Table 1
Grey values as measured along the lines reported in Fig.4 and fig.5 are plotted in Fig.6. A lower voltage gives a higher contrast between late and early wood in spruce, as well as other denser features such as purfling and material layers over the f-holes.
2.4. Detector Binning
The analysis of violin features has close similarities to defect detection and characterization in industrial manufacturing. As in cast or forged metal parts, the shapes and dimensions of “defects” are important char-acteristics. A crucial role is played by the voxel size: to be properly detected and measured, a feature should be at least 2-3 times larger than the voxel size. For a given multi-resolution CT system and a given violin, a smaller voxel size means also longer acquisition time and larger dataset to deal with. For the CT system used in this work, the dataset dimension for a whole violin scanned at 110 mm is around 24 GB.
Fig.6 Fig.4 Fig.5
Binning Options Combined pixels on the CCD Chip None
2 x 2 (4 pixels = 1) 3 x 3 (9 pixels = 1)
4 x 4 (16 pixels = 1)
Where 𝛮� is the number of voxels across the sample largest dimen-sion. This formula does not apply in the case of detector shift and/or in helical scans. After the scan, concerning the reconstruction part of the process, NSI efX proprietary software was used. With this soft-ware, it is possible to use filters and to set certain corrections, such as a beam hardening correction that reduces the beam hardening effect.
Lastly, the reconstructed volume was imported into Volume Graphics with a 16bit unsigned map, which is consistent with the acquired 16bit quality images (related to the detector used).
2.6. Multi-Material Surface Determination
Surface determination is a fundamental step in quantitative CT analy-ses. Every measurement performed on a CT volume requires a surface, defined as the separation between the part of interest and the sur-rounding material (e.g., air). Work-pieces can be composed by one or many components and/or made with materials with heterogeneous densities. Ebony fingerboard, filler materials or neck nails are exam-ples of components with densities that are very different from the rest of the bowed stringed instrument. Surfaces are therefore defined as the boundary between different components (such as top, back, bass-bar, neck graft and fingerboard) that can be made of the same or different materials. Even the same material can show great variation in density, such as early- and late-wood in the example of spruce, resulting in a locally heterogeneous material.
The simplest surface determination uses global thresholding algo-rithms [10]: for instance, a single grey value ISO50 can be assigned to the surface, calculated as the average of the background and material peak in the grey-value histogram (see Fig.10). Bowed stringed instruments are rarely made of homogeneous material, at least due to the inherent varia-tion in wood density. In their grey-value histograms, the region belong-ing to material exhibits at least a couple of peaks. This is evident in Fig.10, showing the frequency distribution of grey values for a region of inter-est in the violin, used in the examples shown above. If the low density peak is used, ISO50 will be closer to the background peak (see ISO501
in Fig.10). If the peak on the right is considered, ISO50 will be super-posed to the lower part of the material histogram (see ISO502 in Fig.10).
Rather than using a single ISO50 grey value, the so-called “local adaptive thresholding” [10] starts from an initially determined ISO50 surface and adapts it locally, defining the surface in correspondence with the grey value maximum gradient. Like other commercial software, VGStudio MAX 3.1 (Volume Graphics GmbH, Germany) uses its own proprietary algorithm for the so-called advanced surface determination. All the mea-surements and volume registrations presented in section 3 are based on this type of surface determination.
The same comparison is performed in Fig.9 in an axial section of the vio-lin back, showing the effect of voxel size in the representation of wood and defect features.
2.5. Other Parameters
The number of projection 𝛮� is the number of images used in a CT scan. A lower number of projections increases the artefacts and de-creases the image quality. The ISO 15708_3 suggests an estimate of the minimum number of projections as:
𝛮� > �2̶ ̶ . 𝛮� (6)
Fig.8 Coronal section of a violin back at three different voxel sizes: 447, 224 and 112 μm (4x-1x mode), from left to right.
Fig.9 Axial section of a violin back at three different voxel sizes: 447, 224 and 112 μm (4x-1x mode), from top to bottom
Fig.8
Fig.9
Global thresholding and advanced determination are used to define the surface of the same violin represented in Fig.8 and Fig.9. A detail of an axial slice of the back edge is shown in Fig.11. The corresponding ISO50 values are plotted as dash-point lines in the histogram in Fig.10. If the high-density peak is considered the refer-ence for the material (ISO502), lower density regions (such as early-growth wood in spruce) will be underestimated in dimension, with the creation of voids and recesses (see middle slice, showing a hole below the purfling). When using ISO501 (low-density peak, slice on the left), surfaces of high-density regions are overestimated. VGStudioMax 3.1 advanced surface determination algorithms create surfaces in the highest grey value gradient regions, and can also avoid the creation of unwanted voids and noise particles.
Fig.12 shows a 3D representation of the same ISO50 and advanced surfaces. The effect of thresholding can be extremely relevant for het-erogeneous materials such as spruce.
Determined surfaces can be exported as STL or point cloud files for reverse engineering or other applications.
3. CT Metrology
X-ray CT has proved to be a useful diagnostic tool in musical inst-rument making and restoration. It has also been used to document the condition of bowed stringed instruments. Non-contact systems like laser scanners and structured light scanners (LS) have positive advantages in terms of portability, device cost and fast acquisition time.
Fig.12
Fig.10
Fig.11
Fig.13
Fig.13 Test sample (right) vs a violin top plate (left), with superposed measurands.
Fig.14 Comparison between LS polygon surface (left) and CT determined surface (right) of the “soundboard” test sample.
Fig.14
both common characteristics of violin surfaces. Therefore, this type of surface should be covered with optically cooperative coatings, which is not always desirable for musical instruments.
Medical CT systems were already used for the reverse engineering of violins, as reported in “The Betts Project” [11]. This kind of applica-tion of medical CT is normally limited by its resoluapplica-tion. Industrial CT may overcome the limitations of medical CT thanks to higher resolution and better radiographic contrast.
The following sections focus on the application of industrial CT in the reverse engineering and measurement of bowed stringed instru-ments, and synthesize findings already presented in [12]. The aim of this work is to evaluate CT as a tool for the dimensional analysis of a violin soundboard. This part of the violin has been chosen because it presents a wide range of common problems related to the dimensional analysis of wooden free-form instruments such as violins or other strings.
3.1. Materials and Methods
We focused on comparing the performance of CT and LS when measur-ing a violin soundboard. In order to assess the accuracy of CT mea-surement results, a tactile coordinate measuring machine (CMM) was used as the reference. Tactile CMMs are well established in industrial coordinate metrology, due to their proven accuracy and to the availabil-ity of internationally accepted standards for performance verification and measurement uncertainty determination (ISO 10360 [13] and ISO 15530 [14]). However, when measuring free-form handmade objects like violins, because of the extreme variability of surface curvature and the presence of non-accessible features, tactile CMMs show several limitations, including the risk of damaging the instruments.
A test sample was designed (Fig.13, right) and machined from red spruce (Fiemme Valley, Italy) with a CNC milling machine. The test sample was conceived to include the typical features measured on a violin top plate, and to be tested by the three systems used in this re-search: CMM, LS and CT.
A set of measurands were defined, each representing a feature of the real violin soundboard, such as the overall dimensions, f-holes positions, plate thickness and elevation maps. In compliance with the similarity requirements stated in [14], the sample can be used to assess the measurement uncertainty for real violin top plates.
CT and structured light analysis of the test object were per-formed in the same conditions and with the same measuring procedure adopted for the analysis of the original violin component. The sample was measured with a ZEISS Prismo tactile CMM and scanned with the NSI X5000 CT system introduced earlier in this chapter. Finally, a set of surfaces was acquired by means of a structured light scanner
repeatability of CT measurements and the stability of the environmen-tal conditions during the scanning process.
Uncertainties according to ISO 15530-3 [14] have been calculated for all measured dimensions. After the uncertainty evaluation, a similar set of measurands were evaluated in a real violin belly (a Nicola Amati, Cremona, 1652); the results are reported in Table 3. In the last column, the uncertainties were calculated using an adapted approach of ISO 15530-3 as suggested in [15, 16], based on repeated CT measurements of the “soundboard” test sample, which was used in substitution of the real violin belly according to the substitution method [16], with refer-ence measurements performed by CMM.
The experimental findings demonstrate that CT provides better results, in terms of measurement repeatability and uncertainty, compared to LS. A major advantage provided by CT is the possibility of extracting information on the inner geometries of bowed stringed instruments, and being able to process dark and shiny surfaces. These types of measure-ment tasks, indeed, are not possible with traditional optical scanners without opening the instrument or altering its optical surface behaviour.
4. Conclusions
The application of industrial X-ray computed tomography to bowed stringed instruments has opened up new possibilities in material analysis, defect diagnostics and metrology of these musical instru- ments. In recent years, industrial CT systems have shown continuous improvements in terms of resolution, acquisition speed, image quality and dimensional accuracy.
Experimental investigations have shown that detector binning al-lows the creation of CT volumes of a complete violin at 0.4 mm voxel resolution in a matter of minutes, making it competitive with medical CT in terms of cost, but still providing better radiographic contrast and overall image quality. With higher voxel resolutions, experimental results showed that the quality of CT reconstructions is significantly enhanced, but at the cost of longer scan time.
When compared to medical scanners, industrial CT systems have great flexibility in terms of tube and detector parameters, as well as in geo-metrical magnification. The effect of these parameters on the final results has to be taken into account when setting them for a specific application.
Dimensional metrology of 3D surfaces is a promising application of industrial CT to bowed stringed instrument, where it has proved its Open Technologies Cronos 3D. For each measuring technique, three
repeated scans were performed. All the results (corresponding to the measurands) acquired with the different techniques were put in com-parison, together with their relative variability.
Deviations of CT and LS from the reference (CMM) were evalu-ated. Furthermore, the corresponding measurands of the inside surface of a Nicola Amati (Cremona, 1652) violin belly were measured using CT and LS. The outside surface of the violin top is too dark and shiny to be scanned with the chosen structured light scanner.
3.2. Results
Average value [mm] s [mm] D [mm]
Measurand CMM CT LS CT LS CT-CMM CT-LS
L1 99.974 99.819 100.144 14 129 26 350
L3 179.654 179.561 180.12 16 75 -92 466
L4 119.782 199.749 120.123 11 77 -33 341
L5 139.755 139.732 140.127 11 47 -23 372
L6 159.54 159.642 160.102 10 33 102 562
Measurands Value [mm] U�� [μm]
The results obtained for measurands L1, L3-L6 (see Fig.13) are reported in Table 2. Temperature and relative humidity were monitored through-out all measuring sessions. Comparing the results obtained with CMM, CT and LS provides several indications. The values from CT have an absolute deviation |Δ| from CMM values ranging from 92 to 102 µm.
LS constantly overestimates the measured dimensions, with a positive Δ deviation ranging from 350 to 560 µm.
Moreover, CT results have a significantly lower standard devia-tion with respect to LS: CT standard deviadevia-tions range from 10 to 16
Table 2
Table 3
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ac k n o w l e d G e M e n t S: The authors would like to thank Manuel Rigodanza for his contribution to the CT metrology application during his master thesis in Product Innovation Engineering at University of Padova, Dr. Valentina Aloisi (University of Padova) for her significant support in CT metrology, Fabrizio Rosi and Luca Passani (TEC-EUROLAB) for the CT and CMM activities, Walter Barbiero for structured light scanning, and Franco Simeoni for providing the Nicola Amati violin.