Measured boundary parameterization based on Poisson's equation  

作　　者：Jun-jie CAO Zhi-xun SU Xiu-ping LIU Hai-chuan BI 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

出　　处：《Journal of Zhejiang University-Science C(Computers and Electronics)》2010年第3期187-198,共12页浙江大学学报C辑（计算机与电子（英文版）

基　　金：supported by the Program for New Century Excellent Talents in University (No. NCET-05-0275);the National Natural Science Foundation of China (Nos. 60533060 and 60673006);the IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR 01647206) from NIH, USA

摘　　要：One major goal of mesh parameterization is to minimize the conformal distortion. Measured boundary parameteri-zations focus on lowering the distortion by setting the boundary free with the help of distance from a center vertex to all the boundary vertices. Hence these parameterizations strongly depend on the determination of the center vertex. In this paper,we introduce two methods to determine the center vertex automatically. Both of them can be used as necessary supplements to the existing measured boundary methods to minimize the common artifacts as a result of the obscure choice of the center vertex. In addition,we propose a simple and fast measured boundary parameterization method based on the Poisson's equation. Our new approach generates less conformal distortion than the fixed boundary methods. It also generates more regular domain boundaries than other measured boundary methods. Moreover,it offers a good tradeoff between computation costs and conformal distortion compared with the fast and robust angle based flattening (ABF++).One major goal of mesh parameterization is to minimize the conformal distortion. Measured boundary parameterizations focus on lowering the distortion by setting the boundary free with the help of distance from a center vertex to all the boundary vertices. Hence these parameterizations strongly depend on the determination of the center vertex. In this paper, we introduce two methods to determine the center vertex automatically. Both of them can be used as necessary supplements to the existing measured boundary methods to minimize the common artifacts as a result of the obscure choice of the center vertex. In addition, we propose a simple and fast measured boundary parameterization method based on the Poisson＇s equation. Our new approach generates less conformal distortion than the fixed boundary methods. It also generates more regular domain boundaries than other measured boundary methods. Moreover, it offers a good tradeoff between computation costs and conformal distortion compared with the fast and robust angle based flattening （ABF＋＋）.

关 键 词：Mesh parameterization Poisson＇s equation Measured boundary 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] TH706[自动化与计算机技术—计算机科学与技术]