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- W2046305987 abstract "In this work, one proves that under quite general assumptions one can deduce the topology of a bounded open set in Rn from a Hausdorff distance approximation of it. For this, one introduces the weak feature size (wfs) that generalizes the notion of local feature size. Our results apply to open sets with positive wfs, which include many sets whose boundaries are not smooth and even nowhere smooth. This class includes also the piecewise analytic open sets which cover many cases encountered in practical applications. The proofs are based on the study of distance functions to closed sets and their critical points. As an application, one gives an algorithmic way, thanks to persistent homology techniques, to compute the homology groups of open sets from noisy samples of points on their boundary." @default.
- W2046305987 created "2016-06-24" @default.
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- W2046305987 date "2005-06-06" @default.
- W2046305987 modified "2023-10-15" @default.
- W2046305987 title "Weak feature size and persistent homology" @default.
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- W2046305987 doi "https://doi.org/10.1145/1064092.1064132" @default.
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