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Image registration is an essential task in medical image analysis. We propose two novel unsupervised diffeomorphic image registration networks, which use deep Residual Networks (ResNets) as numerical approximations of the underlying continuous diffeomorphic setting governed by ordinary differential equations (ODEs), viewed as a Eulerian discretization scheme. While considering the ODE-based parameterizations of diffeomorphisms, we consider both stationary and non-stationary (time varying) velocity fields as the driving velocities to solve the ODEs, which give rise to our two proposed architectures for diffeomorphic registration. We also employ Lipschitz-continuity on the Residual Networks in both architectures to define the admissible Hilbert space of velocity fields as a Reproducing Kernel Hilbert Spaces (RKHS) and regularize the smoothness of the velocity fields. We apply both registration networks to align and segment the OASIS brain MRI dataset. Experimental results demonstrate that our models are computational efficient and achieve comparable registration results with a smoother deformation field. 

Diffeomorphic registration faces challenges for high dimensional images, especially in terms of memory limits. Existing approaches either downsample/crop original images or approximate underlying transformations to reduce the model size. To mitigate this, we propose a Dividing and Down-sampling mixed Registration network (DDR-Net), a general architecture that preserves most of the image information at multiple scales while reducing memory cost. DDR-Net leverages the global context via downsampling the input and utilizes local details by dividing the input images to subvolumes. Such design fuses global and local information and obtains both coarse- and fine-level alignments in the final deformation fields. We apply DDR-Net to the OASIS dataset. The proposed simple yet effective architecture is a general method and could be extended to other registration architectures for better performance with limited computing resources. 

We introduce a neural network framework, utilizing adversarial learning to partition an image into two cuts, with one cut falling into a reference distribution provided by the user. This concept tackles the task of unsupervised anomaly segmentation, which has attracted increasing attention in recent years due to their broad applications in tasks with unlabelled data. This Adversarial-based Selective Cutting network (ASC-Net) bridges the two domains of cluster-based deep learning methods and adversarial-based anomaly/novelty detection algorithms. We evaluate this unsupervised learning model on BraTS brain tumor segmentation, LiTS liver lesion segmentation, and MS-SEG2015 segmentation tasks. Compared to existing methods like the AnoGAN family, our model demonstrates tremendous performance gains in unsupervised anomaly segmentation tasks. Although there is still room to further improve performance compared to supervised learning algorithms, the promising experimental results shed light on building an unsupervised learning algorithm using user-defined knowledge.