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A Probabilistic Rating System for Team Competitions with Individual Contributions Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Fréchet Filters for Color and Hyperspectral Images Filtering

Authors : Ekaterina Ostheimer, Valeriy Labunets, Denis Komarov, Tat’yana Fedorova

Published in: Analysis of Images, Social Networks and Texts

Publisher: Springer International Publishing

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Abstract

Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this paper, we extend the notion of the Fréchet vector median to the general Fréchet vector median, which minimizes the Fréchet cost function (FCF) in the form of an aggregation function instead of the ordinary sum. Moreover, we propose to use an aggregation distance instead of the classical one. We use the generalized Fréchet median for constructing new nonlinear filters based on an arbitrary pair of aggregation operators that can be changed independently. For each pair of parameters, we get the unique class of new nonlinear filters.

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previous chapter Transform Coding Method for Hyperspectral Data: Influence of Block Characteristics to Compression Quality
next chapter Fast Global Image Denoising Algorithm on the Basis of Nonstationary Gamma-Normal Statistical Model
Appendix
Available only for authorised users
Literature
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Labunets V. G.: Filters based on aggregation operators Part 1. Aggregation operators. In: 24th International Crimean Conference Microwave and Telecommunication Technology (CriMiCo2014), Sevastopol, Crimea, Russia, vol. 24, pp. 1239–1240 (2014)
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Labunets, V.G., Gainanov, D.N., Ostheimer, E.: Filters based on aggregation operators. Part 2. The kolmogorov filters. In: 24th International Crimean Conference Microwave and Telecommunication Technology (CriMiCo2014), Sevastopol, Crimea, Russia, vol. 24, pp. 1241–1242 (2014)
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Labunets, V.G., Gainanov, D.N., Tarasov A.D., Ostheimer E.: Filters based on aggregation operators. Part 3. The heron filters. In: 24th International Crimean Conference “Microwave and Telecommunication Technology” (CriMiCo2014), Sevastopol, Crimea, Russia, vol. 24, pp. 1243–1244 (2014)
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Labunets, V.G., Gainanov, D.N., Arslanova, R.A., Ostheimer, E.: Filters based on aggregation operators. Part 4. Generalized vector median filters. In: 24th International Crimean Conference Microwave and Telecommunication Technology (CriMiCo2014), Sevastopol, Crimea, Russia, vol. 24, pp. 1245–1246 (2014)
Metadata
Title
Fréchet Filters for Color and Hyperspectral Images Filtering
Authors
Ekaterina Ostheimer
Valeriy Labunets
Denis Komarov
Tat’yana Fedorova
Copyright Year
2015
Book
Analysis of Images, Social Networks and Texts

Print ISBN: 978-3-319-26122-5

Electronic ISBN: 978-3-319-26123-2

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-26123-2_6

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