Deep Compatible Learning for Partially-Supervised Medical Image Segmentation

Partially-supervised learning can be challenging for segmentation due to the lack of supervision for unlabeled structures, and the methods directly applying fully-supervised learning could lead to incompatibility, meaning ground truth is not in the solution set of the optimization problem given the loss function. To address the challenge, we propose a deep compatible learning (DCL) framework, which trains a single multi-label segmentation network using images with only partial structures annotated. We first formulate the partially-supervised segmentation as an optimization problem compatible with missing labels, and prove its compatibility. Then, we equip the model with a conditional segmentation strategy, to propagate labels from multiple partially-annotated images to the target. Additionally, we propose a dual learning strategy, which learns two opposite mappings of label propagation simultaneously, to provide substantial supervision for unlabeled structures. The two strategies are formulated into compatible forms, termed as conditional compatibility and dual compatibility, respectively. We show this framework is generally applicable for conventional loss functions. The approach attains significant performance improvement over existing methods, especially in the situation where only a small training dataset is available. Results on three segmentation tasks have shown that the proposed framework could achieve performance matching fully-supervised models.