Numerical computation of the cut locus via a variational approximation of the distance function-Reference-Cited by-同舟云学术

Numerical computation of the cut locus via a variational approximation of the distance function

Published:2022-01 Issue:1 Volume:56 Page:105-120
ISSN:0764-583X
Container-title:ESAIM: Mathematical Modelling and Numerical Analysis
language:
Short-container-title:ESAIM: M2AN

Author:

Générau François,Oudet Edouard^ORCID,Velichkov Bozhidar

Abstract

We propose a new method for the numerical computation of the cut locus of a compact submanifold of ℝ3 without boundary. This method is based on a convex variational problem with conic constraints, with proven convergence. We illustrate the versatility of our approach by the approximation of Voronoi cells on embedded surfaces of ℝ3.

Publisher

EDP Sciences

Subject

Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics

Link

https://www.esaim-m2an.org/10.1051/m2an/2021088/pdf

Reference18 articles.

1. On the stability of the cut locus

2. Andersen E.D. and Andersen K.D., The mosek interior point optimizer for linear programming: an implementation of the homogeneous algorithm. In: High Performance Optimization Springer (2000) 197–232.

3. Attali D. and Montanvert A., Modeling noise for a better simplification of skeletons. In: Proceedings of 3rd IEEE International Conference on Image Processing. Vol. 3. IEEE (1996) 13–16.

4. Bonnard B., Cots O. and Jassionnesse L., Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces. In: Geometric Control Theory and Sub-Riemannian Geometry. Springer (2014) 53–72.

5. Simplicial structure of the real analytic cut locus

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A Convex Optimization Framework for Regularized Geodesic Distances;Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Proceedings;2023-07-23

2. Cut Locus on Compact Manifolds and Uniform Semiconcavity Estimates for a Variational Inequality;Archive for Rational Mechanics and Analysis;2022-10-01

3. Computing the cut locus of a Riemannian manifoldviaoptimal transport;ESAIM: Mathematical Modelling and Numerical Analysis;2022-09-14