Optimum Multilevel Thresholding for Medical Brain Images Based on Tsallis Entropy, Incorporating Bayesian Estimation and the Cauchy Distribution

Entropy-based thresholding is a widely used technique for medical image segmentation. Its principle is to determine the optimal threshold by maximizing or minimizing the image’s entropy, dividing the image into different regions or categories. The intensity distributions of objects and backgrounds often overlap and contain many outliers, making segmentation extremely difficult. In this paper, we introduce a novel thresholding method that incorporates the Cauchy distribution into the Tsallis entropy framework based on Bayesian estimation. By introducing Bayesian prior probability estimation to address the overlap in intensity distributions between the two classes, we enhance the estimation of the probability that a pixel belongs to either class. Additionally, we utilize the Cauchy distribution, known for its heavy-tailed characteristics, to fit grayscale pixel distributions with outliers, enhancing tolerance to extreme values. The optimal threshold is derived through the optimization of an information measure formulated using updated Tsallis entropy. Experimental results demonstrate that the proposed method, called Cauchy-TB, achieves significant superiority to existing approaches on two public medical brain image datasets.