Cumulative Chord Piecewise-Quartics for Length and Curve Estimation

  • Ryszard Kozera
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2756)


We discuss the problem of estimating an arbitrary regular parameterized curve and its length from an ordered sample of interpolation points in n-dimensional Euclidean space. The corresponding tabular parameters are assumed to be unknown. In this paper the convergence rates for estimating both curve and its length with cumulative chord piecewise-quartics are established for different types of unparameterized data including ε-uniform samplings. The latter extends previous results on cumulative chord piecewise-quadratics and piecewise-cubics. The numerical experiments carried out for planar and space curves confirm sharpness of the derived asymptotics. A high quality approximation property of piecewise-quartic cumulative chords is also experimentally verified on sporadic data. Our results may be of interest in computer vision (e.g. in edge and range image segmentation or in tracking), digital image processing, computer graphics, approximation and complexity theory or digital and computational geometry.


shape length curve interpolation image analysis and features 


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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ryszard Kozera
    • 1
  1. 1.School of Computer Science and Software EngineeringThe University of Western AustraliaCrawleyAustralia

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