Titlebook: Shapes and Diffeomorphisms; Laurent Younes Textbook 2019Latest edition Springer-Verlag GmbH Germany, part of Springer Nature 2019 68T10, 5

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Distances and Group Actions,In this chapter we discuss metric comparisons between deformable objects and their relation to the registration methods that we have studied in the previous chapters. We will start with a discussion on general metric spaces, and follow with local considerations involving Riemannian geometry.

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Metamorphosis,This chapter introduces metamorphoses, which refer to Riemannian metrics based on transformations in which objects can change under the action of diffeomorphisms (or other transformation groups) but also under independent variations, allowing for more flexibility in the evolution.

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Laurent YounesSuitable for an advanced undergraduate course in the differential geometry of curves and surfaces, featuring applications that are rarely treated in standard texts.Provides a graduate-level theoretica

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Local Properties of Surfaces,hese elements are special cases of the abstract discussion of submanifolds in Appendix B, but are given here a more elementary presentation to ensure that this important material can be read independently.

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Textbook 2019Latest editionctional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diff

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Local Properties of Surfaces,ree dimensions. It presents several results on the local differential geometry of such objects, including metric properties and integration. Some of these elements are special cases of the abstract discussion of submanifolds in Appendix B, but are given here a more elementary presentation to ensure

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Deformable Templates,o the space of transformations. The models that are presented in this chapter are linear versions of this approach, and can be seen as precursors of the nonlinear constructions, based on diffeomorphism groups,, that will be the main focus of the rest of this book.