Image Algebra.

Abstract

Enormous increases in image processing activities in the military, industrial, and academic communities have resulted in a deluge of different image processing architectures, operations, and systems of notation. There is little use of any standardized, mathematically rigorous, efficient algebraic system that is specifically designed to express image manipulation. The purpose of this project is to develop such standardized Image Algebra capable of expressing all image processing transformations and which will establish a comprehensive mathematical structure which can then serve as the mathematical basis for a universally acceptable image processing language. Such an algebraic system for the representation of image processing transformations will serve as a highly useful tool for expressing and for analyzing developed algorithms. It will clarify similarities among alternative algorithms as well as highlight their differences. A programming language based upon such an algebra will be capable of expressing the most complicated image processing algorithms in just a few lines rather than in multiple pages of code. A set of 14 basic binary operations are defined. These basic operations provide for computation between images, between an image and a template, or between templates. Many algebraic properties and relationships are determined. Translations of various image processing transformations into the Image Algebra are provided illustrating the use and the potential of an Image Algebra.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1986
Accession Number
ADA176152

Entities

People

  • Gerhard X. Ritter
  • Maurice A. Shrader-frechette
  • Paul D. Gader

Organizations

  • University of Florida

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Communities
  • Computations
  • Computer Programming
  • Image Processing
  • Information Processing
  • Language
  • Mathematical Analysis
  • Mathematics
  • Notation
  • Programming Languages
  • Structural Components
  • Template Patterns
  • Translations

Readers

  • Computational Linguistics
  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design