# Accuracy Improvements for Convolutional and Differential Distance Function Approximations

arXiv: https://arxiv.org/abs/2412.09200 · HTML: https://mlsanity.com/paper/2412.09200/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 3 of 3)

- [Laplace Meets Moreau: Smooth Approximation to Infimal Convolutions Using Laplace's Method](https://mlsanity.com/paper/2406.02003/) (2024)
- [A fast algorithm for All-Pairs-Shortest-Paths suitable for neural networks](https://mlsanity.com/paper/2308.07403/) (2023)
- [Walk on Spheres for PDE-based Path Planning](https://mlsanity.com/paper/2406.01713/) (2024)

## Built on by (most cited first, 1 of 1)

- [Points as Tori: Fast Pointwise Signed Distance for Point Clouds](https://mlsanity.com/paper/2607.16946/) (2026)

## Abstract (arXiv)

Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for both the schemes, accuracy improvements are proposed and evaluated. Asymptotics of Laplace integrals and Taylor series extrapolations are used to achieve the improvements.