Explicit rigid and similarity image registration

Abstract

Most of the suggested image registration methods are based on the optimization of an objective function. Drawbacks of this approach are the problem of local minima and the need to initialize the transformation close to the true solution. This paper presents a method for N-dimensional rigid and similarity image registration that is not optimization-based and consequently it doesn't involve local minima and initialization. Instead of obtaining the transformation parameters implicitly through an iterative optimization process, they are obtained explicitly. The proposed method has advantages over existing explicit methods. The explicit expressions for transformation parameters involve image integrals and no image derivatives, which makes the method robust to noise. It is shown that the method has a few desired properties including symmetry and transitivity, and that it is invariant to initial alignment of the images. The method has been tested on simulated and real brain 2D and 3D MR image pairs and the achieved average registration error was one voxel.