Non-Rigid Image Registration Using Gaussian Mixture Models

Non-rigid mutual information (MI) based image registration is prone to converge to local optima due to Parzen or histogram based density estimation used in conjunction with estimation of a high dimensional deformation field. We describe an approach for non-rigid registration that uses the log-likelihood of the target image given the deformed template as a similarity metric, wherein the distribution is modeled using a Gaussian mixture model (GMM). Using GMMs reduces the density estimation step to that of estimating the parameters of the GMM, thus being more computationally efficient and requiring fewer number of samples for accurate estimation. We compare the performance of our approach (GMM-Cond) with that of MI with Parzen density estimation (Parzen-MI), on inter-subject and inter-modality (CT to MR) mouse images. Mouse image registration is challenging because of the presence of a rigid skeleton within non-rigid soft tissue, and due to major shape and posture variability in inter-subject registration. The results show that GMM-Cond has higher registration accuracy than Parzen-MI in terms of sum of squared difference in intensity and dice coefficients of overall and skeletal overlap. The GMM-Cond approach is a general approach that can be considered a semi-parametric approximation to MI based registration, and can be used an alternative to MI for high dimensional non-rigid registration.