个人信息Personal Information
教授
博士生导师
硕士生导师
主要任职:软件学院(大连理工大学-立命馆大学国际信息与软件学院)党委书记
性别:女
毕业院校:吉林大学
学位:博士
所在单位:软件学院、国际信息与软件学院
学科:软件工程. 计算数学. 计算机应用技术
办公地点:大连理工大学开发区校区信息楼309室
联系方式:nalei@dlut.edu.cn
电子邮箱:nalei@dlut.edu.cn
Discrete Lie flow: A measure controllable parameterization method
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论文类型:期刊论文
发表时间:2019-06-01
发表刊物:COMPUTER AIDED GEOMETRIC DESIGN
收录刊物:SCIE、EI
卷号:72
页面范围:49-68
ISSN号:0167-8396
关键字:Measure controllable parameterization; Area-preserving parameterization; Discrete Lie advection; Optimal transport
摘要:Computing measure controllable parameterizations for general surface is a fundamental task for medical imaging and computer graphics, which is designed to control the measures of the regions of interest in the parameterization domain for more accurate and thorough detection and examination of data. Previous works usually handle just some certain kind of topology and boundary shapes, or are computationally complex. In this paper, a modified approach based on the technique of lie advection is presented for the measure controllable parameterization of geometry objects in the general context of 2-manifold surfaces. Given a general surface with arbitrary initial parameterization without flips but usually with great area distortion, the Lie derivative is introduced to eliminate the difference between the initial parameterization and the prescribed measure. The vertices flow in the directions derived through the Lie derivative and finally converge to the ideal measure, and by its geometric meaning, this method will be called as DLF (Discrete Lie Flow) intuitively. Compared with previous methods based on Lie derivative, two key modifications were made: an adaptive step-length scheme resulting in a substantive acceleration and robustness and a measure controllable function. Area preserving mapping can be generated easily through our DLF algorithm as a special case for measure controllable parameterization. With various algorithms developed for mesh parameterization based on energy optimization approaches in recent years, our DLF is the minority that is supported by a solid differential geometric theory. We tested our method on plenty of cases, including disk models with convex and non-convex boundaries, and spherical models. Experimental results demonstrate the efficiency of the proposed algorithm. (C) 2019 Elsevier B.V. All rights reserved.