## 3 Experiments
### Results
#### 3.3.3 Note Recognition  
To evaluate the performance of the proposed note recognition stage which contains two CNNs, another CNN system was used for comparison [21]. The system contained only a single CNN, which transcribes music frame-by-frame and returns a list of notes with pitches and onset. This system will be referred to as Sigtia. Actually, the note recognition stage can be treated as a piano transcription system, which takes no account of the individual to be transcribed. To make a comprehensive comparison, two state-of-the-art transcription methods were also used. Both were submitted to MIREX and evaluated in the task of piano tracking. [PERSON]'s method uses a variable-Q transform representation as input and employs probabilistic latent component analysis in transcription [42].  
Figure 7: Results of multi-pitch estimation (MPE): (**a–c**) the output of CNN, DNN, and RNN, respectively; (**d**) the corresponding ground truth piano roll representation.  
[PERSON]'s system is based on Microsoft's ResNet, and it has achieved the best performance in MIREX. For [PERSON]'s method, we trained a CNN using parameters he described in [21]. We have access to the code of [PERSON]'s method, and the second baseline system was implemented by the code. For [PERSON]'s system, the results were obtained from the transcription software named AnthemScore [43].  
All of the note-based results of transcription are presented in Table 3. In general, the performance of the proposed note recognition stage is acceptable. Among these four methods, [PERSON] approach performed the worst on each evaluation measure. This is because [PERSON] model is trained for multiple instruments instead of piano, and the pre-shifted templates are not helpful for piano transcription. The proposed note recognition module outperformed [PERSON]'s method on all evaluation metrics, which indicates that two independent CNNs are superior to a single one in AMT. [PERSON]'s method yielded the best performance, and it outperformed us by only 0.14% on F-measure. On the metrics of precision, our proposed note recognition stage was inferior to [PERSON]'s system. Therefore, we can use a note verification stage to reduce the false positive notes and improve the precision of transcription.  
Figure 8 shows the transcription of the MAPS_MUS-bk_xmas5_ENSTDkCl excerpt using the top two systems in Table 3. The corresponding ground truth has been shown in Figure 7d. Compared with the ground truth, the false positive notes are marked using red crosses and the false negative notes are marked using a blue dashed line. We can observe that the onset of notes in Figure 8a are detected more accurately than that in Figure 8b. This can be attributed to the CNN for onset detection in our system. In the excerpt's first 8.8 s, the transcription result of [PERSON]'s system is better than that of our two consecutive CNNs. There are eight false negative errors and five false positive errors in Figure 8a. Correspondingly, there are only three false negative notes and two false positive notes in Figure 8b. One solution to reduce the false negative errors is to apply a small threshold to the output of the second CNN. This will bring more false positive notes, so an additional note verification stage is necessary. In the excerpt's last 1.2 s, the performance of our note recognition stage was much better than [PERSON]'s system. As the duration of notes here are short, the accurate onset is essential for transcribing them. This also indicates the advantage of our CNNs on short-note transcription.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Recall** & **Precision** & **F-Measure** \\ \hline CNNs & 0.7524 & 0.8593 & 0.8023 \\ Sigtia & 0.6786 & 0.8023 & 0.7353 \\ Benetos & 0.5857 & 0.6305 & 0.6073 \\ Troxel & 0.7477 & 0.8687 & 0.8037 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance on piano transcription.