Consistent digital rays

Jinhee Chun, Matias Korman, Martin Nöllenburg, Takeshi Tokuyama

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p. Each digital ray dig(op) approximates the Euclidean line segment op̄ between o and p. The set of all digital rays satisfies a set of axioms analogous to the Euclidean axioms. We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight Θ(log n) bound in the n × n grid. The proof of the bound is based on discrepancy theory and a simple construction algorithm. Without a monotonicity property for digital rays the bound is improved to O(1). Digital rays enable us to define the family of digital star-shaped regions centered at o, which we use to design efficient algorithms for image processing problems.

Original languageEnglish
Pages (from-to)359-378
Number of pages20
JournalDiscrete and Computational Geometry
Volume42
Issue number3
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • Digital geometry
  • Discrete geometry
  • Star-shaped regions
  • Tree embedding

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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