6533b7dafe1ef96bd126e9cd

RESEARCH PRODUCT

Stability and Finiteness Properties of Medial Axis and Skeleton

F. ChazalR. Soufflet

subject

Numerical AnalysisPure mathematicsControl and OptimizationAlgebra and Number TheoryOpen setStructure (category theory)Skeleton (category theory)CombinatoricsHypersurfaceControl and Systems EngineeringMedial axisBounded functionPoint (geometry)Local feature sizeMathematics

description

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

yearjournalcountryeditionlanguage
2004-04-01Journal of Dynamical and Control Systems
https://doi.org/10.1023/b:jods.0000024119.38784.ff