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Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Gary P. T. Choi

    (Massachusetts Institute of Technology, Department of Mathematics)

  • Lok Ming Lui

    (The Chinese University of Hong Kong, Department of Mathematics)

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.

Suggested Citation

  • Gary P. T. Choi & Lok Ming Lui, 2023. "Recent Developments of Surface Parameterization Methods Using Quasi-conformal Geometry," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 43, pages 1483-1523, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_113
    DOI: 10.1007/978-3-030-98661-2_113
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