A likelihood maximization approach to image registration is developed in this paper. It is assumed that the voxel values in two images in registration are probabilistically related. The principle of maximum likelihood is then exploited to find the optimal registration: the likelihood that given image f, one has image g and given image g, one has image f is optimized with respect to registration parameters. All voxel pairs in the overlapping volume or a portion of it can be used to compute the likelihood. A knowledge-based method and a self-consistent technique are proposed to obtain the probability relation. In the knowledge-based method, prior knowledge of the distribution of voxel pairs in two registered images is assumed, while such knowledge is not required in the self-consistent method. The accuracy and robustness of the likelihood maximization approach is validated by single modality registration of single photon emission computed tomographic (SPECT) images and magnetic resonance (MR) images and by multimodality registration (MR/SPECT). The results demonstrate that the performance of the likelihood maximization approach is comparable to that of the mutual information maximization technique. Finally the relationship between the likelihood approach and the entropy, conditional entropy, and mutual information approaches is discussed.

Cross-entropy (CE), an information-theoretic measure, quantifies the difference between two probability density functions. This measure is applied to volume image registration. When a good prior estimation of the joint distribution of the voxel values of two images in registration is available, the CE can be minimized to find an optimal registration. If such a prior estimation is not available, one seeks the registration which gives a joint distribution different from unlikely ones as much as possible, i.e., the CE is maximized to find an optimal registration. When the unlikely distribution is a uniform one, CE maximization reduces to joint entropy minimization; when the unlikely distribution is proportional to one of the marginal distributions, it reduces to conditional entropy minimization; when the unlikely distribution is the product of two marginal distributions, it degenerates to mutual-information maximization. These different CEs are added together and are used as criteria for image registration. The accuracy and robustness of this new approach are tested and compared using a likely joint distribution and various unlikely joint distributions and their combinations.