Fourier interpolation of a Plane Curve


Ghosh and Jain (1) showed how to charactize a simple, closed, piece-wise linear curve as a Fourier series in a single parametric variable. Such a formulation allows:

We intend to use the Fourier fit scheme as a way to simplify and characterize the outlines of moving animals. The animals will be videotaped. The videotape will then be analysed to extract the outline of the animal, Fourier fit the outline, then use the low bandwidth components to characterize the motion. For example, the DC components give the position of the animal. The fundamental frequency coefficients of the fit give the ellipse (2) which best fits the animal outline.


A matlab program was written to animate a test object, extract its outline, then do the Fourier fit.


The shape that was animated was chosen to be a very simple approximation of a insect larvae turning. There are 4 reconstructions linked below:


  1. Ghosh, PK and Jain, PK (1993) An Algebra of Geometric Shapes, IEEE Computer Graphics and Applications, vol 13 pp 50-59, issue 5
  2. Rouben Rostamian, Equation of an Ellipse,