Three-Dimensional Digital Topology: The Genus.

Abstract

This report is one of a series on the geometrical and topological properties of three-dimensional digital images. In this report, we define the genus of a subset of a three-dimensional array and show that the properties of this digital genus are consistent which those of the genus in ordinary (continuous) topology. Since the approach here is different than that normally used in two dimensions, we also present the two-dimensional case. The derivation of the three-dimensional genus allows us to make explicit what is meant by a hole in an object (e.g., the hole in a ring). We also give algorithms for computing the three-dimensional digital genus and discuss the importance of three-dimensional genus in contrast with the two-dimensional genus. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1980
Accession Number
ADA094339

Entities

People

  • David G. Morgenthaler

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Cartesian Coordinates
  • Computer Science
  • Computer Vision
  • Construction
  • Digital Images
  • Geometry
  • Image Processing
  • Images
  • Object Recognition
  • Orientation (Direction)
  • Pattern Recognition
  • Recognition
  • Three Dimensional
  • Topology
  • Two Dimensional
  • X-Ray Computed Tomography

Readers

  • Computer Vision.
  • Graph Algorithms and Convex Optimization.