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Graph-based approaches in image analysis: a review

Graph-based approaches in image analysis: a review. ANR Project. Navidomass. Salim Jouili Supervisor S.A. Tabbone. QGAR – LORIA Nancy. Réunion Navidomass Paris, le 21 Mars 2008. Outline. Introduction Graph-based representation Similarity measures of graphs Edit distance

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Graph-based approaches in image analysis: a review

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  1. Graph-based approaches in image analysis: a review ANR Project Navidomass Salim Jouili Supervisor S.A. Tabbone QGAR – LORIA Nancy Réunion Navidomass Paris, le 21 Mars 2008

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

  3. introduction • 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)

  4. Graph-based representation • Bunke ,PAMI’82 [1]: • (x,y) = verticesattributes • 1,2 and 3 = vertices labels • 1= Final point • 2= angle • 3 = T intersection 2 2 (30,100) (50,100) 1 3 1 (45,80) (50,80) (55,80) 1 3 1 (45,78) (50,78) (55,78) 2 (50,58) 2 (70,58) 2 2 (70,38) (30,38)

  5. Graph-based representation • Karray, Master 2006 [2]: Multilayer segmentation Homogeneous zones

  6. Graph-based representation • Region adjacency Graphs: • Fauqueur, PhD 2003 [3]: Original image a RAG Representation Of the segmented image

  7. Graph-based representation • Region adjacency Graphs: • Llados, PAMI’01 [4]: • Extraction regions of a plane graph by Jiang and Bunke algorithm [5]. V1 e1 V2 R1 e8 e2 V3 V6 R2 e7 e3 e6 e4 V5 e5 V4 • A RAG G’: • Vertices :represent the regions in G • Edges : represent the regions adjacency in G R3 A plane Graph G representing line drawing

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

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

  10. Similaritymeasures for graphs • Edit distance: • Maximal common subgraph (MCS) 1 operation Edge deletion 1 operation Vertex Substitution G1 G2 D(G1,G2) = 2 G1 G2 Dmcs(G1,G2) = 1- (3/4)=0.25

  11. Similaritymeasures for graphs • Papadoupolos and Manolopoulos Measure: [7] • Sorted graph histogram : • SH1= {V5(3), V4(3), V1(3), V6(2), V3(2), V2(1)} V2 V1 V3 • Sorted graph histogram : • SH 2= {V4(4), V3(4), V1(4), V6(3), V5(3), V2(2)} V5 V6 V4 V2 V1 Dpa. & Mano(G1,G2) =L1(SH1,SH2)=6 V3 V4 Primitive operations are : vertex insertion , vertex deletion and vertex update V6 V5

  12. Similaritymeasures for graphs • 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) = (n0,n1,n2,…) where ni=|{v∈V |deg(v) =i}| Dprobing(G1,G2) =L1(PR(G1),PG(G2)

  13. Median Graph • The generalized median graph aims to extract essential information from a whole of set of graphs in only one prototype The generalized median graph A set of graphs

  14. Median Graph • GGM = arg mingUi=1 d(g,gi) • 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]

  15. Applications • 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] • ...

  16. conclusion • 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.

  17. REFERENCES • [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 1982. • [2] A. Karray. Recherche de lettrines par le contenu. Master'sthesis, Laboratoire L3i, Universités de La Rochelle et de Sfax, France et Tunisie, 2006. • [3] J. Fauqueur. Contributions pour la Recherche d'Images par Composantes Visuelles. PhDthesis, INRIA -Université Versailles St Quentin, 2003. • [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. 553-558. • [6] J. Pan, H.Yang, C. Faloutsos, and P. Duygulu. Gcap : Graph-basedautomatic image captioning. In Proceedingsof the 4th International Workshop on Multimedia Data and Document Engineering, 2004. • [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 174178, Septembre 1999. • [8] D. Lopresti and G. Wilfong. A fast technique for comparing graph representations with applications to perform evaluation. IJDAR, 6:219–229, 2004. • [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, 2003. • [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, 2001. • [12] P. F. Felzenszwalb and D. P. Huttenlocher. Efficient graph-based image segmentation. International Journal of Computer Vision, 59(2), Septembre 2004.

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