Though deep learning has achieved advanced performance recently, it remains a challenging task in the field of medical imaging, as obtaining reliable labeled training data is time-consuming and expensive. In this paper, we propose a double-uncertainty weighted method for semi-supervised segmentation based on the teacher-student model. The teacher model provides guidance for the student model by penalizing their inconsistent prediction on both labeled and unlabeled data. We train the teacher model using Bayesian deep learning to obtain double-uncertainty, i.e. segmentation uncertainty and feature uncertainty. It is the first to extend segmentation uncertainty estimation to feature uncertainty, which reveals the capability to capture information among channels. A learnable uncertainty consistency loss is designed for the unsupervised learning process in an interactive manner between prediction and uncertainty. With no ground-truth for supervision, it can still incentivize more accurate teacher's predictions and facilitate the model to reduce uncertain estimations. Furthermore, our proposed double-uncertainty serves as a weight on each inconsistency penalty to balance and harmonize supervised and unsupervised training processes. We validate the proposed feature uncertainty and loss function through qualitative and quantitative analyses. Experimental results show that our method outperforms the state-of-the-art uncertainty-based semi-supervised methods on two public medical datasets.
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