Optimal Transport and Central Moment Consistency Regularization for Semi-Supervised Medical Image Segmentation

Semi-supervised learning leverages insights from unlabeled data to enhance generalizability of the model, thereby decreasing the dependence on extensive labeled datasets. Most existing methods overly focus on local representations while neglecting the learning of global structures. On the one hand, given that labeled and unlabeled images are presumed to originate from the same distribution, it is probable that similar regional features observed in both types of images correspond to the same label. Current label propagation techniques, which predominantly propagate label information through the construction of graph structures or similarity matrices, heavily depend on localized information and are prone to converge to local optima. In contrast, optimal transport considers the entire distribution. This facilitates more comprehensive and efficient label propagation. On the other hand, current consistency regularization-based methods focus on the local view, we believe learning from a global geometric view may capture more information. Geometric moment information of the sample itself can constrain the overall geometric structure. Inspired by these observations, this paper introduces a semi-supervised medical image segmentation framework that integrates optimal transport and central moment consistency regularization (OTCMC) from a global perspective. Firstly, we pass label information from labeled data to unlabeled data by optimal transport. Secondly, we incorporate central moment consistency regularization to focus the network on the geometric structure of images. Our method achieves the state-of-the-art (SOTA) performance on a series of datasets, including the NIH pancreas, left atrium, brain tumor, and skin lesion dermoscopy datasets.