3. Algebraic Structures for Shape Description

  1. Pijush K. Ghosh1 and
  2. Koichiro Deguchi2

Published Online: 28 JAN 2010

DOI: 10.1002/9780470823095.ch3

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics

How to Cite

Ghosh, P. K. and Deguchi, K. (2008) Algebraic Structures for Shape Description, in Mathematics of Shape Description: A Morphological Approach to Image Processing and Computer Graphics, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470823095.ch3

Author Information

  1. 1

    National Centre for Software Technology (now Centre for Development of Advanced Computing), India

  2. 2

    Graduate School of Information Sciences, Tohoku University, Japan

Publication History

  1. Published Online: 28 JAN 2010
  2. Published Print: 26 MAR 2008

ISBN Information

Print ISBN: 9780470823071

Online ISBN: 9780470823095

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Keywords:

  • algebraic structures for shape description;
  • algebraic composition law - function fκ as a special function;
  • algebraic structure or algebraic system;
  • “isometry” - geometric transformation preserving distance;
  • algebraic system properties or composition law properties;
  • algebraic system morphisms - two algebraic system morphism;
  • consequential algebra of symmetry;
  • identifying algebraic system - as a group;
  • symmetry groups - order of permutation groups of solids in three dimensions;
  • rotation of point in three-dimensional space

Summary

This chapter contains sections titled:

  • What is an Algebraic Structure?

  • Properties of Algebraic Systems

  • Morphisms of Algebraic Systems

  • Semigroups and Monoids: Two Simple Algebraic Systems

  • Groups

  • Symmetry Groups

  • Proper Rotations of Regular Solids

  • Rings