# 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
The training time depends on multiple factors such as the convergence of the model, the size of the training set, the network model, and the underlying hardware. In our experiments, the training time ranged from half an hour, for the simplest cases, up to 10 h, being the size of the input patch the most relevant factor in this regard. Although the training time may become important in some scenarios because it imposes restrictions on parameter optimization and evaluation, \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(\text{F}_{1}^{\text{M}}\) (\%)} & \multicolumn{4}{c}{**Pixels (\(\times 10^{9}\)) Per Second**} \\ \cline{3-11}
**Input Size (px)** & **Number of Filters** & \multicolumn{4}{c}{**Kernel Size (px)**} & \multicolumn{4}{c}{**Kernel Size (px)**} \\ \cline{3-11}  & & **3 \(\times\) 3** & **5 \(\times\) 5** & **7 \(\times\) 7** & **9 \(\times\) 9** & **11 \(\times\) 11** & **3 \(\times\) 3** & **5 \(\times\) 5** & **7 \(\times\) 7** & **9 \(\times\) 9** & **11 \(\times\) 11** \\ \hline \(51\times 51\) & & 86.0 & 87.2 & 86.9 & 85.6 & 86.6 & 7 & 6 & 6 & 5 & 5 \\ \(51\times 75\) & & 85.1 & 86.4 & 86.7 & 84.5 & 86.0 & 6 & 5 & 4 & 4 & 3 \\ \(75\times 51\) & 32 & 86.0 & 86.6 & 86.2 & 86.7 & 86.1 & 6 & 5 & 4 & 4 & 3 \\ \(51\times 101\) & & 86.9 & 86.7 & 86.8 & 85.4 & 86.4 & 5 & 4 & 4 & 3 & 3 \\ \(101\times 51\) & & 86.6 & 86.6 & 86.3 & 84.7 & 85.7 & 4 & 4 & 4 & 3 & 3 \\ \hline \(51\times 51\) & & 86.6 & 85.5 & 87.0 & 86.1 & 85.4 & 5 & 4 & 4 & 3 & 3 \\ \(51\times 75\) & & 87.8 & 86.5 & 83.8 & 83.3 & 84.3 & 4 & 3 & 3 & 2 & 2 \\ \(75\times 51\) & 64 & 86.5 & 86.3 & 86.3 & 85.8 & 85.6 & 3 & 3 & 3 & 2 & 2 \\ \(51\times 101\) & & 86.8 & 85.6 & 84.8 & 81.7 & 86.0 & 3 & 3 & 2 & 2 & 2 \\ \(101\times 51\) & & 87.7 & 87.2 & 87.6 & 84.8 & 87.1 & 3 & 3 & 2 & 2 & 2 \\ \hline \(51\times 51\) & & 87.0 & 87.0 & 87.5 & 87.7 & 86.8 & 3 & 3 & 2 & 1 & 1 \\ \(51\times 75\) & & 87.5 & 85.5 & 86.5 & 87.1 & 86.4 & 2 & 2 & 1 & 1 & 1 \\ \(75\times 51\) & 128 & 86.9 & 85.4 & 87.0 & 84.6 & 83.7 & 2 & 2 & 1 & 1 & 1 \\ \(51\times 101\) & & 87.3 & 86.7 & 86.5 & 86.6 & 85.4 & 2 & 2 & 0.9 & 0.8 & 0.8 \\ \(101\times 51\) & & 86.3 & 85.4 & 84.1 & 86.6 & 86.2 & 2 & 2 & 0.9 & 0.9 & 0.8 \\ \hline \(51\times 51\) & & 86.5 & 87.5 & 86.0 & 86.8 & 86.7 & 2 & 1 & 1 & 0.6 & 0.5 & 0.5 \\ \(51\times 75\) & & 87.7 & 87.4 & 87.0 & 85.8 & 85.1 & 1 & 1 & 0.6 & 0.5 & 0.5 \\ \(75\times 51\) & 256 & 87.0 & 86.7 & 86.7 & 84.9 & 86.8 & 1 & 1 & 0.6 & 0.5 & 0.5 \\ \(51\times 101\) & & 88.0 & 85.3 & 87.4 & 87.4 & 82.8 & 0.9 & 0.9 & 0.5 & 0.4 & 0.3 \\ \(101\times 51\) & & 87.6 & 86.1 & 86.7 & 87.0 & 85.5 & 0.9 & 0.9 & 0.5 & 0.4 & 0.3 \\ \hline \(51\times 51\) & & 87.0 & 85.1 & 82.7 & 84.0 & 85.1 & 0.8 & 0.7 & 0.3 & 0.1 & 0.1 \\ \(51\times 75\) & & 85.2 & 84.8 & 83.6 & 81.3 & 86.2 & 0.6 & 0.5 & 0.1 & 0.1 & 0.1 \\ \(75\times 51\) & 512 & 87.4 & 87.2 & 86.4 & 86.6 & 85.9 & 0.6 & 0.5 & 0.1 & 0.1 & 0.06 \\ \(51\times 101\) & & 86.4 & 84.7 & 82.0 & 85.8 & 86.0 & 0.4 & 0.4 & 0.1 & 0.1 & 0.04 \\ \(101\times 51\) & & 87.1 & 86.9 & 86.0 & 72.7 & 81.9 & 0.5 & 0.4 & 0.1 & 0.1 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results in terms of \(\text{F}_{1}^{\text{M}}\) and pixels per second of the different configurations. All CNN were configured to five layers and one convolution per layer. Results reported represent averages from a five-fold cross-validation scheme over Einsiedlen corpus. in this article, we are more concerned about the network topology and the parameter values that allow to achieve the best accuracy in our corpora.