Graphbased approaches in image analysis: a review

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
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Outline

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

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introduction

• Powerful structured-based representation
• Used with flexibility in processing of a large
  variety of images 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)

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Graph-based representation

• Bunke ,PAMI82 1
• (x,y) vertices attributes
• 1,2 and 3 vertices labels
• 1 Final point
• 2 angle
• 3 T intersection

5
Graph-based representation

• Karray, Master 2006 2

Multilayer segmentation Homogeneous zones
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Graph-based representation

• Region adjacency Graphs
• Fauqueur, PhD 2003 3

Original image
a RAG Representation Of the segmented image
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Graph-based representation

• Region adjacency Graphs
• Llados, PAMI01 4
• Extraction regions of a plane graph by Jiang and
  Bunke algorithm 5.

V1
e1
V2
R1
e8
e2
V3
V6
R2
e7
e3
e4
e6
V5
V4
e5

• A RAG G
• Vertices represent the regions in G
• Edges represent the regions adjacency in G

R3
A plane Graph G representing line drawing
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Graph-based representation

• GCap Graph-based Automatic Image Captioning, J.
  Pan, MDDE04 6.

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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
• ...

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Similarity measures 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
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Similarity measures for graphs

• Papadoupolos and Manolopoulos Measure 7

• Sorted graph histogram
• SH 1 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
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Similarity measures for graphs

• Graph Probing, Lopresti, IJDAR2004 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 niv?V deg(v) i

Dprobing(G1,G2) L1(PR(G1),PG(G2)
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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
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Median Graph

• GGM arg ming?U?i1 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, GbR99 9
• Hlaoui proposed a solution based on the
  decomposition of the problem of minimizing the
  sum of distances in two parts, nodes and edges.
  GbR03 10

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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. PAMI2001 11.
• Segmention
• Felzenszwalb proposed a complete graph-based
  approach for the segmentation of colour images.
  12
• ...

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conclusion

• Graph-based representation flexible, universal
  (documents 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.

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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'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,
  6219229, 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 225234, 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)10891105, 2001.
• 12 P. F. Felzenszwalb and D. P. Huttenlocher.
  Efficient graph-based image segmentation.
  International Journal of Computer Vision, 59(2),
  Septembre 2004.