Contents
1 Graph theory concepts and definitions used in image processing and analysis
Olivier Lézoray and Leo Grady
1.4 Paths, Trees, and Connectivity
1.5 Graph Models in Image Processing and Analysis
2 Graph Cuts—Combinatorial Optimization in Vision
Hiroshi Ishikawa
2.3 Basic Graph Cuts: Binary Labels
3 Higher-Order Models in Computer Vision
Pushmeet Kohli and Carsten Rother
3.2 Higher-Order Random Fields
3.3 Patch and Region-Based Potentials
3.4 Relating Appearance Models and Region-Based Potentials
3.6 Maximum a Posteriori Inference
3.7 Conclusions and Discussion
4 A Parametric Maximum Flow Approach for Discrete Total Variation Regularization
Antonin Chambolle and Jérôme Darbon
5 Targeted Image Segmentation Using Graph Methods
Leo Grady
5.1 The Regularization of Targeted Image Segmentation
6 A Short Tour of Mathematical Morphology on Edge and Vertex Weighted Graphs
Laurent Najman and Fernand Meyer
6.3 Neighborhood Operations on Graphs
6.5 Connected Operators and Filtering with the Component Tree
6.7 MSF Cut Hierarchy and Saliency Maps
6.8 Optimization and the Power Watershed
7 Partial difference Equations on Graphs for Local and Nonlocal Image Processing
Abderrahim Elmoataz, Olivier Lézoray, Vinh-Thong Ta, and Sébastien Bougleux
7.2 Difference Operators on Weighted Graphs
7.3 Construction of Weighted Graphs
7.4 p-Laplacian Regularization on Graphs
8 Image Denoising with Nonlocal Spectral Graph Wavelets
David K. Hammond, Laurent Jacques, and Pierre Vandergheynst
8.2 Spectral Graph Wavelet Transform
8.4 Hybrid Local/Nonlocal Image Graph
8.6 Applications to Image Denoising
Jue Wang
9.2 Graph Construction for Image Matting
9.3 Solving Image Matting Graphs
10 Optimal Simultaneous Multisurface and Multiobject Image Segmentation
Xiaodong Wu, Mona K. Garvin, and Milan Sonka
10.2 Motivation and Problem Description
10.3 Methods for Graph-Based Image Segmentation
11 Hierarchical Graph Encodings
Luc Brun and Walter Kropatsch
11.3 Irregular Pyramids Parallel construction schemes
11.4 Irregular Pyramids and Image properties
12 Graph-Based Dimensionality Reduction
John A. Lee and Michel Verleysen
12.4 Nonlinearity through Graphs
13 Graph Edit Distance—Theory, Algorithms, and Applications
Miquel Ferrer and Horst Bunke
13.2 Definitions and Graph Matching
13.3 Theoretical Aspects of GED
14 The Role of Graphs in Matching Shapes and in Categorization
Benjamin Kimia
14.2 Using Shock Graphs for Shape Matching
14.3 Using Proximity Graphs for Categorization
15 3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching
Avinash Sharma, Radu Horaud, and Diana Mateus
15.3 Spectral Graph Isomorphism
15.4 Graph Embedding and Dimensionality Reduction
15.8 Appendix: Permutation and Doubly- stochastic Matrices
15.9 Appendix: The Frobenius Norm
15.10 Appendix: Spectral Properties of the Normalized Laplacian
16 Modeling Images with Undirected Graphical Models
Marshall F. Tappen
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
17 Tree-Walk Kernels for Computer Vision
Zaid Harchaoui and Francis Bach
17.2 Tree-Walk Kernels as Graph Kernels
17.3 The Region Adjacency Graph Kernel as a Tree-Walk Kernel