Spherical Area-Preserving Parameterization via Energy Minimization
Abstract
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.
Fields of Study & Subjects
3D Shape Modeling and Analysis
Medical Image Segmentation Techniques
Digital Image Processing Techniques
Publication details
- Journal / source
- SIAM Journal on Imaging Sciences
- Volume
- 19
- Issue
- 1
- Pages
- 207–235
- Publication date
- 7 January 2026
- Language
- EN