# Improving Prostate Image Segmentation Based on Equilibrium Optimizer and Cross-Entropy
## 1 Introduction
The approaches that make use of MCE can determine if a particular set of thresholds minimizes the cross-entropy of the histogram's partition. Therefore, MCE is just an entropic criterion, not a whole methodology for thresholding by itself. MCE could be used in an exhaustive search to evaluate all possible combinations of threshold values, but this is, of course, impractical. To alleviate the computational burden of such a kind of search, stochastic optimization algorithms (SOAs) are often applied to this task. SOAs use stochasticity in their operators to help to find optimal solutions to complex problems in reasonable times. We can see in the literature multiple approaches that employ randomness and domain-specific rules that help to identify optimal solutions quickly, and they are often referred to as metaheuristic algorithms. We can find examples of SOAs applied to the multilevel thresholding of images in [12; 13; 14; 15; 16; 17; 18]. Specific to the field of health care, we can find a plethora of implementations. For instance, we can find a modification of the Slime Mould Algorithm (SMA) used to perfom image thresholding over breast thermograms [19]. Ref. [20] uses a variant of the manta ray foraging optimization algorithm (MRFO) to segment computer tomographies (CT) from COVID-19 patients using Otsu as the objective function. [PERSON] et al. proposed an accurate cluster chaotic optimization approach for digital mammograms, lymphoblastic leukemia images, and brain MRIs using cross-entropy as the non-parametric criterion [21]. [PERSON] et al. presented a hybrid algorithm called the hybrid adaptive cuckoo search-squirrel search algorithm (ACS-SA) to segment T-2 weighted axial brain MR images [22]. [PERSON] et al. used a modification of the chimp optimization algorithm (COA) for the segmentation of breast thermographic images [23]. Despite these advances, challenges remain in achieving both high accuracy and computational efficiency in medical image segmentation. The balance between exploration and exploitation in SOAs is critical for their success in specific applications, but it is not always straightforward to adapt general-purpose algorithms to the domain of medical imaging. Moreover, the performance of these algorithms is highly dependent on the problem at hand, making it necessary to assess their applicability in the context of specific medical conditions and imaging modalities. SOAs and specifically metaheuristic algorithms are often presented in the academic literature using a set of standard benchmark functions designed to stress the algorithm and to determine if the proposed approach is better than previous approaches in a general sense. Although usual comparisons give us a glimpse of the algorithm potential, the actual performance can only be assessed in application to a specific problem [24]. Unfortunately, it is impractical to evaluate every new algorithm on all possible applications. However, guided by the general results of the proposal, if we analyze how the algorithm has been applied to other areas, we can identify potential candidates for successful implementations. The equilibrium optimizer (EO) is a SOA inspired by control volume mass balance models [25]. EO has been successfully applied over a wide range of applications, including topics in energy, manufacturing design, artificial intelligence, and even image processing. In electrical and energy applications, the EO has been applied to solve the optimal power flow in hybrid AC/DC grids, where many objectives are considered, such as the generation cost, environmental emissions, power losses, and the deviation of bus voltages [26]. In [27], the EO is used to model a proton exchange fuel cell; the model is tested on various commercial fuel cells with competitive results. In [28], the EO helps to determine critical parameters of Shottky barrier diodes. Ref. [29] introduces the use of EO for solar photovoltaic parameter estimation.