## 6 Discussion  
Current state-of-the-art OMR technologies, which are based on Convolutional Recurrent Neural Networks (CRNN), typically follow an end-to-end approach that operates at the staff level: they map the series of symbols that appear in an image of a single staff to a sequence of music symbol labels. Most commonly, these methods consider an agnostic music representation that defines every symbol as a 2-tuple element that encodes its two graphic components: shape and height. However, as mentioned in Section 1, holistic OMR systems [12; 16; 20] do not take advantage of this double dimension since each possible combination of shape and height is represented as a unique category. This leads to a recognition formulation completely equivalent to the one used in fields as text recognition [21]; hence, the particularities of this data and notation are neglected in the framework. Nevertheless, we consider that exploitation of this trademark of music notation could increase the recognition rates, as recent work have provided insights about its benefits [22; 23; 24; 25]. Considering the end-to-end neural-based framework by [PERSON] et al. [20] as a starting point, we pose the following hypothesis: devoting independent CRNN schemes to separately exploit the two aforementioned graphical components of agnostic labeling and, in time, gathering them at the actual neural level might boost the overall performance of the model. In a practical sense, the considered CRNN architectures for each graphical component are equivalent to that of the starting point to perform a fair performance comparison between both the existing and proposed approaches. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**PreRNN**} & \multicolumn{2}{c}{**InterRNN**} & \multicolumn{2}{c}{**PostRNN**} \\ \cline{2-7}  & **Raw** & **Pretrained** & **Raw** & **Pretrained** & **Raw** & **Pretrained** \\ \hline Baseline & = & = & \(>\) & \(>\) & \(>\) & \(>\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical improvement over the base neural model of the different proposed schemes considering the Wilcoxon signed-rank test with a significance value of \(p<0.05\) for the symbol error rate metric. The symbols = and \(>\) represent that the error of the method in the row (the base neural architecture) is not significantly different or is significantly greater than that of the column, respectively. In this work, we empirically evaluated three different integration policies differing in the point in which the specialized branches are merged: the _PreRNN_, which merges the information after the convolutional stage; the _InterRNN_, which joins the different branches after a first recurrent layer; and the _PostRNN_, which gathers the information after a second recurrent stage. These architectures are evaluated on two collections of monophonic early music manuscripts, namely the _Capitan_ and the _Il Lauro Secco_ corpora. The results presented in Section 5 show that the merging point affects the performance, as both the _InterRNN_ and _PostRNN_ models significantly improve the results of the baseline considered. Moreover, the _InterRNN_ model yields the best overall performance, reducing the baseline error rate by 25.6% and 14.4% for the _Capitan_ and _Il Lauro Secco_ corpora, respectively. In spite of this benefit, the proposed framework entails an increase in the network complexity with respect to the base model considered. Nevertheless, this increase does not imply more training data as each part of the network is meant to specialize in certain features of the staff image. Moreover, regarding processing time, the increase in the complexity of the network does not affect the inference phase, as the different branches work concurrently. The main drawback in this case though is the training lapse, which is certainly expanded. However, note that this drawback is assumable given the remarkable error rate decrease with respect to the figures obtained with the baseline considered.