# Fourier Descriptors

Fourier Descriptors

Fourier descriptors are a way of encoding the shape of a two-dimensional object by taking the Fourier transform of the boundary, where every point on the boundary is mapped to a complex number . 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.

(x,y)

x+iy

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.