Maximum Likelihood Estimation of Hidden Markov Model Parameters, with Application to Medical Image Segmentation

We address the problem of a non-supervised bidimensional segmentation method based upon a discrete-level unilateral Markov field model for the labels and conditionaly Gaussian densities for the observed voxels. Such models have been shown to yield numerically efficient algorithms, for segmentation and for estimation of the model parameters as well. Our contribution is twofold. First, we deal with the degeneracy of the likelihood function with respect to the parameters of the Gaussian densities, which is a well-known problem for such mixture models. We introduce a bounded penalized likelihood function that has been recently shown to provide a consistent estimator in the simpler cases of independent Gaussian mixtures. On the other hand, implementation with EM reestimation formulas remains possible with only limited changes with respect to the standard case. Second, we propose a telegraphic parameterization of the unilateral Markov field. On a theoretical level, this parameterization ensures that some important properties of the field (e.g., stationarity) do hold. On a practical level, it reduces the computational complexity of the algorithm used in the segmentation and parameter estimation stages of the procedure. In addition, it decreases the number of model parameters that must be estimated, thereby improving convergence speed and accuracy of the corresponding estimation

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