Curvature and torsion estimators based on parametric curve fitting

Curvature and torsion estimators based on parametric curve fitting
Thomas Lewiner, João Gomes, Hélio Lopes, Marcos Craizer

Abstract:

Many applications of geometry processing and computer vision rely on geometric properties of curves, particularly their curvature. Several methods have already been proposed to estimate the curvature of a planar curve, most of them for curves in digital spaces. This work proposes a new scheme for estimating curvature and torsion of planar and spatial curves, based on weighted least-squares fitting and local arc-length approximation. The method is simple enough to admit a convergence analysis that takes into account the effect of noise in the samples. The implementation of the method is compared to other curvature estimation methods showing a good performance. Applications to prediction in geometry compression are presented both as a practical application and as a validation of this new scheme.

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BibTeX:

@article{curvature_cg,
    author = {Thomas Lewiner and João Gomes and Hélio Lopes and Marcos Craizer},
    title = {Curvature and torsion estimators based on parametric curve fitting},
    year = {2005},
    month = {october},
    journal = {Computers & Graphics},
    volume = {29},
    number = {5},
    pages = {641--655},
    publisher = {Elsevier},
    doi = {10.1016/j.cag.2005.08.004},
    url = {\url{http://thomas.lewiner.org/pdfs/curvature_cg.pdf}}
}