Abstract
Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve introduced by Calabi et al. in (Int. J. Comput. Vision, 26: 107–135, 1998) 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 parameterizing the three dimensional version of the Euclidean signature curve, namely the curvature, the torsion and their derivatives with respect to arc length.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S. 1998. Differential and numerically invariant signature curves applied to object recognition. Int. J. Comput. Vision, 26:107–135.
Carmo, M.P. Do. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall.
Cartan, É. 1935. Laméethode du repère mobile, la théorie des groupes continues et les espaces généralisés Exposés de géométrie No. 5. Hermann, Paris.
Eves. H. 1965. A Survey of Geometry, II. Allyn and Bacon.
Friedman, M. and Kandel, A. 1993. Fundamentals of Computer Numerical Analysis. CRC: Boca Raton.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boutin, M. Numerically Invariant Signature Curves. International Journal of Computer Vision 40, 235–248 (2000). https://doi.org/10.1023/A:1008139427340
Issue Date:
DOI: https://doi.org/10.1023/A:1008139427340