We propose a new similarity measure for iconic medical image registration, an Edgeworth-based third order approximation of Mutual Information (MI) and named 3-EMI. Contrary to classical Edgeworth-based MI approximations, such as those proposed for independent component analysis, the 3-EMI measure is able to deal with potentially correlated variables. The performance of 3-EMI is then evaluated and compared with the Gaussian and B-Spline kernel-based estimates of MI, and the validation is leaded in three steps. First, we compare the intrinsic behavior of the measures as a function of the number of samples and the variance of an additive Gaussian noise. Then, they are evaluated in the context of multimodal rigid registration, using the RIRE data. We finally validate the use of our measure in the context of thoracic monomodal non-rigid registration, using the database proposed during the MICCAI EMPIRE10 challenge. The results show the wide range of clinical applications for which our measure can perform, including non-rigid registration which remains a challenging problem. They also demonstrate that 3-EMI outperforms classical estimates of MI for a low number of samples or a strong additive Gaussian noise. More generally, our measure gives competitive registration results, with a much lower numerical complexity compared to classical estimators such as the reference B-Spline kernel estimator, which makes 3-EMI a good candidate for fast and accurate registration tasks.