Window-Based Methods for Parameter Estimation of Markov Random Field Images

Ken-Chung HO; Bin-Chang CHIEU

Window-Based Methods for Parameter Estimation of Markov Random Field Images

Ken-Chung HO, Bin-Chang CHIEU

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The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.

Publication: IEICE TRANSACTIONS on Information Vol.E79-D No.10 pp.1462-1476

Publication Date: 1996/10/25

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Type of Manuscript: PAPER

Category: Image Processing,Computer Graphics and Pattern Recognition

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Ken-Chung HO, Bin-Chang CHIEU, "Window-Based Methods for Parameter Estimation of Markov Random Field Images" in IEICE TRANSACTIONS on Information, vol. E79-D, no. 10, pp. 1462-1476, October 1996, doi: .
Abstract: The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_10_1462/_p

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@ARTICLE{e79-d_10_1462,
author={Ken-Chung HO, Bin-Chang CHIEU, },
journal={IEICE TRANSACTIONS on Information},
title={Window-Based Methods for Parameter Estimation of Markov Random Field Images},
year={1996},
volume={E79-D},
number={10},
pages={1462-1476},
abstract={The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Window-Based Methods for Parameter Estimation of Markov Random Field Images
T2 - IEICE TRANSACTIONS on Information
SP - 1462
EP - 1476
AU - Ken-Chung HO
AU - Bin-Chang CHIEU
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1996
AB - The estimation of model parameter is essentially important for an MRF image model to work well. Because the maximum likelihood estimate (MLE), which is statistically optimal, is too difficult to implement, the conventional estimates such as the maximum pseudo-likelihood estimate (MPLE), the coding method estimate (CME), and the least-squares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixel-based estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two window-based estimators to improve the estimation accuracy: the adjoining-conditional-window (ACW) scheme and the separated-conditional-window (SCW) scheme. The replacement of the pixel probabilities by the joint probabilities of window pixels was inspired by the fact that the pixels in an image present information in a joint way and hence the more pixels we deal with the joint probabilities of, the more accurate the estimate should be. The window-based estimators include the pixel-based ones as special cases. We present respectively the relationship between the MLE and each of the two window-based estimates. Through the relationships we provide a unified view that the conventional pixel-based estimates and our window-based estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the cross-scheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the in-scheme superiority that an ACW (or SCW) estimate more accurate than another ACW (or SCW) estimate which uses smaller window size. The experimental results showed the two types of superiority and particularly the significant improvement in estimation accuracy due to using window probabilities instead of pixel probabilities.
ER -