2. Image Transformations

  1. Maria Petrou and
  2. Costas Petrou

Published Online: 27 JAN 2011

DOI: 10.1002/9781119994398.ch2

Image Processing: The Fundamentals, Second Edition

Image Processing: The Fundamentals, Second Edition

How to Cite

Petrou, M. and Petrou, C. (2010) Image Transformations, in Image Processing: The Fundamentals, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994398.ch2

Publication History

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

ISBN Information

Print ISBN: 9780470745861

Online ISBN: 9781119994398

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Keywords:

  • discrete Fourier transform (DFT);
  • even antisymmetric discrete sine transform (EDST);
  • image processing;
  • odd DST (ODST);
  • singular value decomposition image (SVD);
  • Walsh

Summary

This chapter is concerned with the development of some of the important tools of linear image processing, namely the ways by which we express an image as the linear superposition of some elementary images. The optimal way to represent an image with as much detail is to use as basis images those that are defined by the image itself, the eigenimages of the singular value decomposition image (SVD). The bases constructed with the help of orthonormal sets of discrete functions (Haar and Walsh) are easy to implement in hardware. However, the basis constructed with the help of the orthonormal set of complex exponential functions is by far the most popular. The representation of an image in terms of it is called discrete Fourier transform (DFT). Even antisymmetric discrete sine transform (EDST) and odd DST (ODST) require the dc component to be transmitted in addition to the coefficients of the expansion.

Controlled Vocabulary Terms

discrete Fourier transforms; Haar transforms; image processing; singular value decomposition; Walsh functions