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Shape Spaces: From Geometry to Biological Plausibility

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Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Abstract

This chapter reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of various approaches at building Riemannian spaces of shapes, with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm, the attention is turned to elastic metrics and to growth models that can be derived from it. In the latter context, a new class of metrics, involving the optimization of a growth tensor, is introduced, and some of its properties are studied.

Nicolas Charon is partially supported by NSF 1945224 and NSF 1953267.

Laurent Younes is partially supported by NIH U19AG033655, R01NS102670, and R01AG055121.

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Authors and Affiliations

  1. Center for Imaging Science, Johns Hopkins University, Baltimore, MD, USA

    Nicolas Charon & Laurent Younes

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  1. Nicolas Charon
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  2. Laurent Younes
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Correspondence to Laurent Younes .

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Editors and Affiliations

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

    Ke Chen

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Carola-Bibiane Schönlieb

  3. Hong Kong Center for Cerebrocardiovascular Health Engineering (COCHE), Shatin, Hong Kong

    Xue-Cheng Tai

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

    Laurent Younes

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Charon, N., Younes, L. (2023). Shape Spaces: From Geometry to Biological Plausibility. In: Chen, K., Schönlieb, CB., Tai, XC., Younes, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-98661-2_118

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