Optimal filters with multiresolution apertures

Stephen Marshall, Alan C. Green, Edward R. Dougherty, David Greenhalgh

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents an extension to the recently introduced class of nonlinear filters known as Aperture Filters. By taking a multiresolution approach, it can be shown that more accurate filtering results (in terms of mean absolute error) may be achieved compared to the standard aperture filter given the same size of training set. Most optimisation techniques for nonlinear filters require a knowledge of the conditional probabilities of the output. These probabilities are estimated from observations of a representative training set. As the size of the training set is related to the number of input combinations of the filter, it increases very rapidly as the number of input variables increases. It can be impossibly large for all but the simplest binary filters. In order to design nonlinear filters of practical use, it is necessary to limit the size of the search space i.e. the number of possible filters (and hence the training set size) by the application of filter constraints. Filter constraints take several different forms, the most general of which is the window constraint where the output filter value is estimated from only a limited range of input variables.
Original languageEnglish
Pages (from-to)237-250
Number of pages14
JournalJournal of Mathematical Imaging and Vision
Volume20
Issue number3
DOIs
Publication statusPublished - May 2004

Keywords

  • nonlinear filtering
  • multiresolution analysis
  • aperture filter
  • statistical estimation
  • imaging

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