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＜電子ブック＞
Handbook of Variational Methods for Nonlinear Geometric Data / edited by Philipp Grohs, Martin Holler, Andreas Weinmann

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	XXVI, 701 p. 159 illus., 125 illus. in color : online resource
著者標目	Grohs, Philipp editor Holler, Martin editor Weinmann, Andreas editor SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Computer vision FREE:Computational Mathematics and Numerical Analysis FREE:Mathematical Applications in Computer Science FREE:Computer Vision
一般注記	1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.­­- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organizedin a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com HTTP:URL=https://doi.org/10.1007/978-3-030-31351-7

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