Comparing curvature estimation techniques.

摘要: This article presents a careful comparative evaluation of two techniques for numerical curvature estimation 2D closed contours (more specifically closed, regular and simple parametric curves). The considered methods are: (a) 1-D Fourier-based approach; (b) 2-D approach involving the embedding contour into surface (presented first time in this article). Both these employ Gaussian smoothing as regularizing condition order to estimate second derivatives needed estimation. These are according multiresolution approach, where standard deviation Gaussians used scale parameters. applied set curves whose analytical curvatures known compare errors approaches. Three kinds considered: (i) with description; (ii) synthesized terms Fourier components curvature; (iii) obtained by splines. A precise comparison methodology is devised which includes adoption common spatial quantization (namely square box quantization) explicit consideration influence related results indicate that 1D not only faster, but also more accurate. However, still interesting reasonably accurate applications situations along whole domains needed. Key-words: Differential geometry, techniques, cuvature estimation, performance evaluation, transform.