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Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20 [Kõva köide]

Volume editor (Technion - Israel Institute of Technology, Israel), Volume editor (Hong Kong Baptist University, Hong Kong, University of Berge, Norway)
  • Formaat: Hardback, 706 pages, kõrgus x laius: 229x152 mm, kaal: 1220 g
  • Sari: Handbook of Numerical Analysis
  • Ilmumisaeg: 15-Oct-2019
  • Kirjastus: North-Holland
  • ISBN-10: 0444641408
  • ISBN-13: 9780444641403
Teised raamatud teemal:
Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20Suurem pilt
  • Formaat: Hardback, 706 pages, kõrgus x laius: 229x152 mm, kaal: 1220 g
  • Sari: Handbook of Numerical Analysis
  • Ilmumisaeg: 15-Oct-2019
  • Kirjastus: North-Holland
  • ISBN-10: 0444641408
  • ISBN-13: 9780444641403
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780444641403.html
Märksõnad:

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more.

  • Covers contemporary developments relating to the analysis and learning of images, shapes and forms
  • Presents mathematical models and quick computational techniques relating to the topic
  • Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods
Contributors xv
Preface xix
1 Diffusion operators for multimodal data analysis
1(40)
Tal Shnitzer
Roy R. Lederman
Gi-Ren Liu
Ronen Talmon
Hau-Tieng Wu
1 Introduction
2(1)
2 Preliminaries: Diffusion Maps
3(2)
3 Alternating Diffusion
5(12)
3.1 Problem formulation: Metric spaces and probabilistic setting
5(1)
3.2 Illustrative example
5(5)
3.3 Algorithm
10(2)
3.4 Common manifold interpretation
12(5)
4 Self-adjoint operators for recovering hidden components
17(6)
4.1 Problem formulation
18(1)
4.2 Operator definition and analysis
19(3)
4.3 Discrete setting
22(1)
5 Applications
23(15)
5.1 Shape analysis
23(2)
5.2 Foetal heart rate recovery
25(2)
5.3 Sleep dynamics assessment
27(11)
References
38(3)
2 Intrinsic and extrinsic operators for shape analysis
41(76)
Yu Wang
Justin Solomon
1 Introduction
42(2)
2 Preliminaries
44(1)
2.1 Extrinsic and intrinsic geometry
44(1)
2.2 Operators and spectra
45(1)
3 Theoretical aspects and numerical analysis
45(13)
3.1 Basics of linear operators
45(4)
3.2 PDEs and Green's functions
49(3)
3.3 Operator derivation and discretization
52(3)
3.4 Operators and geometry
55(1)
3.5 Inverse problems
56(2)
4 Spectral shape analysis and applications
58(18)
4.1 Spectral analysis: From Euclidean space to manifold
58(1)
4.2 Spectral data analysis
59(3)
4.3 Spectral analysis: Point embedding, signature, and geometric descriptors
62(4)
4.4 Shape analysis and geometry processing
66(6)
4.5 Other aspects of spectral shape analysis
72(1)
4.6 Numerical aspects
73(3)
5 Relevant geometric operators
76(16)
5.1 Identity operator, area form, and mass matrix
76(2)
5.2 Laplace-Beltrami (intrinsic Laplacian)
78(2)
5.3 Combinatorial and graph Laplacians
80(1)
5.4 Restricted Laplacian
80(1)
5.5 Scale invariant Laplacian
81(1)
5.6 Affine and equi-affine invariant Laplacian
81(1)
5.7 Anisotropic Laplacian
82(1)
5.8 Hessian and normal-restricted Hessian: A family of linearized energies
83(1)
5.9 Modified Dirichlet energy
83(1)
5.10 Hamiltonian operator and Schrodinger operator
84(1)
5.11 Curvature Laplacian
85(1)
5.12 Concavity-aware Laplacian
85(1)
5.13 Extrinsic and relative Dirac operators
86(2)
5.14 Intrinsic Dirac operator D
88(1)
5.15 Volumetric (extrinsic) Laplacian
88(1)
5.16 Hessian energy
89(1)
5.17 Single layer potential operator and kernel method
90(1)
5.18 Dirichlet-to-Neumann operator (Poincare-Steklov operator)
91(1)
5.19 Other extrinsic methods
92(1)
6 Summary and experiments
92(11)
6.1 Experiments
93(1)
6.2 Eigenfunctions
93(3)
6.3 Heat kernel signatures
96(1)
6.4 Segmentation
97(3)
6.5 Distance or dissimilarity
100(3)
7 Conclusion and future work
103(1)
7.1 Summary
103(1)
7.2 Future work
104(1)
Acknowledgements
104(1)
References
105(12)
3 Operator-based representations of discrete tangent vector fields
117(32)
Mirela Ben-Chen
Omri Azencot
1 Introduction
119(1)
1.1 Organization
120(1)
2 Smooth functional vector fields
120(8)
2.1 Notation
120(1)
2.2 Directional derivative of functions
121(1)
2.3 Functional vector fields
121(1)
2.4 Flow maps
122(1)
2.5 Functional flow maps
123(3)
2.6 Lie bracket
126(2)
3 Discrete functional vector fields
128(8)
3.1 Notation
128(3)
3.2 Directional derivative of functions
131(1)
3.3 Functional vector fields
131(2)
3.4 Flow maps
133(1)
3.5 Functional flow maps
133(2)
3.6 Lie bracket
135(1)
4 Divergence-based functional vector fields
136(10)
4.1 Smooth DFVF
136(1)
4.2 Discrete DFVF
136(1)
4.3 Mixed Lie bracket operator
137(5)
4.4 The Lie bracket as a linear transformation on vector fields
142(2)
4.5 Integrating the Lie bracket operator
144(1)
4.6 Outlook
145(1)
5 Conclusion and future work
146(1)
References
146(3)
4 Active contour methods on arbitrary graphs based on partial differential equations
149(42)
Christos Sakaridis
Nikos Kolotouros
Kimon Drakopoulos
Petros Maragos
1 Introduction
150(1)
2 Background and related work
151(4)
3 Active contours on graphs via geometric approximations of gradient and curvature
155(14)
3.1 Geometric gradient approximation on graphs
155(8)
3.2 Geometric curvature approximation on graphs
163(3)
3.3 Gaussian smoothing on graphs
166(3)
4 Active contours on graphs using a finite element framework
169(9)
4.1 Problem formulation and numerical approximation
169(5)
4.2 Locally constrained contour evolution
174(4)
5 Experimental results
178(8)
6 Conclusion
186(1)
References
187(4)
5 Fast operator-splitting algorithms for variational imaging models: Some recent developments
191(42)
Roland Glowinski
Shousheng Luo
Xue-Cheng Tai
1 Introduction
192(1)
2 Regularizers and associated variational models for image restoration
193(5)
2.1 Generalities
193(1)
2.2 Total variation regularization
194(1)
2.3 The Euler elastica regularization
195(1)
2.4 L1-Mean curvature and L1-Gaussian curvature energies
196(1)
2.5 Willmore bending energy
197(1)
2.6 Summary
198(1)
3 Basic results, notations and an introduction to operator-splitting methods
198(5)
3.1 Basic results and notations
198(2)
3.2 The Lie and Marchuk-Yanenko operator-splitting schemes for the time discretization of initial value problems
200(1)
3.3 Time discretization of the initial value problem (17) by the Lie scheme
201(1)
3.4 Asymptotic properties of the Lie and Marchuk-Yanenko schemes
202(1)
4 Operator splitting method for Euler elastica energy functional
203(7)
4.1 Formulation of the problem and operator-splitting solution methods
203(4)
4.2 On the solution of problem (44)
207(1)
4.3 On the solution of problem (45)
208(2)
4.4 On the solution of problem (46)
210(1)
5 An operator-splitting method for the Willmore energy-based variational model
210(7)
5.1 Formulation of the problem and operator-splitting solution methods
210(3)
5.2 On the solution of problem (77)
213(2)
5.3 On the solution of problem (78)
215(1)
5.4 Estimating
216(1)
6 An operator-splitting method for the &£1-mean curvature variational model
217(4)
7 Operator-splitting methods for the ROF model
221(6)
7.1 Generalities: synopsis
221(1)
7.2 A first operator-splitting method
222(2)
7.3 A second operator-splitting method
224(3)
8 Conclusion
227(1)
Acknowledgements
227(1)
References
227(6)
6 From active contours to minimal geodesic paths: New solutions to active contours problems by Eikonal equations
233(40)
Da Chen
Laurent D. Cohen
1 Introduction
234(2)
1.1 Outline
235(1)
2 Active contour models
236(7)
2.1 Edge-based active contour model
236(4)
2.2 The piecewise smooth Mumford-Shah model and the piecewise constant reduction model
240(3)
3 Minimal paths for edge-based active contours problems
243(4)
3.1 Cohen-Kimmel minimal path model
243(2)
3.2 Finsler and Randers minimal paths
245(2)
4 Minimal paths for alignment active contours
247(6)
4.1 Randers alignment minimal paths
247(4)
4.2 Riemannian alignment minimal paths
251(2)
5 Orientation-lifted Randers minimal paths for Euler-Mumford elastica problem
253(8)
5.1 Euler-Mumford elastica problem and its Finsler metric interpretation
254(1)
5.2 Finsler elastica geodesic path for approximating the elastica curve
255(2)
5.3 Data-driven Finsler elastica metric
257(4)
6 Randers minimal paths for region-based active contours
261(7)
6.1 Hybrid active contour model
261(2)
6.2 A Randers metric interpretation to the hybrid energy
263(1)
6.3 Practical implementations
264(1)
6.4 Application to image segmentation
265(3)
7 Conclusion
268(1)
Acknowledgements
269(1)
References
269(4)
7 Computable invariants for curves and surfaces
273(42)
Oshri Halimi
Dan Raviv
Yonathan Aflalo
Ron Kimmel
1 Introduction
274(3)
2 Scale invariant metric
277(8)
2.1 Scale invariant arc-length for planar curves
277(1)
2.2 Scale invariant metric for implicitly defined planar curves
278(1)
2.3 Scale invariant metric for surfaces
279(1)
2.4 Approximating the scale invariant Laplace-Beltrami operator for surfaces
280(5)
3 Equi-affine invariant metric
285(3)
3.1 Equi-affine invariant arc-length
285(1)
3.2 Equi-affine metric for surfaces
286(2)
4 Affine metric
288(6)
4.1 Affine invariant arc-length
288(1)
4.2 Affine metric for surfaces
289(3)
4.3 Approximating the Gaussian curvature
292(2)
5 Applications
294(16)
5.1 Self functional maps: A song of shapes and operators
294(11)
5.2 Object recognition
305(5)
6 Summary
310(1)
Acknowledgements
310(1)
References
311(4)
8 Solving PDEs on manifolds represented as point clouds and applications
315(36)
Rongjie Lai
Hongkai Zhao
1 Introduction
316(2)
2 Solving PDEs on manifolds represented as point clouds
318(6)
2.1 Moving least square methods
318(2)
2.2 Local mesh method
320(4)
3 Solving Fokker-Planck equation for dynamic system
324(7)
3.1 Double well potential
327(2)
3.2 Rugged Mueller potential
329(2)
4 Solving PDEs on incomplete distance data
331(6)
5 Geometric understanding of point clouds data
337(6)
5.1 Construction of skeletons from point clouds
338(1)
5.2 Construction of conformal mappings from point clouds
339(1)
5.3 Nonrigid manifolds registration using LB eigenmap
340(3)
6 Conclusion
343(2)
Acknowledgements
345(1)
References
345(6)
9 Tighter continuous relaxations for MAP inference in discrete MRFs: A survey
351(50)
Hariprasad Kannan
Nikos Komodakis
Nikos Paragios
1 LP relaxation
354(8)
1.1 Tightening the polytope
357(5)
2 Cluster pursuit algorithms
362(7)
3 Cycles in the graph
369(8)
3.1 Searching for frustrated cycles
372(2)
3.2 Efficient MAP inference in a cycle
374(1)
3.3 Planar subproblems
375(2)
4 Tighter subgraph decompositions
377(3)
4.1 Global higher-order cliques
378(2)
5 Semidefinite programming-based relaxation
380(14)
5.1 Rounding schemes for SDP relaxation
392(1)
5.2 Problems where SDP relaxation has helped
393(1)
6 Characterizing tight relaxations
394(2)
7 Conclusion
396(1)
References
396(5)
10 Lagrangian methods for composite optimization
401(36)
Shoham Sabach
Marc Teboulle
1 Introduction
402(2)
2 The Lagrangian framework
404(10)
2.1 Lagrangian-based methods: Basic elements and mechanism
404(3)
2.2 Proximal mappings and minimization
407(4)
2.3 Application examples
411(3)
3 The convex setting
414(10)
3.1 Preliminaries on the convex model (CM)
414(2)
3.2 Proximal method of multipliers and fundamental Lagrangian-based schemes
416(2)
3.3 One scheme for all: A perturbed PMM and its global rate analysis
418(4)
3.4 Special cases of the perturbed PMM: Fundamental schemes
422(2)
4 The nonconvex setting
424(9)
4.1 The nonconvex nonlinear composite optimization--- Preliminaries
425(2)
4.2 ALBUM---Adaptive Lagrangian-based multiplier method
427(2)
4.3 A methodology for global analysis of Lagrangian-based methods
429(2)
4.4 ALBUM in action: Global convergence of Lagrangian-based schemes
431(2)
Acknowledgements
433(1)
References
433(4)
11 Generating structured nonsmooth priors and associated primal-dual methods
437(66)
Michael Hintermuller
Kostas Papafitsoros
1 Introduction
438(11)
1.1 Context
438(11)
1.2 Main contributions and organization of this chapter
449(1)
2 Nonsmooth priors
449(13)
2.1 Total Variation
449(4)
2.2 Total generalized variation
453(2)
2.3 Dualization
455(6)
2.4 Dualization of the variational regularization problems
461(1)
3 Numerical algorithms
462(7)
4 Bilevel optimization
469(11)
4.1 Background
469(4)
4.2 Bilevel optimization---A monolithic approach
473(7)
5 Numerical examples
480(14)
5.1 Discrete operators for (Pjv)
481(4)
5.2 Bilevel TV numerical experiments
485(3)
5.3 Discrete operators for (Pjcv)
488(3)
5.4 Bilevel TGV numerical experiments
491(3)
References
494(9)
12 Graph-based optimization approaches for machine learning, uncertainty quantification and networks
503(30)
Andrea L. Bertozzi
Ekaterina Merkurjev
1 Introduction
504(1)
2 Graph theory
505(2)
3 Recent methods for semisupervised and unsupervised data classification
507(11)
3.1 Semisupervised learning and the Ginzburg-Landau graph model
508(3)
3.2 The graph MBO scheme for data classification and image processing
511(2)
3.3 Heat kernel pagerank method
513(1)
3.4 Unsupervised learning and the Mumford-Shah model
514(1)
3.5 Imposing volume constraints
515(3)
4 Total variation methods for semisupervised and unsupervised data classification
518(4)
5 Uncertainty quantification within the graphical framework
522(1)
6 Networks
523(3)
7 Conclusion
526(1)
Acknowledgements
527(1)
References
527(6)
13 Survey of fast algorithms for Euler's elastica-based image segmentation
533(20)
Sung Ha Kang
Xue-Cheng Tai
Wei Zhu
1 Introduction
534(1)
2 Piecewise constant representation and interface problems to illusory contour with curvature term
535(5)
3 Euler's elastica-based segmentation models and fast algorithms
540(7)
4 Discussion
547(1)
References
548(5)
14 Recent advances in denoising of manifold-valued images
553(26)
R. Bergmann
F. Laus
J. Persch
C. Steidl
1 Introduction
554(3)
2 Preliminaries on Riemannian manifolds
557(4)
2.1 General notation
557(3)
2.2 Convexity and Hadamard manifolds
560(1)
3 Intrinsic variational restoration models
561(3)
4 Minimization algorithms
564(8)
4.1 Subgradient descent
564(1)
4.2 Half-quadratic minimization
565(2)
4.3 Proximal point and Douglas-Rachford algorithm
567(5)
5 Numerical examples
572(2)
6 Conclusions
574(1)
References
574(5)
15 Image and surface registration
579(34)
Ke Chen
Lok Ming Lui
Jan Modersitzki
1 Introduction
580(3)
2 Mathematical background
583(2)
2.1 Continuous and discrete images
583(2)
2.2 A mathematical framework for image registration
585(1)
3 Distance measures
585(5)
3.1 Volumetric differences
585(3)
3.2 Feature-based differences
588(2)
4 Regularization
590(7)
4.1 Regularization by ansatz-spaces, parametric registration
590(1)
4.2 Quadratic regularizer
591(1)
4.3 Nonquadratic regularizer
592(2)
4.4 Registration penalties and constraints
594(1)
4.5 Penalties for locally invertible maps
594(1)
4.6 Diffeomorphic registration
595(1)
4.7 Registration by inverse consistent approach
596(1)
5 Surface registration
597(6)
5.1 Brief introduction to surface geometry
597(2)
5.2 Parameterization-based approaches
599(1)
5.3 Laplace-Beltrami eigenmap approaches
600(1)
5.4 Metric approaches
600(1)
5.5 Functional map approaches
601(1)
5.6 Relationship between SR and IR
601(2)
6 Numerical methods
603(2)
7 Deep learning-based registration
605(1)
8 Conclusions
606(1)
References
606(7)
16 Metric registration of curves and surfaces using optimal control
613(34)
Martin Bauer
Nicolas Charon
Laurent Younes
1 Introduction
614(2)
2 Building metrics via submersions
616(3)
3 Optimal control framework
619(3)
4 Chordal metrics on shapes
622(4)
4.1 Motivation
622(1)
4.2 General principle
623(1)
4.3 Oriented varifold distances
624(2)
4.4 Numerical aspects
626(1)
5 Intrinsic metrics
626(9)
5.1 Reparametrization-invariant metrics on parametrized shapes
627(2)
5.2 The metric on the space of unparametrized shapes
629(1)
5.3 The induced geodesic distance
630(1)
5.4 The geodesic equation
631(1)
5.5 An optimal control formulation of the geodesic problem on the space of unparametrized shapes
632(1)
5.6 Numerical aspects
633(2)
6 Outer deformation metric models
635(4)
7 A hybrid metric model
639(2)
8 Conclusion
641(1)
Acknowledgements
642(1)
References
642(5)
17 Efficient and accurate structure preserving schemes for complex nonlinear systems
647(24)
Jie Shen
1 Introduction
647(2)
2 The SAV approach
649(6)
2.1 Suitable energy splitting
653(1)
2.2 Adaptive time stepping
654(1)
3 Several extensions of the SAV approach
655(11)
3.1 Problems with global constraints
655(3)
3.2 L1 minimization via hyper regularization
658(1)
3.3 Free energies with highly nonlinear terms
659(2)
3.4 Coupling with other physical conservation laws
661(3)
3.5 Dissipative/conservative systems which are not driven by free energy
664(2)
4 Conclusion
666(1)
Acknowledgements
666(1)
References
666(5)
Index 671
Ron Kimmel is a Professor of Computer Science at the Technion where he holds the Montreal Chair in Sciences. He held a post-doctoral position at UC Berkeley and a visiting professorship at Stanford University. He has worked in various areas of image and shape analysis in computer vision, image processing, and computer graphics. Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging and computational biometry, numerical optimization of problems with a geometric flavor, and applications of metric geometry, deep learning, and differential geometry. Kimmel is an IEEE Fellow for his contributions to image processing and non-rigid shape analysis. He is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing Lab. and a founder and advisor of several successful image processing and analysis companies. Professor Tai Xue-Cheng is a member of the Department of Mathematics at the Hong Kong Baptist University, Hong Kong and also the University of Bergen of Norway. His research interests include Numerical partial differential equations, optimization techniques, inverse problems, and image processing. He is the winner for several prizes for his contributions to scientific computing and innovative researches for image processing. He served as organizing and program committee members for many international conferences and has been often invited for international conferences. He has served as referee and reviewers for many premier conferences and journals.