# Optical Medieval Music Recognition Using Background Knowledge
## 8 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Detection**} & \multicolumn{3}{c}{**Type**} & **Position in Staff** & \multicolumn{3}{c}{**Sequence**} \\
**Post-Processing** & **Archit.** & \(\textbf{F}_{1}^{all}\) & \(\textbf{F}_{1}^{note}\) & \(\textbf{F}_{1}^{clef}\) & \(\textbf{F}_{1}^{Accalis}\) & \(\textbf{Acc}_{ente}\) & \(\textbf{Acc}_{cldf}\) & \(\textbf{Acc}_{cont}\) & \(\textbf{Acc}_{cldf}\) & \(\textbf{hS}\) & \(\textbf{A}\) & \(\textbf{d}\)\(\textbf{SAR}\) & \(\textbf{m}\)\(\boldsymbol{AR}\) \\ \hline \multirow{3}{*}{no} & FCN & 98.3 & 98.4 & 93.3 & 3.0 & n/a & 96.4 & 96.7 & 1 & 93.0 & n/a & 84.4 \\  & Eff-b3 & 99.2 & 99.4 & 98.3 & 48.0 & n/a & 96.4 & 96.9 & 99.9 & 95.0 & n/a & 90.4 \\ \hline \multirow{3}{*}{yes} & FCN & 98.5 & 98.6 & 96.2 & 3.0 & n/a & 94.9 & 98.9 & 1 & 95.3 & n/a & 89.4 \\  & Eff-b3 & 99.3 & 99.4 & 99.1 & 46 & n/a & 96.1 & 98.9 & 1 & 97.0 & n/a & 93.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mixed model experiments on the Pa904 dataset with and without post-processing; that is, no training data for fine-tuning were used. Only the model of Table 4 was used for predictions and evaluated solely on the Pa904 dataset (all metrics in %). The recognition rate of the accidents is very low, especially with the FCN, since this was already low in the “mixed model” due to the low amount of training instances. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Model** & **Document Specific (Section 8.3)** & **Mixed Model (Section 8.4)** \\
**Architecture** & **FCN** & **Eff-b3** & **FCN** & **Eff-b3** \\ \hline Post-processing step (compare Section 5) & & & & \\ None & 88.8 & 90.5 & 84.4 & 90.4 \\ (1) Correct symbols in wrong layout blocks & 88.8+ & 90.5 & 84.5 & 90.4 \\ (2) Correct overlapping symbols & 89.3 & 90.6 & 84.7 & 90.5 \\ (3) Correct position in staff of cefs & 88.8 & 90.5 & 84.6 & 90.4 \\ (4) Correct missing clefs & 91.2 & 91.8 & 86.3 & 91.3 \\ (5) Correct looped graphical connection & n/a & n/a & 85.9 & 90.7 \\ (6) Correct PIS stacked notes & 91.3 & 93.2 & 87.8 & 92.5 \\ All combined & 94.6 & 95.8 & 89.4 & 93.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Influence of the individual post-processing steps on the mAR in % of the Pa904 dataset. Each post-processing step is evaluated individually. The entry marked with a plus has improved, but the improvement was too small to be shown in the table. Two models are evaluated: The “Document specific” model which adds a document specific fine-tuning to the mixed model and the “Mixed model”, without fine-tuning, which has been trained on different datasets and subsequently evaluated on this dataset. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & & **FCN** & **+/\(-\)** & **Eff-b3** & **+/\(-\)** \\ \hline Post-proc. & no & yes & no & yes \\ \hline TP (bsar) & 93.78 & 96.59 & & 94.55 & 97.42 \\ \hline \multirow{4}{*}{FN} & Missing Notes & 1.10 & 1.10 & 0\% & 0.93 & 0.74 & 20\% \\  & Wrong PiS & 2.08 & 0.74 & 64\% & 1.80 & 0.63 & 65\% \\  & Missing Clef & 0.14 & 0.10 & 28\% & 0.08 & 0.05 & 29\% \\  & Missing Acid & 0.16 & 0.16 & 0\% & 0.09 & 0.09 & 0\% \\ \hline \multirow{4}{*}{FP} & Sum & 3.48 & 2.10 & 39\% & 2.90 & 1.51 & 48\% \\ \cline{2-6}  & Add. Notes & 0.63 & 0.52 & 17\% & 0.71 & 0.39 & 45\% \\ \cline{1-1}  & Wrong PiS & 2.08 & 0.74 & 64\% & 1.80 & 0.63 & 65\% \\ \cline{1-1}  & Add. Clef & 0.04 & 0.03 & 9\% & 0.04 & 0.04 & 0\% \\ \cline{1-1}  & Add. Accid & 0 & 0 & 0\% & 0 & 0 & 0\% \\ \hline \multirow{4}{*}{FP} & Sum & 2.75 & 1.30 & 53\% & 2.55 & 1.06 & 59\% \\ \cline{1-1}  & Overall Sum & 6.23 & 3.40 & 45\% & 5.45 & 2.57 & 53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Listing of symbol segmentation error types of the models and their quantity in %. The +/\(-\) columns indicate the improvement percentage by which the error type can be reduced by post-processing. The best performing model of the “FCN” and the “Eff-b3” architecture were used (fine-tuning + post-processing).