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Fourier Shape Analysis

Shape Analysis by Fourier Descriptors computation.


  1. Shape Analysis by Fourier Descriptors and Curvature Computation
  2. Elliptic Fourier Descriptor (EFD)


Thomas Boudier and Ben Tupper (EFD)


  • Fourier descriptors
  • Elliptic Fourier Descriptors
  • Curvature

A Shape-Smoothin plugin based on EFD is available at : ShapeSmoothing


Fourier Descriptor

This plugin computes the Fourier Descriptors and the curvature from a closed curve. It can smooth a curve restraining the number of Fourier values. The first values are the double of the center of the shape, the second values corresponds to the fitting by a ellipse. The computation is based on the description taken from the chapter 6 page 24 of the book Image Analysis in the Biological Sciences.

If the save curvature box is activated, the curvature values are saved in a text file named curvature.txt.

You need to draw a closed ROI before running the plugin. You can use Interpolate and Fit Spline to optimize a selection.

Elliptic Fourier Descriptor

The EFD provides a normalized set of coefficients that are rotation, translation and scale invariant. The first coefficient relates to the centroid of the input shape before the EFD is computed and can be ignored. The second EFD coefficient relates to a circle circumscribed about the centroid before the EFD computation. After the EDF computation the second EFD is always 2 and can be ignored. That leaves the remaining EFD coefficients for use in comparing shapes.

Reference : Feature Extraction and Image Processing, 2nd Ed, by Mark Nixon and Alberto Aguado, Academic Press 2008, ISBN 978-0-1237-2538-7

Fourier Shape Analysis


Download fourier2.5_.jar to your plugins directory and then restart ImageJ or use the Update Menu command.

The sources are included in the jar file.





2014-06-12 : Display curvatures information in a image. Computes both raw and Fourier-filtered curvatures.

2014-05-22 : Bug in curvature display. Plugins are now under “Plugins/Analyze”.

2013-07-15 : Extra column “ax” removed

2009-11-19 : Ben Tupper added the Elliptic Fourier Descriptors

Known Bugs

Contact me for any questions or suggestions :

plugin/analysis/fourier_shape_analysis/start.txt · Last modified: 2020/05/19 05:47 by tboudier

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