Image Processing and Analysis with Graphs : Theory and Practice book cover
1st Edition

Image Processing and Analysis with Graphs
Theory and Practice

ISBN 9781315217284
Published July 12, 2017 by CRC Press
570 Pages 16 Color & 169 B/W Illustrations

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Book Description

Covering the theoretical aspects of image processing and analysis through the use of graphs in the representation and analysis of objects, Image Processing and Analysis with Graphs: Theory and Practice also demonstrates how these concepts are indispensible for the design of cutting-edge solutions for real-world applications.

Explores new applications in computational photography, image and video processing, computer graphics, recognition, medical and biomedical imaging

With the explosive growth in image production, in everything from digital photographs to medical scans, there has been a drastic increase in the number of applications based on digital images. This book explores how graphs—which are suitable to represent any discrete data by modeling neighborhood relationships—have emerged as the perfect unified tool to represent, process, and analyze images. It also explains why graphs are ideal for defining graph-theoretical algorithms that enable the processing of functions, making it possible to draw on the rich literature of combinatorial optimization to produce highly efficient solutions.

Some key subjects covered in the book include:

  • Definition of graph-theoretical algorithms that enable denoising and image enhancement
  • Energy minimization and modeling of pixel-labeling problems with graph cuts and Markov Random Fields
  • Image processing with graphs: targeted segmentation, partial differential equations, mathematical morphology, and wavelets
  • Analysis of the similarity between objects with graph matching
  • Adaptation and use of graph-theoretical algorithms for specific imaging applications in computational photography, computer vision, and medical and biomedical imaging

Use of graphs has become very influential in computer science and has led to many applications in denoising, enhancement, restoration, and object extraction. Accounting for the wide variety of problems being solved with graphs in image processing and computer vision, this book is a contributed volume of chapters written by renowned experts who address specific techniques or applications. This state-of-the-art overview provides application examples that illustrate practical application of theoretical algorithms. Useful as a support for graduate courses in image processing and computer vision, it is also perfect as a reference for practicing engineers working on development and implementation of image processing and analysis algorithms.

Table of Contents

Graph Theory Concepts and Definitions Used in Image Processing and Analysis, O. Lezoray and L. Grady


Basic Graph Theory

Graph Representation

Paths, Trees, and Connectivity

Graph Models in Image Processing and Analysis

Graph Cuts—Combinatorial Optimization in Vision,
H. Ishikawa


Markov Random Field

Basic Graph Cuts: Binary Labels

Multi-Label Minimization


Higher-Order Models in Computer Vision,
P. Kohli and C. Rother


Higher-Order Random Fields

Patch and Region-Based Potentials

Relating Appearance Models and Region-Based Potentials

Global Potentials

Maximum a Posteriori Inference

A Parametric Maximum Flow Approach for Discrete Total Variation Regularization,
A. Chambolle and J. Darbon


Idea of the approach

Numerical Computations


Targeted Image Segmentation Using Graph Methods,
L. Grady

The Regularization of Targeted Image Segmentation

Target Specification


A Short Tour of Mathematical Morphology on Edge and Vertex Weighted Graphs,
L. Najman and F. Meyer


Graphs and lattices

Neighborhood Operations on Graphs


Connected Operators and Filtering with the Component Tree

Watershed Cuts

MSF Cut Hierarchy and Saliency Maps

Optimization and the Power Watershed

Partial Difference Equations on Graphs for Local and Nonlocal Image Processing,
A. Elmoataz, O. Lezoray, V.-T. Ta, and S. Bougleux


Difference Operators on Weighted Graphs

Construction of Weighted Graphs

p-Laplacian Regularization on Graphs


Image Denoising with Nonlocal Spectral Graph Wavelets,
D.K. Hammond, L. Jacques, and P. Vandergheynst


Spectral Graph Wavelet Transform

Nonlocal Image Graph

Hybrid Local/Nonlocal Image Graph

Scaled Laplacian Model

Applications to Image Denoising



Image and Video Matting,
J. Wang


Graph Construction for Image Matting

Solving Image Matting Graphs

Data Set

Video Matting

Optimal Simultaneous Multisurface and Multiobject Image Segmentation
, X. Wu, M.K. Garvin, and M. Sonka


Motivation and Problem Description

Methods for Graph-Based Image Segmentation

Case Studies



Hierarchical Graph Encodings
, L. Brun and W. Kropatsch


Regular Pyramids

Irregular Pyramids Parallel construction schemes

Irregular Pyramids and Image properties

Graph-Based Dimensionality Reduction,
J.A. Lee and M. Verleysen



Classical methods

Nonlinearity through Graphs

Graph-Based Distances

Graph-Based Similarities

Graph embedding

Examples and comparisons

Graph Edit Distance—Theory, Algorithms, and Applications,
M. Ferrer and H. Bunke


Definitions and Graph Matching

Theoretical Aspects of GED

GED Computation

Applications of GED

The Role of Graphs in Matching Shapes and in Categorization,
B. Kimia


Using Shock Graphs for Shape Matching

Using Proximity Graphs for Categorization



3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching
, A. Sharma, R. Horaud, and D. Mateus


Graph Matrices

Spectral Graph Isomorphism

Graph Embedding and Dimensionality Reduction

Spectral Shape Matching

Experiments and Results


Appendix: Permutation and Doubly- stochastic Matrices

Appendix: The Frobenius Norm

Appendix: Spectral Properties of the Normalized Laplacian

Modeling Images with Undirected Graphical Models
, M.F. Tappen



Graphical Models for Modeling Image Patches

Pixel-Based Graphical Models

Inference in Graphical Models

Learning in Undirected Graphical Models

Tree-Walk Kernels for Computer Vision,
Z. Harchaoui and F. Bach


Tree-Walk Kernels as Graph Kernels

The Region Adjacency Graph Kernel as a Tree-Walk Kernel

The Point Cloud Kernel as a Tree-Walk Kernel

Experimental Results



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Olivier Lézoray received his B.Sc. in mathematics and computer science, as well as his M.Sc. and Ph.D. degrees from the Department of Computer Science, University of Caen, France, in 1992, 1996, and 2000, respectively. From September 1999 to August 2000, he was an assistant professor with the Department of Computer Science at the University of Caen. From September 2000 to August 2009, he was an associate professor at the Cherbourg Institute of Technology of the University of Caen, in the Communication Networks and Services Department. In July 2008, he was a visiting research fellow at the University of Sydney, Australia. Since September 2009, he has been a full professor at the Cherbourg Institute of Technology of the University of Caen, in the Communication Networks and Services Department. He also serves as Chair of the Institute Research Committee. In 2011 he cofounded Datexim and is a member of the scientific board of the company, which brought state-of-art image and data processing to market with applications in digital pathology. His research focuses on discrete models on graphs for image processing and analysis, image data classification by machine learning, and computer-aided diagnosis.

Leo Grady received his B.Sc. degree in electrical engineering from the University of Vermont in 1999 and a Ph.D. degree from the Cognitive and Neural Systems Department at Boston University in 2003. Dr. Grady was with Siemens Corporate Research in Princeton, where he worked as a Principal Research Scientist in the Image Analytics and Informatics division. He recently left Siemens to become Vice President of R&D at HeartFlow. The focus of his research has been on the modeling of images and other data with graphs. These graph models have generated the development and application of tools from discrete calculus, combinatorial/continuous optimization, and network analytics to perform analysis and synthesis of the images/data. The primary applications of his work have been in computer vision and biomedical applications. Dr. Grady currently holds 30 granted patents with more than 40 additional patents currently under review. He has also contributed to more than 20 Siemens products that target biomedical applications and are used in medical centers worldwide.