Accuracy Improvements for Convolutional and Differential Distance Function Approximations

TL;DR

This paper proposes accuracy enhancements for convolutional and differential distance function approximation schemes within bounded domains, utilizing asymptotic analysis and Taylor series extrapolation to improve estimation precision.

Contribution

It introduces novel accuracy improvement techniques for convolutional and differential distance estimations using asymptotic and Taylor series methods.

Findings

Accuracy improvements demonstrated through theoretical analysis.

Enhanced estimation precision validated in experiments.

Method applicable to various boundary domain problems.

Abstract

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.