Efficient Convolution-Based Pairwise Elastic Image Registration on Three Multimodal Similarity Metrics

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 gradient metric 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