## 3 Methodology
### Recognition Architectures
#### 3.2.2 Proposed Approach  
This section presents the different neural architectures proposed for exploiting the individual shape and height properties when considering an agnostic representation of music notation. For that, we modify the base CRNN architecture introduced in Section 3.2.1 by adding different layers to adequately exploit such pieces of information with the aim of improving the overall recognition rate. More precisely, our hypothesis is that having two CRNN models that are specialized in retrieving the shape and height features may be beneficial with respect to having a unique system that deals with the task as a whole. The input staff image is individually processed by each model, and the different characteristics obtained by each single model may be gathered at some point of the neural model before the actual classification process. Based on that premise, we propose three different end-to-end architectures that basically differ on the point in which the two CRNN models are joined: (i) the _PreRNN_ one, which joins the extracted features by each model right before the recurrent block; (ii) the _InterRNN_ one, which performs this process after the first recurrent layer; and (iii) the _PostRNN_ one, which gathers both sources of information after the recurrent block. These proposals are graphically shown in Figure 3.  
As it may be noted, all models depict three differentiated parts. Out of these three parts, two of them constitute complete CRNN models specialized on a certain type of information (either shape or height) while the third one is meant to join the previous sources of information for eventual classification. These parts are thoroughly described below:  
* Shape branch: a first CRNN model that focuses on the holistic classification of musical symbols in terms of their shape labels. Its input is the initial staff \(x\in\mathcal{X}\), while its output is a sequence \(\mathbf{z}^{s}\in\Sigma_{5}^{s}\) of shape symbols. Figure 3: Graphicaldescription of the three CRNN-based architectures proposed. The _Concat_ block concatenates the input features from each branch. Gray layers represent the ones that are only considered during the training stage of the model. * Height branch: the other CRNN model devoted to recognition of the vertical position labels. In this case, a sequence \(\mathbf{z}^{h}\in\Sigma_{H}^{*}\) of height symbols is retrieved out of the initial staff \(x\in\mathcal{X}\). * Combined branch: the one that combines the extracted features of the other two branches to perform joint estimation of music symbols in terms of their combined <shape:height> labels. Thus, given an initial input staff \(x\in\mathcal{X}\), the branch retrieves a sequence \(\mathbf{z}\in\Sigma_{T}^{*}\) of combined labels. Note that all branches are separately trained using the same set of staves \(\mathcal{T}\) with the CTC learning algorithm, simply differing on the output vocabulary considered. This way, we somehow bias the different _shape_ and _height_ CRNN branches to learn specific features for those pieces of information, whereas in the case of the _combined_ branch, the training stage is expected to learn how to properly merge those separate pieces of information. In a practical sense, in this work, we consider two different policies for training the introduced models: a first scenario in which the parameters of the entire architecture are learned from scratch, i.e., we sequentially train the different branches without any particular initialization, and a second case in which the shape and height branches are separately trained and, after their convergence, the same procedure of the first scenario is reproduced. In this regard, we may assess how influential the initial training stage of the different branches of the scheme is on the overall performance of the system. It must be remarked that all proposed architectures perform the feature-merging operation after the convolutional block, having discarded other policies which may affect this stage.