On Local Definitions of Length of Digital Curves

  • Mohamed Tajine
  • Alain Daurat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


In this paper we investigate the ‘local’ definitions of length of digital curves in the digital space r2 where r is the resolution of the discrete space. We prove that if μ r is any local definition of the length of digital curves in r2, then for almost all segments S of ℝ2, the measure μ r (S r ) does not converge to the length of S when the resolution r converges to 0, where S r is the Bresenham discretization of the segment S in r2. Moreover, the average errors of classical local definitions are estimated, and we define a new one which minimizes this error.


Digital segments local length estimation frequency of factors convergence 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mohamed Tajine
    • 1
  • Alain Daurat
    • 1
  1. 1.LSIIT UMR 7005 CNRS-ULP, Pôle APIIllkirch-GraffenstadenFrance

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