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by Leo Grady, Olivier Lezoray
Image Processing and Analysis with Graphs
Cover
Half Title
Title Page
Copyright Page
Dedication
Preface
The Editors
Contributors
Table of Contents
1 Graph theory concepts and definitions used in image processing and analysis
1.1 Introduction
1.2 Basic Graph Theory
1.3 Graph Representation
1.4 Paths, Trees, and Connectivity
1.5 Graph Models in Image Processing and Analysis
1.6 Conclusion
Bibliography
2 Graph Cuts—Combinatorial Optimization in Vision
2.1 Introduction
2.2 Markov Random Field
2.3 Basic Graph Cuts: Binary Labels
2.4 Multi-Label Minimization
2.5 Examples
2.6 Conclusion
Bibliography
3 Higher-Order Models in Computer Vision
3.1 Introduction
3.2 Higher-Order Random Fields
3.3 Patch and Region-Based Potentials
3.4 Relating Appearance Models and Region-Based Potentials
3.5 Global Potentials
3.6 Maximum a Posteriori Inference
3.7 Conclusions and Discussion
Bibliography
4 A Parametric Maximum Flow Approach for Discrete Total Variation Regularization
4.1 Introduction
4.2 Idea of the approach
4.3 Numerical Computations
4.4 Applications
Bibliography
5 Targeted Image Segmentation Using Graph Methods
5.1 The Regularization of Targeted Image Segmentation
5.2 Target Specification
5.3 Conclusion
Bibliography
6 A Short Tour of Mathematical Morphology on Edge and Vertex Weighted Graphs
6.1 Introduction
6.2 Graphs and lattices
6.3 Neighborhood Operations on Graphs
6.4 Filters
6.5 Connected Operators and Filtering with the Component Tree
6.6 Watershed Cuts
6.7 MSF Cut Hierarchy and Saliency Maps
6.8 Optimization and the Power Watershed
6.9 Conclusion
Bibliography
7 Partial difference Equations on Graphs for Local and Nonlocal Image Processing
7.1 Introduction
7.2 Difference Operators on Weighted Graphs
7.3 Construction of Weighted Graphs
7.4 p-Laplacian Regularization on Graphs
7.5 Examples
7.6 Concluding Remarks
Bibliography
8 Image Denoising with Nonlocal Spectral Graph Wavelets
8.1 Introduction
8.2 Spectral Graph Wavelet Transform
8.3 Nonlocal Image Graph
8.4 Hybrid Local/Nonlocal Image Graph
8.5 Scaled Laplacian Model
8.6 Applications to Image Denoising
8.7 Conclusions
8.8 Acknowledgments
Bibliography
9 Image and Video Matting
9.1 Introduction
9.2 Graph Construction for Image Matting
9.3 Solving Image Matting Graphs
9.4 Data Set
9.5 Video Matting
9.6 Conclusion
Bibliography
10 Optimal Simultaneous Multisurface and Multiobject Image Segmentation
10.1 Introduction
10.2 Motivation and Problem Description
10.3 Methods for Graph-Based Image Segmentation
10.4 Case Studies
10.5 Conclusion
10.6 Acknowledgments
Bibliography
11 Hierarchical Graph Encodings
11.1 Introduction
11.2 Regular Pyramids
11.3 Irregular Pyramids Parallel construction schemes
11.4 Irregular Pyramids and Image properties
11.5 Conclusion
Bibliography
12 Graph-Based Dimensionality Reduction
12.1 Summary
12.2 Introduction
12.3 Classical methods
12.4 Nonlinearity through Graphs
12.5 Graph-Based Distances
12.6 Graph-Based Similarities
12.7 Graph embedding
12.8 Examples and comparisons
12.9 Conclusions
Bibliography
13 Graph Edit Distance—Theory, Algorithms, and Applications
13.1 Introduction
13.2 Definitions and Graph Matching
13.3 Theoretical Aspects of GED
13.4 GED Computation
13.5 Applications of GED
13.6 Conclusions
Bibliography
14 The Role of Graphs in Matching Shapes and in Categorization
14.1 Introduction
14.2 Using Shock Graphs for Shape Matching
14.3 Using Proximity Graphs for Categorization
14.4 Conclusion
14.5 Acknowledgment
Bibliography
15 3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching
15.1 Introduction
15.2 Graph Matrices
15.3 Spectral Graph Isomorphism
15.4 Graph Embedding and Dimensionality Reduction
15.5 Spectral Shape Matching
15.6 Experiments and Results
15.7 Discussion
15.8 Appendix: Permutation and Doubly- stochastic Matrices
15.9 Appendix: The Frobenius Norm
15.10 Appendix: Spectral Properties of the Normalized Laplacian
Bibliography
16 Modeling Images with Undirected Graphical Models
16.1 Introduction
16.2 Background
16.3 Graphical Models for Modeling Image Patches
16.4 Pixel-Based Graphical Models
16.5 Inference in Graphical Models
16.6 Learning in Undirected Graphical Models
16.7 Conclusion
Bibliography
17 Tree-Walk Kernels for Computer Vision
17.1 Introduction
17.2 Tree-Walk Kernels as Graph Kernels
17.3 The Region Adjacency Graph Kernel as a Tree-Walk Kernel
17.4 The Point Cloud Kernel as a Tree-Walk Kernel
17.5 Experimental Results
17.6 Conlusion
17.7 Acknowledgments
Bibliography
Index
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Image Processing and Analysis with Graphs
Image Processing and Analysis with Graphs
THEORY
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PRACTICE
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