Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations

We present an algorithm for automatic elastic registration of three-dimensional (3D) medical images. Our algorithm initially recovers the global spatial mismatch between the reference and floating images, followed by hierarchical octree-based subdivision of the reference image and independent registration of the floating image with the individual subvolumes of the reference image at each hierarchical level. Global as well as local registrations use the six-parameter full rigid-body transformation model and are based on maximization of normalized mutual information (NMI). To ensure robustness of the subvolume registration with low voxel counts, we calculate NMI using a combination of current and prior mutual histograms. To generate a smooth deformation field, we perform direct interpolation of six-parameter rigid-body subvolume transformations obtained at the last subdivision level. Our interpolation scheme involves scalar interpolation of the 3D translations and quaternion interpolation of the 3D rotational pose. We analyzed the performance of our algorithm through experiments involving registration of synthetically deformed computed tomography (CT) images. Our algorithm is general and can be applied to image pairs of any two modalities of most organs. We have demonstrated successful registration of clinical whole-body CT and positron emission tomography (PET) images using this algorithm. The registration accuracy for this application was evaluated, based on validation using expert-identified anatomical landmarks in 15 CT–PET image pairs. The algorithm’s performance was comparable to the average accuracy observed for three expert-determined registrations in the same 15 image pairs.