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Shape spaces: From geometry to biological plausibility

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arxiv 2205.01237 v1 pith:663VOBSS submitted 2022-05-02 math.DG math.OC

Shape spaces: From geometry to biological plausibility

Nicolas Charon , Laurent Younes This is my paper
classification math.DG math.OC
keywords metricscontextdiffeomorphicgrowthriemannianshapespacesalgorithm
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This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of 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.

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