  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.
