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Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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.

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Acknowledgements

This work was supported in part by the National Science Foundation under Grant No. DMS-2002103 (to Gary P. T. Choi) and HKRGC GRF under project ID 2130549 (to Lok Ming Lui).

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Gary P. T. Choi

  2. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China

    Lok Ming Lui

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  1. Gary P. T. Choi
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  2. Lok Ming Lui
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Correspondence to Lok Ming Lui .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK

    Ke Chen

  2. Dept Appl Math & Theoretical Phys, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Xue-Cheng Tai

  4. Department of Applied Mathematics & Stat, Johns Hopkins University, Baltimore, MD, USA

    Laurent Younces

Section Editor information

  1. Department of Mathematical Sciences, University of Liverpool Mathematical Sciences Building, Liverpool, UK

    Ke Chen Ph.D

  2. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, USA

    Laurent Younes

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Xuecheng Tai Ph.D

  4. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom

    Carola-Bibiane Schönlieb Ph.D

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Choi, G.P.T., Lui, L.M. (2022). Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_113-1

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  • DOI: https://doi.org/10.1007/978-3-030-03009-4_113-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03009-4

  • Online ISBN: 978-3-030-03009-4

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