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.

Brain shift makes the pre-operative MRI navigation highly inaccurate hence the intraoperative modalities are adopted in surgical theatre. Due to the excellent economic and portability merits, the Ultrasound imaging is used at our collaborating hospital, Charing Cross Hospital, Imperial College London, UK. However, it is found that intraoperative diagnosis on Ultrasound images is not straightforward and consistent, even for very experienced clinical experts. Hence, there is a demand to design a Computer-aided-diagnosis system to provide a robust second opinion to help the surgeons. The proposed CAD system based on "Mixed-Attention Res-U-net with asymmetric loss function" achieves the state-of-the-art results comparing to the ground truth by classification at pixel-level directly, it also outperforms all the current main stream pixel-level classification methods (e.g. U-net, FCN) in all the evaluation metrices.