Salim Jouili

SupervisorS.A. Tabbone

QGAR – LORIANancy

Navidomass

ANR Project

Réunion NavidomassParis, le 21 Mars 2008

Introduction Graph-based representation Similarity measures of graphs

Edit distancePapadopolous and Manolopoulos measureMaximal common SubgraphGraph 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 segmentationHomogeneous 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]. V1 V2

V3V6

V5 V4

A plane Graph Grepresenting line drawing

e1

e8

e3

e2

e5

e4e6

e7

R1

R2

R3

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 :ClassifyMatch Index ...

Edit distance:

Maximal common subgraph (MCS)

G1 G2

1 operation

Edge deletion

1 operation

Vertex Substitution

D(G1,G2) = 2

G1 G2 Dmcs(G1,G2) = 1- (3/4)=0.25

Papadoupolos and Manolopoulos Measure: [7]

V1

V5

V4

V2

V3

V6

Sorted graph histogram :SH 1= {V5(3), V4(3), V1(3), V6(2), V3(2), V2(1)}

V1

V5

V4

V2

V3

V6

Sorted graph histogram :SH 2 = {V4(4), V3(4), V1(4), V6(3), V5(3), V2(2)}

Dpa. & Mano(G1,G2) =L1(SH1,SH2)=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) = (n0,n1,n2,…) where ni=|{v∈V |deg(v) =i}|

Dprobing(G1,G2) =L1(PR(G1),PG(G2)

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 mingUi=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]

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 1982.

[2] A. Karray. Recherche de lettrines par le contenu. Master's thesis, 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. PhD thesis, 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-based automatic image captioning. In Proceedings of 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.