# Convolutional Neural Networks: A Roundup and Benchmark of Their Pooling Layer Variants
## 4 Results  
### Details Retention  
As previously described, three metrics were used as a means of comparison for how well details are preserved after pooling the original input. The first one is the Root-Mean-Squared Contrast (RMSC) [44], which is the standard deviation of the pixel intensities, which indicates how well the contrast levels are maintained between the input and output. The second, the Peak-Noise-to-Signal Ratio (PSNR) [45], shows how strong the original image signal is compared to the introduced noise due to pooling. Lastly, the Structural Similarity Index (SSIM) [46] can range from \(-1\) to \(1\) and shows the actual similarity between the input and output of the pooling layer.  
In Table 4, Average pooling appears to be the best choice, since it shows the best SSIM values across all dataset tests. Furthermore, it achieved a top ranking PSNR as well for two out of the three datasets--which can be interpreted as a low level of introduced noise. When it comes to the RMSC, though other methods achieved better values, Average pooling kept up, and as we can see in the pooling layers' output examples, higher contrast is not always good, at least when it comes to comparing similarities with the original image.  
In Figures 7-9, a sample input of each dataset is presented, as well as the respective output for each pooling layer. Each method might have a tendency to favor higher or lower values of the input pixels, while some increase the contrast significantly.  
Combined with the results of Table 4, it seems that Average pooling indeed achieved a result that was very close to the original image. On the other hand, tree, l2, fuzzy, and spectral pooling introduced a much higher contrast to the image, generating an output that was very different from the original input.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**MNIST**} & \multicolumn{3}{c}{**CIFAR10**} & \multicolumn{3}{c}{**CIFAR100**} \\  & **RMSC** & **PSNR** & **SSIM** & **RMSC** & **PSNR** & **SSIM** & **RMSC** & **PSNR** & **SSIM** \\ \hline Max & 0.35 & 65.66 & 0.76 & 0.17 & 68.69 & 0.82 & 0.26 & 66.84 & 0.80 \\ Adaptive Max & 0.35 & 65.66 & 0.76 & 0.17 & 68.69 & 0.82 & 0.26 & 66.84 & 0.80 \\ Fractional Max & 0.35 & 65.66 & 0.76 & 0.17 & 68.69 & 0.82 & 0.26 & 66.84 & 0.80 \\ Average & 0.28 & 69.47 & **0.89** & 0.15 & **75.52** & **0.86** & 0.26 & **70.80** & **0.84** \\ Mixed & 0.16 & 70.54 & 0.85 & 0.16 & 70.54 & 0.85 & 0.26 & 69.03 & 0.82 \\ Gated & 0.30 & 68.49 & 0.83 & 0.14 & 72.24 & 0.85 & 0.26 & 69.22 & 0.82 \\ Tree (Level 2) & 0.53 & 60.57 & 0.69 & **0.33** & 53.74 & 0.62 & 0.46 & 54.84 & 0.73 \\ LP (L2) & **0.57** & 58.66 & 0.61 & 0.29 & 55.02 & 0.66 & 0.52 & 52.43 & 0.66 \\ Stochastic & 0.15 & **70.67** & 0.83 & 0.15 & 70.66 & 0.83 & 0.26 & 68.91 & 0.81 \\ Fuzzy & 0.55 & 59.95 & 0.68 & 0.29 & 55.20 & 0.67 & 0.52 & 52.58 & 0.66 \\ Overlapping Max & 0.40 & 60.46 & 0.56 & 0.18 & 64.92 & 0.70 & 0.25 & 62.01 & 0.58 \\ Spectral & 0.58 & 58.72 & 0.66 & 0.30 & 55.08 & 0.61 & **0.53** & 52.53 & 0.57 \\ Wavelet & 0.26 & 69.47 & 0.89 & 0.15 & 72.52 & **0.86** & 0.26 & **70.80** & **0.84** \\ Local Importance & 0.31 & 67.76 & 0.81 & 0.15 & 71.51 & **0.86** & 0.26 & 70.01 & **0.84** \\ Soft & 0.29 & 62.92 & 0.65 & 0.15 & 67.87 & 0.67 & 0.27 & 65.91 & 0.63 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The details’ retention indicators of our benchmark. The best value for each metric in each separate dataset is highlighted.