Marshall, Stephen and Green, Alan C. and Dougherty, Edward R. and Greenhalgh, David (2004) *Optimal filters with multiresolution apertures.* Journal of Mathematical Imaging and Vision, 20 (3). pp. 237-250. ISSN 0924-9907

## 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.

Item type: | Article |
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ID code: | 3481 |

Keywords: | nonlinear filtering, multiresolution analysis, aperture filter, statistical estimation, imaging, Electrical engineering. Electronics Nuclear engineering, Mathematics, Modelling and Simulation, Geometry and Topology, Applied Mathematics, Computer Vision and Pattern Recognition, Statistics and Probability, Condensed Matter Physics |

Subjects: | Technology > Electrical engineering. Electronics Nuclear engineering Science > Mathematics |

Department: | Faculty of Engineering > Electronic and Electrical Engineering Unknown Department Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 21 Jun 2007 |

Last modified: | 04 Sep 2014 12:14 |

URI: | http://strathprints.strath.ac.uk/id/eprint/3481 |

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