Multichannel image registration is an important challenge in medical image analysis. Multichannel images result from modalities such as dual-energy CT or multispectral microscopy. Besides, multichannel feature images can be derived from acquired images, for instance, by applying multiscale feature banks to the original images to register. Multichannel registration techniques have been proposed, but most of them are applicable to only two multichannel images at a time. In the present study, we propose to formulate multichannel registration as a groupwise image registration problem. In this way, we derive a method that allows the registration of two or more multichannel images in a fully symmetric manner (i.e., all images play the same role in the registration procedure), and therefore, has transitive consistency by definition. The method that we introduce is applicable to any number of multichannel images, any number of channels per image, and it allows to take into account correlation between any pair of images and not just corresponding channels. In addition, it is fully modular in terms of dissimilarity measure, transformation model, regularisation method, and optimisation strategy. For two multimodal datasets, we computed feature images from the initially acquired images, and applied the proposed registration technique to the newly created sets of multichannel images. MIND descriptors were used as feature images, and we chose total correlation as groupwise dissimilarity measure. Results show that groupwise multichannel image registration is a competitive alternative to the pairwise multichannel scheme, in terms of registration accuracy and insensitivity towards registration reference spaces.

In image registration the optimal transformation parameters of a given transformation model are typically obtained by minimizing a cost function. Stochastic gradient descent (SGD) is an efficient optimization algorithm for image registration. In SGD optimization, stochastic approximations of the cost function derivative are used in each iteration to update the transformation parameters. The stochastic approximation error leads to large variance in the parameters. To enforce convergence nonetheless, SGD methods are typically implemented in combination with a gradually decreasing update step size. However, selecting a proper sequence of step sizes is a major challenge in practice. An alternative strategy in numerical optimization is to use a constant step size and enforce convergence by averaging the parameters obtained by SGD over several iterations. It was proven mathematically that the highest possible rate of convergence is achieved in this way. Inspired by this work, we propose an averaged SGD (Avg-SGD) method for efficient image registration. In the Avg-SGD approach, a constant step size is used, in combination with an exponentially weighted iterate averaging scheme. Experiments on 3D lung CT scans demonstrate the effectiveness of the Avg-SGD method in terms of convergence rate, accuracy and precision.