Consistent digital rays

Jinhi Jiyon, Cozzetti Matias Korman, Martin Nöllenburg, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 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 op 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 ⊖ (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
Title of host publicationProceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08
Pages355-364
Number of pages10
DOIs
Publication statusPublished - 2008 Dec 12
Event24th Annual Symposium on Computational Geometry, SCG'08 - College Park, MD, United States
Duration: 2008 Jun 92008 Jun 11

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other24th Annual Symposium on Computational Geometry, SCG'08
CountryUnited States
CityCollege Park, MD
Period08/6/908/6/11

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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  • Cite this

    Jiyon, J., Korman, C. M., Nöllenburg, M., & Tokuyama, T. (2008). Consistent digital rays. In Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08 (pp. 355-364). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1377676.1377737