Fourier Descriptors

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Fourier Descriptors

• David Fu
• 2002/1/9

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Content

• 0. Introduction
• 1. Overview of the Fourier descriptors methods
• a. Transformation to the tangent space
• b. Complex Fourier descriptors
• 2. Testing the algorithm
• a. High frequencies limitation
• b. Crossovers problem
• 3. Conclusions

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Introduction

• Articles mentioned image processing or meachine
  vision
• Identification or counting of sprites
• Give good results with the complex method for
  describing closed curves.
• Commonly used for pattern recognition
• chromosome classification,
• identification of aircrafts
• identification of particules.
• Main issue is how many terms should be kept from
  the Fourier transform so the description is
  efficient.

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Overview of the Fourier descriptors methods

• Transformation to the tangent space

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Overview of the Fourier descriptors methods

• rho-theta graph
• Figure. rho-theta graph

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Overview of the Fourier descriptors methods

• rho-theta graph

f(x) a0 a1Cos(q) b1Sin(q) a2Cos(2q)
b2Sin(2q) a3Cos(3q) b3Sin(3q) c q2pix
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The shape is now described by a set of N vertices
z(i) i 1,,N corresponding to N points of
the outline. The Fourier descriptors c(k) k
-N/2 1,,N/2 are the coefficients of the
Fourier transform of z
The inverse relationship exists between c(k) and
z(i)
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Testing the algorithm
There are three different parameters 1. N The
number of points you draw (in blue) 2. M The
number of Fourier descriptors you want to use 3.
L The number of points you want to reconstruct
(in red)
The reconstructed points are denoted and
their indice, l is restricted to the interval 0,
L-1
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High frequencies limitation
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Crossovers problem
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Conclusion
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Conclusion
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Conclusion