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.

翻译：我们研究了伪标签及其泛化形式在半监督医学图像分割中的应用。伪标签通过将无标注数据的原始推理结果作为伪标签进行自训练，在半监督学习中取得了显著的实证成功。本文构建了伪标签与期望最大化算法之间的关联，部分解释了其经验成功的原因。由此我们发现，原始伪标签方法本质上是对其完整理论公式的经验估计。基于这一见解，我们提出了在贝叶斯原理下伪标签的完整泛化形式，称为贝叶斯伪标签。随后，我们通过学习阈值筛选高质量伪标签，提供了一种变分方法来近似学习贝叶斯伪标签。在论文后续部分，我们展示了伪标签及其泛化形式——贝叶斯伪标签在医学图像半监督分割中的应用实例：1) 基于CT体数据的肺血管三维二值分割；2) 基于MRI体数据的脑肿瘤二维多类别分割；3) 基于MRI体数据的脑肿瘤三维二值分割。研究同时表明，伪标签能够增强学习表示的鲁棒性。