Edgeworth-based approximation of Mutual Information for medical image registration

Mutual Information (MI) has been extensively used as a similarity measure in image registration and motion estimation, and it is particularly robust for 3D multimodal medical image registration. However, MI estimators are known i) to have a high variance and ii) to be computationally costly. In order to overcome these drawbacks, we propose a new similarity measure based on an Edgeworth-based third order expansion of MI and named 3-EMI in the following. This kind of approximation is well known in signal processing, and especially in Independent Components Analysis (ICA), but its computation is easier since data can be prewhitened contrary to images in registration. The performance of affine and non-rigid registrations based on the 3-EMI metric is studied through computer results in the context of cardiac multislice computed tomography. In fact, an estimate of the 3-EMI metric using sample statistics is compared to a histogram-based estimate of the standard normalized MI, showing a better robustness of the 3-EMI measure with respect to the range of the searched deformation. In addition, in practice, one part of the floating image may be missing regarding the reference image. Computer results show that our approach is less sensitive to such a practical problem.