Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
| Autor: | Jeff Calder, Sangmin Park, Dejan Slepčev |
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| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
65N75 62G20 65N12 65N15 65D99 Numerical Analysis Applied Mathematics General Engineering Machine Learning (stat.ML) Mathematics - Statistics Theory Numerical Analysis (math.NA) Statistics Theory (math.ST) Theoretical Computer Science Computational Mathematics Computational Theory and Mathematics Statistics - Machine Learning FOS: Mathematics Mathematics - Numerical Analysis Software |
| Zdroj: | Journal of Scientific Computing. 92 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-022-01894-9 |
| Popis: | We investigate identifying the boundary of a domain from sample points in the domain. We introduce new estimators for the normal vector to the boundary, distance of a point to the boundary, and a test for whether a point lies within a boundary strip. The estimators can be efficiently computed and are more accurate than the ones present in the literature. We provide rigorous error estimates for the estimators. Furthermore we use the detected boundary points to solve boundary-value problems for PDE on point clouds. We prove error estimates for the Laplace and eikonal equations on point clouds. Finally we provide a range of numerical experiments illustrating the performance of our boundary estimators, applications to PDE on point clouds, and tests on image data sets. 53 pages, 14 figures |
| Databáze: | OpenAIRE |
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