LEADER 05354nam 22005895 450 001 996418277603316 005 20200704001554.0 010 $a3-030-31351-4 024 7 $a10.1007/978-3-030-31351-7 035 $a(CKB)4100000010858798 035 $a(DE-He213)978-3-030-31351-7 035 $a(MiAaPQ)EBC6157442 035 $a(PPN)243763093 035 $a(EXLCZ)994100000010858798 100 $a20200403d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHandbook of Variational Methods for Nonlinear Geometric Data$b[electronic resource] /$fedited by Philipp Grohs, Martin Holler, Andreas Weinmann 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XXVI, 701 p. 159 illus., 125 illus. in color.) 311 $a3-030-31350-6 327 $a1. 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.ญญ- 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. 330 $aThis 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. 606 $aComputer mathematics 606 $aComputer science?Mathematics 606 $aOptical data processing 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aMath Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17044 606 $aImage Processing and Computer Vision$3https://scigraph.springernature.com/ontologies/product-market-codes/I22021 606 $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110 615 0$aComputer mathematics. 615 0$aComputer science?Mathematics. 615 0$aOptical data processing. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aMath Applications in Computer Science. 615 24$aImage Processing and Computer Vision. 615 24$aMathematical Applications in Computer Science. 676 $a515.64 702 $aGrohs$b Philipp$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aHoller$b Martin$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aWeinmann$b Andreas$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418277603316 996 $aHandbook of Variational Methods for Nonlinear Geometric Data$92377951 997 $aUNISA