Convergence of an iterative algorithm for teichmüller maps via harmonic energy optimization
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AbstractFinding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüuller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichmüller map between Riemann surfaces of finite type are theoretically guaranteed (see Fletcher and Markovic, Quasiconformal maps and Teichmüller theory, Oxford Graduate Texts in Math., vol. 11, Oxford University Press, Oxford, 2007). Recently, a simple iterative algorithm for computing the Teichmüller maps between connected Riemann surfaces with given boundary value was proposed by Lui, Lam, Yau, and Gu in Teichmüller extremal mapping and its applications to landmark matching registration, arXiv:1211.2569. Numerical results were reported in the paper to show the effectiveness of the algorithm. The method was successfully applied to landmarkmatching registration. The purpose of this paper is to prove the iterative algorithm proposed in loc. cit., indeed converges.
All Author(s) ListLui L.M., Gu X., Yau S.-T.
Journal nameMathematics of Computation
Volume Number84
Issue Number296
PublisherAmerican Mathematical Society
Place of PublicationUnited States
Pages2823 - 2842
LanguagesEnglish-United Kingdom

Last updated on 2021-11-01 at 01:57