Elsevier

Pattern Recognition Letters

Volume 3, Issue 5, September 1985, Pages 323-326
Pattern Recognition Letters

A simple proof of Rosenfeld's characterization of digital straight line segments

https://doi.org/10.1016/0167-8655(85)90063-7Get rights and content

Abstract

A digital straight line segment is defined as the grid-intersect quantization of a straight line segment in the plane. Let S be a set of pixels on a square grid. Rosenfeld [8] showed that S is a digital straight line segment if and only if it is a Digital arc having the chord property. Then Kim and Rosenfeld [3,6] showed that S has the chord properly if and if for every p, qϵS there is a digital straight line segment CS such that p and q are the extremities of C.

We give a simple proof of these two results based on the Transversal Theorem of Santaló. We show how the underlying methodology can be generalized to the case of (infinite) digital straight lines and to the quantization of hyperplanes in an n-dimensional space for n ≥ 3.

References (11)

  • L Dantzer et al.

    Helly's Theorem and its relatives

  • H Freeman

    On the encoding of arbitrary Geometric Configurations

    IRE Trans. Electronic Computers

    (1961)
  • C.E Kim

    Digital convexity, straightness and convex polygons

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1982)
  • C.E Kim

    Three-dimensional digital line segments

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1983)
  • C.E Kim

    Three-dimensional digital planes

    IEEE Trans. Pattern Anal. Mach. Intell.

    (1984)
There are more references available in the full text version of this article.

Cited by (13)

  • Digital straightness - A review

    2004, Discrete Applied Mathematics
  • Digital straightness

    2001, Electronic Notes in Theoretical Computer Science
  • Discrete Geometry for Image Processing

    1999, Advances in Imaging and Electron Physics
  • Detecting the straightness of digital curves in O(N) steps

    1989, Computer Vision, Graphics and Image Processing
  • Picture processing: 1985.

    1986, Computer Vision, Graphics, & Image Processing
  • STRONG CHORD PROPERTY FOR 4-CONNECTED CONVEX DIGITAL SETS.

    1986, Computer vision, graphics, and image processing
View all citing articles on Scopus
View full text