## 4 Results and Analysis
### Experimental Analysis Based on Multi-Level Thresholding  
To assess the performance of the proposed COSGO algorithm against other methods, multiple quantitative metrics were used, such as the Peak Signal-to-Noise Ratio (PSNR), the Feature Similarity Index (FSIM), the Structural Similarity Index Measure (SSIM), dice, and the Jaccard index and accuracy, along with the optimal objective function values and their associated variances. In this regard, ten images were selected from the BSD500 dataset [40]. For ease of interpretation and comparative analysis, the best results averaged over 10 independent runs are highlighted in bold in the subsequent tables. Table 4 presents the average and standard deviation fitness function values for all compared methods across thresholding levels 2, 3, 4, and 5 evaluated on all images using two objective functions: Otsu's method and Kapur's entropy. Moreover, the proposed COSGO algorithm demonstrates lower computational time at threshold level 2 and level 3. Based on the obtained results of the running time of each algorithm, which are presented in Table 5, the COSGO algorithm achieves superior performance in terms of execution time. The segmentation results based on Otsu and Kapur entropy are shown in Table 6, along with the PSNR, SSIM, and FSIM values. A traditional statistic for assessing image quality is the PSNR. It determines how segmented and original photos differ from one another. The segmented image is more like the original when the PSNR value is higher. In this way, the higher value of the PSNR proves the algorithm efficiently. In addition, the mean square error (MSE) was calculated for each algorithm with two objective functions. The obtained results were also in the same running condition, with 100 iteration numbers and 30 search agent numbers. It was observed that the proposed COSGO algorithm showed better performance in terms of higher PSNR and lower MSE values in comparison to the other algorithms. The Structural Similarity Index Measure (SSIM) evaluates the perceived quality of an image by incorporating luminance, contrast, and structural information. A higher SSIM value closer to 1 indicates a greater structural similarity between the segmented image and the original image. The Feature Similarity Index Measure (FSIM), which is widely used for image quality assessment, particularly in terms of texture and detail preservation, quantifies the similarity based on low-level image features, such as phase congruency and gradient magnitude. Table 7 presents the obtained value for each algorithm with two different objective functions as Otsu and Kapur entropy functions. In Table 8, the dice coefficient and Jaccard index are shown. The dice coefficient and Jaccard index (intersection over union) are widely used metrics for evaluating image segmentation performance by measuring the similarity between the predicted segmentation and the ground truth. In contrast, the Jaccard index measures the ratio of the intersection to the union of the same sets. Both metrics range from 0 to 1, with higher values indicating greater similarity, and they are especially important in assessing the spatial accuracy of segmentation methods. Table 9 presents the quantitative evaluation of the segmentation accuracy achieved by each algorithm across the test image dataset. The evaluation is based on two widely recognized overlap-based similarity metrics: the dice coefficient and the Jaccard index. These metrics assess how closely the segmented regions produced by the algorithms align with the ground truth masks. Higher values in both metrics indicate superior segmentation performance, reflecting better boundary adherence and region consistency. The table highlights the comparative strengths of each method and provides a comprehensive understanding of their effectiveness in accurately delineating the target regions.