# A Novel Perturbation Consistency Framework in Semi-Supervised Medical Image Segmentation
## 1 Introduction  
Semantic segmentation is a technique that aims to provide pixel-level predictions for images, treating it as a dense pixel classification task. It is crucial in natural image processing for facilitating real-world applications like autonomous driving. The segmentation of internal structures from medical images, such as radiography, computed tomography (CT), or magnetic resonance imaging (MRI), holds significant importance for a plethora of clinical applications [1]. Numerous image semantic segmentation techniques based on fully supervised learning have been proposed [2; 3]. However, traditional fully supervised scenarios [4; 5] heavily rely on images meticulously labeled by human annotators, posing a significant barrier to their extensive application in the medical image domain. Annotating a large number of images is prohibitively costly, with some requiring annotation by clinicians with extensive expertise. Consequently, semi-supervised segmentation has emerged as a prominent area of interest in recent years, gaining traction in the field of medical image analysis. In semi-supervised segmentation methods, the objective is to symmetrically train both labeled and unlabeled data in a consistent manner. For instance, pseudo-label generation by the teacher model supervises the unlabeled data in the student model. This work focuses on the consistent regularization framework, generalized in the field of semi-supervised classification by FixMatch [6]. This approach aims to showcase the utility of unlabeled data by augmenting it with varying degrees of enhancement and then imposing consistency constraints on the predictions. Specifically, predictions generated from a weakly perturbedversion \(X_{w}\) supervise strongly perturbed unlabeled images \(X_{s}\). The UniMatch [7] study found that strongly augmented data are more effective for learning and added two branches to the FixMatch approach, incorporating a novel strong enhancement branch and a feature-level perturbation branch. Regarding strong perturbations, the CutMix [8] method utilized in UniMatch employs a straightforward data processing technique known as copy and paste (CP). This approach reinforces the consistency of weakly and strongly augmented pairs between unlabeled and labeled data. Traditional CP methods often overlook a unified learning strategy for labeled and unlabeled data, limiting their effectiveness. CP methods aim to enhance the network's generalization ability but are constrained by low-precision pseudo-labels. An effective strategy involves motivating unlabeled data to learn common semantics present in labeled data, achieving distributional alignment through a consistent learning strategy. This is accomplished by implementing a hybrid copy-paste (HCP) methodology within the auxiliary-main framework, where portions of labeled and unlabeled images are interchanged. The auxiliary network compares pseudo-labels of the unlabeled image with real labels, providing a supervisory signal to the main network. By interchanging parts of labeled and unlabeled images, HCP effectively increases the model's ability to learn local features, thereby enhancing the contribution of unlabeled data during training. This approach ensures that the model can learn from finer details present in the images, improving the overall consistency of the model. The two hybrid images enable the network to learn the shared semantics between labeled and unlabeled data, both bidirectionally and symmetrically. For the weakly perturbed branch, UniMatch halts gradient backpropagation and uses weakly perturbed images to supervise other branches. We introduce an additional branch integrated into a semi-supervised contrastive learning framework for medical image segmentation. This method, based on group-based sampling [9], constructs pixel groups and samples proportionally based on class distribution. The main concept involves partitioning images into grids, sampling semantically proximate pixels within the same grid while minimizing memory footprint.