Applied Graph Theory in Computer Vision and Pattern Recognition

1. Front Matter

   Pages I-X

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2. Applied Graph Theory for Low Level Image Processing and Segmentation

   1. Front Matter

      Pages 1-1

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   2. Multiresolution Image Segmentations in Graph Pyramids

      • Walter G. Kropatsch, Yll Haxhimusa, Adrian Ion

      Pages 3-41

   3. A Graphical Model Framework for Image Segmentation

      • Rui Huang, Vladimir Pavlovic, Dimitris N. Metaxas

      Pages 43-63

   4. Digital Topologies on Graphs

      • Alain Bretto

      Pages 65-82

3. Graph Similarity, Matching, and Learning for High Level Computer Vision and Pattern Recognition

   1. Front Matter

      Pages 84-84

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   2. How and Why Pattern Recognition and Computer Vision Applications Use Graphs

      • Donatello Conte, Pasquale Foggia, Carlo Sansone, Mario Vento

      Pages 85-135

   3. Efficient Algorithms on Trees and Graphs with Unique Node Labels

      • Gabriel Valiente

      Pages 137-149

   4. A Generic Graph Distance Measure Based on Multivalent Matchings

      • Sébastien Sorlin, Christine Solnon, Jean-Michel Jolion

      Pages 151-181

   5. Learning from Supervised Graphs

      • Joseph Potts, Diane J. Cook, Lawrence B. Holder

      Pages 183-201

4. Special Applications

   1. Front Matter

      Pages 204-204

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   2. Graph-Based and Structural Methods for Fingerprint Classification

      • Gian Luca Marcialis, Fabio Roli, Alessandra Serrau

      Pages 205-226

   3. Graph Sequence Visualisation and its Application to Computer Network Monitoring and Abnormal Event Detection

      • Horst Bunke, P. Dickinson, A. Humm, Ch. Irniger, M. Kraetzl

      Pages 227-245

   4. Clustering of Web Documents Using Graph Representations

      • Adam Schenker, Horst Bunke, Mark Last, Abraham Kandel

      Pages 247-265

Graph theory has strong historical roots in mathematics, especially in topology. Its birth is usually associated with the “four-color problem” posed by Francis Guthrie 1 in 1852, but its real origin probably goes back to the Seven Bridges of Konigsber ¨ g 2 problem proved by Leonhard Euler in 1736. A computational solution to these two completely different problems could be found after each problem was abstracted to the level of a graph model while ignoring such irrelevant details as country shapes or cross-river distances. In general, a graph is a nonempty set of points (vertices) and the most basic information preserved by any graph structure refers to adjacency relationships (edges) between some pairs of points. In the simplest graphs, edges do not have to hold any attributes, except their endpoints, but in more sophisticated graph structures, edges can be associated with a direction or assigned a label. Graph vertices can be labeled as well. A graph can be represented graphically as a drawing (vertex=dot,edge=arc),but,aslongaseverypairofadjacentpointsstaysconnected by the same edge, the graph vertices can be moved around on a drawing without changing the underlying graph structure. The expressive power of the graph models placing a special emphasis on c- nectivity between objects has made them the models of choice in chemistry, physics, biology, and other ?elds.

• Matching
• algorithm
• algorithms
• classification
• cognition
• computer vision
• fingerprint
• graph theory
• graphs
• image processing
• image segmentation
• learning
• network
• pattern
• pattern recognition

• Computer Science & Engineering Department, University of South Florida, Tampa, USA

  Abraham Kandel

• Institute of Computer Science and Applied Mathematics (IAM), Bern, Switzerland

  Horst Bunke

• Department of Information Systems Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

  Mark Last

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