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On the Estimation of Markov Random Field Parameters
March 1999 (vol. 21 no. 3)
pp. 216-224

Abstract—We examine the histogram method proposed in [1] for estimating the parameters associated with a Markov random field. This method relies on the estimation of the local interaction sums from histogram data. We derive an estimator for these quantities that is optimal in a well-defined sense. Furthermore, we show that the final step of the histogram method, the solution of a least-squares problem, can be done substantially faster than one might expect if no equation culling is used. We also examine the use of weighted least-squares and see that this seems to lead to better estimates even with small amounts of data.

[1] H. Derin and H. Elliott, "Modelling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp. 39-55, Jan. 1987.
[2] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistical Soc., Series B, vol. 2, 1974.
[3] G. Cross and A. Jain, "Markov Random Field Texture Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 1, 1983.
[4] M. Gurelli and L. Onural, "On a Parameter Estimation Method for Gibbs-Markov Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 4, Apr. 1994.
[5] C. Gauss, "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae," Classics in Applied Mathematics, SIAM, 1995.
[6] B. Calder, L. Linnett, S. Clarke, and D. Carmichael, "Improvements in Markov Random Field Parameter Estimation," IEE E4 Colloquium on Multiresolution Image Processing.London: IEE, Apr. 1995, no. 1995/077.
[7] G. Golub and C. Van Loan, Matrix Computations, third ed. Baltimore: Johns Hopkins Univ. Press, 1996.

Index Terms:
Markov random fields, parameter estimation.
Citation:
Carlos F. Borges, "On the Estimation of Markov Random Field Parameters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 3, pp. 216-224, March 1999, doi:10.1109/34.754587
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