A Robust Hessian-based Trust Region Algorithm for Spherical Conformal Parameterizations
Numerical Analysis
2023-12-01 v1 Numerical Analysis
Abstract
Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical conformal parameterizations of simply connected closed surfaces of genus-. In addition, we give the sparsity structure of the Hessian matrix, which leads to a robust Hessian-based trust region algorithm for the computation of spherical conformal maps. Numerical experiments demonstrate the local quadratic convergence of the proposed algorithm with low conformal distortions. We subsequently propose an application of our method to surface registrations that still maintains local quadratic convergence.
Cite
@article{arxiv.2311.18474,
title = {A Robust Hessian-based Trust Region Algorithm for Spherical Conformal Parameterizations},
author = {Zhong-Heng Tan and Tiexiang Li and Wen-Wei Lin and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2311.18474},
year = {2023}
}