On the Number of Digital Straight Line Segments

  • Authors:
  • Carlos A. Berenstein;David Lavine

  • Affiliations:
  • Univ. of Maryland, College Park;LNK Corporation, Inc., Riverdale, MD

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1988

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Abstract

A closed-form expression has been reported in the literature for L/sub N/, the number of digital line segments of length N that correspond to lines of the form y=ax+ beta , Oor= alpha , beta 1. The authors prove an asymptotic estimate for L/sub N/ that might prove useful for many applications, namely, L/sub N/=N/sup 3// pi /sup 2/+O(N/sup 2/ log N). An application to an image registration problem is given.