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 introduction Problematics

• 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 (IR)
  systems
• only textual

Indexing Graphical Documents
6
General introduction Problematics
root
7
General introduction Graphical 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 introduction Documents representation
Document Representation Unit
Three approaches

• Syntactic approach Sciasco-04

Linet1 Linet2 Linet3
Linet4 Linet5 polygon0,01,1.71t5

• Structural approach Fonseca-03

• Statistical approach Dosch-04, Fonseca-Grec05

Vectorial signatures
9
General introduction Conclusion
Approach Advantages Drawbacks Documents
syntactic -Strongly discriminating -Simple Shapes -Simple Shapes
Structural -Complex Shapes -High complexity -Relations weakly discriminating -Complex Shapes
Statistical -Strongly discriminating according to features -Difficult to choice features -Simple Shapes
Vectorial graphical documentcomplexity, 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 Construction Fonseca 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
Regions Graph ConstructionOur Approach
Definition of the vectorial information

• Based on Weindorfs work
• Using Vectorial information Direct Angle.

Definition Direct direction
anticlockwise
Example
16
Regions Graph ConstructionOur Approach Minimum
Direct Angle

• Algorithm

• Three cases
• Colinear
• Perpendicular or acute

getRangle
17
Regions Graph ConstructionOur Approach Finding
elementary cycles

• Exploiting the minimum Direct Angle between 2
  Lines to build a new Line Graph
• Principle

a(2-1)
e4,b1
L1
L1
e
b
b2,e1
L1
b
e1,b2
e
b1,e4
b
e
a(1-2)
e
e
b
e
e
L5
L4
L5
L2
L4
L2
L5
L2
L4
e
b
b
b
e
b
L3
L3
L3
Line Graph
Vector Graphic document
Specialized Line Graph
b beginning of a Line
aDirect angle between 2 Lines
e end of a Line
18
Regions Graph ConstructionOur Approach Finding
elementary cycles

• Exploiting the minimum Direct Angle between 2
  Lines to build a new Line Graph
• Principle

a(2-1)
L1
L1
e
b
L1
b
e
b
e
a(1-2)
e
e
b
e
e
L5
L4
L5
L2
L4
L2
L5
L2
L4
e
b
b
b
e
b
L3
L3
L3
Line Graph
Vector Graphic document
Specialized Line Graph
b beginning of a Line
aDirect 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.
a(2-1)
a(1-4)
L1
L1
a(1-2)
a(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 gt1 then choose the edge
which has the Minimum Direct Angle
a(2-1)
a(1-4)
L1
L1
a(1-2)
a(4-1)
L5
L2
L4
L4
L5
L2
L3
L3
Specialized Line Graph
Vector Graphic document
21
Regions Graph Construction Temporal 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 therere vectors the more theres a big
  gap in terms of runtime

22
Regions Graph Construction Spatial Relations
determination
Clementini-93
a
b
a
b
a
b
a
b
adjacency
overlap
strict and tangential inclusion
23
Regions Graph Construction Spatial Relations
determination
Clementini-93
a
b
a
b
a
b
a
b
adjacency
overlap
strict and tangential inclusion
Adjacency relation determination
24
Regions Graph Construction Spatial Relations
determination
Clementini-93
a
b
a
b
a
b
a
b
adjacency
overlap
strict and tangential inclusion
inclusion relation determination
Necessary and sufficient condition Xmin lt Xmin
Xmax gt Xmax
Ymin lt Ymin Ymax gt 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
Experimentation Introduction

• 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
Experimentation Hand-sketched documents
Documents vary from 5 to 78 vectors
Comparison with a classic algorithm
Results
28
Experimentation Hand-sketched documents
Example of Region Graph obtained from a LineGraph
(78,255)
29
Experimentation Randomly generated documents
Documents vary from 462 to 2708 vectors

• Comparison with results found by
  Fonseca/Ferreira
• C
• Not the same documents

Fonsecas approach
our approach
30
Experimentation Randomly 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)