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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Charon, N., Younes, L. (2022). Shape Spaces: From Geometry to Biological Plausibility. In: Chen, K., Schönlieb, CB., Tai, XC., Younces, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-03009-4_118-1
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