1st Edition

Image Processing and Analysis with Graphs Theory and Practice

Edited By Olivier Lezoray, Leo Grady Copyright 2012
    570 Pages 16 Color & 169 B/W Illustrations
    by CRC Press

    570 Pages 16 Color & 169 B/W Illustrations
    by CRC Press

    570 Pages 16 Color & 169 B/W Illustrations
    by CRC Press

    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.

    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




    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.