1 / 25

Hubert  CARDOT

Graph Signature: A Simple Approach for Clustering Similar Graphs Applied to Graphic Symbols Recognition. Rashid-Jalal QURESHI. JY- RAMEL. Hubert  CARDOT. Université François Rabelais de Tours, Laboratoire d'Informatique 64, Avenue Jean Portalis, 37200 TOURS – France.

toviel
Download Presentation

Hubert  CARDOT

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Graph Signature: A Simple Approach for Clustering Similar Graphs Applied to Graphic Symbols Recognition Rashid-Jalal QURESHI JY- RAMEL Hubert  CARDOT Université François Rabelais de Tours, Laboratoire d'Informatique 64, Avenue Jean Portalis, 37200 TOURS – France Pascal workshop (June 14, 2007)

  2. Plan _ Introduction _ Graph Based Symbol’s Representation Graphics Primitives Extraction + Attributed Graph Generation + _ Proposed Graph Matching Methods + Graph Mining for Feature Vector Extraction + Graph Matching using G-Signature _ Results & Conclusion _ Perspectives ( Future Works) Pascal workshop (June 14, 2007) 2

  3. Introduction Document Image Analysis Text Part Graphics Part Character recognition Lines recognition Logos recognition Symbols recognition Professional softwares already exist Graphic Symbols Attributed Graph Graph Matching Using G-Signature for Recognition Pascal workshop (June 14, 2007) 3

  4. Introduction Symbols can be simple 2D binary shapes composed of lines, arcs and filled areas, that represent something in a specific application domain. Architectural Symbols Electrical Symbols Pascal workshop (June 14, 2007) 4

  5. Graph Based Symbol’s Representation 1/6 Vectorization and Quadrilaterals For contours vectorization, we have used a method suggested by K. Wall [13] Quadrilaterals built by matching the corresponding vectors in term of slope, distance and area criteria. i.e., vectors which are close to each other and have opposite directions are fused together to form a quadrilateral Symbol Vectorization of contours Quadrilaterals [13] K. Wall, P. Danielsson, “A fast sequential method for polygonal approximation of digitized curves”, Computer Vision, Graphics and Image Processing, vol. 28, 1984, pp. 220 – 221. Pascal workshop (June 14, 2007) 5

  6. Graph Based Symbol’s Representation 2/6 Linear graphics symbols and their representation by quadrilaterals Pascal workshop (June 14, 2007) 6

  7. Graph Based Symbol’s Representation 3/6 Zone of Influence of a Quadrilateral Each quadrilateral has attributes like length ( ) of the median axis, angles of the two vectors, width on each side and a zone of influence Zone of influence of quadrilateral Pascal workshop (June 14, 2007) 7

  8. Graph Based Symbol’s Representation 4/6 Quadrilaterals Nodes Zone of influence of quadrilaterals and their corresponding sub-graphs Fusing sub-graphs together, a complete neighbourhood graph Pascal workshop (June 14, 2007) 8

  9. Graph Based Symbol’s Representation 5/6 Nodes Attribute (Relative Length ) Edges Attributes (Connection Type , Relative Angles) Junction Pascal workshop (June 14, 2007) 9

  10. L T L L Graph Based Symbol’s Representation 6/6 Attributed graph of quadrilaterals with symbolic and numeric attributes Pascal workshop (June 14, 2007) 10

  11. Graph Matching Motivation Behind Graph Signature Graph Isomorphism, Subgraph Isomorphism, Maximum Common Subgraph + Optimal Solution - NP Complete - No robustness to noise and distortion Error-tolerant Methods… Graph edit distance + Robust to vectorial distortion - NP-Complete in Worst case Similarity Measure Based Methods… + Robust to noise/distortion - Sub-optimal solution Pascal workshop (June 14, 2007) 11

  12. Greedy Algorithm, Score of mappings vertex-to-vertex similarity edge-to-edge similarity Splits as penalties Pascal workshop (June 14, 2007) 12

  13. Greedy Algorithm, SimGraph Pascal workshop (June 14, 2007) 13

  14. 1 1.0 85 0.8 2 SimGraph Continue… A 1.0 90 0.9 B 0.5 45 C A-1 2 0 0 0 2 A-1,B-2 2+1.8=3.8 0.98 0 0 4.6 A-1,B-2 3.8+1.4=5.2 0.98 2 0 4.18 C-2 Pascal workshop (June 14, 2007) 14

  15. SimGraph Continue… Working with 50 different symbols of GREC2003 database, a set of 1100 examples of different levels of distortion, geometric transformations and common noises were generated. The proposed novel similarity measure, and Simgraph Algorithm is devised to perform inexact matching of attributed graphs in Polynomial time Pascal workshop (June 14, 2007) 15

  16. Graph Signature (G - Signature) Graph Signature or G-Signature is the transformation of graph representation of graphic symbol to 1-Dimentional features vector, which is rather easy to store and manipulate. Three types of discriminating features were extracted A. Quantitative Features It consist of number of vertices in a graph, number of edges in the graph, number of vertices connected to 1, 2, 3, 4 or greater than 4 vertices ( i.e., degree of vertices). B. Symbolic Features The study of the symbolic attributes associated with edges.These consist of number of edges having L, P, T, X, or S as edge label. C. Range Features These features are based on the frequency of relative lengths (nodes) and relative angle (edges) in a certain interval. Pascal workshop (June 14, 2007) 16

  17. Graph Signature (G - Signature) A. Quantitative Features B. Symbolic Features C. Range Features # of vertices in a graph # of edges having label “L” # of vertices with RL (0.0 - 0.2) # of edges in a graph # of edges having label “P” # of vertices with RL (0.2 - 0.4) # of vertices with degree 1 # of edges having label “T” # of vertices with RL (0.4 - 0.6) # of vertices with degree 2 # of edges having label “X” # of vertices with RL (0.6 - 0.8) # of vertices with degree 3 # of edges having label “S” # of vertices with RL (0.8 - 1.0) # of vertices with degree 4 # of edges with RA (0° - 30°) # of vertices with degree > 4 # of edges with RA (30° - 60°) # of edges with RA (60° - 90°) # of edges with RA (90° - 120°) # of edges with RA (120° - 150°) # of edges with RA (150° - 180°) Pascal workshop (June 14, 2007) 17

  18. Graph Signature (G - Signature) Pascal workshop (June 14, 2007) 18

  19. Graph Signature (G - Signature) GREC-2003 Models Distances of hand-drawn architectural and electrical symbols vs. their respective models Pascal workshop (June 14, 2007) 19

  20. Graph Signature (G - Signature) The nearest neighbour rule (NNR) for classification, i.e., Two graphic symbols are similar if the Euclidean distance of their feature vectors is relatively small. d (Si , x) = MINi (d(Si ,x)) Pascal workshop (June 14, 2007) 20

  21. Results Performance of the proposed G-signature Pascal workshop (June 14, 2007) 21

  22. Improvementsuggested G – Signature Cluster of Similar Symbols Greedy Algorithm Closest Matching Symbol Pascal workshop (June 14, 2007) 22

  23. Conclusions Due to relative attributes on graph’s vertices and edges, our graph based symbols representations are invariant of rotation and scaling. G-signature is very fast to compute from an attributed graph The technique is fairly general and can be used to cluster similar graphs Higher precision can be achieved when it is coupled with other polynomial time graph matching algorithms. A weighted distance measure, or some other statistical classifier can also be use to improve performance (tests under study) Pascal workshop (June 14, 2007) 23

  24. Thats it ! Thanks for listening Questions ? Suggestions ? Pascal workshop (June 14, 2007)

  25. SimGraph Continue… 3/4 The New Similarity measure ( continue…) : is the score of the mapping computed C : is a cardinality function (# of vertices or edges) : represent the number of attributes associated to a vertex and an edge Pascal workshop (June 14, 2007) 14

More Related