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Minimum-Length Polygons in Approximation Sausages

  • Tetsuo Asano
  • Yasuyuki Kawamura
  • Reinhard Klette
  • Koji Obokata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2059)

Abstract

The paper introduces a new approximation scheme for planar digital curves. This scheme defines an approximating sausage ‘around’ the given digital curve, and calculates a minimum-length polygon in this approximating sausage. The length of this polygon is taken as an estimator for the length of the curve being the (unknown) preimage of the given digital curve. Assuming finer and finer grid resolution it is shown that this estimator converges to the true perimeter of an r-compact polygonal convex bounded set. This theorem provides theoretical evidence for practical convergence of the proposed method towards a ‘correct’ estimation of the length of a curve. The validity of the scheme has been verified through experiments on various convex and non-convex curves. Experimental comparisons with two existing schemes have also been made.

Keywords

Digital geometry digital curves multigrid convergence length estimation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tetsuo Asano
    • 1
  • Yasuyuki Kawamura
    • 1
  • Reinhard Klette
    • 2
  • Koji Obokata
    • 1
  1. 1.School of Information ScienceJAISTAsahidaiJapan
  2. 2.CITRUniversity of AucklandAucklandNew Zealand

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