## 2 Related Work
### Global Thresholding Based on Intensity Histograms  
[PERSON]'s method [22] is a classic non-parametric unsupervised algorithm for automatic image thresholding, calculating the optimal threshold by maximizing the between-class  
Figure 1: The histogram of medical images consists of histograms of different components, whose distributions overlap and contain many outliers.  
Figure 2: The major steps of the proposed method, Cauchy-TB. The green arrow indicates the direction of flow in the recursive process.  
variance of the image. Several improvements have been proposed to enhance its performance. [PERSON] [28] introduced a two-dimensional histogram to consider pixel neighborhood information, improving the Otsu method's performance in noise handling. [PERSON] [29] improved the algorithm by using image histograms and global thresholding techniques, reducing computation time and improving segmentation quality. [PERSON] [30] weighted cumulative probability parameters to improve segmentation for single-peaked histograms. [PERSON] [31] proposed a method combining 3D Otsu and multi-scale image representation, demonstrating stable results and robustness to noise.  
The entropy-based algorithm is also widely utilized, finding the optimal threshold through entropy. [PERSON] [21] proposed the maximum entropy method, achieving good results even for non-ideal bimodal histograms. However, it lacks consideration of spatial information, leading to poor noise robustness. [PERSON] [32] used the Cuckoo Search Algorithm to enhance the Maximum Entropy method, improving both its accuracy and its efficiency. The MHUE method [23] integrates grayscale class uncertainty and spatial uniformity into an energy function. It shows excellent performance in segmenting fuzzy images and medical images. [PERSON] [33] proposed a segmentation method based on fuzzy entropy that considered inter-class and intra-class differences, and in 2012, they improved the method with a new energy function [24]. [PERSON] [25] introduced a Tsallis entropy-based method, while [PERSON] [26] applied 2D Tsallis entropy to multi-threshold problems. [PERSON] [34] developed a Tsallis-entropy-based threshold segmentation method that utilizes multi-scale and multi-directional Gabor transformations. Recently, new methods such as Masi entropy [27] have been utilized. [PERSON] [35] compared the performance of eight thresholding methods on microscopic medical images and found that [PERSON]'s entropy threshold performed the best. [PERSON] [36] introduced a multilevel thresholding method based on non-entropy maximization, utilizing threshold scores. They used the AO-PSO optimizer to reduce computational costs for multi-class segmentation. [PERSON] [37] proposed an enhanced version of the Barnacle Mating Optimizer, which made substantial advancements in both precision and efficiency.  
Recently, [PERSON] [38] proposed a deep learning model called the Deep Threshold Prediction Network (DTP-Net) for threshold prediction. The model takes grayscale images as input, with the goal of determining the optimal grayscale threshold by maximizing the Dice similarity index (DSI) between the segmented image and the ground truth.