Stability-guaranteed learning for partially supervised cardiac image segmentation via decomposition and conditional propagation.

Partially-supervised learning can be challenging for image segmentation due to the lack of supervision for unlabeled structures. From the perspective of optimization, directly applying conventional loss functions in fully-supervised learning could lead to the unstable training problem in partially-supervised segmentation, since the ground truth is not in the solution set of the optimization problem. To address this challenge, we propose a stability-guaranteed learning (SGL) framework, which trains a single multi-label segmentation network using images with only partial annotations. We first give the definition of stability and propose a stable loss formulation for partially-supervised segmentation. Specifically, we decompose the stable loss into two basic components, i.e., the positive loss and the negative loss. The former targets pixels with the positive ground truth, and the latter is for pixels with the negative ground truth. Then, we propose a prior loss based on the negative loss, which captures inter-class information from inclusiveness and exclusiveness relationships among images via label propagation. Additionally, we extend the proposed framework via a dual learning strategy, to provide substantial supervision for unlabeled structures. We show that this framework is applicable to different loss functions used in fully-supervised and partially-supervised segmentation. Results on three cardiac segmentation datasets (ACDC, MSCMRseg, and MMWHS) demonstrate that our SGL outperformed state-of-the-art partially-supervised segmentation methods, and could achieve performance matching fully-supervised models.