Abstract
Image binarization is a common operation in the preprocessing stage in most Optical Music Recognition (OMR) systems. The choice of an appropriate binarization method for handwritten music scores is a difficult problem. Several works have already evaluated the performance of existing binarization processes in diverse applications. However, no goal-directed studies for music sheets documents were carried out. This paper presents a novel binarization method based in the content knowledge of the image. The method only needs the estimation of the staffline thickness and the vertical distance between two stafflines. This information is extracted directly from the gray level music score. The proposed binarization procedure is experimentally compared with several state of the art methods.

Abstract
Ordinal data classification (ODC) has a wide range of applications in areas where human evaluation plays an important role, ranging from psychology and medicine to information retrieval. In ODC the output variable has a natural order, however, there is not a precise notion of the distance between classes. The recently proposed method for ordinal data, Kernel Discriminant Learning Ordinal Regression (KDLOR), is based on Linear Discriminant Analysis (LDA), a simple tool for classification. KDLOR brings LDA to the forefront in the ODC field, motivating further research. This paper compares three LDA based algorithms for ODC. The first method uses the generic framework of Frank and Hall for ODC instantiated with a kernel version of LDA. Similarly, the second method is based on the also generic Data Replication framework for ODC instantiated with the same kernel version of LDA. Both the Frank and Hall and Data Replication methods address the ODC problem by the use of a base binary classifier. Finally, the third method under comparison is KDLOR. The experiments are carried out on synthetic and real datasets. A comparison between the performances of the three systems is made based on t-statistics. The performance and running time complexity of the methods do not support any advantage of KDLOR over the other two methods. © 2012 IEEE.

Abstract
While ordinal classification problems are common in many situations, induction of ordinal decision trees has not evolved significantly. Conventional trees for regression settings or nominal classification are commonly induced for ordinal classification problems. On the other hand a decision tree consistent with the ordinal setting is often desirable to aid decision making in such situations as credit rating. In this work we extend a recently proposed strategy based on constraints defined globally over the feature space. We propose a bootstrap technique to improve the accuracy of the baseline solution. Experiments in synthetic and real data show the benefits of our proposal. © 2011 IEEE.

Abstract
For centuries, music has been shared and remembered by two traditions: aural transmission and in the form of written documents normally called musical scores. Many of these scores exist in the form of unpublished manuscripts and hence they are in danger of being lost through the normal ravages of time. To preserve the music some form of typesetting or, ideally, a computer system that can automatically decode the symbolic images and create new scores is required. Programs analogous to optical character recognition systems called optical music recognition (OMR) systems have been under intensive development for many years. However, the results to date are far from ideal. Each of the proposed methods emphasizes different properties and therefore makes it difficult to effectively evaluate its competitive advantages. This article provides an overview of the literature concerning the automatic analysis of images of printed and handwritten musical scores. For self-containment and for the benefit of the reader, an introduction to OMR processing systems precedes the literature overview. The following study presents a reference scheme for any researcher wanting to compare new OMR algorithms against well-known ones. © 2012, Springer-Verlag London Limited.

Abstract
Ordinal classification is a form of multiclass classification for which there is an inherent order between the classes, but not a meaningful numeric differerence between them. The performance of such classifiers is usually assessed by measures appropriate for nominal classes or for regression. Unfortunately, these do not account for the true dimension of the error. The goal of this work is to show that existing measures for evaluating ordinal classification models surffer from a number of important shortcomings. For this reason, we propose an alternative measure defined directly in the confusion matrix. An error coefficient appropriate for ordinal data should capture how much the result diverges from the ideal prediction and how "inconsistent" the classifier is in regard to the relative order of the classes. The proposed coefficient results from the observation that the performance yielded by the Misclassification Error Rate coefficient is the benefit of the path along the diagonal of the confusion matrix. We carry out an experimental study which confirms the usefulness of the novel metric.

Abstract
Although Optical Music Recognition (OMR) has been the focus of much research for decades, the processing of handwritten musical scores is not yet satisfactory. The efforts made to find robust symbol representations and learning methodologies have not found a similar quality in the learning of the dissimilarity concept. Simple Euclidean distances are often used to measure dissimilarity between different examples. However, such distances do not necessarily yield the best performance. In this paper, we propose to learn the best distance for the k-nearest neighbor (k-NN) classifier. The distance concept will be tuned both for the application domain and the adopted representation for the music symbols. The performance of the method is compared with the support vector machine (SVM) classifier using both real and synthetic music scores. The synthetic database includes four types of deformations inducing variability in the printed musical symbols which exist in handwritten music sheets. The work presented here can open new research paths towards a novel automatic musical symbols recognition module for handwritten scores. © 2011 IEEE.