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TaBLE 1: Success rates of the extraction algorithm for samples written in the notation styles of Britto and Sanz. he distance of the contour points to the centroid, a fixed sercentage of the wavelet transform coefficients, the Fourier ransform coefficients and the two sets of angular-radial ransform coefficients. Three different values of neighbors « have been employed: 1, 3, and 5. In Table 2, the correct classification rates are shown.

Table 1 Success rates of the extraction algorithm for samples written in the notation styles of Britto and Sanz. he distance of the contour points to the centroid, a fixed sercentage of the wavelet transform coefficients, the Fourier ransform coefficients and the two sets of angular-radial ransform coefficients. Three different values of neighbors « have been employed: 1, 3, and 5. In Table 2, the correct classification rates are shown.

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Ficure 1: Fragments of scores in white mensural notation showing the two different notation styles analyzed in this work.
Ficure 1: Fragments of scores in white mensural notation showing the two different notation styles analyzed in this work.
Frcure 3: Examples of the most common imperfections encountered in digitized images. From (a) to (b): extraneous elements, fungi and mold darkening the background, unaligned staves and folds, and distorted staves due to the irregular leveling of the sheet.
Frcure 3: Examples of the most common imperfections encountered in digitized images. From (a) to (b): extraneous elements, fungi and mold darkening the background, unaligned staves and folds, and distorted staves due to the irregular leveling of the sheet.
Figure 4: Example of the selection of the active area. (a) selection of the polygon; (b) results of the rectangular minimal area retrieval
Figure 4: Example of the selection of the active area. (a) selection of the polygon; (b) results of the rectangular minimal area retrieval
Figure 5: Example of blanking unessential red elements. (a) original score. (b) processed image.
Figure 5: Example of blanking unessential red elements. (a) original score. (b) processed image.
Figure 6: Example of compensation of the illumination. (a) original image (grayscale); (b) grid for the estimation of the illumination (45 cells), the location of the data points used to interpolate the illumination mask is marked; (c): average illumination levels of each cell; (d) illumination mask with interpolated illumination levels.
Figure 6: Example of compensation of the illumination. (a) original image (grayscale); (b) grid for the estimation of the illumination (45 cells), the location of the data points used to interpolate the illumination mask is marked; (c): average illumination levels of each cell; (d) illumination mask with interpolated illumination levels.
the image of a score where the parameters described are indicated. 3.1.1. Estimation of the Thickness of the Staff Lines. Now, we consider that the preliminary corrections of image distortions are sufficient to permit a proper detection of the thickness of the lines. In Figure 10, two examples of the shape of row histograms for distorted and corrected images of the same staff are shown. In Figure 10(a), the lines are widely superimposed and their discrimination is almost impossible, unlike the row histogram in Figure 10(b). In this case, the K-means algorithm [21] is applied to the distances between consecutive local maxima of the histogram over the histogram threshold to find two clusters. The centroids of these clusters, represent the average distance between the staff lines and the average distance between the staves. The histogram threshold is obtained using the technique described in the previous task (task 1) of the isolation of staves procedure).
the image of a score where the parameters described are indicated. 3.1.1. Estimation of the Thickness of the Staff Lines. Now, we consider that the preliminary corrections of image distortions are sufficient to permit a proper detection of the thickness of the lines. In Figure 10, two examples of the shape of row histograms for distorted and corrected images of the same staff are shown. In Figure 10(a), the lines are widely superimposed and their discrimination is almost impossible, unlike the row histogram in Figure 10(b). In this case, the K-means algorithm [21] is applied to the distances between consecutive local maxima of the histogram over the histogram threshold to find two clusters. The centroids of these clusters, represent the average distance between the staff lines and the average distance between the staves. The histogram threshold is obtained using the technique described in the previous task (task 1) of the isolation of staves procedure).
‘IGURE 8: Example of the application of the Hough transform on a score. The original image (a) and its Hough transform in 2D (b) and 3D c) views. The two sets of peaks corresponding to ~180° and ~270° are marked.
‘IGURE 8: Example of the application of the Hough transform on a score. The original image (a) and its Hough transform in 2D (b) and 3D c) views. The two sets of peaks corresponding to ~180° and ~270° are marked.
Ficure 9: Row histograms computed on a sample score (b). Row histograms for white and black pixels are plotted in (a) and (c), respectively.
Ficure 9: Row histograms computed on a sample score (b). Row histograms for white and black pixels are plotted in (a) and (c), respectively.
Ficure 10: Example of the influence of the distortion of the image on the row histograms.
Ficure 10: Example of the influence of the distortion of the image on the row histograms.
Figure 11: Example of the determination of the threshold for the row histogram: The detection threshold is the arithmetic mean betwee: the centroids of the second and the third clusters, obtained using K-means.
Figure 11: Example of the determination of the threshold for the row histogram: The detection threshold is the arithmetic mean betwee: the centroids of the second and the third clusters, obtained using K-means.
Figure 14: The height of the staff is computed on the basis of the line thickness, the line distances and the staff distances.
Figure 14: The height of the staff is computed on the basis of the line thickness, the line distances and the staff distances.
Fircure 12: Example of the process of detection of the thickness of the lines. For each peak (in the image only the first peak is treated as example), the distance between the two points of intersection with the fixed threshold is computed. The distances extracted are used in a K-means clustering stage, with two clusters, to obtain a measure of the thickness of the lines of the whole staff.
Fircure 12: Example of the process of detection of the thickness of the lines. For each peak (in the image only the first peak is treated as example), the distance between the two points of intersection with the fixed threshold is computed. The distances extracted are used in a K-means clustering stage, with two clusters, to obtain a measure of the thickness of the lines of the whole staff.
Figure 13: Example of the process of detection of the distance between the staff lines and between the staves. After the threshold is fixed, the distances between the points of intersection with the thresholds are obtained and a clustering process is used to group the values regarding the same measures.
Figure 13: Example of the process of detection of the distance between the staff lines and between the staves. After the threshold is fixed, the distances between the points of intersection with the thresholds are obtained and a clustering process is used to group the values regarding the same measures.
FIGURE 15: Example of the usage of the row histogram of the white pixels to detect errors in the computation of the staff position. In (a) the staff is correctly extracted and the first and the last row histogram values are equal to the maximum. In (b), the staff is badly cut and the value of the histogram of the last row is smaller than the maximum value.
FIGURE 15: Example of the usage of the row histogram of the white pixels to detect errors in the computation of the staff position. In (a) the staff is correctly extracted and the first and the last row histogram values are equal to the maximum. In (b), the staff is badly cut and the value of the histogram of the last row is smaller than the maximum value.
Absolute frequency (white pixels per row)
Absolute frequency (white pixels per row)
(b) Column histogram of the black pixels. The threshold (solid line), the minima under the threshold (circles), the line that divide the staff in equal parts (thick line) and the optimal division lines found (dashed lines) are shown. The arrows show the shift from the initial position of the division lines to their final location.
(b) Column histogram of the black pixels. The threshold (solid line), the minima under the threshold (circles), the line that divide the staff in equal parts (thick line) and the optimal division lines found (dashed lines) are shown. The arrows show the shift from the initial position of the division lines to their final location.
(a) Sample staff with optimal vertical divisions (dashed line)
(a) Sample staff with optimal vertical divisions (dashed line)
Ficure 17: An example of the correction of the rotation of staff fragments: the inclination values of the fragments of the staff (a) are detected using the Hough transform and corrected (b).
Ficure 17: An example of the correction of the rotation of staff fragments: the inclination values of the fragments of the staff (a) are detected using the Hough transform and corrected (b).
Figure 18: Moving window used to track the staff lines. The window is shifted rightward and vertically, depending on the amount of black pixels in it.
Figure 18: Moving window used to track the staff lines. The window is shifted rightward and vertically, depending on the amount of black pixels in it.
Ficure 20: Blanking of extraneous elements. (a) Initial staff fragment. (b) Staff fragment after the removal of the extraneous elements. Figure 19: An example of blanking the staff lines. (a) original image. (b) processed image.
Ficure 20: Blanking of extraneous elements. (a) Initial staff fragment. (b) Staff fragment after the removal of the extraneous elements. Figure 19: An example of blanking the staff lines. (a) original image. (b) processed image.
Ficure 21: Row and column histograms for two differently tagged fragments of a half-note. Both, column and row histograms, are partially overlapped.
Ficure 21: Row and column histograms for two differently tagged fragments of a half-note. Both, column and row histograms, are partially overlapped.
FiGurE 22: Two examples of music symbols composed by horizontal bands. The key of C and the double whole (shaded areas in the staff).
FiGurE 22: Two examples of music symbols composed by horizontal bands. The key of C and the double whole (shaded areas in the staff).
FicureE 23: Row and Column histograms for two differently tagged fragments of a double whole. Column histograms are nearly completely overlapped, while the row ones are separated a distance which is smaller than the separation between the staff lines.
FicureE 23: Row and Column histograms for two differently tagged fragments of a double whole. Column histograms are nearly completely overlapped, while the row ones are separated a distance which is smaller than the separation between the staff lines.
Ficure 24: Example of the processing stages aimed to track the contour of a half-note.
Ficure 24: Example of the processing stages aimed to track the contour of a half-note.
IGURE 25: Figure 25: Example of the process aimed to extract the coordinates of the contour of a symbol. The dilation of the complex ructure of the G clef leads to the presence of a hole, that has to be corrected before edge tracking.
IGURE 25: Figure 25: Example of the process aimed to extract the coordinates of the contour of a symbol. The dilation of the complex ructure of the G clef leads to the presence of a hole, that has to be corrected before edge tracking.
Figure 26: A half-note symbol represented in a polar reference system, suitable for the calculation of the ART coefficients.
Figure 26: A half-note symbol represented in a polar reference system, suitable for the calculation of the ART coefficients.
Figure 28: An example of incorrectly extracted symbols. Line fragments link two notes. Figure 27: Example of the determination of the line/space membership of a quarter-note (in gray) for pitch detection. The row histogran of the black pixels of the note (dashed line) shows a maximum close to the third line, identified by the third peak of the row histogram of th black pixels of the staff (solid line).
Figure 28: An example of incorrectly extracted symbols. Line fragments link two notes. Figure 27: Example of the determination of the line/space membership of a quarter-note (in gray) for pitch detection. The row histogran of the black pixels of the note (dashed line) shows a maximum close to the third line, identified by the third peak of the row histogram of th black pixels of the staff (solid line).
TABLE 2: Correct classification rates for the k-NN method for symbols correctly extracted and partially extracted. The methods employed for the extraction of the vectors of features are: the Fourier descriptor, with the edge function computed by distance from the centroid (FD1), the Wavelet transform coefficients (WTC), the Fourier transform coefficients (FTC) and the two sets of angular-radial transform coefficients based on center of gravity of the edges (ART1) and on the center of the bounding box (ART2).
TABLE 2: Correct classification rates for the k-NN method for symbols correctly extracted and partially extracted. The methods employed for the extraction of the vectors of features are: the Fourier descriptor, with the edge function computed by distance from the centroid (FD1), the Wavelet transform coefficients (WTC), the Fourier transform coefficients (FTC) and the two sets of angular-radial transform coefficients based on center of gravity of the edges (ART1) and on the center of the bounding box (ART2).
TABLE 3: Correct classification rates for the classifier based on the Mahalanobis distance. The vectors of features are obtained from the angular-radial transform coefficients, with reference on the center of gravity of the contour (ART1) and on the center of the bounding box (ART2).
TABLE 3: Correct classification rates for the classifier based on the Mahalanobis distance. The vectors of features are obtained from the angular-radial transform coefficients, with reference on the center of gravity of the contour (ART1) and on the center of the bounding box (ART2).
TABLE 4: Correct classification rates for the Fisher method for both the symbols correctly extracted and partially extracted. The vectors of features employed are the Fourier descriptors of the distance to the centroid of the contour points (FD1) and the two sets of angular-radial transform coefficients with center at the centroid of the contour and at the center of bounding box, ART1 and ART2, respectively. The choice of the membership is done using a k-NN and Gaussian approach. score in modern notation and, with minimum changes, the score in white mensural notation can also be obtained [49]. Additionally, the program can also generate the MIDI file of the typed score [50] so that the recognized score can be listened. represent western music notation from the 17th century onwards. WEDELMUSIC [45] is a XML compliant format which can include the image of the score and an associated WAV or MIDI file and it is mainly aimed to support the development of new emerging applications. GUIDO [46] is a general purpose language for representing scores. More recently, MPEG-SMR (Symbolic Music Representation) [47] aims to become a real standard to cope with computer music representation and the related emerging needs of new interactive music applications.
TABLE 4: Correct classification rates for the Fisher method for both the symbols correctly extracted and partially extracted. The vectors of features employed are the Fourier descriptors of the distance to the centroid of the contour points (FD1) and the two sets of angular-radial transform coefficients with center at the centroid of the contour and at the center of bounding box, ART1 and ART2, respectively. The choice of the membership is done using a k-NN and Gaussian approach. score in modern notation and, with minimum changes, the score in white mensural notation can also be obtained [49]. Additionally, the program can also generate the MIDI file of the typed score [50] so that the recognized score can be listened. represent western music notation from the 17th century onwards. WEDELMUSIC [45] is a XML compliant format which can include the image of the score and an associated WAV or MIDI file and it is mainly aimed to support the development of new emerging applications. GUIDO [46] is a general purpose language for representing scores. More recently, MPEG-SMR (Symbolic Music Representation) [47] aims to become a real standard to cope with computer music representation and the related emerging needs of new interactive music applications.
Figure 29: Original images for the recognition and transcription example.
Figure 29: Original images for the recognition and transcription example.
Ficure 30: Sample Lilypond code (ASCII) to engrave the score in white mensural notation and in modern notation.
Ficure 30: Sample Lilypond code (ASCII) to engrave the score in white mensural notation and in modern notation.
Figure 31: Scores transcribed in both white mensural notation and modern notation of the original score shown in Figure 29.
Figure 31: Scores transcribed in both white mensural notation and modern notation of the original score shown in Figure 29.
Related topics:
Computer ScienceOptical Music RecognitionElectrical and Electronic Engineering
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