Efficient convolution-based pairwise elastic image registration on three multimodal similarity metrics

•Convolutional formulation for 2D multimodal pairwise image registration problems based on the free-form deformation paradigm.•The proposed method uses simple 1D convolution operations instead of the classical implementation based on tensor products, leading to a large reduction in runtime.•The convolutional approach is adapted to three different multimodal metrics, namely, normalized cross correlation, mutual information and normalized mutual information. Moreover, a sufficient condition on the gradient of metric is provided for further extension to other metrics.•Reformulated functions are the spatial transformation, the regularization term, as well as the corresponding gradient functions; all of these are evaluated at each iteration of the optimization process during the image registration procedure. This paper proposes a complete convolutional formulation for 2D multimodal pairwise image registration problems based on free-form deformations. We have reformulated in terms of discrete 1D convolutions the evaluation of spatial transformations, the regularization term, and their gradients for three different multimodal registration metrics, namely, normalized cross correlation, mutual information, and normalized mutual information. A sufficient condition on the metric gradient is provided for further extension to other metrics. The proposed approach has been tested, as a proof of concept, on contrast-enhanced first-pass perfusion cardiac magnetic resonance images. Execution times have been compared with the corresponding execution times of the classical tensor product formulation, both on CPU and GPU. The speed-up achieved by using convolutions instead of tensor products depends on the image size and the number of control points considered, the larger those magnitudes, the greater the execution time reduction. Furthermore, the speed-up will be more significant when gradient operations constitute the major bottleneck in the optimization process.