@article{7dd58da90c644888a425632d1cb3ff64,
title = "Convergent Conformal Energy Minimization for the Computation of Disk Parameterizations",
abstract = "Surface conformal parameterizations have been widely applied to various tasks in computer graphics. In this paper, we develop a convergent conformal energy minimization (CCEM) iterative algorithm via the line-search gradient descent method with a quadratic approximation for the computation of disk-shaped conformal parameterizations of simply connected open triangular meshes. In addition, we prove the global convergence of the proposed CCEM iterative algorithm. Moreover, under some mild assumptions, we prove the existence of a nontrivial solution, which is a local minimum of the conformal energy with a bijective boundary map. The numerical experiments indicate that the efficiency of the proposed CCEM algorithm is greatly improved and that the accuracy is competitive with that of state-of-the-art algorithms.",
keywords = "conformal energy minimization, disk conformal parameterization, simply connected open surface",
author = "Kuo, {Yueh Cheng} and Lin, {Wen Wei} and Yueh, {Mei Heng} and Yau, {Shing Tung}",
note = "Funding Information: \ast Received by the editors April 26, 2021; accepted for publication (in revised form) September 7, 2021; published electronically December 2, 2021. https://doi.org/10.1137/21M1415443 Funding: This work was partially supported by the Ministry of Science and Technology, the National Center for Theoretical Sciences, the ST Yau Center in Taiwan, the Nanjing Center for Applied Mathematics, and the Center of Mathematical Sciences and Applications at Harvard University. \dagger Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, Taiwan (yckuo@nuk.edu.tw). \ddagger Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan, and Nanjing Center for Applied Mathematics, Nanjing 211135, People's Republic of China (wwlin@math.nctu.edu.tw). \S Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan (yue@ntnu.edu.tw). \P Department of Mathematics, Harvard University, Cambridge, MA 02138 USA, and Nanjing Center for Applied Mathematics, Nanjing 211135, People's Republic of China (yau@math.harvard.edu). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics.",
year = "2021",
doi = "10.1137/21M1415443",
language = "English",
volume = "14",
pages = "1790--1815",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}