## 5 Experiments
### Staff Line Detection
#### 5.2.4 Data Amount  
In this section, the effect of increasing the amount of training examples is investigated. The results are summarised in Table 5. Each value is computed by first averaging all cross-folds of a single part and then taking the mean of all three respective experiments for all parts.  
As expected, if no additional data is available, an increasing number of training examples yields a higher \(F_{1}\) score. The model trained on only one page already detects staves with \(F_{1}^{\text{D}}=98.3\%\) and the length of a detected line matches with \(F_{1}^{\text{LF}}=96.9\%\). Applying data augmentation on this data improves the results significantly, resulting in a \(F_{1}^{\text{D}}\) of over 99% and a \(F_{1}^{\text{LF}}\) of 98.0% if one page is used. Using more pages slightly increases the total \(F_{1}\)-score up to 97.9%.  
Of course using a pretrained model on the remaining data (PT) or including the remaining data into the data set (Inc.) clearly outperforms the standard training without data augmentation. However, it shows that including the data is in general better than just using a pretrained model if only one or two pages are available, which makes this approach more robust for few pages. If more data is used the error differences are caused by the training process itself for instance by choosing the random seed for initialisation of the model. But it is to be expected that if many GT pages are available PT  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{**Detection**} & \multicolumn{3}{c}{**Length Fit**} \\  & **Train** & **Test** & **Prec.** & **Rec.** & \(F_{1}^{\text{D}}\) & **Prec.** & **Rec.** & \(F_{1}^{\text{LF}}\) & **Total F\({}_{1}\)** \\ \hline \multirow{4}{*}{\(F_{1}^{\text{LF}}\)-score} & 2, 3 & 1 & 1.000 & 1.000 & 1.000 & 0.977 & 0.990 & 0.983 & 0.983 \\  & 1, 3 & 2 & 0.986 & 0.993 & 0.990 & 0.982 & 0.995 & 0.988 & 0.978 \\  & 1, 2 & 3 & 1.000 & 0.978 & 0.988 & 0.990 & 0.990 & 0.990 & 0.978 \\ \hline \multirow{4}{*}{\(F_{1}^{\text{LF}}\)-score} & \multicolumn{3}{c}{Mean} & \multicolumn{3}{c}{0.993} & \multicolumn{3}{c}{0.987} & \multicolumn{3}{c}{0.980} \\  & 2, 3 & 1 & 1.000 & 1.000 & 1.000 & 0.976 & 0.993 & 0.984 & 0.984 \\  & 1, 3 & 2 & 0.959 & 0.978 & 0.968 & 0.968 & 0.997 & 0.982 & 0.951 \\  & 1, 2 & 3 & 0.989 & 0.967 & 0.977 & 0.988 & 0.995 & 0.991 & 0.969 \\ \hline \multicolumn{4}{c}{Mean} & \multicolumn{3}{c}{0.982} & \multicolumn{3}{c}{0.986} & \multicolumn{3}{c}{0.968} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparing staff line detection using cross data set training: Two parts are chosen for training while the remainder is chosen as the test data set. The training data is split into five cross folds (four folds training, one for validation) of which the average scores are shown. The total score is computed as the product of the individual \(F_{1}\)-scores. The lower half of the table shows the results when using data augmentation.  
is superior since the model can fit directly on the respective data. Data augmentation improves the results when PT is used, however not if the data is added to the dataset.  
In general, it is remarkable that using \(N_{\text{train}}=0\), that is, only using data of the other parts for training, yields very competitive results compared to any other experiment. Similar results are achieved if only training on one page of a single part but using data augmentation. Therefore, in practice it can be expected that the staff detection algorithm generalised well on unseen layouts.