Similarity metrics and efficient optimization for simultaneous registration

We address the alignment of a group of images with simultaneous registration. Therefore, we provide further insights into a recently introduced class of multivariate similarity measures referred to as accumulated pair-wise estimates (APE) and derive efficient optimization methods for it. More specifically, we show a strict mathematical deduction of APE from a maximum-likelihood framework and establish a connection to the congealing framework. This is only possible after an extension of the congealing framework with neighborhood information. Moreover, we address the increased computational complexity of simultaneous registration by deriving efficient gradient-based optimization strategies for APE: Gauss-Newton and the efficient second-order minimization (ESM). We present next to SSD, the usage of the intrinsically non-squared similarity measures NCC, CR, and MI, in this least-squares optimization framework. Finally, we evaluate the performance of the optimization strategies with respect to the similarity measures, obtaining very promising results for ESM.