## 3 Results
### Quantitative Evaluation  
In order to comprehensively evaluate the success of the proposed method in this study, both perceptually and structurally, various reference-free image quality metrics were used. Each of these metrics allows us to evaluate the performance of the methods by measuring different aspects of image quality. Integrated Local Natural Image Quality Evaluator (IL-NIQE) [31] is a completely blind quality indicator and measures the deviation from natural scene statistics; lower IL-NIQE values indicate that noise, blur and color errors are reduced, and the perceived quality is increased. Average Gradient (AG) [20] measures the average of spatial gradient sizes in the image; high AG values indicate that detail richness and edge sharpness are improved. However, when the AG values increase excessively, this increase can sometimes be caused by unwanted noise; so, it should be interpreted together with IL-NIQE. Underwater Image Quality Measure (UIQM) [6] is a composite metric based on the human-eye model developed for underwater images and is calculated as a weighted sum of elements such as the underwater image colorfulness measure (UICM), the underwater image contrast measure (UIConM) and the underwater image sharpness measure (UISM); therefore, higher UIQM values indicate increased overall enhancement quality. UICM [6] specifically measures color shifts and color saturation; higher UICM values indicate that color aberrations are eliminated and color vibrancy is increased. Information Entropy (IE) [32] measures the information content of the image and the uncertainty in tone distribution; higher IE generally means wider dynamic range and increased information. _Metric comparison_: Table 2 presents the average values of IE, IL-NIQE, AG, and UIQM and its sub-component UICM metrics calculated for 60 underwater images in the Test-C60 dataset, and Table 3 presents the average values of 184 underwater images in the OceanDark dataset. These tables clearly demonstrate the performance superiority of the proposed method over 14 other underwater image enhancement methods in terms of these five metrics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Test-C60**} \\ \hline  & IE \(\uparrow\) & UIQM \(\uparrow\) & UICM \(\uparrow\) & ILNIQE \(\downarrow\) & AG \(\downarrow\) \\ \hline IBLA & 14.3913 & 0.5144 & 5.8387 & 35.6136 & 30.8885 \\ CBF & 14.7693 & 0  
When the scores presented in Table 2 are examined, it is seen that our proposed method produces the results closest to natural scene statistics by obtaining the lowest value (25.46) in IL-NIQE and records the highest value (0.997) in UIQM, proving that it improves color, contrast and sharpness in a balanced manner. The detail preservation ability of the method is confirmed by the best score of 51.60 reached in the average gradient (AG) metric; and in UICM, representing color accuracy, the second-best value (11.05) is achieved right after the aggressive color compensation of HFM. Although it remains in the third place in terms of entropy (15.32), the low value of IL-NIQE and the high value of AG show that this information is due to a balanced contrast increase and does not consist of excessive noise. Other compared methods either produced blur while increasing color saturation (HFM) or were insufficient in providing detail [11]. The results show that the proposed method achieves consistent success in both objective and perceptual metrics by finding the optimum point in the color-detail trade-off on the Test-C60 dataset. The average scores calculated on 183 low-light and dense scattering images in the OceanDark dataset in Table 3 show that the proposed method outperforms its competitors by 2.6-19 points, achieving the lowest value of 23.06 in IL-NIQE. It surpasses the second-ranked [11] by \(\approx\)13% and HFM by \(\approx\)23% in UIQM with a score of 1.1182, indicating that it improves color, contrast and sharpness in a balanced manner.