A variational approach for optimizing quadratic mutual information for medical image registration

This paper explores the use of quadratic mutual information as a similarity criterion for dense, non-rigid registration of medical images. Quadratic mutual information between two random variables has been recently proposed as Euclidean distance between the joint density and the product of the marginals. It has been shown to have a smooth sample estimator, that can be computed without having to use numerical approximation techniques for computing the integral over densities. In this paper, we derive Euler-Lagrange equations for optimizing quadratic mutual information in a variational framework. We then obtain a dense deformation field for registering 3D tomography images. Our results demonstrate the applicability of this criterion for such a task, and yield ground for further analysis and research.