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Sharpness in Trajectory Estimation by Piecewise-quadratics(-cubics) and Cumulative Chords

  • Ryszard Kozera
  • Mateusz Śmietanka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7594)

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).

Keywords

Convergence Rate Interpolation Scheme Length Estimation Fast Convergence Rate Asymptotic Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ryszard Kozera
    • 1
  • Mateusz Śmietanka
    • 1
  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

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