# Genetic Programming to Remove Impulse Noise in Color Images
## 5 Experimental Results
### Performance of the Proposed Filter
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Filter**} & \multicolumn{2}{c}{\(\mathbf{p=0.05}\)} & \multicolumn{2}{c}{\(\mathbf{p=0.10}\)} & \multicolumn{2}{c}{\(\mathbf{p=0.15}\)} & \multicolumn{2}{c}{\(\mathbf{p=0.20}\)} \\ \cline{3-11}  & & **SSIM** & **FSIM** & **SSIM** & **FSIM** & **SSIM** & **FSIM** & **SSIM** & **FSIM** \\ \hline \multirow{4}{*}{**FMM**} & IDCNN [33] & **0.9902** & 0.9928 & 0.9788 & 0.9846 & 0.9461 & 0.9659 & 0.8297 & 0.9056 \\  & & GP & 0.9792 & 0.9872 & 0.9681 & 0.9819 & 0.9365 & 0.9682 & 0.8642 & 0.9360 \\  & DBAIN [25] & **0.9919** & **0.9957** & **0.9875** & **0.9935** & **0.9819** & **0.9905** & **0.9745** & **0.9864** \\  & NARSM [22] & 0.9888 & **0.9938** & **0.9828** & **0.9908** & **0.9770** & **0.9874** & **0.9712** & **0.9836** \\  & GSAPA [17] & 0.9681 & 0.9710 & 0.9610 & 0.9656 & 0.9476 & 0.9576 & 0.9256 & 0.9485 \\  & FMPGF [20] & 0.9475 & 0.9647 & 0.8679 & 0.9244 & 0.7452 & 0.8589 & 0.6209 & 0.7855 \\  & VMF [16] & 0.9472 & 0.9680 & 0.9146 & 0.9566 & 0.8162 & 0.9227 & 0.6514 & 0.8505 \\ \hline \multirow{4}{*}{**FMM**} & IDCNN [33] & **0.9907** & **0.9930** & **0.9829** & **0.9866** & **0.9729** & **0.9795** & **0.9537** & **0.9693** \\  & GP & **0.9748** & **0.9866** & **0.9609** & **0.9824** & 0.9371 & 0.9753 & 0.9010 & **0.9633** \\  & DBAIN [25] & 0.6042 & 0.8595 & 0.4702 & 0.7747 & 0.3899 & 0.7143 & 0.3318 & 0.6689 \\  & NARSM [22] & 0.6036 & 0.8591 & 0.4693 & 0.7734 & 0.3888 & 0.7127 & 0.3307 & 0.6674 \\  & GSAPA [The average results presented in Tables 4 and 5 encompass a diverse set of 360 test color images with different features such as size, shape, color texture, light conditions, edge characteristics, etc. The complete set of resulting filtered images, along with their original sizes and denoised versions, is available in the Supplementary Materials. However, four test images with different distinguishable characteristics were selected for illustrative purposes to visually analyze the filters' efficiency: Baboon, Goldhill, Pepper, and Caps. Figure 3 shows the visual results of some of the comparison filters applied to the Baboon image, considering the salt-and-pepper, uniform, and correlated noise models from top to bottom, respectively. Since the Baboon image has more profound and larger textured areas compared to the other test images, robust filters such as the VMF exhibited lower performance. Because of this, the resulting images of this filter were visually omitted. Among the filtered images, Figure 3a closely resembles the version of the image before adding noise. On the other hand, some filtered images show additional artifacts, e.g., Figure 3g. The ICDNN filter (Figure 3j-l) and the proposed GP filter (Figure 3m-o) excelled in noise removal while preserving the details of the images across the three different noise models. Figure 4 shows the resulting images produced by some of the comparison filters applied to the Goldhill image, arranged according to the three noise models from top to bottom. The Goldhill image has similar color tonalities to the Baboon image but has a few smooth areas and complex geometric patterns, resulting in significant contrast differences. For this reason, the filtered images shown here exhibit similar visual behavior to the filtered Baboon images. As observed in the filtered images, the NAFSM filter performed the best for salt-and-pepper noise (very close to the version of the image before adding noise). Although the IDCNN filter (Figure 4j-l) excelled in noise removal while preserving the details of the images for uniform and correlated noise, the proposed GP (Figure 4m-o) filter maintained consistent performance across the three different noise models. In general, the proposed GP filter ranked second for uniform noise and achieved some of the best MAE values for correlated noise.