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Recent Development of Medical Shape Analysis via Computational Quasi-Conformal Geometry

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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Abstract

Medical analysis is closely related to mathematics in many aspects. Over the past decades, mathematicians have designed numerous mathematical models and algorithms to aid medical researches. However, the space for joint-forcing mathematics with the medical industry is very limited in early years due to immature implementation and technological support. Those models are mostly limited to simple applications of the probability and statistics theory. It is until recent years when computational geometry comes into appliance, and it opens up a huge room for the incorporation of mathematics with medical analysis. For instance, medical imaging, geometric modeling for medical surfaces, and machine learning for disease classification are crucial topics nowadays having heavy reliance on image processing and geometric analysis. There are many streams in applying the study of geometry. Among those, the application of the quasi-conformal Teichmüller theory has shown to be very successful in recent years. This article serves to conclude some most updated models having solid contributions to the medical science in different aspects.

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Authors and Affiliations

  1. Chinese University of Hong Kong, Hong Kong, China

    Hei-Long Chan & Lok-Ming Lui

Authors
  1. Hei-Long Chan
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  2. Lok-Ming Lui
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Corresponding author

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. No affiliation provided

    Xue-Cheng Tai Ph.D

  2. No affiliation provided

    Carola-Bibiane Schönlieb Ph.D

  3. No affiliation provided

    Ke Chen Ph.D

  4. No affiliation provided

    Laurent Younes

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Chan, HL., Lui, LM. (2021). Recent Development of Medical Shape Analysis via Computational 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_70-1

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  • DOI: https://doi.org/10.1007/978-3-030-03009-4_70-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03009-4

  • Online ISBN: 978-3-030-03009-4

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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