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