A continuous method for reducing interpolation artifacts in mutual information-based rigid image registration

We propose an approach for computing mutual information in rigid multimodality image registration. Images to be registered are modeled as functions defined on a continuous image domain. Analytic forms of the probability density functions for the images and the joint probability density function are first defined in 1D. We describe how the entropies of the images, the joint entropy, and mutual information can be computed accurately by a numerical method. We then extend the method to 2D and 3D. The mutual information function generated is smooth and does not seem to have the typical interpolation artifacts that are commonly observed in other standard models. The relationship between the proposed method and the partial volume (PV) model is described. In addition, we give a theoretical analysis to explain the nonsmoothness of the mutual information function computed by the PV model. Numerical experiments in 2D and 3D are presented to illustrate the smoothness of the mutual information function, which leads to robust and accurate numerical convergence results for solving the image registration problem.