Figure 1
Different measurement solutions: (a) simple ‘crackmeter’ (source: www.avongard.com), (b) measurement solution of SHM-X company (source: www.shmsystem.pl), (c) electronic extensometers in a 3D measurement system and (d) SisGeo linear extensometer (source: www.sisgeo.com).
Figure 2
Block diagram of the procedure determining displacement parameters
Figure 3
Pattern image used for calibration
Figure 4
An example of an image used for camera calibration: (a) original image, (b) image with detected and numbered dots and (c) image with residual error and scale in pixels
Figure 5
QR codes with coded text information: (a) ‘MQR: N:00001 S:50.00’ (marker number: 00001; size: 50.00 mm × 50.00 mm) and (b) ‘MQR: N:00002 S:50.00’ (marker number: 00002; size: 50.00 mm × 50.00 mm).
Figure 6
Illustration of geometric transformations made to set down NMI
Figure 7
Diagram of a geometric system in which markers were photographed
Figure 8
Distribution of a probability density function concerning determined mutual position values of markers, based on photos taken for Case A (blue) and Case B (orange)
Table 1
Case A (number of pictures: 42; number of analysed pairs of pictures: 439)
| Average | Standard deviation | Minimum | Maximum | |
|---|---|---|---|---|
| Tx [mm] | 110.852 | 0.020 | 110.813 | 110.917 |
| Ty [mm] | −1.999 | 0.008 | −2.024 | −1.978 |
| Tz [mm] | 2.220 | 0.028 | 2.150 | 2.291 |
| Rx [deg] | −0.014 | 0.011 | −0.050 | 0.018 |
| Ry [deg] | −0.057 | 0.023 | −0.121 | −0.010 |
| Rz [deg] | 0.227 | 0.006 | 0.215 | 0.240 |
Table 2
Case B (number of pictures: 44; number of analysed pairs of pictures: 467)
| Average | Standard deviation | Minimum | Maximum | |
|---|---|---|---|---|
| Tx [mm] | 110.839 | 0.010 | 110.811 | 110.870 |
| Ty [mm] | −1.982 | 0.011 | −2.009 | −1.946 |
| Tz [mm] | 2.233 | 0.022 | 2.172 | 2.291 |
| Rx [deg] | −0.005 | 0.010 | −0.037 | 0.019 |
| Ry [deg] | −0.072 | 0.018 | −0.114 | −0.013 |
| Rz [deg] | 0.230 | 0.005 | 0.214 | 0.243 |
Figure 9
Distribution of a probability density function concerning the values determined for mutual positions of markers, based on photos taken for Case C
Figure 10
Distribution of a probability density function for determining distances for Case C
Figure 11
Diagram of a geometric system in which the photos of markers were taken (Case C).
Table 3
Case C (number of photos: 36; number of photo pairs: 160)
| Average | Standard deviation | Minimum | Maximum | |
|---|---|---|---|---|
| Tx [mm] | 90.999 | 0.027 | 90.921 | 91.059 |
| Ty [mm] | −12.118 | 0.025 | −12.184 | −12.060 |
| Tz [mm] | −78.360 | 0.028 | −78.454 | −78.306 |
| Rx [deg] | −2.636 | 0.017 | −2.680 | −2.593 |
| Ry [deg] | 89.827 | 0.019 | 89.776 | 89.872 |
| Rz [deg] | −6.549 | 0.007 | −6.572 | −6.533 |
| Distance [mm] | 120.698 | 0.020 | 120.645 | 120.760 |