PDE methods for extracting normal vector fields and distance functions of shapes

TL;DR

This paper reviews PDE-based techniques for deriving geometric features like normal vectors and distance functions of shapes, highlighting recent advances and generalizations of classical methods.

Contribution

It summarizes recent PDE methods for extracting shape features, including novel approaches to normal vector and distance function computation.

Findings

Normal vector fields can be extracted using elliptic and heat equations.

Distance functions can be obtained from elliptic equations, generalizing Varadhan's formula.

The methods enhance geometric feature extraction from shapes.

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.