Optimum Windows for Image Registration

Two-dimensional cross-correlation techniques are applied to the problem of image registration under the assumption of small geometric distortion. Optimum window functions are derived for two performance measures of interest: peak-to-sidelobe ratio and mean-square registration error. The latter is examined in terms of the contribution caused by noise and the contribution caused by geometric distortion. A generalized Lagrange multiplier approach is used to derive approximate solutions assuming random images. The case of Gaussian autocorrelation functions is examined in detail. Results of applying the theoretically derived window functions to real data are presented, showing significant improvement in correlator performance.