Salim Jouili Supervisor S.A. Tabbone QGAR – LORIA Nancy Navidomass ANR Project Réunion Navidomass Paris, le 21 Mars 2008

 Introduction  Graph-based representation  Similarity measures of graphs  Edit distance  Papadopolous and Manolopoulos measure  Maximal common Subgraph  Graph probing  Median Graph  Applications  Conclusion

 Powerful structured-based representation  Used with flexibility in processing of a large variety of image’s types (the ancient documents, the electric and architectural plans, natural images, medical images...).  Preserves topographic information of the image as well as the relationship between the components.  In the two last decades many works have been developed.  Step in very subfield of image analysis :  Pattern Recognition  Segmentation  CBIR (Content-based image retrieval)

 Bunke,PAMI’82 [1]: (x,y) = vertices attributes 1,2 and 3 = vertices labels  1= Final point  2= angle  3 = T intersection 2 (50,100) 3 (50,80) 3 (50,78) 2 (50,58) 2 (70,58) 2 (70,38) 2 (30,38) 2 (30,100) 1 (45,80) 1 (45,78) 1 (55,80) 1 (55,78)

 Karray, Master 2006 [2]: Multilayer segmentation Homogeneous zones

 Region adjacency Graphs:  Fauqueur, PhD 2003 [3]: Original image a RAG Representation Of the segmented image

 Region adjacency Graphs:  Llados, PAMI’01 [4]:  Extraction regions of a plane graph by Jiang and Bunke algorithm [5]. V1V1 V2V2 V3V3 V6V6 V5V5 V4V4 A plane Graph G representing line drawing e1e1 e8e8 e3e3 e2e2 e5e5 e4e4 e6e6 e7e7 R1R1 R2R2 R3R3 A RAG G’: Vertices :represent the regions in G Edges : represent the regions adjacency in G

 GCap: Graph-based Automatic Image Captioning, J. Pan, MDDE’04 [6].

 Most of works in graph-based representation, notably in document analysis, sought some resemblance measures between represented objects in order to :  Classify  Match  Index ...

 Edit distance:  Maximal common subgraph (MCS) G1G1 G2G2 1 operation Edge deletion 1 operation Vertex Substitution D(G 1,G 2 ) = 2 G1G1 G2G2 D mcs (G 1,G 2 ) = 1- (3/4)=0.25

 Papadoupolos and Manolopoulos Measure: [7] V1V1 V5V5 V4 V2V2 V3V3 V6V6  Sorted graph histogram :  SH 1 = {V 5 (3), V 4 (3), V 1 (3), V 6 (2), V 3 (2), V 2 (1)} V1V1 V5V5 V4 V2V2 V3V3 V6V6  Sorted graph histogram :  SH 2 = {V 4 (4), V 3 (4), V 1 (4), V 6 (3), V 5 (3), V 2 (2)} D pa. & Mano (G 1,G 2 ) =L1(SH 1,SH 2 )=6 Primitive operations are : vertex insertion, vertex deletion and vertex update

 Graph Probing, Lopresti, IJDAR’2004 [8]:  “How many vertices with degree n are present in graph G= (V,E)?” PR collect the response from the graphs  PR(G) = (n 0,n 1,n 2,…) where n i =|{v ∈ V |deg(v) =i}| D probing (G 1,G 2 ) =L1(PR(G 1 ),PG(G 2 )

 The generalized median graph aims to extract essential information from a whole of set of graphs in only one prototype A set of graphs The generalized median graph

 GGM = arg min g  U  i=1 d(g,g i )  Where U is the set of all the graphs that can be built from the original set of graphs.  Jiang Propose a genetic algorithm, GbR’99 [9]  Hlaoui proposed a solution based on the decomposition of the problem of minimizing the sum of distances in two parts, nodes and edges. GbR’03 [10]

 Content-based image retrieval : Berretti proposed a technique of graph matching and indexing dedicated to the graph-models in content- based retrieve. Using m-tree indexing method. PAMI’2001 [11].  Segmention: Felzenszwalb proposed a complete graph-based approach for the segmentation of colour images. [12] ...

 Graph-based representation : flexible, universal (document’s type), spatial information.  Useful in many field in image analysis.  Many solution in measurement of similarity between graphs  depends from the data stored in graphs.  Ambitious research field notably for Content- based image retrieval.

 [1] H. Bunke. Attributed of programmed graph grammars and their application to schematic diagram interpretation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(6), Novembre  [2] A. Karray. Recherche de lettrines par le contenu. Master's thesis, Laboratoire L3i, Universités de La Rochelle et de Sfax, France et Tunisie,  [3] J. Fauqueur. Contributions pour la Recherche d'Images par Composantes Visuelles. PhD thesis, INRIA - Université Versailles St Quentin,  [4] J. Lladòs, E. Martí, and J. J. Villanueva. Symbol recognition by error-tolerant subgraph matching betweenregion adjacency graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10),2001.  [5] Jiang, X.Y., Bunke, H., An Optimal Algorithm for Extracting the Regions of a Plane Graph, Pattern Recognition Letters (14), 1993, pp  [6] J. Pan, H.Yang, C. Faloutsos, and P. Duygulu. Gcap : Graph-based automatic image captioning. In Proceedings of the 4th International Workshop on Multimedia Data and Document Engineering,  [7] A. N. Papadopoulos and Y. Manolopoulos. Structure-based similarity search with graph histograms. Proceedings of International Workshop on Similarity Search (DEXA IWOSS'99), pages , Septembre  [8] D. Lopresti and G. Wilfong. A fast technique for comparing graph representations with applications to perform evaluation. IJDAR, 6:219–229,  [9] X. Jiang, A. Munger, and H. Bunke. Scomputing the generalized median of a set of graphs. 2nd IAPR-TC- IS Workshop on Graph Based Representations.  [10] A. Hlaoui and S.Wang. A new median graph algorithm. IAPR Workshop on GbRPR, LNCS 2726, pages 225–234,  [11] S. Berretti, A. D. Bimbo, and E. Vicario. Efficient matching and indexing of graph models in content- based retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10):1089–1105,  [12] P. F. Felzenszwalb and D. P. Huttenlocher. Efficient graph-based image segmentation. International Journal of Computer Vision, 59(2), Septembre 2004.