Abstract
In this paper we verify sharpness of the theoretical results concerning the asymptotic orders of trajectory approximation of the unknown parametric curve γ in arbitrary Euclidean space. The pertinent interpolation schemes (based on piecewise-quadratics and piecewise-cubics) are here considered for the so-called reduced data. The latter forms an ordered collection of points without provision of the associated interpolation knots. To complement such data i.e. to determine the missing knots, cumulative chord parameterization is invoked. Sharpness of cubic and quartic orders of convergence are demonstrated for piecewise-quadratics and piecewise-cubics, respectively. This topic has its ramification in computer vision (e.g. image segmentation), computer graphics (e.g. trajectory modeling) or in engineering (e.g. robotics).
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© 2012 Springer-Verlag Berlin Heidelberg
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Kozera, R., Śmietanka, M. (2012). Sharpness in Trajectory Estimation by Piecewise-quadratics(-cubics) and Cumulative Chords. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds) Computer Vision and Graphics. ICCVG 2012. Lecture Notes in Computer Science, vol 7594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33564-8_18
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DOI: https://doi.org/10.1007/978-3-642-33564-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33563-1
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