# Weak feature size and persistent homology: computing homology of solids in Rn from noisy data samples

@article{Chazal2005WeakFS, title={Weak feature size and persistent homology: computing homology of solids in Rn from noisy data samples}, author={Fr{\'e}d{\'e}ric Chazal and Andr{\'e} Lieutier}, journal={Proceedings of the twenty-first annual symposium on Computational geometry}, year={2005} }

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…

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