# Effective Implementation of Edge-Preserving Filtering on CPU Microarchitectures
## 7 Experimental Results
### Influence of Denormalized Numbers
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} & \multicolumn{3}{c}{**(b)**} & \multicolumn{3}{c}{**(c)**} \\ \hline \(r\) & 4 & 8 & 16 & \(r\) & \(\sigma_{r}\) & 4 & 8 & 16 & \(r\) & \(\sigma_{r}\) & 4 & 8 & 16 \\ \hline
12 & 16.76 & 16.83 & 16.85 & 12 & 63.95 & 48.69 & 48.09 & 12 & 3.82 & 2.89 & 2.85 \\
24 & 42.53 & 42.40 & 42.39 & 24 & 207.54 & 185.16 & 181.40 & 24 & 4.88 & 4.37 & 4.28 \\
48 & 143.24 & 143.01 & 142.58 & 48 & 741.42 & 717.41 & 685.18 & 48 & 5.18 & 5.02 & 4.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational time and speedup ratio of Gaussian range filter in the range computing (RC) implementation using AVX512 for various parameters. These results were obtained on an Intel Core i9 7980 XE. If the ratio exceeds 1, the proposed methods are faster than the straightforward implementation (none) for each parameter. Image size is 768 \(\times\) 512. (**a**) Computational time (proposed) [ms]; (**b**) Computational time (none) [ms]; (**c**) Speedup ratio. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} & \multicolumn{3}{c}{**(b)**} & \multicolumn{3}{c}{**(c)**} \\ \hline \(r\) & 4 & 8 & 16 & \(r\) & \(\sigma_{s}\) & \(\sigma_{r}\) & 4 & 8 & 16 & \(r\) & \(\sigma_{s}\) & \(\sigma_{r}\) & 4 & 8 & 16 \\ \hline
4 & 17.48 & 17.57 & 17.63 & 4 & 66.48 & 51.36 & 50.24 & 4 & 3.80 & 2.92 & 2. To verify the accuracy of the proposed methods, we compared the scalar implementation in double-precision with the proposed methods and other approaches regarding peak signal-to-noise ratio (PSNR). The results are shown in Figure 11. The proposed methods hardly affect accuracy. Note that the accuracies of the RqL and MqL implementation are slightly lower than those of the other types of implementation because the LUTs are approximated. In these types, the accuracy deterioration is not significant because human vision does not sense differences higher than 50 dB [51; 52]. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} & \multicolumn{3}{c}{**(b)**} & \multicolumn{3}{c}{**(c)**} \\ \cline{2-10} \(\sigma_{s}\) & \(h\) & \(4\sqrt{2}\) & \(8\sqrt{2}\) & \(16\sqrt{2}\) & \(\sigma_{s}\) & \(h\) & \(4\sqrt{2}\) & \(8\sqrt{2}\) & \(16\sqrt{2}\) & \(\sigma_{s}\) & \(h\) & \(4\sqrt{2}\) & \(8\sqrt{2}\) & \(16\sqrt{2}\) \\ \hline
4 & 40.20 & 40.05 & 39.92 & 4 & 99.14 & 84.85 & 82.85 & 4 & 2.47 & 2.12 & 2.08 \\
8 & 133.61 & 133.02 & 132.85 & 8 & 340.29 & 311.72 & 301.38 & 8 & 2.55 & 2.34 & 2.27 \\
16 & 496.86 & 496.57 & 495.89 & 16 & 1166.17 & 1191.36 & 1163.34 & 16 & 2.35 & 2.40 & 2.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computational time and speedup ratio of the bilateral non-local means filter in the MC implementation using AVX512 for various parameters. These results were calculated using an Intel Core i9 7980 XE. If the ratio exceeds 1, the proposed methods are faster than the straightforward implementation (none) for each parameter. Template window size is \((3,3)\); search window size is \((2\times 3\sigma_{s}+1,2\times 3\sigma_{s}+1)\); and image size is 768 \(\times\) 512. (**a**) Computational time (proposed) [ms]; (**b**) Computational time (none) [ms]; (**c**) Speedup ratio. Figure 11: PSNRs of the bilateral filter, Gaussian range filter, non-local means filter and bilateral non-local means filter: (**a**) bilateral filter; (**b**) Gaussian range filter; (**c**) non-local means filter; (**d**) bilateral non-local means filter. Note that the maximal value in (**a–d**) is infinity.