Dual-layer ℓ₁-graph embedding for semi-supervised image labeling

In non-local patch-based (NLPB) labeling, a target voxel can fuse its label from the manual labels of the atlas voxels in accordance to the patch-based voxel similarities. Although state-of-the-art NLPB method mainly focuses on labeling a single target image by many atlases, we propose a novel semi-supervised strategy to address the realistic case of only a few atlases yet many unlabeled targets. Specifically, we create an ℓ₁-graph of voxels, such that each target voxel can fuse its label from not only atlas voxels but also other target voxels. Meanwhile, each atlas voxel can utilize the feedbacks from the graph to check whether its expert labeling needs to be corrected. The ℓ₁-graph is built by applying (duallayer) sparsity learning to all target and atlas voxels represented by their surrounding patches. By embedding the voxel labels to the graph, the target voxels can jointly compute their labels. In the experiment, our method with the capabilities of (1) joint labeling and (2) atlas label correction has enhanced the accuracy of NLPB labeling significantly.