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

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Applied Mathematical Scienceshttp://image.papertrans.cn/s/image/866389.jpg

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鄙视读作

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Computations on Triangulated Surfaces,Triangulated surfaces provide a three-dimensional generalization of polygons in two dimensions. Surfaces are usually stored on computers in the form of triangulated surfaces, and these are the kinds of objects that must be handled in practical applications.

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Celiac-Plexus

Ordinary Differential Equations and Groups of Diffeomorphisms,This chapter begins our discussion of diffeomorphic shape analysis with the introduction of spaces of diffeomorphisms, notably those associated with flows of ordinary differential equations. This chapter relies heavily on concepts presented in Appendix C that the reader may want consult at this point.

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Building Admissible Spaces,This chapter presents several explicit constructions of admissible spaces, focusing on Hilbert spaces. We will in particular introduce the notion of reproducing kernels associated to an admissible space, which will provide a powerful computational tool. Several important properties associated with such kernels are also discussed.

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Diffeomorphic Matching,This chapter discusses variational registration methods, minimizing registration costs with a guarantee that the optimal solution is a diffeomorphism. The main focus will be on methods optimizing over flows associated with differential equations, using concepts introduced in the previous chapters.