Extension of the modified-histogramming method for multilevel Markov random fields

A very useful method for the estimation of Markov random field (MRF) parameters has been proposed by H. Derin and H. Elliott (1987). A bias reduction based modification of that method, called the modified-histogramming (MH) method, has been proposed by M.I. Gurelli and L. Onural (1994) for binary MRFs mainly to obtain better performance in the case of small amounts of image data. In this correspondence, an extension of the MH method for multilevel MRFs is proposed. Also, a data merging technique is given to increase the performance of the method.