2. Mathematical Preliminaries

  1. Frank Y. Shih

Published Online: 4 AUG 2010

DOI: 10.1002/9780470590416.ch2

Image Processing and Pattern Recognition

Image Processing and Pattern Recognition

How to Cite

Shih, F. Y. (2010) Mathematical Preliminaries, in Image Processing and Pattern Recognition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470590416.ch2

Publication History

  1. Published Online: 4 AUG 2010
  2. Published Print: 12 APR 2010

ISBN Information

Print ISBN: 9780470404614

Online ISBN: 9780470590416



  • cosine transform;
  • Fourier transform;
  • Laplace transform;
  • mathematical preliminaries;
  • wavelet transform;
  • Z-transform


Most images are recorded and processed in the time domain or spatial domain. The spatial domain refers to the aggregate of pixels composing an image, and the spatial domain processing involves operations that apply directly on these pixels. However, it is sometimes convenient and efficient to process images in the frequency domain because edge pixels generally correspond to high-frequency components and interior pixels of an object region correspond to low-frequency components. In this chapter, the mathematical preliminaries that are often used in image processing for converting an image from spatial domain to frequency domain are introduced. These include Laplace transform, Fourier transform, Z-transform, cosine transform, and wavelet transform.

Controlled Vocabulary Terms

fourier transform optics; laplace transforms; wavelet transforms; Z transforms