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Length Estimation for Curves with ε-Uniform Sampling

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Computer Analysis of Images and Patterns (CAIP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2124))

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Abstract

This paper discusses the problem of how to approximate the length of a parametric curve γ: [0, T] → ℝn from points q i =γ(t i), where the parameters t i are not given. Of course, it is necessary to make some assumptions about the distribution of the t i: in the present paper ε-uniformity. Our theoretical result concerns an algorithm which uses piecewise-quadratic interpolants. Experiments are conducted to show that our theoretical estimates are sharp, and that the assumption of ε-uniformity is needed. This work may be of interest in computer graphics, approximation and complexity theory, digital and computational geometry, and digital image processing.

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Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, 6009, WA, Australia

    Lyle Noakes

  2. Department of Computer Science & Software Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, 6009, WA, Australia

    Ryszard Kozera

  3. Centre for Image Technology & Robotics, The University of Auckland, Tamaki Campus, Building 731, Auckland, New Zealand

    Reinhard Klette

Authors
  1. Lyle Noakes
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  2. Ryszard Kozera
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  3. Reinhard Klette
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Editor information

Editors and Affiliations

  1. Faculty of Electronics and Information Technology Institute of Radioelectronics, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665, Warsaw, Poland

    Władysław Skarbek

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© 2001 Springer-Verlag Berlin Heidelberg

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Noakes, L., Kozera, R., Klette, R. (2001). Length Estimation for Curves with ε-Uniform Sampling. In: Skarbek, W. (eds) Computer Analysis of Images and Patterns. CAIP 2001. Lecture Notes in Computer Science, vol 2124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44692-3_63

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  • DOI: https://doi.org/10.1007/3-540-44692-3_63

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42513-7

  • Online ISBN: 978-3-540-44692-7

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