Probabilistic image processing by extended Gauss-Markov random fields

Kazuyuki Tanaka; Nicolas Morin; Muneki Yasuda; D. M. Titterington

doi:10.1109/SSP.2009.5278499

Probabilistic image processing by extended Gauss-Markov random fields

Kazuyuki Tanaka, Nicolas Morin, Muneki Yasuda, D. M. Titterington

INF - Applied Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.

Original language	English
Title of host publication	2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
Pages	618-621
Number of pages	4
DOIs	https://doi.org/10.1109/SSP.2009.5278499
Publication status	Published - 2009
Event	2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09 - Cardiff, United Kingdom Duration: 2009 Aug 31 → 2009 Sept 3

Publication series

Name	IEEE Workshop on Statistical Signal Processing Proceedings

Conference

Conference	2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
Country/Territory	United Kingdom
City	Cardiff
Period	09/8/31 → 09/9/3

Keywords

Bayesian image analysis
Bayesian network
Gauss-Markov random fields

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10.1109/SSP.2009.5278499

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title = "Probabilistic image processing by extended Gauss-Markov random fields",

abstract = "We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.",

keywords = "Bayesian image analysis, Bayesian network, Gauss-Markov random fields",

author = "Kazuyuki Tanaka and Nicolas Morin and Muneki Yasuda and Titterington, {D. M.}",

year = "2009",

doi = "10.1109/SSP.2009.5278499",

language = "English",

isbn = "9781424427109",

series = "IEEE Workshop on Statistical Signal Processing Proceedings",

pages = "618--621",

booktitle = "2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09",

note = "2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09 ; Conference date: 31-08-2009 Through 03-09-2009",

}

Tanaka, K, Morin, N, Yasuda, M & Titterington, DM 2009, Probabilistic image processing by extended Gauss-Markov random fields. in 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09., 5278499, IEEE Workshop on Statistical Signal Processing Proceedings, pp. 618-621, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09, Cardiff, United Kingdom, 09/8/31. https://doi.org/10.1109/SSP.2009.5278499

Probabilistic image processing by extended Gauss-Markov random fields. / Tanaka, Kazuyuki; Morin, Nicolas; Yasuda, Muneki et al.
2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09. 2009. p. 618-621 5278499 (IEEE Workshop on Statistical Signal Processing Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Probabilistic image processing by extended Gauss-Markov random fields

AU - Tanaka, Kazuyuki

AU - Morin, Nicolas

AU - Yasuda, Muneki

AU - Titterington, D. M.

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Y1 - 2009

N2 - We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.

AB - We propose an extension of the Gauss-Markov random field (GMRF) models by introducing next-nearest neighbour interactions. The values of the next-nearest neighbour interactions are set to positive real numbers with the expectation that this will lead to some noise reduction while preserving the edges. Values for the hyperparameters in the proposed model are determined by using the EM algorithm in order to maximize the marginal likelihood. In addition, a measure of mean squared error, which quantifies the statistical performance of our proposed model, is derived analytically as an exact explicit expression by means of the multi-dimensional Gaussian integral formulas.

KW - Bayesian image analysis

KW - Bayesian network

KW - Gauss-Markov random fields

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BT - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09

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Y2 - 31 August 2009 through 3 September 2009

ER -

Probabilistic image processing by extended Gauss-Markov random fields

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