3. Statistical Description of Images

  1. Maria Petrou and
  2. Costas Petrou

Published Online: 27 JAN 2011

DOI: 10.1002/9781119994398.ch3

Image Processing: The Fundamentals, Second Edition

Image Processing: The Fundamentals, Second Edition

How to Cite

Petrou, M. and Petrou, C. (2010) Statistical Description of Images, in Image Processing: The Fundamentals, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994398.ch3

Publication History

  1. Published Online: 27 JAN 2011
  2. Published Print: 9 APR 2010

ISBN Information

Print ISBN: 9780470745861

Online ISBN: 9781119994398



  • image processing;
  • independent component analysis (ICA);
  • Karhunen-Loeve (K-L) transform;
  • random process;
  • statistical properties


This chapter provides the necessary background for the statistical description of images from the signal processing point of view. It treats each image as the outcome of some random process, and it shows how one can reason about images using concepts from probability and statistics, in order to express a whole collection of images as composites of some basic images. In some cases it treats an image as the only available version of a large collection of similar images and reasons on the statistical properties of the whole collection. The Karhunen-Loeve (K-L) transform leads to an orthogonal basis of uncorrelated elementary images, in terms of which we may express any image that shares the same statistical properties as the image used to construct the transformation matrix. Independent component analysis (ICA) allows one to construct independent components from an ensemble of data.

Controlled Vocabulary Terms

image processing; Karhunen-Loeve transforms; random processes