Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2003, March 27.

Abstract:
The medial axis is a geometric object associated to any bounded open set in $\R^n$ which has various applications in computer science. We study it from a mathematical point of view. We give some results about its geometrical structure when the open set is subanalytic and we prove that it is stable under $\core^2$-perturbations when the open set is bounded by a an hypersurface with positive local feature size.

Mathematics Subject Classification (2000): 32B20, 65D17, 65D18, 52C45.

Keywords and Phrases: medial axis, subanalytic sets, stability problems, shape modeling.

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