Woo
AU - Lee, Seong Whan
PY - 2000
Y1 - 2000
N2 - 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 "essential part" 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.
AB - 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 "essential part" 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.
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U2 - 10.1109/ICPR.2000.903503
DO - 10.1109/ICPR.2000.903503
M3 - Article
AN - SCOPUS:33750915078
VL - 15
SP - 135
EP - 138
JO - Proceedings - International Conference on Pattern Recognition
JF - Proceedings - International Conference on Pattern Recognition
SN - 1051-4651
IS - 3
ER -