Abstract-Mutual Information (MI) is popular for registration via function optimization. This work proposes an inverse compositional formulation of MI for Levenberg-Marquardt optimization. This yields a constant Hessian, which may be precomputed. Speed improvements of 15 percent were obtained, with convergence accuracies similar those of the standard formulation.

BACKGROUND AND PURPOSE:There is significant interest in whether diffusion-weighted MR imaging indices, such as the minimum apparent diffusion coefficient, may be useful clinically for preoperative tumor grading and treatment planning. To help establish the pathologic correlate of minimum ADC, we undertook a study investigating the relationship between minimum ADC and maximum FDOPA PET uptake in patients with newly diagnosed glioblastoma multiforme.

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Abstract. Many variants of MI exist in the literature. These vary primarily in how the joint histogram is populated. This paper places the four main variants of MI: Standard sampling, Partial Volume Estimation (PVE), In-Parzen Windowing and Post-Parzen Windowing into a single mathematical framework. Jacobians and Hessians are derived in each case. A particular contribution is that the non-linearities implicit to standard sampling and post-Parzen windowing are explicitly dealt with. These non-linearities are a barrier to their use in optimisation. Side-byside comparison of the MI variants is made using eight diverse data-sets, considering computational expense and convergence. In the experiments, PVE was generally the best performer, although standard sampling often performed nearly as well (if a higher sample rate was used). The widely used sum of squared differences metric performed as well as MI unless large occlusions and non-linear intensity relationships occurred. The binaries and scripts used for testing are available online.

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