Accurately segmenting tissue structures or lesion areas in medical images plays a crucial role in physician diagnosis and treatment planning. However, supervised learning algorithms heavily rely on a large amount of annotated data for training, and accurate labeling of medical images requires significant time and effort due to their high complexity and diversity. This severely limits the application and development of supervised learning in medical image segmentation. To overcome this limitation, this article aims to investigate a semi-supervised 3-D medical image segmentation algorithm with a small amount of annotated data. The proposed method incorporates geometric constraints into the segmentation process, which outperforms other semi-supervised segmentation methods. We hope that this work can contribute to computer-aided diagnosis and treatment.

Semi-supervised learning (SSL) algorithms have received extensive attention in medical image segmentation because they can be trained with unlabeled data. However, most existing SSL methods underestimate the importance of small branches and boundary regions, resulting in unsatisfactory boundaries and nonsmooth objects. We observe that the voxels of the target boundary have relative uncertainty. When the foreground map and background map of an object have the same voxel, that voxel must be in the edge region. Therefore, in this study, we propose a novel SSL framework based on the uncertainty of bounding voxels, which we call the boundary-aware network (BoANet). Specifically, we use a dual-task network that predicts the segmentation map and background map of objects. For unlabeled data, because the geometric contour information of the target object is obtained by elementwise multiplication of the segmentation map and the background map, geometric constraints are imposed on the segmentati...