1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment

A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems.