A varifold approach to surface approximation

DOI10.1007/s00205-017-1141-0zbMath1378.49052arXiv1609.03625OpenAlexW2520360888MaRDI QIDQ1675110

Simon Masnou, Blanche Buet, Gian Paolo Leonardi

Publication date: 26 October 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03625

zbMATH Keywords

varifoldapproximate mean curvature vectordiscrete varifoldfirst variation of varifoldgeneralized mean curvature vectormass of varifoldrectifiable varifold

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Integration on manifolds; measures on manifolds (58C35) Length, area, volume, other geometric measure theory (28A75) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (10)

Intrinsic finite element method for advection-diffusion-reaction equations on surfaces ⋮ Mean curvature motion of point cloud varifolds ⋮ Weak and approximate curvatures of a measure: a varifold perspective ⋮ Discretization and approximation of surfaces using varifolds ⋮ Corrected curvature measures ⋮ Partial differential equations and variational methods for geometric processing of images ⋮ Recovering the homology of immersed manifolds ⋮ Approximation of the Willmore energy by a discrete geometry model ⋮ Recovering measures from approximate values on balls ⋮ Representation of surfaces with normal cycles and application to surface registration

Uses Software

• Eigen
• MeshLab
• nanoflann

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(C^{1+\alpha}\)-regularity for two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Convergence of curvatures in secant approximations
• Second fundamental measure of geometric sets and local approximation of curvatures
• Integral and current representation of Federer's curvature measures
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Sharp stability inequalities for planar double bubbles
• Generalized Wasserstein distance and its application to transport equations with source
• Generalized curvatures
• On the first variation of a varifold
• The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration
• Improved convergence theorems for bubble clusters. I. The planar case
• Parameter-Free and Multigrid Convergent Digital Curvature Estimators
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• The approximation power of moving least-squares
• Computing Discrete Minimal Surfaces and Their Conjugates
• Inference of Curvature Using Tubular Neighborhoods
• Improved convergence theorems for bubble clusters. II. The three-dimensional case
• Optimal Transport
• Quantitative conditions of rectifiability for varifolds

This page was built for publication: A varifold approach to surface approximation