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Deformable image registration can be time consuming and often needs extensive parameterization to perform well on a specific application. We present a deformable registration method based on a 3-D convolutional neural network, together with a framework for training such a network. The network directly learns transformations between pairs of 3-D images. The network is trained on synthetic random transformations which are applied to a small set of representative images for the desired application. Training, therefore, does not require manually annotated ground truth information on the deformation. The framework for the generation of transformations for training uses a sequence of multiple transformations at different scales that are applied to the image. This way, complex transformations with large displacements can be modeled without folding or tearing images. The methodology is demonstrated on public data sets of inhale-exhale lung CT image pairs which come with landmarks for evaluation of the registration quality. We show that a small training set can be used to train the network, while still allowing generalization to a separate pulmonary CT data set containing data from a different patient group, acquired using a different scanner and scan protocol. This approach results in an accurate and very fast deformable registration method, without a requirement for parameterization at test time or manually annotated data for training.

Error estimation in nonlinear medical image registration is a nontrivial problem that is important for validation of registration methods. We propose a supervised method for estimation of registration errors in nonlinear registration of three-dimensional (3-D) images. The method is based on a 3-D convolutional neural network that learns to estimate registration errors from a pair of image patches. By applying the network to patches centered around every voxel, we construct registration error maps. The network is trained using a set of representative images that have been synthetically transformed to construct a set of image pairs with known deformations. The method is evaluated on deformable registrations of inhale-exhale pairs of thoracic CT scans. Using ground truth target registration errors on manually annotated landmarks, we evaluate the method's ability to estimate local registration errors. Estimation of full domain error maps is evaluated using a gold standard approach. The two evaluation approaches show that we can train the network to robustly estimate registration errors in a predetermined range, with subvoxel accuracy. We achieved a root-mean-square deviation of 0.51 mm from gold standard registration errors and of 0.66 mm from ground truth landmark registration errors.

We propose a framework for rotation and translation covariant deep learning using SE(2) group convolutions. The group product of the special Euclidean motion group SE(2) describes how a concatenation of two roto-translations results in a net roto-translation. We encode this geometric structure into convolutional neural networks (CNNs) via SE(2) group convolutional layers, which fit into the standard 2D CNN framework, and which allow to generically deal with rotated input samples without the need for data augmentation. We introduce three layers: a lifting layer which lifts a 2D (vector valued) image to an SE(2)-image, i.e., 3D (vector valued) data whose domain is SE(2); a group convolution layer from and to an SE(2)-image; and a projection layer from an SE(2)-image to a 2D image. The lifting and group convolution layers are SE(2) covariant (the output roto-translates with the input). The final projection layer, a maximum intensity projection over rotations, makes the full CNN rotation invariant. We show with three different problems in histopathology, retinal imaging, and electron microscopy that with the proposed group CNNs, state-of-the-art performance can be achieved, without the need for data augmentation by rotation and with increased performance compared to standard CNNs that do rely on augmentation.

Retinal image analysis is a challenging problem due to the precise quantification required and the huge numbers of images produced in screening programs. This paper describes a series of innovative brain-inspired algorithms for automated retinal image analysis, recently developed for the RetinaCheck project, a large-scale screening program for diabetic retinopathy and other retinal diseases in Northeast China. The paper discusses the theory of orientation scores, inspired by cortical multi-orientation pinwheel structures, and presents applications for automated quality assessment, optic nerve head detection, crossing-preserving enhancement and segmentation of retinal vasculature, arterio-venous ratio, fractal dimension, and vessel tortuosity and bifurcations. Many of these algorithms outperform state-of-the-art techniques. The methods are currently validated in collaborating hospitals, with a rich accompanying base of metadata, to phenotype and validate the quantitative algorithms for optimal classification power.