Image Registration using Bayes Theory and a Maximum Likelihood Framework with an EM Algorithm

A novel image registration algorithm that uses two kinds of information is presented: One kind is the shape information of an object and the other kind is the intensity information of a voxel and its neighborhoods consisting of the object. We, first, segment the medical volume data using the Markov random field model and the ICM algorithm and extract the surface region of the object from a segmented volume data. Second, we use the hidden labeling variables and likelihood method to statistically model the intensity distribution of each voxel at the surface region. We adopt the Bernoulli probability model to formulate a prior distribution of the labeling variable for the transformed voxels. The Gaussian mixture model is taken as a probability distribution function for the intensity of the transformed voxel. We use the EM algorithm to get the proper estimators for the parameters of the complete-data log likelihood function. The EM algorithm consists of two steps: the E-step and M-step. In the E-step, we compute the posterior distribution of the labeling variable by taking the expectation for the log-likelihood function. Next, we drive the estimators for all of the parameters by maximizing this function iteratively in the M-step. Then, we define a new registration measure with the Q-function obtained by the EM algorithm. We evaluate the precision of the proposed approach by comparing the registration traces of the Q- function obtained from the original image and its transformed image with respect to x-translation and rotation. The experimental results show that our method has great potential power to register various medical images given by different modalities.