A General Preconditioning Scheme for Difference Measures in Deformable Registration

Abstract

We present a preconditioning scheme for improving the efficiency of optimization of arbitrary difference measures in deformable registration problems. This is of particular interest for high-dimensional registration problems with statistical difference measures such as MI, and the demons method, since in these cases the range of applicable optimization methods is limited. The proposed scheme is simple and computationally efficient: It performs an approximate normalization of the point-wise vectors of the difference gradient to unit length. The major contribution of this work is a theoretical analysis which demonstrates the improvement of the condition by our approach, which is furthermore shown to be an approximation to the optimal case for the analyzed model. Our scheme improves the convergence speed while adding only negligible computational cost, thus resulting in shorter effective runtimes. The theoretical findings are confirmed by experiments on 3D brain data.