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arXiv · 2403.11726

Riemannian gradient descent for spherical area-preserving mappings

Marco Sutti·Mei-Heng Yueh
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Abstract

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 3-dimensional Euclidean space. Numerical experiments on several mesh models demonstrate the accuracy and stability of the proposed framework. Comparisons with two 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.

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Marco Sutti, Mei-Heng Yueh. 2024-03-18. Riemannian gradient descent for spherical area-preserving mappings. https://doi.org/10.3934/math.2024946

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