Spherical Area-Preserving Parameterization via Energy Minimization

Abstract

We propose a novel method, called spherical authalic energy minimization (SAEM), for computing spherical area-preserving parameterizations of genus-zero closed surfaces, with strong theoretical foundations. The global convergence of the associated computational algorithm is theoretically guaranteed. In addition, we introduce a Riemannian bijective correction method that ensures the bijectivity of the resulting mapping under mild assumptions. Numerical experiments show that SAEM effectively minimizes area distortion and achieves bijective mappings, outperforming state-of-the-art methods. Finally, we demonstrate the practical utility of SAEM in shape description.