# Optical Medieval Music Recognition Using Background Knowledge
## 8 Results
### Error Analysis  
The error distribution of the best performing \"FCN\" and \"Eff-b3\" model of the Pa 904 dataset is listed in Table 9. Both the error rate with and without post-processing is specified. The edit distance was used to count the number of insertions, deletions and replacements to obtain the Ground Truth sequence. Replacements are counted as one insertion and one deletion. Therefore, correctly segmented symbols, that were predicted with a wrong type (e.g., instead of a c-clef, an f-clef), are counted as two errors (FN and FP). In general, more errors are caused by missing symbols rather than by the detection of additional symbols. This is the case for the models without post-processing as well as for those with post-processing. The post-processing pipeline balances the ratio between FN and FP, but is still in favor of FN. Missing notes are one of the main errors of the symbol recognition. This was expected, since some of the documents are heavily affected by bleed-through noise. Because the contrast between the background and the symbols is sometimes too weak, this effect is intensified. In addition to that, symbols can protrude the text, often overlapping them, which means that they can only be recognized with the usage of context knowledge. After that, the most probable errors were wrongly predicted PIS of symbols with a relative amount of 24.5% (absolute 0.63%) in total (FP and FN). This is reasonable, because the decision if a note is, for example, on a staff line or between two lines can often only be decided based on context. Especially with single note neumes, it is difficult to correct PIS errors. Some first experiments were conducted using a simple language model with transitional probabilities of n-gram sequence pitches of the notes to correct those errors. However, we did not manage to incorporate this knowledge with a positive effect to the mAR, since it caused about the same number of errors that we were able to correct with it. Without post-processing, clefs were the third-largest source of error on average, with an error rate of about 0.12%. This is still high, considering that clefs usually occur at most 1-2 times per line. Using post-processing, the error-rate decreases by about 25%. That was also to be expected, since a missing clef, especially those at the beginning, can be corrected relatively well with background knowledge. Altogether, errors concerning accidentals occur the least, which is not surprising since they only occur very rarely. That is also the reason why additional accidentals are not recognized, since the network has to be very confident to segment an accidental. With the different encoder architectures, two things in particular could be observed: The more complex architectures recognize symbols better with a sufficient amount of training. Additionally, a finer localization of the note components could be observed when using these networks. This resulted in less PIS errors, since a poor localization of symbols sharing roughly the same horizontal position (this can, for example, be observed in a Podatus neume) can result in a sequence error. Moreover, reading order errors happen less, and are mainly caused by stacked NCs (e.g., a so-called PES or Scandicus neume), in which, e.g., the upper note is sung first because of a poor localization segmentation, but should in reality be sung later. Since it is very important to recognize the clef correctly because wrong or unrecognized clefs cause subsequent errors, these errors were examined more closely. Without post-processing, one-third to one-fourth of all clef errors were missing clefs in the beginning of a staff line. In most cases, the clefs are located close to the text, whereby it is missed or recognized as one symbol. Clef errors that can be attributed to drop capitals, as these are close to each other, amount to about 10%. That seems logical, since a clef often occurs after a drop capital and can cause errors as a result. The second most common mistakes are wrong symbol types in the staff.