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Registration is a fundamental step in image processing systems where there is a need to match two or more images. Applications include motion detection, target recognition, video processing, and medical imaging. Although a vast number of publications have appeared on image registration, performance analysis is usually performed visually, and little attention has been given to statistical performance bounds. Such bounds can be useful in evaluating image registration techniques, determining parameter regions where accurate registration is possible, and choosing features to be used for the registration. In this paper, Crame´r-Rao bounds on a wide variety of geometric deformation models, including translation, rotation, shearing, rigid, more general affine and nonlinear transformations, are derived. For some of the cases, closed-form expressions are given for the maximum-likelihood (ML) estimates, as well as their variances, as space permits. The bounds are also extended to unknown original objects. Numerical examples illustrating the analytical performance bounds are presented.