## 4 Results and Discussion
In this case, the staff line needs to be interpolated/reconstructed, but the scheme proposed did not perform the interpolation properly or did not perform the interpolation at all. * False detection: at a certain location, the scheme presented marked a pixel as corresponding to a staff line and the binary image presented a level corresponding to the image foreground but a pixel of a ground truth staff line was not found at a close vertical position. * False interpolation: at a certain location, the scheme presented marked a pixel as corresponding to a staff line, the binary image presented a level corresponding to the image background at the same location and no ground truth staff line pixel was found at a close vertical position. Note that additionally, we will use the term 'correct reconstruction' to refer to the union of the sets with correctly detected and correctly interpolated staff pixels. Figure 9: Example of staff line ground truth data drawn on the original image. Sample excerpt. Due to the way in which they are created, the ground truth staff lines may not lay at the vertical center of the images' staff lines. Consequently, in order to perform the evaluation, this fact is taken into account by considering correct detection and interpolation when the ground truth pixel is at a position that is close to the reconstructed pixel in the vertical direction, namely, the maximum vertical separation allowed for that estimated average staff line width at the current image. The behavior of such vertical distance between the ground truth pixels and the detected pixels was observed in order to gather some detailed information about it. The histogram found is shown in Figure 10. This figure shows that the maximum separation allowed between the ground truth and the reconstructed staves is enough to embrace all the situations that can happen in our scheme (note that the estimated thickness of the staff lines ranges between 6.50 and 12.86 px, with 10.25 as global average) and that the ground truth is mostly correctly created with its staff lines running through the vertical center of the (reconstructed) staff lines or displaced only 1 pixel in most cases. Regarding the separation between staff lines, the estimated average separation between them in a staff ranges between 51.33 and 62.506 px, with 62.04 on average. The result of the evaluation of the performance of the scheme developed using the described ground truth is shown in Table 3. Observe that the percentage of staff line pixels (all the pixels in the reconstructed staff lines) is very close to 100%: 98.10%, this difference is partly due to the slightly smaller length of the reconstructed staff lines that the scheme produces. Note that this number could also be larger than 100% if the number of reconstructed staff line pixels becomes larger than the number of ground truth pixels. The percentage of correctly detected pixels, which includes correctly detected and interpolated pixels, is also close to 100%: 97.55%. This fact points that the system performs correctly. Observe that \begin{table}
\begin{tabular}{l c} \hline Staves & 69 \\ \hline Staff lines & 276 \\ \hline Total \# control points & 3919 \\ \hline Mean control points per staff line & 14.2 \\ \hline Standard deviation of \# control points per staff line & 3.31 \\ \hline Minimum \# control points per staff line & 6 \\ \hline Maximum \# control points per staff line & 21 \\ \hline Mean control points per staff & 56.8 \\ \hline Standard deviation of \# control points per staff line & 12.8 \\ \hline Minimum \# control points per staff line & 24 \\ \hline Maximum \# control points per staff line & 83 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the ground truth data creation parameters.