Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry

Gary P. T. Choi () and Lok Ming Lui ()
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Gary P. T. Choi: Massachusetts Institute of Technology, Department of Mathematics
Lok Ming Lui: The Chinese University of Hong Kong, Department of Mathematics

Chapter 43 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 1483-1523 from Springer

Abstract: Abstract Surface parameterization is of fundamental importance for many tasks in computer vision and imaging. In recent years, computational quasi-conformal geometry has become an emerging tool for the design of efficient and accurate parameterization methods for both surface meshes and point clouds. More specifically, using quasi-conformal (QC) theory, it is possible to reduce the geometric distortion and achieve conformal parameterizations for surfaces with different topology easily. It is also possible to achieve surface parameterizations that satisfy certain prescribed conditions, such as landmark constraints, with a minimal quasi-conformal distortion. In this article, we give an overview of the recent advances in surface parameterization using quasi-conformal geometry.

Keywords: Surface parameterization; Quasi-conformal geometry; Conformal map; Quasi-conformal map; Mesh; Point cloud (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_113

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DOI: 10.1007/978-3-030-98661-2_113

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