Minimizing Estimated Risks on Unlabeled Data: A New Formulation for Semi-Supervised Medical Image Segmentation

Supervised segmentation can be costly, particularly in applications of biomedical image analysis where large scale manual annotations from experts are generally too expensive to be available. Semi-supervised segmentation, able to learn from both the labeled and unlabeled images, could be an efficient and effective alternative for such scenarios. In this work, we propose a new formulation based on risk minimization, which makes full use of the unlabeled images. Different from most of the existing approaches which solely explicitly guarantee the minimization of prediction risks from the labeled training images, the new formulation also considers the risks on unlabeled images. Particularly, this is achieved via an unbiased estimator, based on which we develop a general framework for semi-supervised image segmentation. We validate this framework on three medical image segmentation tasks, namely cardiac segmentation on ACDC2017, optic cup and disc segmentation on REFUGE dataset and 3D whole heart segmentation on MM-WHS dataset. Results show that the proposed estimator is effective, and the segmentation method achieves superior performance and demonstrates great potential compared to the other state-of-the-art approaches. Our code and data will be released via https://zmiclab.github.io/projects.html, once the manuscript is accepted for publication.