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

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

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

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

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 Vectorization and Quadrilaterals Symbol Vectorization of contoursQuadrilaterals [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. Graph Based Symbol’s Representation 1/6 Pascal workshop (June 14, 2007) 5

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

Zone of Influence of a Quadrilateral Zone of influence of 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 Pascal workshop (June 14, 2007) 7 Graph Based Symbol’s Representation 3/6

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

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

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

Graph Matching Motivation Behind Graph Signature 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 Graph Isomorphism, Subgraph Isomorphism, Maximum Common Subgraph + Optimal Solution - NP Complete - No robustness to noise and distortion Pascal workshop (June 14, 2007) 11

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

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

A B C A-1,B = A A-1,B = C-2 SimGraph Continue… Pascal workshop (June 14, 2007) 14

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. Model Symbol Query Symbol Detected correctly Missed Recognition Rate Rotation % Scaling % Noise Level % Level % Level % Distortion % 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 SimGraph Continue…

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. 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. Graph Signature (G - Signature) Pascal workshop (June 14, 2007) 16 Three types of discriminating features were extracted

# of vertices in a graph # of edges in a graph # of vertices with degree 1 # of vertices with degree 2 # of vertices with degree 3 # of vertices with degree 4 # of vertices with degree > 4 A. Quantitative Features B. Symbolic FeaturesC. Range Features # of edges having label “L” # of edges having label “P” # of edges having label “T” # of edges having label “X” # of edges having label “S” # of vertices with RL ( ) # of vertices with RL ( ) # of vertices with RL ( ) # of vertices with RL ( ) # of vertices with RL ( ) # of edges with RA (0° - 30°) # 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 Graph Signature (G - Signature)

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

d (S i, x) = MIN i (d(S i,x)) 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. Pascal workshop (June 14, 2007) 20 Graph Signature (G - Signature)

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

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

Conclusions Due to relative attributes on graph’s vertices and edges, our graph based symbols representations are invariant of rotation and scaling. The technique is fairly general and can be used to cluster similar graphs G-signature is very fast to compute from an attributed graph Pascal workshop (June 14, 2007) 23 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)

Thats it ! Pascal workshop (June 14, 2007)

: 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 The New Similarity measure ( continue…) Pascal workshop (June 14, 2007) 14 SimGraph Continue… 3/4