Fourier descriptors

1
Fourier descriptors

• Ahmad Alkhodre Mostefa Belarbi
• Insa Lyon
• Georg Langs Srdan Tosovic
• Vienna University
• Nicolas Sicard
• Pavia University
• Lecturer Alberto Aguado
• University of Surrey

2
Contents

• Introduction
• Fourier descriptors
• Classification
• Occlusion
• Suggestions
• Conclusion

3
Introduction

• Using shapes
• Advantages
• Drawbacks

4
Fourier decomposition
?

...
5
Fourier descriptors
decomposed to real imaginary part
original picture
border
Fourier coefficients
Fourier descriptors
6
Fourier decomposition(of Nicolas)
Processing
Processing
7
Invariance (Rotation)work in progress
8
Reconstruction (of Nicolas)
9
Classification

• Database of Fourier descriptors with 14 airplanes
  and 1 Nicolas.
• Evaluation function for matching the test object
  with one object or Nicolas in the database.
• Astonishing results

10
Occlusion problem

• Random results, when classifying occluded curves

• How much is occluded?
• Which part of the original curve?
• Which airplane?

11
Classification occlusions
database building
Create databases of subcurves for each airplane
Alpha-beta decomposition
12
Curve represented by subcurve descriptors
database building
1.
2.
3.
4.
beta
alpha
5.
13
Processing of input
matching
Process the curve as an interval from a to b, for
every (a,b) couple present in the database
n x
Store results in a datastructure similar to the
database
14
Matching
matching
Input image
15
Search for lowest point
matching
a
b
16
Results
matching
inputshape
match
b
a
17
Problems, observations
matching

• Symmetry
• Descriptors are invariant against mirroring
• Time for more testing
• Tests were performed on one airplane
• Matching is dependent on number of airplanes in
  the database
• Weigthing algorithm for lowest point search
• Robustness

18
Conclusion

• What we have done
• Shape extraction
• Fourier coefficients
• Invariant Fourier descriptors
• Shape reconstruction
• Classification
• Proposition for occlusion problem
• What we still need to do
• Generalization of alpha-beta decomposition