# Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images
## 3 Results and Discussion
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Noise**} & \multicolumn{2}{c}{**Gauss \(\sigma=5\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=10\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=20\)**} & \multicolumn{2}{c}{**Gauss \(\sigma=30\)**} \\  & \multicolumn{2}{c}{**Impulsive \(p=0.05\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.1\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.2\)**} & \multicolumn{2}{c}{**Impulsive \(p=0.3\)**} \\ \hline Filter & MAE & PSNR & NCD & MAE & PSNR & NCD & MAE & PSNR & NCD & MAE & PSNR & NCD \\ None & 7.75 & 21.26 & 8.29 & 14.56 & 18.48 & 15.72 & 27.19 & 15.23 & 29.37 & 38.36 & 13.22 & 40.92 \\ FRF-FPGA & **3.01** & **32.9** & 3.19 & **4.61** & **30.59** & **4.19** & **7.92** & **26.87** & 7. Figure 6: Method outputs. Lena image contaminated with impulse \(p\) and Gaussian noise \(\sigma\). (**a**) Lena. (**b**) Noisy \(p=0.05,\sigma=5\). (**c**) Filter output. (**d**) Noisy \(p=0.1\), \(\sigma=10\). (**e**) Filter output. (**f**) Noisy \(p=0.2\), \(\sigma=20\). (**g**) Filter output. (**h**) Noisy \(p=0.3\), \(\sigma=30\). (**i**) Filter output. Figure 7: Method outputs. Image Flower contaminated with impulse \(p\) and Gaussian noise \(\sigma\). (**a**) Flower. (**b**) Noisy \(p=0.05,\sigma=5\). (**c**) Filter output. (**d**) Noisy \(p=0.1\), \(\sigma=10\). (**e**) Filter output. (**f**) Noisy \(p=0.2\), \(\sigma=20\). (**g**) Filter output. (**h**) Noisy \(p=0.3\), \(\sigma=30\). (**i**) Filter output. We also analyzed the filtering capabilities of the new technique when the images were contaminated only with impulses and only with Gaussian noise. The results of these experiments for Lena image are shown in Figures 8-10. Similar findings were achieved for the other test images. For the Gaussian noise, the proposed filter can compete in results of PSNR, MAE, and NCD with the methods specifically designed to reduce pure Gaussian noise (APF, C-BM3 DF, and FWSDF), and it provides better outputs than the rest of the filters. In some cases, depending on the amount of noise, the proposed method improves the methods specifically designed to reduce Gaussian noise, and in other cases does not improve them. FRF-FPGA presents a better performance than APF, C-BM3 DF, and FWSDF, when the noise is high (\(\sigma=20,30\)). However, its performance decreases a little for lower noise. Nevertheless, the difference in this case is not significant. This illustrates the filter practical utility to denoise images contaminated only with Gaussian distortion. Filter outputs for visual inspection are shown in Figures 11 and 12. It may be observed that the new method is capable of decreasing Gaussian noise without blurring the edges of the image. In relation to images contaminated only with impulsive noise, the new filter is also competitive (Figures 13 and 14). The only filters performing a little better, in some cases, than the new method, are the IPCSVF, which is expressly designed to suppress impulsive noise, and the PBTVMF. Compared to the other methods  
Figure 10: Comparison of normalized color difference (NCD) obtained by state-of-the-art methods when restoring Lena contaminated only with Gaussian noise \(\sigma\) or impulse noise \(p\). (**a**) Lena contaminated only by Gaussian \(\sigma\). (**b**) Lena contaminated only with impulse \(p\). Figure 9: Comparison of PSNR obtained by state-of-the-art methods when restoring Lena contaminated only with Gaussian noise \(\sigma\) or impulse noise \(p\). (**a**) Lena contaminated only with Gaussian \(\sigma\). (**b**) Lena contaminated only with impulse \(p\). Figure 11: Method outputs using test image Flower contaminated with various intensities of Gaussian \(\sigma\). (**a**) Flower. (**b**) Noisy \(\sigma=5\). (**c**) Filter output. (**d**) Noisy \(\sigma=10\). (**e**) Filter output. (**f**) Noisy \(\sigma=20\). (**g**) Filter output. (**h**) Noisy \(\sigma=30\). (**i**) Filter output. Figure 12: Method outputs using test image Parrots contaminated with various intensities of Gaussian \(\sigma\). (**a**) Parrots.