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Shape Spaces: From Geometry to Biological Plausibility

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

Author

Listed:
  • Nicolas Charon

    (Johns Hopkins University, Center for Imaging Science)

  • Laurent Younes

    (Johns Hopkins University, Center for Imaging Science)

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.

Suggested Citation

  • Nicolas Charon & Laurent Younes, 2023. "Shape Spaces: From Geometry to Biological Plausibility," 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 53, pages 1929-1958, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_118
    DOI: 10.1007/978-3-030-98661-2_118
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