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WindowBased Methods for Parameter Estimation of Markov Random Field Images
KenChung HO BinChang CHIEU
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E79D
No.10
pp.14621476 Publication Date: 1996/10/25 Online ISSN:
DOI: Print ISSN: 09168532 Type of Manuscript: PAPER Category: Image Processing,Computer Graphics and Pattern Recognition Keyword: Markov random field, parameter estimation, maximum likelihood estimation, multiwindow image partitioning,
Full Text: PDF(1.2MB)>>
Summary:
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 pseudolikelihood estimate (MPLE), the coding method estimate (CME), and the leastsquares estimate (LSE) are all based on the (conditional) pixel probabilities for simplicity. However, the conventional pixelbased estimators are not very satisfactorily accurate, especially when the interactions of pixels are strong. We therefore propose two windowbased estimators to improve the estimation accuracy: the adjoiningconditionalwindow (ACW) scheme and the separatedconditionalwindow (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 windowbased estimators include the pixelbased ones as special cases. We present respectively the relationship between the MLE and each of the two windowbased estimates. Through the relationships we provide a unified view that the conventional pixelbased estimates and our windowbased estimates all approximate the MLE. The accuracy of all the estimates can be described by two types of superiority: the crossscheme superiority that an ACW estimate is more accurate than the SCW estimate with the same window size, and the inscheme 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.

