Shape matching of 3D contours using normalized Fourier descriptors

In this paper, we develop a simple, eigenspace matching algorithm for closed 3D contours. Our algorithm relies on a novel method which normalizes the Fourier descriptors (FDs) of a 3D contour with respect to two of its FD coefficients corresponding to the lowest non-zero frequencies. The remaining matching task only involves vertex shift and rotation about the z-axis. Our approach is inspired by the observation that the traditional Fourier transform of a 1D signal is equivalent to the decomposition of the signal into a linear combination of the eigenvectors of a smoothing operator. It turns out that our FD normalization is equivalent to aligning the limit plane approached by the sequence of progressively smoothed 3D contours with the xy-plane.