Globally Optimal Rigid Intensity Based Registration: A Fast Fourier Domain Approach

High computational cost is the main obstacle to adapting globally optimal branch-and-bound algorithms to intensity-based registration. Existing techniques to speed up such algorithms use a multiresolution pyramid of images and bounds on the target function among different resolutions for rigidly aligning two images. In this paper, we propose a dual algorithm in which the optimization is done in the Fourier domain, and multiple resolution levels are replaced by multiple frequency bands. The algorithm starts by computing the target function in lower frequency bands and keeps adding higher frequency bands until the current subregion is either rejected or divided into smaller areas in a branch and bound manner. Unlike spatial multiresolution approaches, to compute the target function for a wider frequency area, one just needs to compute the target in the residual bands. Therefore, if an area is to be discarded, it performs just enough computations required for the rejection. This property also enables us to use a rather large number of frequency bands compared to the limited number of resolution levels used in the space domain algorithm. Experimental results on real images demonstrate considerable speed gains over the space domain method in most cases.