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The accuracy and computational complexity of mutual information (MI) estimation are critical factors in multi-modality non-rigid image registration. This paper discusses the accuracy and complexity of MI estimation approaches based on non-rigid registration functions. General formulations have been derived for Shannon's and Renyi's definitions of MI, as well as Cauchy- Schwartz quadratic MI. The results obtained indicate that a fuzzy histogram binning estimation approach is significantly faster and more accurate than the conventional non-parametric Parzen window estimation approach. The analytical formulations obtained for various MI definitions are continuously differentiable and are shown to be computationally efficient for high-dimensional optimization problems particularly for non-rigid image registration.