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.

chapter 1|24 pages

Graph theory concepts and definitions used in image processing and analysis

ByOlivier Lézoray, Leo Grady

chapter 2|39 pages

Graph Cuts—Combinatorial Optimization in Vision

ByHiroshi Ishikawa

chapter 3|28 pages

Higher-Order Models in Computer Vision

ByPushmeet Kohli, Carsten Rother

chapter 4|17 pages

A Parametric Maximum Flow Approach for Discrete Total Variation Regularization

ByChambolle Antonin, Jérôme Darbon

chapter 5|30 pages

Targeted Image Segmentation Using Graph Methods

ByLeo Grady

chapter 6|33 pages

A Short Tour of Mathematical Morphology on Edge and Vertex Weighted Graphs

ByLaurent Najman, Fernand Meyer

chapter 7|32 pages

Partial difference Equations on Graphs for Local and Nonlocal Image Processing

ByAbderrahim Elmoataz, Olivier Lézoray, Vinh-Thong Ta, Sébastien Bougleux

chapter 8|30 pages

Image Denoising with Nonlocal Spectral Graph Wavelets

ByDavid K. Hammond, Laurent Jacques, Pierre Vandergheynst

chapter 9|26 pages

Image and Video Matting

ByJue Wang

chapter 10|39 pages

Optimal Simultaneous Multisurface and Multiobject Image Segmentation

ByXiaodong Wu, Mona K. Garvin, Milan Sonka

chapter 11|45 pages

Hierarchical Graph Encodings

ByLuc Brun, Walter Kropatsch

chapter 12|28 pages

Graph-Based Dimensionality Reduction

ByJohn A. Lee, Michel Verleysen

chapter 13|40 pages

Graph Edit Distance—Theory, Algorithms, and Applications

ByMiquel Ferrer, Horst Bunke

chapter 14|18 pages

The Role of Graphs in Matching Shapes and in Categorization

ByBenjamin Kimia

chapter 15|34 pages

3D Shape Registration Using Spectral Graph Embedding and Probabilistic Matching

ByAvinash Sharma, Radu Horaud, Diana Mateus

chapter 16|24 pages

Modeling Images with Undirected Graphical Models

ByMarshall F. Tappen

chapter 17|29 pages

Tree-Walk Kernels for Computer Vision

ByZaid Harchaoui, Francis Bach