Data-driven deep learning approaches to image registration can be less accurate than conventional iterative approaches, especially when training data is limited. To address this issue and meanwhile retain the fast inference speed of deep learning, we propose VR-Net, a novel cascaded variational network for unsupervised deformable image registration. Using a variable splitting optimization scheme, we first convert the image registration problem, established in a generic variational framework, into two sub-problems, one with a point-wise, closed-form solution and the other one being a denoising problem. We then propose two neural layers (i.e. warping layer and intensity consistency layer) to model the analytical solution and a residual U-Net (termed generalized denoising layer) to formulate the denoising problem. Finally, we cascade the three neural layers multiple times to form our VR-Net. Extensive experiments on three (two 2D and one 3D) cardiac magnetic resonance imaging datasets show that VR-Net outperforms state-of-the-art deep learning methods on registration accuracy, whilst maintaining the fast inference speed of deep learning and the data-efficiency of variational models.

MOTIVATION: Localization microscopy data is represented by a set of spatial coordinates, each corresponding to a single detection, that form a point cloud. This can be analyzed either by rendering an image from these coordinates, or by analyzing the point cloud directly. Analysis of this type has focused on clustering detections into distinct groups which produces measurements such as cluster area, but has limited capacity to quantify complex molecular organization and nano-structure. RESULTS: We present a segmentation protocol which, through the application of persistence-based clustering, is capable of probing densely packed structures which vary in scale. An increase in segmentation performance over state-of-the-art methods is demonstrated. Moreover we employ persistent homology to move beyond clustering, and quantify the topological structure within data. This provides new information about the preserved shapes formed by molecular architecture. Our methods are flexible and we demonstrate this by applying them to receptor clustering in platelets, nuclear pore components, endocytic proteins and microtubule networks. Both 2D and 3D implementations are provided within RSMLM, an R package for pointillist-based analysis and batch processing of localization microscopy data. AVAILABILITY AND IMPLEMENTATION: RSMLM has been released under the GNU General Public License v3.0 and is available at https://github.com/JeremyPike/RSMLM. Tutorials for this library implemented as Binder ready Jupyter notebooks are available at https://github.com/JeremyPike/RSMLM-tutorials. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.