## 1 Introduce  
Pathologists can analyze morphological features such as cell size, texture, and shape to assist in diagnosing malignant tumors, determining treatment methods, or conducting in-depth research [1]. Specifically, through instance segmentation of cells, researchers can accurately quantify cellular characteristics, including the cell count and size within tumor tissues, thereby supporting the quantitative analysis, grading, and staging of malignancies [2]. The prerequisite for these procedures involves large-scale cellular-level analysis of digital tissue samples, which renders manual cell analysis practically infeasible due to its high labor intensity and significant inter-observer variability. This necessitates the urgent development of automated cell analysis methods [3]. Most existing fully supervised automated cell analysis algorithms are based on convolutional neural networks (CNNs), which have achieved remarkable progress in the medical field and digital pathology [4; 5; 6]. Among them, UNet [7], a widely used CNN architecture for image segmentation, has been applied to cell instance segmentation [8]. Researchers have also proposed numerous UNet-based variants, such as UNet++ [9] and UNet3+ [10]. In these methods, the semantic gap between feature maps of encoder and decoder sub-networks is reduced by redesigning skip connections, thereby enhancing segmentation performance. However, despite merging coarse-grained deep features and fine-grained shallow features at the same scale via skip connections, UNet-based encoder-decoder networks exhibit inefficient non-local contextual modeling across arbitrary positions, limiting their performance in segmenting complex histopathological images [11]. To address these challenges, researchers have developed novel approaches. For example, Hover-Net [12] uses a fully convolutional neural network to extract image features and identifies candidate cell regions through post-processing. These candidate regions are further processed and filtered to generate final segmentation masks, achieving instance segmentation of individual cells. CIA-Net [13] incorporates two decoders, with each responsible for segmenting nuclei or contours. By bidirectionally aggregating specific features, it leverages spatial and textural dependencies between nuclei and contours to enhance performance on both tasks. Nevertheless, such methods rely on complex pixel grouping post-processing to extract object instances, and their performance is highly dependent on segmentation results and grouping strategies [14]. Fully supervised deep learning methods have significantly enhanced the automation level of cell segmentation through end-to-end feature learning. However, these methods rely heavily on large quantities of high-quality annotated data for training, which enables models to achieve high segmentation accuracy even in complex backgrounds. This reliance on extensive annotations poses challenges, including high costs, time-consuming processes, and inconsistent annotation quality due to the need for pathologist involvement in medical image labeling. To address these limitations, semi-supervised learning methods have gradually gained attention. These methods integrate a small amount of labeled data with a large volume of unlabeled data, reducing data acquisition costs while enhancing model generalization and robustness. For example, Mean Teacher [15] leverages consistency regularization to utilize unlabeled data for performance improvement, FixMatch [16] combines pseudo-labeling with strong-weak data augmentation strategies to significantly boost segmentation accuracy, and Cross Pseudo Supervision [17] mitigates pseudo-label noise via mutual supervision between dual networks. Additionally, generative adversarial network (GAN)-based methods such as SegAN [18] exploit distributional information in unlabeled data through adversarial training mechanisms, thereby further improving segmentation model robustness. Despite these advances, efficiently leveraging unlabeled data remains a challenge.