###### Abstract  
In this study, we delve into the realm of image segmentation, a field characterized by a multitude of approaches; one frequently used technique is thresholding-based image segmentation. This process divides intensity levels into different regions based on a specified threshold value. Minimum Cross-Entropy Thresholding (MCET) stands out as an independent objective function that can be applied with any distribution and is regarded as a mean-based thresholding method. In certain cases, images exhibit diverse structures that result in different histogram distributions. Some images possess symmetric histograms, while others feature asymmetric ones. Traditional mean-based thresholding methods are well-suited for symmetric image histograms, relying on Gaussian distribution definitions for mean estimations. However, in situations involving asymmetric distributions, such as left and right-skewed histograms, a different approach is required. In this paper, we propose the utilization of a Maximum Likelihood Estimation (MLE) of [PERSON]'s distribution or Extreme Value Type I (EVI) distribution for the objective function of an MCET. Our goal is to introduce a dedicated image-thresholding model designed to enhance the accuracy and efficiency of image-segmentation tasks. This model determines optimal thresholds for image segmentation, facilitating precise data analysis for specific image types and yielding improved segmentation results by considering the impact of mean values on thresholding objective functions. We compare our proposed model with original methods and related studies in the literature. Our model demonstrates better performance in terms of segmentation accuracy, as assessed through both unsupervised and supervised evaluations for image segmentation. images segmentation; minimum cross-entropy; Gumbel distribution; improving segmentation methods; skewed histogram; extreme value distribution (EVI) +
Footnote †: journal:  
0000-0002-4000  
skin lesions and other types of images. For instance, in some medical images, the skewness of a histogram can be influenced by factors such as the image acquisition parameters. When Magnetic Resonance Imaging (MRI) a brain, the segmentation task is affected if the intensity dissimilarity between adjacent glioma regions is small; this challenge was solved using U-Net to propose attention layers for small-intensity dissimilarities [7]. Moreover, Computed Tomography (CT) scan images can indeed vary depending on multiple factors, including the stage and type of infection, while the proportion of infected pixels in CT images is small [8]. Images of these kinds often present similar segmentation challenges, particularly when employing mean-based thresholding techniques while adhering to the Gaussian definition for a mean estimation [9]. The performance of mean-based thresholding methods in achieving superior segmentation results can be influenced by the choice of the probability distribution. For instance, the Gaussian distribution tends to perform optimally when dealing with symmetric intensity levels, whereas the utilization of the log-normal distribution can lead to improved mean estimations in cases involving right-skewed intensity levels, ultimately enhancing the effectiveness of mean-based objective functions [10]. However, Gumbel maximum and log-normal distributions do not necessarily have the same mean value, even for a right-skewed histogram. The mean value of a probability distribution is a measure of its central tendency and it can vary depending on the specific parameters of each distribution. The novelty of using the Gumbel distribution and Maximum Likelihood Estimation (MLE) lies in their ability to address these limitations effectively. Mitigating these limitations refines the thresholding function, improving the precision of image segmentation and target object detection, particularly in medical imaging and remote sensing. The Gumbel distribution is commonly used for model estimation, and relies on mode and scale parameters.