PDE methods for extracting normal vector fields and distance functions of shapes
Analysis of PDEs
2025-06-25 v1 Optimization and Control
Abstract
Partial differential equations can be used for extracting geometric features of shapes. This article summarizes recent methods to extract the normal vector field from an elliptic equation proposed by Yamada and from the heat equation, and also a method to extract the (signed) distance function from an elliptic equation that generalizes Varadhan's in 1967.
Cite
@article{arxiv.2506.19323,
title = {PDE methods for extracting normal vector fields and distance functions of shapes},
author = {Takahiro Hasebe and Jun Masamune and Hiroshi Teramoto and Takayuki Yamada},
journal= {arXiv preprint arXiv:2506.19323},
year = {2025}
}