Spherical Authalic Energy Minimization for Area-Preserving Parameterization

TL;DR

This paper introduces SAEM, a novel method for computing area-preserving spherical parameterizations of genus-zero surfaces, with guaranteed convergence and improved bijectivity, supported by theoretical and experimental validation.

Contribution

The paper presents SAEM, a new energy minimization approach with theoretical guarantees and a bijective correction method for better area-preserving surface parameterization.

Findings

SAEM effectively minimizes area distortion.

SAEM guarantees convergence.

SAEM improves bijectivity over existing methods.

Abstract

We propose a new effective method called spherical authalic energy minimization (SAEM) for computing spherical area-preserving parameterizations of genus-zero surfaces. The proposed SAEM has solid theoretical support and guaranteed convergence. In addition, we develop a Riemannian bijective correction method to ensure the bijectivity of the produced mapping under mild assumptions. Numerical experiments showed that the SAEM effectively minimized area distortion with improved bijectivity compared to other state-of-the-art methods.