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

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

Author

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  • Hei-Long Chan

    (Chinese University of Hong Kong)

  • Lok-Ming Lui

    (Chinese University of Hong Kong)

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.

Suggested Citation

  • Hei-Long Chan & Lok-Ming Lui, 2023. "Recent Development of Medical Shape Analysis via Computational 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 41, pages 1413-1436, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_70
    DOI: 10.1007/978-3-030-98661-2_70
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