Dual-Scale Volume Priors with Wasserstein-Based Consistency for Semi-Supervised Medical Image Segmentation

Despite signi cant progress in semi-supervised medical image segmentation, most existing segmentation networks overlook e ective methodological guidance for feature extraction and important prior information from datasets. In this paper, we develop a semi-supervised medical image segmentation framework that e ectively integrates spatial regularization methods and volume priors. Speci cally, our approach integrates a strong explicit volume prior at the image scale and Threshold Dynamics spatial regularization, both derived from variational models, into the backbone segmentation network. The target region volumes for each unlabeled image are estimated by a regression network, which e ectively regularizes the backbone segmentation network through an image-scale Wasserstein distance constraint, ensuring that the class ratios in the segmentation results for each unlabeled image match those predicted by the regression network. Additionally, we design a dataset-scale Wasserstein distance loss function based on a weak implicit volume prior, which enforces that the volume distribution predicted for the unlabeled dataset is similar to that of labeled dataset. Experimental results on the 2017 ACDC dataset, PROMISE12 dataset, and thigh muscle MR image dataset show the superiority of the proposed method.

Interpretable Small Training Set Image Segmentation Network Originated from Multi-Grid Variational Model

The main objective of image segmentation is to divide an image into homogeneous regions for further analysis. This is a significant and crucial task in many applications such as medical imaging. Deep learning (DL) methods have been proposed and widely used for image segmentation. However, these methods usually require a large amount of manually segmented data as training data and suffer from poor interpretability (known as the black box problem). The classical Mumford-Shah (MS) model is effective for segmentation and provides a piece-wise smooth approximation of the original image. In this paper, we replace the hand-crafted regularity term in the MS model with a data adaptive generalized learnable regularity term and use a multi-grid framework to unroll the MS model and obtain a variational model-based segmentation network with better generalizability and interpretability. This approach allows for the incorporation of learnable prior information into the network structure design. Moreover, the multi-grid framework enables multi-scale feature extraction and offers a mathematical explanation for the effectiveness of the U-shaped network structure in producing good image segmentation results. Due to the proposed network originates from a variational model, it can also handle small training sizes. Our experiments on the REFUGE dataset, the White Blood Cell image dataset, and 3D thigh muscle magnetic resonance (MR) images demonstrate that even with smaller training datasets, our method yields better segmentation results compared to related state of the art segmentation methods.