### Abstract

Original language | English |
---|---|

Pages (from-to) | 237-250 |

Number of pages | 14 |

Journal | Journal of Mathematical Imaging and Vision |

Volume | 20 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 2004 |

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### Keywords

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

### Cite this

*Journal of Mathematical Imaging and Vision*,

*20*(3), 237-250. https://doi.org/10.1023/B:JMIV.0000024041.44525.e6

}

*Journal of Mathematical Imaging and Vision*, vol. 20, no. 3, pp. 237-250. https://doi.org/10.1023/B:JMIV.0000024041.44525.e6

**Optimal filters with multiresolution apertures.** / Marshall, Stephen; Green, Alan C.; Dougherty, Edward R.; Greenhalgh, David.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal filters with multiresolution apertures

AU - Marshall, Stephen

AU - Green, Alan C.

AU - Dougherty, Edward R.

AU - Greenhalgh, David

PY - 2004/5

Y1 - 2004/5

N2 - 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.

AB - 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.

KW - nonlinear filtering

KW - multiresolution analysis

KW - aperture filter

KW - statistical estimation

KW - imaging

U2 - 10.1023/B:JMIV.0000024041.44525.e6

DO - 10.1023/B:JMIV.0000024041.44525.e6

M3 - Article

VL - 20

SP - 237

EP - 250

JO - Journal of Mathematical Imaging and Vision

JF - Journal of Mathematical Imaging and Vision

SN - 0924-9907

IS - 3

ER -