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.     

Image Correlation with Geometric Distortion Part II: Effect on Local Accuracy

The effect of geometric distortion on the local accuracy of the image registration algorithms using cross correlation is presented. Using a probabilistic model describing images as homogeneous random patterns, expressions for the mean and covariance of the local error vector in terms of image and noise autocorrelation functions, geometric distortion, and reference image area are derived. The geometric distortions considered are those represented by an affine transformation of image coordinates. It is shown that for a fixed geometric distortion there is an image size (integration area) that minimizes the local error. The optimum area decreases with increasing geometric distortion.