Estimating derivatives and curvature of open curves

摘要

This article presents an effective spectral approach to estimate derivatives and curvature of open parametric curves. As the method is based on the discrete Fourier transform, the discontinuities of the curve (as well as of its derivatives) must be controlled to minimize the Gibbs phenomenon. We address this problem by obtaining a smooth extension of the curve in such a way as to suitably close it, which is done through a variational approach taking into account the spectral energy of differentiated versions of the extended curves. This novel method presents potential for applications in a broad class of problems, ranging from applied and experimental physics to image analysis.