Riemannian gradient descent for spherical area-preserving mappings
<|reference_start|>Riemannian gradient descent for spherical area-preserving mappings: 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.<|reference_end|>
@article{sutti2024riemannian,
    title={Riemannian gradient descent for spherical area-preserving mappings},
    author={Marco Sutti and Mei-Heng Yueh},
    journal={arXiv preprint arXiv:2403.11726},
    year={2024},
    doi={10.3934/math.2024946},
    archivePrefix={arXiv},
    eprint={2403.11726},
    primaryClass={math.NA cs.NA}
}