Semi-supervised learning (SSL) is a promising machine learning paradigm to address the issue of label scarcity in medical imaging. SSL methods were originally developed in image classification. 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. Therefore, it is a not trivial to straightforwardly adapt existing SSL image classification methods in segmentation. 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 first 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 when only 6.25\% of the total labels are used. In a second experiment, we show that U-net based MisMatch outperforms state-of-the-art methods on an MRI-based brain tumour segmentation task. In a third experiment, we show that a 3D MisMatch outperforms a previous method using input level augmentations, on a left atrium segmentation task. Lastly, we find that the performance improvement of MisMatch over the baseline might originate from its better calibration.

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