Numerically Invariant Signature Curves

1999/03/18 by Mireille Boutin, Boutin, Mireille
Computer Science · Mathematics · Physics and Astronomy · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Physical sciences #Mathematical Physics (math-ph) #cs.CV #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9903036

21 pages, amsart, uses verbatim, amsmath, latexsym, amssymb, epsf 55 pictures

arxiv created 1999/03/19 · arxiv updated 2009/11/30

Abstract

Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve proposed by E.Calabi et. al are presented. The new formulas are valid for fine but otherwise arbitrary partitions of the curve. We also give numerically invariant expressions for the four differential invariants parametrizing the three dimensional version of the Euclidean signature curve, namely the curvature, the torsion and their derivatives with respect to arc length.

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