## 5 Results and Discussion
### Results with the Structural Dissimilarity Measure (DSSIM)
The results obtained with PSNR and DSSIM are shown in Figures 11 and 12 (for PSNR, a higher value is better, whilst for DSSIM, a lower value is better). In Figures 11 and 12, the curve representing the compressed image expresses the relevance of the models. In fact, in the case of PSNR, this relevance is provided by a model that gives results above the compressed image and, up to the case of DSSIM, by a model that gives results below the compressed image. However, the use of Gaussian filtering does not satisfy these conditions. In the worst case, the others are generally confused by the compressed image. Finally, we observed, with the help of Table 7, using the standard deviation, the stability of the results on all the databases used in this work. Table 8 shows the average execution times achieved by our model on the image databases used. The algorithm still needs to be optimized to reduce the time required to process an image. The average processing time observed is approximately 10 min per image. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Berkeley Databases**} & \multicolumn{2}{c}{**KODAK Databases**} & \multicolumn{2}{c}{**USC-SIPI Databases**} \\ \hline  & **DSSIM** & **PSNR** & **DSSIM** & **PSNR** & **DSSIM** & **PSNR** \\ \hline
10\% & 0.13 (0.02) & 26.23 (2.07) & 0.1 (0.01) & 28.31 (2.3) & 0.09 (0.01) & 30.07 (2.63) \\
20\% & 0.07 (0.013) & 28.28 (2.19) & 0.05 (0.009) & 30.64 (2.44) & 0.05 (0.009) & 32.7 (2.97) \\
30\% & 0.05 (0.01) & 29.49 (2.23) & 0.03 (0.007) & 32 (2.45) & 0.04 (0.008) & 34.14 (3.15) \\
40\% & 0.04 (0.01) & 30.37 (2.22) & 0.03 (0.005) & 32.9 (2.43) & 0.03 (0.007) & 35 (3.19) \\
50\% & 0.04 (0.009) & 31.13 (2.19) & 0.02 (0.005) & 33.72 (2.39) & 0.03 (0.007) & 35.6 (3.18) \\
60\% & 0.03 (0.009) & 31.93 (2.14) & 0.02 (0.004) & 34.52 (2.33) & 0.02 (0.007) & 36.36 (3.16) \\
70\% & 0.03 (0.008) & 33.07 (2.03) & 0.02 (0.004) & 35.58 (2.22) & 0.02 (0.007) & 37.23 (3.08) \\
80\% & 0.03 (0.008) & 34.81 (1.84) & 0.01 (0.003) & 37.15 (2) & 0.02 (0.007) & 38.41 (2.9) \\
90\% & 0.02 (0.008) & 38.07 (1.41) & 0.01 (0.003) & 39.88 (1.5) & 0.02 (0.007) & 40.58 (2.33) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Illustration of the mean values and standard deviations on DSSIM and PSNR criteria obtained after image processing by our proposed model on the Berkeley (120 images), Kodak (24 images), and USC-SIPI (13 images) databases. Figure 10: Illustration of the effects of the use of static \(\lambda\) and dynamic \(\lambda\) on the Lena image. (**Left side**) \(\lambda=1.0\); (**Right side**) \(\lambda\) is dynamic. Figure 11: Results on the evolution of the PSNR according to the quality of compression. Figure 12: Results on the evolution of the DSSIM according to the quality of the compression. When using the PSNR parameter, the visual rendering is improved for compression with a quality between 10% and 70%. The use of the DSSIM parameter shows that, for a quality of between 10% and 30%, the proposed model improves. In any case, for compression with high information loss, our proposal gives better PSNR and DSSIM values than the just compressed image. As soon as the compression becomes low, we see that it is no longer necessary to use our proposal, since it provides values that are lower than those given by the compressed image. The work focuses on the proposal of an adaptive control operator for the smoothing strength of the p(x)-Laplacian method. Tests were carried out on the three following image databases: Berkeley, USC-SIPI, and KODAK. We degraded the images of these three databases by applying compression levels with losses. The results in Figures 11 and 12 show a higher efficiency of the p(x)-Laplacian method with our adaptive controller compared to other smoothing methods in the literature with respect to the PSNR and DSSIM evaluation operators. We showed that the p(x)-Laplacian operator with our control operator produces better results than the p(x)-Laplacian with a static \(\lambda\).