Elliptic Fourier features of a closed contour

A direct procedure for obtaining the Fourier coefficients of a chain-encoded contour is presented. Advantages of the procedure are that it does not require integration or the use of fast Fourier transform techniques, and that bounds on the accuracy of the image contour reconstruction are easy to specify. Elliptic properties of the Fourier coefficients are shown and used for a convenient and intuitively pleasing procedure of normalizing a Fourier contour representation. Extension of the contour representation to arbitrary objects at arbitrary aspect angle is discussed. The procedures have direct application to a variety of pattern recognition problems that involve analysis of well-defined image contours.