Asymmetric fourier descriptor of non-closed segments

The Fourier descriptor is an efficient and effective way to describe a closed boundary. However, for a non-closed segment, since the two non-adjacent end points result in signal discontinuity, after eliminating the high-frequency part, the reconstructed segment has large error near the two ends. In this paper, we propose a warping method to connect the two ends and perform odd-symmetric extension to smooth the warped segment around them. With these modifications, the high-frequency components near the two ends can be much reduced and we can obtain the reconstructed segment with accurate end-point locations even when only the low frequency coefficients are preserved. This method could also be used for a closed boundary with a pre-segmentation process, and the experimental result shows that with the same boundary compression rate, our method has better reconstruction quality than directly extracting Fourier descriptors on the closed boundary.