In this paper, we study pseudo-labelling. Pseudo-labelling employs raw inferences on unlabelled data as pseudo-labels for self-training. We elucidate the empirical successes of pseudo-labelling by establishing a link between this technique and the Expectation Maximisation algorithm. Through this, we realise that the original pseudo-labelling serves as an empirical estimation of its more comprehensive underlying formulation. Following this insight, we present a full generalisation of pseudo-labels under Bayes' theorem, termed Bayesian Pseudo Labels. Subsequently, we introduce a variational approach to generate these Bayesian Pseudo Labels, involving the learning of a threshold to automatically select high-quality pseudo labels. In the remainder of the paper, we showcase the applications of pseudo-labelling and its generalised form, Bayesian Pseudo-Labelling, in the semi-supervised segmentation of medical images. Specifically, we focus 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 whole brain tumours from MRI volumes; and (4) 3D binary segmentation of prostate from MRI volumes. We further demonstrate that pseudo-labels can enhance the robustness of the learned representations. The code is released in the following GitHub repository: https://github.com/moucheng2017/EMSSL.

Supervised machine learning methods have been widely developed for segmentation tasks in recent years. However, the quality of labels has high impact on the predictive performance of these algorithms. This issue is particularly acute in the medical image domain, where both the cost of annotation and the inter-observer variability are high. Different human experts contribute estimates of the "actual" segmentation labels in a typical label acquisition process, influenced by their personal biases and competency levels. The performance of automatic segmentation algorithms is limited when these noisy labels are used as the expert consensus label. In this work, we use two coupled CNNs to jointly learn, from purely noisy observations alone, the reliability of individual annotators and the expert consensus label distributions. The separation of the two is achieved by maximally describing the annotator's "unreliable behavior" (we call it "maximally unreliable") while achieving high fidelity with the noisy training data. We first create a toy segmentation dataset using MNIST and investigate the properties of the proposed algorithm. We then use three public medical imaging segmentation datasets to demonstrate our method's efficacy, including both simulated (where necessary) and real-world annotations: 1) ISBI2015 (multiple-sclerosis lesions); 2) BraTS (brain tumors); 3) LIDC-IDRI (lung abnormalities). Finally, we create a real-world multiple sclerosis lesion dataset (QSMSC at UCL: Queen Square Multiple Sclerosis Center at UCL, UK) with manual segmentations from 4 different annotators (3 radiologists with different level skills and 1 expert to generate the expert consensus label). In all datasets, our method consistently outperforms competing methods and relevant baselines, especially when the number of annotations is small and the amount of disagreement is large. The studies also reveal that the system is capable of capturing the complicated spatial characteristics of annotators' mistakes.

Semi-supervised learning (SSL) is a promising machine learning paradigm to address the ubiquitous issue of label scarcity in medical imaging. The state-of-the-art SSL methods in image classification utilise consistency regularisation to learn unlabelled predictions which are invariant to input level perturbations. However, image level perturbations violate the cluster assumption in the setting of segmentation. Moreover, existing image level perturbations are hand-crafted which could be sub-optimal. In this paper, we propose MisMatch, a semi-supervised segmentation framework based on the consistency between paired predictions which are derived from two differently learnt morphological feature perturbations. MisMatch consists of an encoder and two decoders. One decoder learns positive attention for foreground on unlabelled data thereby generating dilated features of foreground. The other decoder learns negative attention for foreground on the same unlabelled data thereby generating eroded features of foreground. We normalise the paired predictions of the decoders, along the batch dimension. A consistency regularisation is then applied between the normalised paired predictions of the decoders. We evaluate MisMatch on four different tasks. Firstly, we develop a 2D U-net based MisMatch framework and 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. Secondly, we show that 2D MisMatch outperforms state-of-the-art methods on an MRI-based brain tumour segmentation task. We then further confirm that 3D V-net based MisMatch outperforms its 3D counterpart based on consistency regularisation with input level perturbations, on two different tasks including, left atrium segmentation from 3D CT images and whole brain tumour segmentation from 3D MRI images. Lastly, we find that the performance improvement of MisMatch over the baseline might originate from its better calibration. This also implies that our proposed AI system makes safer decisions than the previous methods.

Recent years have seen increasing use of supervised learning methods for segmentation tasks. However, the predictive performance of these algorithms depends on the quality of labels. This problem is particularly pertinent in the medical image domain, where both the annotation cost and inter-observer variability are high. In a typical label acquisition process, different human experts provide their estimates of the ``true'' segmentation labels under the influence of their own biases and competence levels. Treating these noisy labels blindly as the ground truth limits the performance that automatic segmentation algorithms can achieve. In this work, we present a method for jointly learning, from purely noisy observations alone, the reliability of individual annotators and the true segmentation label distributions, using two coupled CNNs. The separation of the two is achieved by encouraging the estimated annotators to be maximally unreliable while achieving high fidelity with the noisy training data. We first define a toy segmentation dataset based on MNIST and study the properties of the proposed algorithm. We then demonstrate the utility of the method on three public medical imaging segmentation datasets with simulated (when necessary) and real diverse annotations: 1) MSLSC (multiple-sclerosis lesions); 2) BraTS (brain tumours); 3) LIDC-IDRI (lung abnormalities). In all cases, our method outperforms competing methods and relevant baselines particularly in cases where the number of annotations is small and the amount of disagreement is large. The experiments also show strong ability to capture the complex spatial characteristics of annotators' mistakes. Our code is available at \url{https://github.com/moucheng2017/LearnNoisyLabelsMedicalImages}.