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Cumulative Chord Piecewise-Quartics for Length and Curve Estimation

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Computer Analysis of Images and Patterns (CAIP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2756))

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Abstract

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.

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Author information

Authors and Affiliations

  1. School of Computer Science and Software Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, 6009 WA, Perth, Australia

    Ryszard Kozera

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  1. Ryszard Kozera
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Editors and Affiliations

  1. Institute of Mathematics and Computing Science, University of Groningen, P.O.Box 800, 9700 AV, Groningen, The Netherlands

    Nicolai Petkov

  2. Institute of Mathematics and Computing Science, University of Groningen, Blauwborgje 3, 9747 AC, Groningen, The Netherlands

    Michel A. Westenberg

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Kozera, R. (2003). Cumulative Chord Piecewise-Quartics for Length and Curve Estimation. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_85

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  • DOI: https://doi.org/10.1007/978-3-540-45179-2_85

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40730-0

  • Online ISBN: 978-3-540-45179-2

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