A sampling theory for compact sets in Euclidean space

Frédéric Chazal, David Cohen-Steiner, André Lieutier
2006 Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06  
We introduce a parameterized notion of feature size that interpolates between the minimum of the local feature size and the recently introduced weak feature size. Based on this notion of feature size, we propose sampling conditions that apply to noisy samplings of general compact sets in euclidean space. These conditions are sufficient to ensure the topological correctness of a reconstruction given by an offset of the sampling. Our approach also yields new stability results for medial axes,
more » ... or medial axes, critical points, and critical values of distance functions.
doi:10.1145/1137856.1137904 dblp:conf/compgeom/ChazalCL06 fatcat:q2ftrmcxfvestehxblvqhsvm2a