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

Ken-Chung HO  Bin-Chang CHIEU  

IEICE TRANSACTIONS on Information and Systems   Vol.E79-D   No.10   pp.1462-1476
Publication Date: 1996/10/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing,Computer Graphics and Pattern Recognition
Markov random field,  parameter estimation,  maximum likelihood estimation,  multiwindow image partitioning,  

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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.