## 2 Background  
Even though the term OMR encompasses a vast range of scenarios--research might vary depending on the music notation system or the engraving mechanism of the manuscripts--most of the existing literature is framed within a multi-stage pipeline that divides the challenge into a series of independent phases [26]. [PERSON] and [PERSON] [9] properly described and formalized the de facto standard workflow, which was later thoroughly reviewed by [PERSON] et al. [10]. This sequential pipeline comprises four main blocks: (i) _image preprocessing_, which aims at palliating problems mostly related to the scanning process and paper quality; (ii) _symbol segmentation and classification_, which focuses on the detection and actual labeling of different elements of the image meant to be recognized; (iii) _reconstruction of the music notation_, which postprocesses the recognition process; and (iv) an _output encoding_ stage that stores the recognized elements into a suitable symbolic format. In this work, we focus on the symbol segmentation and classification one.  
The inclusion of deep learning strategies in the OMR field produced a shift towards the use of end-to-end or holistic systems for symbol recognition [27]. Some examples of work addressing the recognition process at a staff level may be found in the literature for common Western notation [12; 16; 28; 29] as well as mensural [20], neumatic [30], and ancient organ tablature [31] handwritten music. While our proposal focuses on staff-line symbol recognition, it must be noted that research efforts are also devoted to addressing the issue of full-page recognition such as the proposal by [PERSON] et al. [21].  
In this context of staff-level holistic approaches for symbol recognition, most approaches rely on the use of architectures based on _Convolutional Recurrent Neural Networks_ (CRNN). Such schemes work on the premise of using the convolutional stage to learn the adequate features for the case at issue, with the recurrent part being devoted to modeling the temporal (or spatial) dependencies of the symbols. This type of design has been mainly exploited using _Sequence-to-Sequence_ (seq2 seq) architectures [22; 25] or considering the _Connectionist Temporal Classification_ (CTC) training mechanism [12; 16; 20; 28]. However, the work by [PERSON] et al. [25] shows that, when targeting the same handwritten corpus, CRNN-seq2 seq models are not competitive against CRNN trained with CTC.  
As previously introduced, music notation depicts a two-dimensional nature since each symbol is actually defined by a combination of a certain shape or glyph and its height or vertical position within the staff lines. While proven to be beneficial, this particularity has been rarely exploited in the literature, with some examples being the work by [PERSON] et al. [23], which shows that separately performing shape and height classification is beneficial in the context of isolated symbol classification of early music manuscripts; by [PERSON] and [PERSON] [22] and [PERSON] et al. [25], in which this conclusion was further reinforced in a context of CRNN-seq2 seq models; and by [PERSON] and [PERSON] [24], which also proved the validity of such an exploitation by integrating the shape and height information at a Language Model level, which was based on Hidden Markov Models rather than on the actual optical estimation.  
For all of the above, this paper presents a novel proposal that takes advantage of the two-dimensional nature of music symbols in the context of neural end-to-end OMR systems at the staff level. The basic premise in this case is that, instead of relying on a single CRNN scheme for processing each staff, we can devote two CRNN schemes to concurrently exploit the shape and height information and to eventually merge them at the actual neural level. As will be shown, this separate exploitation of the music symbol information provides a remarkable improvement in terms of recognition performance when compared to the baseline in which this duality is not considered.