# Deep Neural Networks for Document Processing of Music Score Images
## 5 Experiments
### CNN Parameterization
#### 5.1.2 Number of Filters, Kernel Size, and Non-Squared Input  
According to the results in the previous section, we fixed the base CNN to five layers, and one convolution operation per layer. We now evaluate the performance with different number of \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{6}{c}{\(\mathrm{F}_{1}^{M}\) **(\%)**} & \multicolumn{6}{c}{**Pixels (\(\times 10^{3}\)) Per Second**} \\ \cline{3-11}
**Input Size (px)** & **Convolution Blocks** & \multicolumn{6}{c}{**Depth (Layers)**} & \multicolumn{6}{c}{**Depth (Layers)**} \\ \cline{3-11}  & & **1** & **2** & **3** & **4** & **5** & **1** & **2** & **3** & **4** & **5** \\ \hline \(11\times 11\) & & & 66.7 & 71.0 & 73.0 & - & - & 24 & 22 & 19 & - & - \\ \(25\times 25\) & & & 70.4 & 76.1 & 81.1 & 82.6 & - & 15 & 16 & 17 & 16 & - \\ \(51\times 51\) & & & 78.9 & 80.9 & 85.1 & 83.2 & 86.9 & 6 & 7 & 8 & 8 & 8 \\ \(75\times 75\) & & & 75.8 & 80.6 & 86.2 & 85.8 & 85.5 & 4 & 4 & 5 & 5 & 5 \\ \(101\times 101\) & & & 74.2 & 83.5 & 84.2 & 86.9 & 86.6 & 2 & 3 & 3 & 3 & 3 \\ \hline \(11\times 11\) & & & 69.1 & 71.8 & 72.2 & - & - & 21 & 18 & 14 & - & - \\ \(25\times 25\) & & & 75.4 & 79.2 & 81.1 & 82.7 & - & 11 & 12 & 12 & 11 & - \\ \(51\times 51\) & 2 & & 81.1 & 82.7 & 85.1 & 86.6 & 86.0 & 4 & 4 & 5 & 5 & 5 \\ \(75\times 75\) & & & 83.9 & 85.6 & 84.4 & 86.9 & 86.1 & 2 & 3 & 3 & 3 & 3 \\ \(101\times 101\) & & & 49.0 & 83.8 & 86.8 & 85.1 & 85.6 & 1 & 2 & 2 & 2 & 2 \\ \hline \(11\times 11\) & & & 72.1 & 71.6 & 72.2 & - & - & 18 & 15 & 12 & - & - \\ \(25\times 25\) & & & 76.4 & 81.5 & 82.8 & 82.6 & - & 9 & 9 & 9 & 8 & - \\ \(51\times 51\) & 3 & & 83.1 & 84.4 & 86.0 & 86.7 & 84.9 & 3 & 3 & 3 & 3 & 3 \\ \(75\times 75\) & & & 81.2 & 85.5 & 84.6 & 85.8 & 86.8 & 2 & 2 & 2 & 2 & 2 \\ \(101\times 101\) & & & 50.9 & 86.6 & 86.9 & 85.7 & 84.6 & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results in terms of \(\mathrm{F}_{1}^{M}\) and pixels per second of the different configurations. All CNN are configured to 32 filters per convolution, \(3\times 3\) kernels and trained with 20,000 random samples per class—being a total of 100,000 prototypes. Results reported represent averages from a five-fold cross-validation scheme over Einsiedeln corpus. filters per convolution and different kernel sizes. In addition, we consider non-squared input sizes, restricting any of the dimensions to 51. The results of this experiment are reported in Table 4.  
The results confirm that these parameters have a less influence than the previous ones on the accuracy, although their relevance is still high for the computation time. Initially, the base CNN improved by adding more filters--to some extent--while the best results maintained smaller kernel sizes. The upward trend of the computational cost is also clear with respect to increasing the number of filters and the size of the kernel, suggesting a much stronger influence on the part of the former. It is also appreciated that considering non-squared image sizes can be beneficial, as the results vary considerably in this regard. This fact is not accidental, as the relevant information to distinguish the category of a pixel is usually found on the horizontal (for example, in the case of text) or the vertical (for example, to find the staff lines) axes of such pixel, so the information of the diagonal neighborhoods is less relevant. The best result in terms of accuracy is obtained when 256 filters per convolution are established, with a kernel size of \(3\times 3\), and input blocks of \(51\times 101\) (height and width, respectively). This configuration improves the accuracy of the base CNN up 1%, from 86.9% to 88.0%. In our experiments, this neural configuration classified 900 pixels per second, on average. In the manuscripts considered (Table 1), this represents a cost of around 6 h to completely classify a whole page. Throughout these experiments, however, we did not make any comments about the time it takes for each model to train.