| Description |
1 online resource (xxvi, 701 pages) |
| Contents |
Part I. Processing Geometric Data -- Geometric Finite Elements -- Non-smooth Variational Regularization for Processing Manifold-Valued Data -- Lifting Methods for Manifold-Valued Variational Problems -- Geometric Subdivision and Multiscale Transforms -- Variational Methods for Discrete Geometric Functionals -- Part II. Geometry as tool -- Variational Methods for Fluid-Structure Interactions -- Convex Lifting-Type Methods for Curvature Regularization -- Assignment flows -- Geometric Methods on Low-Rank Matrix and Tensor Manifolds -- Part IV. Shapes Spaces and the Analysis of Geometric Data -- Shape Analysis of Functional Data -- Statistical Analysis of Trajectories of Multi-Modality Data -- Geometric Metrics for Topological Representations -- On Geometric Invariants, Learning, and Recognition of shapes and forms -- Sub-Riemannian Methods in Shape Analysis -- Part V. Optimization Algorithms and Numerical Methods -- First Order Methods for Optimization on Riemannian Manifolds -- Recent Advances in Stochastic Riemannian Optimization -- Averaging Symmetric Positive-Definite Matrices -- Rolling Maps and Nonlinear Data -- Part VI. Applications -- Manifold-Valued Data in Medical Imaging Applications -- The Riemannian and Affine Geometry of Facial Expression and action recognition -- Biomedical Applications of Geometric Functional Data Analysis |
| Summary |
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 organized in 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 |
| Notes |
Print version record |
| Subject |
Calculus of variations -- Handbooks, manuals, etc
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Geometry -- Handbooks, manuals, etc
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Maths for computer scientists.
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Image processing.
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Mathematical modelling.
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Numerical analysis.
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Computers -- Data Processing.
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Computers -- Computer Graphics.
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Mathematics -- Applied.
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Mathematics -- Counting & Numeration.
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Modelos matemáticos
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Geometría
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Ordenadores -- Datos-Tratamiento
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Calculus of variations
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Geometry
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| Genre/Form |
Electronic books
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handbooks.
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Handbooks and manuals
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Handbooks and manuals.
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Guides et manuels.
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| Form |
Electronic book
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| Author |
Grohs, Philipp
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Holler, Martin
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Weinmann, Andreas
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| ISBN |
9783030313517 |
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3030313514 |
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