Hyperbolic Hausdorff distance for medial axis transform

Choi, Sung Woo; Seidel, Hans-Peter

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Hyperbolic Hausdorff distance for medial axis transform

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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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MPI-I-2000-4-003.pdf
(全文テキスト（全般）), 347KB

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引用

Choi, S. W., & Seidel, H.-P.(2000). Hyperbolic Hausdorff distance for medial axis transform (MPI-I-2000-4-003). Saarbrücken: Max-Planck-Institut für Informatik.

引用: https://hdl.handle.net/11858/00-001M-0000-0014-6D4A-A

要旨

Although the Hausdorff distance is a popular device to measure the differences between sets, it is not natural for some specific classes of sets, especially for the medial axis transform which is defined as the set of all pairs of the centers and the radii of the maximal balls contained in another set. In spite of its many advantages and possible applications, the medial axis transform has one great weakness, namely its instability under the Hausdorff distance when the boundary of the original set is perturbed. Though many attempts have been made for the resolution of this phenomenon, most of them are heuristic in nature and lack precise error analysis.