# Improving Prostate Image Segmentation Based on Equilibrium Optimizer and Cross-Entropy
## 1 Introduction  
Image processing of medical images has become an exciting research topic due to its importance in the detection, diagnosis, and staging of health conditions. Medical images cover a wide range of technologies designed to generate a visual representation of internal morphology or function with the specific purpose of assisting health care practitioners. Many technologies utilize non-invasive approaches, such as magnetic resonances (MR), ultrasonography, and positron emission tomography (PET), among others. From these alternatives, MR images (MRIs) are often used to analyze anatomical structures as they provide high spatial distribution. However, the acquisition of high-quality MRIs is quite challenging, since MRIs are known to suffer from movements of the patient and the presence of artifacts [1], which can compromise the quality of the scans and subsequently the accuracy of diagnoses and treatment plans. These challenges necessitate the use of advanced techniques for image segmentation, which is a crucial step in interpreting medical images and assisting in diagnosis, particularly in diseases like prostate cancer, which is the second most common and deadly cancer in men after lung cancer [2]. Prostate cancer is known for its silent development, and it is often diagnosed at an advanced stage. According to global cancer statistics from 2022, 1,466,680 new cases of prostate cancer were diagnosed that year [3]. Early detection is crucial, as it significantly improves survival rates; however, challenges in this area remain, due to the subtle nature of early-stage tumors in imaging. Accurate analysis of prostate MRIs is therefore essential to improving diagnostic accuracy and reducing the need for invasive biopsies. The use of computer-aided diagnostic tools (CAD) as a complementary means to medical imaging can help health practitioners to avoid or reduce biopsy rates while also saving time [4]. Research around the design of CAD centers on three main topics: denoising, segmentation, and classification. Segmentation is a fundamental task in medical image processing and plays a critical role in separating different regions of interest within an image, especially when the boundaries are not clearly defined [5]. Traditional segmentation methods, such as thresholding, offer simplicity but face limitations in the context of complex medical images, particularly when distinguishing between subtle tissue variations in MRI scans. Thresholding stands as a simple yet powerful methodology meant to separate two or more regions of an image. This approach first transforms a given image into a frequency representation over an intensity histogram. The histogram is the input of thresholding methods, while the core idea is to find a threshold value (_th_) that accurately divides the histogram into two or more classes. Each class will homogeneously share the same intensity value. Traditionally, thresholding approaches have been named bilevel or multilevel thresholding (MTH) according to the number of thresholds that the implementation possesses. The solution of a MTH problem involves the finding of the optimal threshold values (_th_) that segment a given image properly. As the number of thresholds increases, so does the computational complexity of the task; thus, the efficient selection of threshold values is a non-trivial task. In the literature, we can find numerous approaches to determine the best threshold values for an image. First, the work proposed by [PERSON] used the between-class variance as a non-parametric criterion [6]. Entropy-based approaches take information theory elements to determine if a given partition of a histogram is good enough. This area started with the basic formulation of the Shannon entropy [7], followed by a multitude of variants, including Kapur [8], Tsallis [9], Renyi [10], and cross-entropy [11]. Cross-entropy has been largely adopted by the image processing community since it was proposed by [PERSON] and [PERSON], and it is often referred to as minimum cross-entropy criterion (MCE).