Recognition as Graph Matching
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The document discusses graph matching in pattern recognition, covering various approaches, algorithms, and applications. It highlights the significance of measuring object similarity through graph representations and introduces various taxonomies such as isomorphism and graph edit distance. It concludes with future research directions and the potential efficiency of focused graph subclasses in practical applications.
Recognition as Graph Matching
- 1. RECOGNITION AS GRAPH MATCHING Presented By- Vishakha Agarwal (Research Scholar) M.Tech, Final Year Department of Computer Science and Information Technology
- 2. OUTLINE Introduction Pattern recognition approaches Graphs in pattern recognition Graph matching taxonomy Graph matching algorithms Graph based recognition: Application taxonomy Graph based recognition: Application Discussions and conclusions References
- 3. INTRODUCTION In many practical problems, there is a need to make some decision about the content of an image or about the classification of an object that it contains. For example, the user of a notebook computer may be able to give input using hand printed characters. The classification process might actually fail, either because the character is badly made, or because the person invented a new character. Recognition means “To Know Again.” A recognition system must contain some memory of the objects that it is to recognize.
- 4. PATTERN RECOGNITION APPROACHES Traditional subdivision of pattern recognition:
- 5. PATTERN RECOGNITION APPROACHES: STATISTICAL APPROACH Advantages: Theoretically well founded. Many powerful algorithms available. Disadvantages Dimension of feature vector fixed. Only unary feature values, but no relations can be modeled.
- 6. PATTERN RECOGNITION APPROACHES: STRUCTURAL APPROACH Advantages Representation size is variable. Higher representation power. Disadvantages: Lack of mathematical structure in the graph domain. Lack of algorithmic tools.
- 7. GRAPHS IN PATTERN RECOGNITION In pattern recognition and computer vision, it is required to measure the similarity of objects. When graphs are used for the representation of structured objects, then the problem of measuring object similarity turns into the problem of computing the similarity of graphs, which is also known as graph matching. If graphs are used for object representation this problem turns into determining the similarity of graphs.
- 8. GRAPHS IN PATTERN RECOGNITION Standard concepts in graph matching include graph isomorphism, subgraph isomorphism, and maximum common subgraph. However, in real world applications we can’t always expect a perfect match between the input and one of the graphs in the database. Therefore, what is needed is an algorithm for error- tolerant matching, or equivalently , a method that computes a measure of similarity between two given graphs.
- 9. GRAPH MATCHING TAXONOMY In graph matching, we used to consider directed and labeled graphs, which are sometimes synonymously referred to as (attributed) relational graphs, or relational structures. If we delete some nodes from a graph, together with their incident edges, we obtain a subgraph g’ ⊆ g.
- 10. GRAPH MATCHING TAXONOMY Graph matching can be done by- Graph Isomorphism- In this, the exact structural correspondence is sought: there must be a bijective mapping between the nodes of the two graphs that preserves the edges of both graphs.
- 11. GRAPH MATCHING TAXONOMY • Subgraph Isomorphism- It requires the existence of an isomorphism between one of the graphs and a subgraph of the other. In other words, one of the graphs may have extra nodes and extra edges linking these new nodes to the rest.
- 12. GRAPH MATCHING TAXONOMY • Monomorphism- In monomorphism, extra edges in the larger graph are allowed also between nodes that do have a correspondent in the smaller graph.
- 13. GRAPH MATCHING TAXONOMY Maximum Common Subgraph- It is the largest subgraph of one of the two graphs that is isomorphic to a subgraph of the other. This kind of matching allows both graphs to have extra nodes and edges, but is also significantly more expensive from a computational viewpoint. Weighted graph matching- Here the edges of the graphs have a weight, and the goal is to find the common subgraph with the largest total weight.
- 14. GRAPH MATCHING TAXONOMY Graph Edit Distance- It measures the similarity of two graphs by computing the minimum-cost set of edit operations needed to transform one of the graphs into the other. The sequence of edit operations that transform g into g’ implies an error-correcting mapping from the nodes of g to the nodes of g’.
- 15. GRAPH MATCHING ALGORITHMS The standard algorithm for graph and subgraph isomorphism detection is the one by Ullman , in which Maximum common subgraph detection has been addressed. Most of these algorithms are particular versions of the A* search procedure, i.e., they rely on some kind of tree search incorporating various heuristic look-ahead techniques in order to prune the search space. Other approaches are based on neural networks such as the Hopfield network or the Kohonen map. Also genetic algorithms have been used in many approximate method based on maximum flow . However, all of these approximate methods may get tracked in local minima and miss the optimal solution.
- 16. GRAPH BASED RECOGNITION: APPLICATION TAXONOMY At least six application areas in which graph matching techniques have been successfully employed can be individuated: 2D and 3D image analysis and processing Document processing Biometric identification Image databases Video analysis Biological and biomedical applications
- 17. GRAPH BASED RECOGNITION: APPLICATION Automatic Transcription of Handwritten Medieval Text Digitization of historical documents has become a focus of intensive research.
- 18. GRAPH BASED RECOGNITION: APPLICATION Challenges in the Transcription of Handwritten Historical Documents Layout analysis and extraction of text Decorations Decay of paper or parchment Faded ink Bleed through Various other artifacts Lack of language model etc.
- 20. GRAPH BASED RECOGNITION: APPLICATION Problems with the conventional approach- Two dimensional shape of the characters is not adequately modeled; no structural relations. Possible Solution: Use skeletons to represent the handwriting by a graph. Transform the graph of a handwritten text into a sequence of feature vectors. Apply HMMs and RNNs to sequence of feature vectors.
- 21. GRAPH BASED RECOGNITION: APPLICATION Graph Extraction- Apply a thinning operator to generate the skeleton of the image. Nodes: Key points: crossings, junctions, end points, left-most points of circular arcs. Secondary points: equidistant points on the skeleton between key points; distance d is a parameter. Edges: Nodes that are neighbors on the skeleton are connected by edges.
- 23. GRAPH BASED RECOGNITION: APPLICATION Comments- In this application, graph-matching based feature extraction could reduce the error rate by about 50% compared to a standard set of features. Because the graphs are rather small, the additional computational cost is moderate (compared to HMM decoding) Recent experiments with alternative graph distance measures have given good results.
- 24. DISCUSSIONS AND CONCLUSIONS Recognition and learning of patterns are subjects of considerable depth and interest to cognitive psychology, pattern recognition, and computer vision. A wide spectrum of graph matching algorithms have become available meanwhile. They range from deterministic approaches, suitable for finding optimal solutions to problems involving graphs with a limited number of nodes and edges, to approximate methods that are applicable to large-scale problems.
- 25. DISCUSSIONS AND CONCLUSIONS It is conjectured that there are many applications in pattern recognition and computer vision where the full representational power of graphs may not be needed. Restricting the focus on special subclasses of graphs may result in more efficient matching procedures. Other promising areas of future research include the automatic inference of edit costs from a set of sample graphs, and the combination of optimal and approximate graph matching methods.
- 26. REFERENCES http://www.cse.nd.edu/Fu_Prize_Seminars/bunke/slides.pdf. Valiente G.,et. al,An Image Similarity for Graph Matching,0- 7695-0746-8/00 ©2010 IEEE. http://www.nptel.ac.in/courses/117104069/chapter_1/1_10.html. Wachinger C.,et.al, Structural Image Representation for Image Registration , 978-1-4244-7028-0/10/ ©2010 IEEE. Conte D.,et.al, Graph Matching Application in Pattern Recognition and Image Processing, 0-7803-7750-8/03 ©2003 IEEE. Bunke H.,et.al,Graph Matching: Theoritical foundations, Algorithms ,and Applications.
- 27. REFERENCES Wiskott L.,et.al,Face Recognition by Elastic Bunch graph Matching,7th intern conference, on Computer Analysis on Images and Patterns, Keil, Germany, September 1997. International Master of Research in Computer Science: Computer Aided Decision Support, Graph for Pattern Recognition, Author: Romain Raveaux , Zeina Abu-Aisheh, in the RFAI groups at the University of Tours ,October 2013. Caetano T.,et.al,Learning Graph Matching,IEEE Transactions on Pattern Analysis and Machine Intelligence, VOL 31, NO. 6, June 2009.
Editor's Notes
- #6: The notion of a statistic is intimately connected to the concept of a probability distribution, generally the distribution of signal amplitudes.