Deformable Image Registration with a Scale-adaptive Convolutional Neural Network

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Multi-resolution hierarchical strategy is typically used in conventional optimization-based image registration to address large deformation and improve the chance of a good local minimum. A rough concept of the scale is captured in deep networks by the reception field of kernels, and it has been realized to be both desirable and challenging to capture convolutions of different scales simultaneously in registration networks. In this study, we propose an image registration network that is conscious of and self-adaptive to deformation of various scales. Dilated inception modules (DIMs) are proposed to incorporate receptive fields of different sizes in a computationally efficient way. Scale adaptive modules (SAMs) are proposed to guide and adjust shallow features using convolutional kernels with spatially adaptive dilation rate learned from deep features. DIMs and SAMs are integrated into the registration network which takes a U-net structure. The network is trained in an unsupervised setting and completes registration with a single evaluation run. Experiment with cardiac MRIs showed that the adaptive dilation rate in SAM corresponded well to the deformation scale. Evaluated with left ventricle segmentation, our method achieved a dice of $(0.93\pm 0.02)$, significantly better than SimpleElastix and networks without DIM or SAM. Assessment with respect to average surface distance was less than 2 millimeters (1.6 pixels), comparable to the best-performing SimpleElastix without statistical significance. Experiment with synthetic data also demonstrated the effectiveness of DIMs and SAMs, which leaded to a significant reduction in target registration error based on dense deformation field. The average registration time was 4 milliseconds for 2D image with size $256\times 256$.