# Genetic Programming to Remove Impulse Noise in Color Images
## 5 Experimental Results
### Discussion  
In this context, overall performance relies on the capacity of a filter to simultaneously detect and remove any impulse noise model (salt and pepper, uniform, or correlated) without a preference or specialization. Therefore, the filtering process for each noise model can be seen as an objective function for a multi-objective problem. Each objective function depends on the image quality metrics used. Since a lower MAE value means fewer lost details in the image, searching for the optimum performance considering the MAE can be seen as a minimization multi-objective problem. Conversely, the cases for the PSNR,  
Figure 5: Output images of the five best filters considering the Peppers image perturbed by salt-and-pepper, uniform, and correlated noise, with a noise density of \(p=0.20\): (**a–c**) NAFSM; (**d–f**) VMF; (**g–i**) IDCNN; (**j–l**) GP.  
Figure 6: Output images of the five best filters considering the Caps image perturbed by salt-and-pepper, uniform, and correlated noise, with a noise density of \(p=0.20\): (**a–c**) NAFSM; (**d–f**) VMF; (**g–i**) IDCNN; (**j–l**) GP.  
SSIM, and FSIM all represent maximization multi-objective problems (see Section 3.2). Figures 7-10 illustrate the extent to which the performance of the comparison filters deviates with respect to a hypothetical optimum, also known as an equilibrium point in the context of multi-objective optimization [45]. In this work, the equilibrium point represents the best values obtained simultaneously for each corresponding noise model.  
Figure 7 presents a three-dimensional Pareto front for the MAE average values, considering the complete set of test images with noise densities \(p=0.05,0.10,0.15\), and \(0.20\). As can be observed, the MAE average values of the proposed GP filter (indicated by a red diamond) are among the closest to the equilibrium point for all noise densities, on par with the IDCNN and GSAPA filters. Given their specialization in salt-and-pepper noise, the NAFSM and DBAIN move away from the equilibrium point as the noise density level increases for the other two noise models. The average values of these two filters are located in a two-dimensional opposite extreme point at \(p=0.20\). Consistent with the results of Table 4, the NAFSM and DBAIN are the furthest from the optimum.  
Similar to the behaviors shown in Figure 7 but oriented in the opposite direction, Figure 8 depicts the three-dimensional Pareto front for the PSNR average values. In this metric, the IDCNN filter demonstrates the best average values for the maximization multi-objective  
Figure 7: Three-dimensional Pareto front for MAE average values by considering the whole set of test images with noise densities \(p=0.05,0.10,0.15\), and \(0.20\).  
problem, followed by the GP filter, for \(p=0.05\) and \(0.10\). However, it is unclear which one of the average values of the IDCNN, GP, or GSAPA filters is the second closest to equilibrium for \(p=0.15\) and \(0.20\). It is also hard to determine which of the filters yields the furthest average values from the optimum. Unlike in Figure 7, the DBAIN is in a two-dimensional extreme point concerning the equilibrium point across all noise densities, followed by the NAFSM. Similarly to Figure 8, but with normalized values, Figures 9 and 10 present the three-dimensional Pareto fronts for the SSIM and FSIM average values, respectively.  
Figure 10: _Cont._  
Figure 9: Three-dimensional Pareto front for SSIM average values by considering the whole set of test images with noise densities \(p=0.05,0.10,0.15,\) and \(0.20\).