caa a22 4500 445331526 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10208-011-9098-0 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9098-0 Geometric Inference for Probability Measures [Elektronische Daten] [Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot] Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows one to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers or with background noise. In this paper, we show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we introduce a notion of distance function to a probability distribution in ℝ d . These functions share many properties with classical distance functions, which make them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, we show that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers. Moreover, in settings where empirical measures are considered, these functions can be easily evaluated, making them of particular practical interest. SFoCM, 2011 Geometric inference nationallicence Computational topology nationallicence Optimal transportation nationallicence Nearest neighbor nationallicence Surface reconstruction nationallicence Chazal Frédéric INRIA Saclay, Saclay, France aut Cohen-Steiner David INRIA Sophia-Antipolis, Nice, France aut Mérigot Quentin Laboratoire Jean Kuntzmann, CNRS/Université de Grenoble I, Grenoble, France aut Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 733-751 1615-3375 11:6<733 2011 11 10208 https://doi.org/10.1007/s10208-011-9098-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9098-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chazal Frédéric INRIA Saclay, Saclay, France aut NATIONALLICENCE 700 1- Cohen-Steiner David INRIA Sophia-Antipolis, Nice, France aut NATIONALLICENCE 700 1- Mérigot Quentin Laboratoire Jean Kuntzmann, CNRS/Université de Grenoble I, Grenoble, France aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 733-751 1615-3375 11:6<733 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer