Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations

TL;DR

This paper introduces a novel authalic energy minimization approach for disk area-preserving surface parameterizations, improving accuracy and efficiency with guaranteed convergence, and demonstrates its practical application in surface registration.

Contribution

It formulates disk area-preserving parameterization as an authalic energy minimization problem and proposes a preconditioned nonlinear conjugate gradient method with proven convergence.

Findings

Enhanced area-preserving accuracy

Improved computational efficiency

Successful application in surface registration

Abstract

An area-preserving parameterization is a bijective mapping that maps a surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an authalic energy minimization (AEM) problem and proposes a novel preconditioned nonlinear conjugate gradient method for the AEM with guaranteed theoretical convergence. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to another state-of-the-art algorithm. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.