Mathematical methods for 2D-3D cardiac image registration

We propose a mathematical formulation aimed at intensity-based slice-to-volume registration, aligning a cross-sectional slice of a 3D volume to a 2D image. The approach is flexible and can accommodate various regularization schemes, similarity measures, and optimizers. We evaluate the framework by registering 2D and 3D cardiac magnetic resonance (MR) images obtained in vivo, aimed at image-guided surgery applications that utilise real-time MR imaging as a visualization tool. Rigid-body and affine transformations are used to validate the parametric model. Target registration error (TRE), Jaccard, and Dice indices are used to evaluate the algorithm and demonstrate the accuracy of the registration scheme on both simulated and clinical data. Registration with the affine model appeared to be more robust than the rigid model in controlled registration experiments. By simply extending the rigid model to an affine model, alignment of the cardiac region generally improved, without the need for complex dissimilarity measures or regularizers