Recovering structure from r-sampled objects
SGP '09 Proceedings of the Symposium on Geometry Processing
Optimal reconstruction might be hard
Proceedings of the twenty-sixth annual symposium on Computational geometry
Reconstructing shapes with guarantees by unions of convex sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Proceedings of the twenty-seventh annual symposium on Computational geometry
Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Preserving geometric properties in reconstructing regions from internal and nearby points
Computational Geometry: Theory and Applications
Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
Computational Geometry: Theory and Applications
Homological reconstruction and simplification in R3
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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, critical points, and critical values of distance functions.