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Fourier Descriptors

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shapes
1
2
3
4
5
6
7
number of descriptors
9
Fourier descriptors are a way of encoding the shape of a two-dimensional object by taking the Fourier transform of the boundary, where every
(x,y)
point on the boundary is mapped to a complex number
x+iy
. The original shape can be recovered from the inverse Fourier transform. However, if only a few terms of the inverse are used, the boundary becomes simplified, providing a way to smooth or filter the boundary.
In this Demonstration, you can select from seven different shapes and reconstruct the shape from a different number of descriptors. When the number is small, the resulting reconstruction is greatly simplified; as the number increases, the reconstruction converges to the original.
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