Riemannian gradient descent for spherical area-preserving mappings

Marco Sutti*, Mei Heng Yueh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is based on the stretch energy functional, and the minimization is constrained on a power manifold of unit spheres embedded in three-dimensional Euclidean space. Numerical experiments on several mesh models demonstrate the accuracy and stability of the proposed framework. Comparisons with three existing state-of-the-art methods for computing area-preserving mappings demonstrate that our algorithm is both competitive and more efficient. Finally, we present a concrete application to the problem of landmark-aligned surface registration of two brain models.

Original languageEnglish
Pages (from-to)19414-19445
Number of pages32
JournalAIMS Mathematics
Issue number7
Publication statusPublished - 2024


  • area-preserving mapping
  • matrix manifolds
  • Riemannian gradient descent
  • Riemannian optimization
  • stretch-energy functional

ASJC Scopus subject areas

  • General Mathematics


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