Stability and Finiteness Properties of Medial Axis and Skeleton

The medial axis is a geometric object associated with any bounded open set in ℝn 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 C2-perturbations when the open set is bounded by a hypersurface with positive local feature size.

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