On the Estimation of Markov Random Field Parameters
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We examine the histogram method proposed in  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.
IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 3, March 1999, pp. 216-224.
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