2. Sets and Functions for Shape Description

  1. Pijush K. Ghosh1 and
  2. Koichiro Deguchi2

Published Online: 28 JAN 2010

DOI: 10.1002/9780470823095.ch2

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) Sets and Functions 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.ch2

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:

  • sets and functions for shape description;
  • concept of set - general and fundamental notion of mathematics;
  • “class,” “aggregate” and “collection” - synonyms of “set”;
  • equality and inclusion of sets;
  • Venn diagram, schematic representation of set by set of points;
  • functions, mappings and operations;
  • geometric transformations as translation, rotation, scaling - viewed as functions;
  • pictorial representation of function - allied to traditional coordinate geometry;
  • one-to-one onto (or bijective function);
  • inverse functions - inverse of composite function

Summary

This chapter contains sections titled:

  • Basic Concepts of Sets

  • Equality and Inclusion of Sets

  • Some Operations on Sets

  • Relations in Sets

  • Functions, Mappings, and Operations