On Cellular Straight Line Segments.

Abstract

We discuss a scheme for digitizing curves that is consistent with a scheme for digitizing regions. It is shown that the cellular image of a region is determined by the cellular image of its boundary by the scheme. It is proved that the chord property is a necessary and sufficient condition for a cellular arc to be a cellular straight line segment. By showing that the chord property and the cellular convexity condition are equivalent, we prove that a cellular arc is a cellular straight line segment if and only if it is cellularly convex. This leads to an algorithm to determine whether or not a cellular complex is a cellular straight line segment in time linear in the number of rows of cells. Finally it is proven that a cellular complex is cellularly convex if and only if any pair of its cells is connected by a cellular straight line segment in the cellular complex. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1980
Accession Number
ADA089511

Entities

People

  • Chul E. Kim

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundaries
  • Computer Science
  • Computers
  • Curvature
  • Digital Images
  • Geometry
  • Grids
  • Image Processing
  • Images
  • Maryland
  • Pattern Recognition
  • Plane Geometry
  • Security
  • Universities

Fields of Study

  • Mathematics

Readers

  • Computer Vision.
  • Graph Algorithms and Convex Optimization.
  • Molecular Genetics