Chapter 5. Two-Dimensional Filters

  1. Maria Petrou1 and
  2. Panagiota Bosdogianni2

Published Online: 17 OCT 2001

DOI: 10.1002/0470841907.ch5

Image Processing: The Fundamentals

Image Processing: The Fundamentals

How to Cite

Petrou, M. and Bosdogianni, P. (2001) Two-Dimensional Filters, in Image Processing: The Fundamentals, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/0470841907.ch5

Author Information

  1. 1

    University of Surrey, Guildford, UK

  2. 2

    Technical University of Crete, Chania, Greece

Publication History

  1. Published Online: 17 OCT 2001

ISBN Information

Print ISBN: 9780471998839

Online ISBN: 9780470841907



  • filter design;
  • approximation theory;
  • linear programming in filter design;
  • IIR filters;
  • FIR filters


Chapter 4 exposes the need for the development of filters which have various desired properties appropriate for images. This chapter covers techniques for 2D filter design so that one may develop filters that have response in preselected frequency bands, while they remain finite and thus appropriate for implementation by convolution. It covers issues like recursive versus non-recursive filters, filter stability to noise and measures of fidelity like the Chebyshev norm. It shows how the filter design problem may be formulated as a linear programming problem and discusses issues like limiting set of equations and La Vallee Poussin theorem.