Sparse linear solvers or generalized deconvolution are fundamental to science and engineering, applied in partial differential equations (PDEs), scientific computing, computer vision, and beyond. Indirect solvers possess characteristics that make them undesirable as stable differentiable modules; existing direct solvers, though reliable, are too expensive to be adopted in neural architectures. We substantially accelerate direct sparse solvers by up to three orders of magnitude, violating common assumptions that direct solvers are too slow. We "condense" a sparse Laplacian matrix into a dense tensor, a compact data structure that batch-wise stores the Dirichlet-to-Neumann matrices, reducing the sparse solving to recursively merging pairs of dense matrices that are much smaller. The batched small dense systems are sliced and inverted in parallel to take advantage of dense GPU BLAS kernels, highly optimized in the era of deep learning. Our method is efficient, qualified as a strong zero-shot baseline for AI-based PDE solving, and a reliable differentiable module integrable into machine learning pipelines.

In magnetic resonance imaging (MRI), slice-to-volume reconstruction (SVR) refers to computational reconstruction of an unknown 3D magnetic resonance volume from stacks of 2D slices corrupted by motion. While promising, current SVR methods require multiple slice stacks for accurate 3D reconstruction, leading to long scans and limiting their use in time-sensitive applications such as fetal fMRI. Here, we propose a SVR method that overcomes the shortcomings of previous work and produces state-of-the-art reconstructions in the presence of extreme inter-slice motion. Inspired by the recent success of single-view depth estimation methods, we formulate SVR as a single-stack motion estimation task and train a fully convolutional network to predict a motion stack for a given slice stack, producing a 3D reconstruction as a byproduct of the predicted motion. Extensive experiments on the SVR of adult and fetal brains demonstrate that our fully convolutional method is twice as accurate as previous SVR methods. Our code is available at github.com/seannz/svr.

Image registration is a fundamental medical image analysis task, and a wide variety of approaches have been proposed. However, only a few studies have comprehensively compared medical image registration approaches on a wide range of clinically relevant tasks. This limits the development of registration methods, the adoption of research advances into practice, and a fair benchmark across competing approaches. The Learn2Reg challenge addresses these limitations by providing a multi-task medical image registration data set for comprehensive characterisation of deformable registration algorithms. A continuous evaluation will be possible at https://learn2reg.grand-challenge.org. Learn2Reg covers a wide range of anatomies (brain, abdomen, and thorax), modalities (ultrasound, CT, MR), availability of annotations, as well as intra- and inter-patient registration evaluation. We established an easily accessible framework for training and validation of 3D registration methods, which enabled the compilation of results of over 65 individual method submissions from more than 20 unique teams. We used a complementary set of metrics, including robustness, accuracy, plausibility, and runtime, enabling unique insight into the current state-of-the-art of medical image registration. This paper describes datasets, tasks, evaluation methods and results of the challenge, as well as results of further analysis of transferability to new datasets, the importance of label supervision, and resulting bias. While no single approach worked best across all tasks, many methodological aspects could be identified that push the performance of medical image registration to new state-of-the-art performance. Furthermore, we demystified the common belief that conventional registration methods have to be much slower than deep-learning-based methods.

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.

This paper presents a framework for automatically learning shape and appearance models for medical (and certain other) images. The algorithm was developed with the aim of eventually enabling distributed privacy-preserving analysis of brain image data, such that shared information (shape and appearance basis functions) may be passed across sites, whereas latent variables that encode individual images remain secure within each site. These latent variables are proposed as features for privacy-preserving data mining applications. The approach is demonstrated qualitatively on the KDEF dataset of 2D face images, showing that it can align images that traditionally require shape and appearance models trained using manually annotated data (manually defined landmarks etc.). It is applied to the MNIST dataset of handwritten digits to show its potential for machine learning applications, particularly when training data is limited. The model is able to handle "missing data", which allows it to be cross-validated according to how well it can predict left-out voxels. The suitability of the derived features for classifying individuals into patient groups was assessed by applying it to a dataset of over 1900 segmented T1-weighted MR images, which included images from the COBRE and ABIDE datasets.

In biomedical research, cell counting is important to assess physiological and pathophysiological information. However, the automated analysis of microscopic images of tissues remains extremely challenging. We propose an automated processing protocol for proper segmentation of individual cells in microscopic images. A Gaussian filter is applied to improve signal to noise ratio (SNR) then an original minmax method is proposed to produce an image in which information describing both cell centers (minima) and boundaries are enhanced. Finally, a contour-based model initialized from minima in the min-max cartography is carried out to achieve cell individualization. This method is evaluated on a NeuN-stained macaque brain section in sub-regions presenting various levels of fraction of neuron surface occupation. Comparison with several methods of reference demonstrates that the performances of our method are superior. A first application to the segmentation of neurons in the hippocampus illustrates the ability of our approach to deal with massive and complex data.