Adaptive Metrics for Adaptive Samples
| Autor: | Nicholas J. Cavanna, Donald R. Sheehy |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Adaptive sampling lcsh:T55.4-60.8 homology inference Computer science Inference adaptive sampling 010103 numerical & computational mathematics 0102 computer and information sciences Homology (mathematics) 01 natural sciences lcsh:QA75.5-76.95 Theoretical Computer Science topological data analysis surface reconstruction lcsh:Industrial engineering. Management engineering 0101 mathematics Numerical Analysis Discrete representation Euclidean space Computational Mathematics Computational Theory and Mathematics 010201 computation theory & mathematics Computer Science - Computational Geometry Topological data analysis lcsh:Electronic computers. Computer science Algorithm Surface reconstruction |
| Zdroj: | Algorithms Volume 13 Issue 8 Algorithms, Vol 13, Iss 200, p 200 (2020) |
| DOI: | 10.48550/arxiv.1807.08208 |
| Popis: | In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on Euclidean space. We prove a near-duality between adaptive samples in the Euclidean metric space and uniform samples in this alternate metric space which results in topological interleavings between the offsets generated by this metric and those generated by an linear approximation of it. After smoothing the distance function associated to the adaptive metric, we apply a result from the theory of critical points of distance functions to the interleaved spaces which yields a computable homology inference scheme assuming one has Hausdorff-close samples of the domain and the landmark set. |
| Databáze: | OpenAIRE |
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