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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.