Shape smoothing using double offsets
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees
Computational Geometry: Theory and Applications
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
Optimal reconstruction might be hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
Geodesic delaunay triangulations in bounded planar domains
ACM Transactions on Algorithms (TALG)
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
Pattern Recognition Letters
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In this work one proves that under quite general assumptions one can deduce the topology of a bounded open set in ${\Bbb R}^n$ from an approximation of it. For this, one introduces the weak feature size (wfs) that extends for nonsmooth objects the notion of local feature size. Our results apply to open sets with positive wfs. This class includes subanalytic open sets which cover many cases encountered in practical applications. The proofs are based upon the study of distance functions to closed sets and their critical points. The notion of critical point is the same as the one used in riemannian geometry [22], [9], [20] and nonsmooth analysis [10]. As an application, one gives a way to compute the homology groups of open sets from noisy samples of points on their boundary.