  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.
