@inproceedings{1b5c7754314f41af9609144e6b9f1064,
title = "Solving PDEs on manifolds with global conformal parametrization",
abstract = "In this paper, we propose a method to solve PDEs on surfaces with arbitrary topologies by using the global conformal parametrization. The main idea of this method is to map the surface conformally to 2D rectangular areas and then transform the PDE on the 3D surface into a modified PDE on the 2D parameter domain. Consequently, we can solve the PDE on the parameter domain by using some well-known numerical schemes on ℝ 2. To do this, we have to define a new set of differential operators on the manifold such that they are coordinates invariant. Since the Jacobian of the conformal mapping is simply a multiplication of the conformal factor, the modified PDE on the parameter domain will be very simple and easy to solve. In our experiments, we demonstrated our idea by solving the Navier-Stoke's equation on the surface. We also applied our method to some image processing problems such as segmentation, image denoising and image inpainting on the surfaces.",
author = "Lui, {Lok Ming} and Yalin Wang and Chan, {Tony F.}",
year = "2005",
doi = "10.1007/11567646_26",
language = "English (US)",
isbn = "3540293485",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "307--319",
booktitle = "Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings",
note = "3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005 ; Conference date: 16-10-2005 Through 16-10-2005",
}