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Jonas De Vylder, Wilfried Philips

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IMPROVED FOURIER DESCRIPTORS FOR 2-D SHAPE REPRESENTATION Jonas De Vylder, Wilfried Philips Ghent University, Dept. Of Telecommunications and Information Processing – PowerPoint PPT presentation

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Title: Jonas De Vylder, Wilfried Philips


1
IMPROVED FOURIER DESCRIPTORS FOR2-D SHAPE
REPRESENTATION
  • Jonas De Vylder, Wilfried Philips

Ghent University, Dept. Of Telecommunications and
Information Processing
Jonas.DeVylder_at_telin.UGent.be
http//telin.ugent.be/ipi
  • Automatic detection of an object in an image is a
    difficult task. If the expected object has a
    certain shape, this shape information can be
    incorporated as a constraint in the detection
    algorithm. Techniques able to use this
    information are
  • Snakes
  • Hough-transform
  • Active Shape Models
  • Retrieve similar shapes out of a database
  • Interpolate between two similar shapes
  • Use the descriptors in a metric to measure
    difference
  • The FDs can be made invariant to
  • translation
  • Scaling
  • Rotation
  • Changing the starting point of S(t)

S(t) is not a uniqueparametisation!
S(tn1)
Approximate s(t)
S(tn)
y
An example of a contour
Improve the FD-approximation by changing the
scanning speed ?(t) of the contour
S(tn-1)
S(t) is a parameterisation of the contour
S(0)
0
x
  • Bn are chosen to minimize the mean squared
    distance between S and SN
  • SN can easily be calculated using the FFT
  • Bn are called Fourier Descriptors (FDs)
  • Gn minimizes
  • SN can be calculated without interpolating S
  • Gn are called Improved Fourier Descriptors
    (IFDs)
  • 436 leaf contours where approximated
  • The database contains 6 different families of
    leaves
  • All leaves where approximated using 10,20,,50
    (Improved) Fourier Descriptors
  • Two different error metrics are used to compare
    the FDs and IFDs
  • A maximum distance between the original and the
    approximation
  • An average distance between the original and the
    approximation
  • For both measurements the IFDs on average
    approximated over 10 better than the FDs

Jonas.devylder_at_telin.ugent.be
10 FDs
Original shape
10 IFDs
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