Riemannian gradient descent for spherical area-preserving mappings
This work provides a more efficient method for computing spherical area-preserving mappings, which is beneficial for applications like surface registration in medical imaging.
This paper introduces a new Riemannian gradient descent method to compute spherical area-preserving mappings of topological spheres. The method demonstrates competitive accuracy and improved efficiency compared to two existing state-of-the-art methods, and is applied to landmark-aligned surface registration of brain models.
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.