This repository contains a simple implementation in MATLAB of the following paper on distance computation using an extension of the Heat distance method.
It provides an implementation using finite difference in the sub-directory 'fd' and implementations using the finite element method in 'fem_2d' and 'fem_3d'. The finite difference-based implementation computes the distance to the boundary of white domains (images). The finite element-based implementation computes the distance to boundary of domains in 2D represented by a triangulation, and domains in 3D represented by a tetrahedra mesh. Examples of meshes are provided in the 'data' sub-directories (the file formats used by Triangle / Tetgen are used).
This is a link to the [paper] (https://www.sciencedirect.com/science/article/pii/S0010448525001290) where the methods were introduced. The corresponding bibtex entry is
@article{Belyaev2025CAD,
title = {Heat method extensions for distance function estimation in planar and space domains},
journal = {Computer-Aided Design},
volume = {190},
pages = {103968},
year = {2026},
issn = {0010-4485},
doi = {https://doi.org/10.1016/j.cad.2025.103968},
author = {Belyaev, Alexander and Fayolle, Pierre-Alain},
}