Handbook of Variational Methods for Nonlinear Geometric Data / edited by Philipp Grohs, Martin Holler, Andreas Weinmann.
- 1st ed. 2020.
- Cham : Springer International Publishing : Imprint: Springer, 2020.
- Mathematics and Statistics (Springer-11649)
1 online resource (XXVI, 701 pages) : 159 illustrations, 125 illustrations in color.
- Computer science -- Mathematics.
Optical data processing.
- Local subjects:
- Computational Mathematics and Numerical Analysis.
Math Applications in Computer Science.
Image Processing and Computer Vision.
Mathematical Applications in Computer Science.
- System Details:
- text file PDF
- 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.
- 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.
- Grohs, Philipp. editor., Editor,
Holler, Martin, editor., Editor,
Weinmann, Andreas. editor., Editor,
SpringerLink (Online service)
- Contained In:
- Springer eBooks
- Other format:
- Printed edition:
- Publisher Number:
- 10.1007/978-3-030-31351-7 doi
- Access Restriction:
- Restricted for use by site license.
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