Volume image registration by cross-entropy optimization

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.