  This paper concerns pseudo labelling in segmentation. Our contribution is
fourfold. Firstly, we present a new formulation of pseudo-labelling as an
Expectation-Maximization (EM) algorithm for clear statistical interpretation.
Secondly, we propose a semi-supervised medical image segmentation method purely
based on the original pseudo labelling, namely SegPL. We demonstrate SegPL is a
competitive approach against state-of-the-art consistency regularisation based
methods on semi-supervised segmentation on a 2D multi-class MRI brain tumour
segmentation task and a 3D binary CT lung vessel segmentation task. The
simplicity of SegPL allows less computational cost comparing to prior methods.
Thirdly, we demonstrate that the effectiveness of SegPL may originate from its
robustness against out-of-distribution noises and adversarial attacks. Lastly,
under the EM framework, we introduce a probabilistic generalisation of SegPL
via variational inference, which learns a dynamic threshold for pseudo
labelling during the training. We show that SegPL with variational inference
can perform uncertainty estimation on par with the gold-standard method Deep
Ensemble.
