Expectation maximisation pseudo labels.

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.