We study pseudo labelling and its generalisation for semi-supervised segmentation of medical images. Pseudo labelling has achieved great empirical successes in semi-supervised learning, by utilising raw inferences on unlabelled data as pseudo labels for self-training. In our paper, we build a connection between pseudo labelling and the Expectation Maximization algorithm which partially explains its empirical successes. We thereby realise that the original pseudo labelling is an empirical estimation of its underlying full formulation. Following this insight, we demonstrate the full generalisation of pseudo labels under Bayes' principle, called Bayesian Pseudo Labels. We then provide a variational approach to learn to approximate Bayesian Pseudo Labels, by learning a threshold to select good quality pseudo labels. In the rest of the paper, we demonstrate the applications of Pseudo Labelling and its generalisation Bayesian Psuedo Labelling in semi-supervised segmentation of medical images on: 1) 3D binary segmentation of lung vessels from CT volumes; 2) 2D multi class segmentation of brain tumours from MRI volumes; 3) 3D binary segmentation of brain tumours from MRI volumes. We also show that pseudo labels can enhance the robustness of the learnt representations.

The lack of labels is one of the fundamental constraints in deep learning based methods for image classification and segmentation, especially in applications such as medical imaging. Semi-supervised learning (SSL) is a promising method to address the challenge of labels carcity. The state-of-the-art SSL methods utilise consistency regularisation to learn unlabelled predictions which are invariant to perturbations on the prediction confidence. However, such SSL approaches rely on hand-crafted augmentation techniques which could be sub-optimal. In this paper, we propose MisMatch, a novel consistency based semi-supervised segmentation method. MisMatch automatically learns to produce paired predictions with increasedand decreased confidences. MisMatch consists of an encoder and two decoders. One decoder learns positive attention for regions of interest (RoI) on unlabelled data thereby generating higher confidence predictions of RoI. The other decoder learns negative attention for RoI on the same unlabelled data thereby generating lower confidence predictions. We then apply a consistency regularisation between the paired predictions of the decoders. For evaluation, we first perform extensive cross-validation on a CT-based pulmonary vessel segmentation task and show that MisMatch statistically outperforms state-of-the-art semi-supervised methods when only 6.25% of the total labels are used. Furthermore MisMatch performance using 6.25% ofthe total labels is comparable to state-of-the-art methodsthat utilise all available labels. In a second experiment, MisMatch outperforms state-of-the-art methods on an MRI-based brain tumour segmentation task.

Simulating images representative of neurodegenerative diseases is important for predicting patient outcomes and for validation of computational models of disease progression. This capability is valuable for secondary prevention clinical trials where outcomes and screening criteria involve neuroimaging. Traditional computational methods are limited by imposing a parametric model for atrophy and are extremely resource-demanding. Recent advances in deep learning have yielded data-driven models for longitudinal studies (e.g., face ageing) that are capable of generating synthetic images in real-time. Similar solutions can be used to model trajectories of atrophy in the brain, although new challenges need to be addressed to ensure accurate disease progression modelling. Here we propose Degenerative Adversarial NeuroImage Net (DaniNet) --- a new deep learning approach that learns to emulate the effect of neurodegeneration on MRI. DaniNet uses an underlying set of Support Vector Regressors (SVRs) trained to capture the patterns of regional intensity changes that accompany disease progression. DaniNet produces whole output images, consisting of 2D-MRI slices that are constrained to match regional predictions from the SVRs. DaniNet is also able to condition the progression on non-imaging characteristics (age, diagnosis, etc.) while it maintains the unique brain morphology of individuals. Adversarial training ensures realistic brain images and smooth temporal progression. We train our model using 9652 T1-weighted (longitudinal) MRI extracted from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. We perform quantitative and qualitative evaluations on a separate test set of 1283 images (also from ADNI) demonstrating the ability of DaniNet to produce accurate and convincing synthetic images that emulate disease progression.

Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surface that have similar temporal dynamics across a patient population, and concurrently estimates an average trajectory of vertex measurements in each cluster. DIVE uniquely outputs a parcellation of the cortex into areas with common progression patterns, leading to a new signature for individual diseases. DIVE further estimates the disease stage and progression speed for every visit of every subject, potentially enhancing stratification for clinical trials or management. On simulated data, DIVE can recover ground truth clusters and their underlying trajectory, provided the average trajectories are sufficiently different between clusters. We demonstrate DIVE on data from two cohorts: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Dementia Research Centre (DRC), UK, containing patients with Posterior Cortical Atrophy (PCA) as well as typical Alzheimer's disease (tAD). DIVE finds similar spatial patterns of atrophy for tAD subjects in the two independent datasets (ADNI and DRC), and further reveals distinct patterns of pathology in different diseases (tAD vs PCA) and for distinct types of biomarker data: cortical thickness from Magnetic Resonance Imaging (MRI) vs amyloid load from Positron Emission Tomography (PET). Finally, DIVE can be used to estimate a fine-grained spatial distribution of pathology in the brain using any kind of voxelwise or vertexwise measures including Jacobian compression maps, fractional anisotropy (FA) maps from diffusion imaging or other PET measures. DIVE source code is available online: https://github.com/mrazvan22/dive

We introduce Disease Knowledge Transfer (DKT), a novel technique for transferring biomarker information between related neurodegenerative diseases. DKT infers robust multimodal biomarker trajectories in rare neurodegenerative diseases even when only limited, unimodal data is available, by transferring information from larger multimodal datasets from common neurodegenerative diseases. DKT is a joint-disease generative model of biomarker progressions, which exploits biomarker relationships that are shared across diseases. As opposed to current deep learning approaches, DKT is interpretable, which allows us to understand underlying disease mechanisms. Here we demonstrate DKT on Alzheimer's disease (AD) variants and its ability to predict trajectories for multimodal biomarkers in Posterior Cortical Atrophy (PCA), in lack of such data from PCA subjects. For this we train DKT on a combined dataset containing subjects with two distinct diseases and sizes of data available: 1) a larger, multimodal typical AD (tAD) dataset from the TADPOLE Challenge, and 2) a smaller unimodal Posterior Cortical Atrophy (PCA) dataset from the Dementia Research Centre (DRC) UK, for which only a limited number of Magnetic Resonance Imaging (MRI) scans are available. We first show that DKT estimates plausible multimodal trajectories in PCA that agree with previous literature. We further validate DKT in two situations: (1) on synthetic data, showing that it can accurately estimate the ground truth parameters and (2) on 20 DTI scans from controls and PCA patients, showing that it has favourable predictive performance compared to standard approaches. While we demonstrated DKT on Alzheimer's variants, we note DKT is generalisable to other forms of related neurodegenerative diseases. Source code for DKT is available online: https://github.com/mrazvan22/dkt.