Computation of Circular Area and Spherical Volume Invariants via Boundary Integrals
| Autor: | Riley O'Neill, Pedro Angulo-Umana, Peter J. Olver, Katrina Yezzi-Woodley, Jeff Calder, Bo Hessburg, Chehrzad Shakiban |
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| Rok vydání: | 2020 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Mathematics - Differential Geometry Computer Vision and Pattern Recognition (cs.CV) General Mathematics Computation Computer Science - Computer Vision and Pattern Recognition 02 engineering and technology Curvature Planar 65D18 65D30 68U05 65N38 FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Mathematics - Numerical Analysis Invariant (mathematics) Physics Applied Mathematics Mathematical analysis Surface integral 020207 software engineering Numerical Analysis (math.NA) Differential Geometry (math.DG) Integral invariants Computer Science - Computational Geometry High Energy Physics::Experiment 020201 artificial intelligence & image processing |
| Zdroj: | Experts@Minnesota |
| ISSN: | 1936-4954 |
| Popis: | We show how to compute the circular area invariant of planar curves, and the spherical volume invariant of surfaces, in terms of line and surface integrals, respectively. We use the Divergence Theorem to express the area and volume integrals as line and surface integrals, respectively, against particular kernels; our results also extend to higher dimensional hypersurfaces. The resulting surface integrals are computable analytically on a triangulated mesh. This gives a simple computational algorithm for computing the spherical volume invariant for triangulated surfaces that does not involve discretizing the ambient space. We discuss potential applications to feature detection on broken bone fragments of interest in anthropology. |
| Databáze: | OpenAIRE |
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