## 1 Introduction
Boundary discontinuity indicates that there are obvious gray changes between different regions, which is the key to the edge detection method. The OSTU algorithm is an efficient region segmentation algorithm [20] and has been applied to the analysis of rock porosity [21]. Through research, researchers have found that the rock physical properties calculated using the threshold-porosity relationship are more accurate than the classical segmentation methods [22; 23]. With the rapid development of deep learning technology [24; 25], image segmentation methods based on deep learning are constantly emerging [26; 27; 28] and are increasingly widely used in the field of digital cores. For example, [PERSON] et al. proposed using the SegNet network to automatically segment digital rock images, effectively improving the accuracy of image processing [29]. [PERSON] et al. further explored the application of convolutional neural networks in the super-resolution segmentation of carbonate rock images [30], providing a new perspective for high-precision geological analysis. The U-Net architecture, due to its excellent image segmentation performance, has been widely used in the field of the automatic segmentation of rock images, especially in the image analysis of rock types such as sandstone [31]. In recent years, researchers have made various innovative improvements to U-Net. For example, in the research by [PERSON] et al. in 2024, Pore-net [32] was proposed, which is an improved model based on U-Net. This model significantly improves the efficiency of pore identification by optimizing the data-reading strategy, increasing the number of convolutional layers, and integrating the Canny edge detection algorithm. In addition, [PERSON] et al. proposed a deep learning method called UR network that combines U-Net and Res_Unet to address the segmentation accuracy problem caused by the adhesion of ore particles and dark areas [33]. This method first uses U-Net to conduct a preliminary ore contour detection and then further refines the contour through Res_Unet to improve the segmentation accuracy. In the research published by [PERSON] et al. in May 2024 [34], a new semantic segmentation network that combines U-Net and Transformer, namely Diamond-Unet, was proposed. This innovative model introduces the Feature Cross Fusion Path (FCFP) to enhance the network's ability to capture fine-grained details and understand coarse-grained semantics in full-scale image segmentation. Although the above methods have achieved remarkable results in the fully supervised learning framework, as the requirements for image segmentation accuracy continue to increase, the traditional fully supervised methods gradually show limitations due to their dependence on a large amount of professionally annotated data. To address this challenge, semi-supervised learning methods have rapidly become the research hotspot due to their potential to reduce annotation requirements while maintaining high segmentation accuracy and have made breakthroughs in multiple fields [35; 36; 37]. Currently, semi-supervised technologies such as pseudo-label technology [38], consistency regularization [39], and graph learning methods [40] are particularly concerned. [PERSON] et al. proposed a semi-supervised learning model SU-Net [41] based on U-Net in 2023 which combines unsupervised and semi-supervised learning strategies and effectively reduces the dependence on a large amount of labeled data. [PERSON] et al. further proposed an improved semi-supervised support vector machine-fuzzy C-means (CSVM-FCM) algorithm [42] which realizes a more refined segmentation of pores and rocks in the image through the optimization of the objective function. In view of the limitations of the pseudo-label technology [43], we have proposed an innovative Adaptive Bagging method, improved the multi-model weight adjustment strategy, and optimized the pseudo-label generation process.