Shape Spaces: From Geometry to Biological Plausibility

Nicolas Charon () and Laurent Younes ()
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Nicolas Charon: Johns Hopkins University, Center for Imaging Science
Laurent Younes: Johns Hopkins University, Center for Imaging Science

Chapter 53 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 1929-1958 from Springer

Abstract: 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.

Keywords: Riemannian shape spaces; Shape analysis; Shape evolution; Diffeomeorphisms; Morphoelasticity; Growth models (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_118

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DOI: 10.1007/978-3-030-98661-2_118

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