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arXiv · 2506.19323

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

Takahiro Hasebe·Jun Masamune·Hiroshi Teramoto·Takayuki Yamada
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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.

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Takahiro Hasebe, Jun Masamune, Hiroshi Teramoto, Takayuki Yamada. 2025-06-24. PDE methods for extracting normal vector fields and distance functions of shapes. https://arxiv.org/abs/2506.19323

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