An Algorithm for building Region Graph from vectorial graphics

1. An Algorithm for building Region Graph from vectorial graphics Master training by Zouba Karim Tutor: Eric Trupin Date : 2005-09-06

2. Context • Last Name: Zouba • First Name: Karim • Post: Master student SATI-GI • Place: PSI Laboratory in Rouen University • In collaboration with: IPI group(Nottingham) • Training period: April-september 2005 • Tutor: Eric Trupin

3. Plan I) General introduction II) Regions Graph Construction III) Experimentation IV) Conclusion and future works

4. Plan I) General introduction II) Regions Graph Construction III) Experimentation IV) Conclusion and future works

5. General introductionProblematics • Problematics: a large abundance of documents on the Web • Definition of Document Indexing :it consists in classifying in a Tree structure documents according to their descriptors, and links on these documents. • Currently documents retrieval & Indexing (I&R) systems =only textual Indexing Graphical Documents

6. General introductionProblematics root

7. General introductionGraphical Documents Definition of Vector Graphic Documents: a document which consists of graphical objects (Lines, points, polygons, curves) with shape, color and position attributes. A wide variety of formats: svg, ClipArt, DXF Several area of application: SIG,Internet, Enterprise,… Properties: Not very voluminous Possibility to enlarge and reduce the size unless loss of quality

8. General introductionDocuments representation Document Representation Unit Three approaches • Syntactic approach [Sciasco-04] Line[t1] Line[t2] Line[t3] Line[t4] Line[t5] polygon[0,01,1.71][t5] • Structural approach [Fonseca-03] • Statistical approach [Dosch-04], [Fonseca-Grec05] Vectorial signatures

9. General introduction Conclusion Vectorial graphical document=complexity, a lot of regions Structural Approach : Regions Graph

10. Plan I) General introduction II) Regions Graph Construction III) Experimentation IV) Conclusion and future works

11. Regions Graph ConstructionPrinciple • Principle: K Lines LineGraph Building Decomposition Finding cycles + relations • Regions Construction • Relations determination

12. Regions Graph ConstructionRegions Construction • Main problem of our study • Based: Polygon detection (Elementary Cycles) • Two approaches [Fonseca-03] - our approach Any a priori information about graphical primitives [Fonseca-03] Exploiting vectorial information between primitives [our approach-05]

13. Regions Graph ConstructionFonseca Approach • region detection= Finding elementary cycles • Algorithm • Input: a set of Lines • Step 1: features extraction + LineGraph Building • Step 2: Finding minimum cycles: all elementary cycles + filtering (greedy algorithm) from LineGraph

14. Regions Graph ConstructionOur Approach • region detection= Finding elementary cycles in exploiting vectorial information between graphical primitives. • Which Vectorial information ? • Finding Elementary Cycles ?

15. Based on Weindorf’s work Using Vectorial information: Direct Angle. Regions Graph ConstructionOur Approach: Definition of the vectorial information Definition: Direct direction anticlockwise Example

16. Algorithm Regions Graph ConstructionOur Approach: Minimum Direct Angle • Three cases • Colinear • Perpendicular or acute getRangle

17. Exploiting the minimum Direct Angle between 2 Lines to build a new Line Graph Principle: Regions Graph ConstructionOur Approach: Finding elementary cycles α(2-1) e4,b1 L1 b L1 e b2,e1 L1 b e1,b2 e b1,e4 α(1-2) e b e e b e e L5 L4 L5 L2 L4 L5 L2 L4 L2 b b e b e b L3 L3 L3 Line Graph Vector Graphic document Specialized Line Graph b: beginning of a Line α:Direct angle between 2 Lines e: end of a Line

18. Exploiting the minimum Direct Angle between 2 Lines to build a new Line Graph Principle: Regions Graph ConstructionOur Approach: Finding elementary cycles α(2-1) L1 b L1 e L1 b e α(1-2) e b e e b e e L5 L4 L5 L2 L4 L5 L2 L4 L2 b b e b e b L3 L3 L3 Line Graph Vector Graphic document Specialized Line Graph b: beginning of a Line α:Direct angle between 2 Lines e: end of a Line

19. Regions Graph ConstructionOur Approach: Finding elementary cycles Elementary cycle for region detection: begin by the extremity of the root Node and end by the other extremity of the root Node. α(2-1) α(1-4) L1 L1 α(1-2) α(4-1) L5 L2 L4 L4 L5 L2 L3 L3 Specialized Line Graph Vector Graphic document

20. Regions Graph ConstructionOur Approach: Finding elementary cycles Some rules: If nbr of outgoing edges =1 then add the extremity Vector If nbr of outgoing edges >1 then choose the edge which has the Minimum Direct Angle α(2-1) α(1-4) L1 L1 α(1-2) α(4-1) L5 L2 L4 L4 L5 L2 L3 L3 Specialized Line Graph Vector Graphic document

21. Regions Graph ConstructionTemporal complexity determination • Depends on 2 variables N: number of Nodes M: number of edges • [Fonseca-03] • Our approach • Expectations: • Same evolution for few vectors • The more there’re vectors the more there’s a big gap in terms of runtime

22. Regions Graph Construction Spatial Relations determination [Clementini-93] a b a b a a b b adjacency overlap strict and tangential inclusion

23. Regions Graph Construction Spatial Relations determination [Clementini-93] a b a b a a b b adjacency overlap strictand tangential inclusion Adjacency relation determination

24. Regions Graph Construction Spatial Relations determination [Clementini-93] a b a b a a b b adjacency overlap strictand tangential inclusion inclusion relation determination Necessary and sufficient condition: [Xmin<Xmin&Xmax>Xmax] & [Ymin <Ymin&Ymax>Ymax] Ymax R2 Ymax R1 Ymin Ymin Xmin Xmin Xmax Xmax

25. Plan I) General introduction II) Regions Graph Construction III) Experimentation IV) Conclusion and future works

26. ExperimentationIntroduction • Type of Documents: SVG • 2 corpus wisely used on the WEB Limited access via Search engine and described by metadata Shapes: Lines, rectangles and polygons Randomly generated Hand-sketched

27. ExperimentationHand-sketched documents Documents vary from 5 to 78 vectors Comparison with a classic algorithm Results:

28. ExperimentationHand-sketched documents Example of Region Graph obtained from a LineGraph (78,255)

29. ExperimentationRandomly generated documents Documents vary from 462 to 2708 vectors • Comparison with results found by Fonseca/Ferreira: • C++ • Not the same documents Fonseca’s approach our approach

30. ExperimentationRandomly generated documents

31. Conclusion and future works • Vectorial approach is better than classic polygon detection • Adapted to complex documents (Technical documents, industrial drawings,…) • Future Work Indexing (Graph Mining) Neighbourhood relation (Voronoi)