Fast registration algorithm using a variational principle for mutual information

A method is proposed for cross-modal image registration based on mutual information (MI) matching criteria. Both conventional and "normalized" MI are considered. MI may be expressed as a functional of a general image displacement field u. The variational principle for MI provides a field equation for u. The method employs a set of "registration points" consisting of a prescribed number of strongest edge points of the reference image, and minimizes an objective function D defined as the sum of the square residuals of the field equation for a at these points, where a is expressed as a sum over a set of basis functions (the affine model is presented here). D has a global minimum when the images are aligned, with a "basin of attraction" typically of width similar to0.3 pixels. By pre-filtering with a low-pass filter, and using a multiresolution image pyramid, the basin may be significantly widened. The Levenberg-Marquardt algorithm is used to minimize D. Tests using randomly distributed misalignments of image pairs show that registration accuracy of 0.02 - 0.07 pixels is achieved, when using cubic B-splines for image representation, interpolation, and Parzen window estimation.