Biomedical Engineering Reference
In-Depth Information
Table 8.1 Error statistics of the calibration algorithms using the data from the laser scanner
system, see also Fig. 8.6
Min
25th p.
Median
75th p.
Max
Translation error (mm)
Tsai-Lenz
1.2812
4.7987
7.6678
10.3164
18.1265
DQ
2.0395
4.7066
6.7426
9.0190
13.3181
QR24 M
4.4768
7.7452
10.6338
15.7291
28.5564
QR24
0.8984
1.1740
1.3517
2.1678
3.3947
QR15
0.8848
1.1702
1.3216
2.1760
3.4044
Rotation error ( )
Tsai-Lenz 0.2883 0.6180 0.8088 0.9393 1.4628
DQ 0.4873 0.7327 0.9475 1.1914 1.4691
QR24 M 0.2442 0.6146 0.8193 0.9869 1.3946
QR24 0.4121 0.6702 0.8574 1.1523 1.4730
QR15 - - - - -
The numbers shown are minimum, 25th percentile, median, 75th percentile, and maximum.
Minimal values for each column are marked in bold
QR24 M
Tsai−Lenz
Dual Quaternion
QR24
QR15
Translation errors on the test data
Rotation errors on the test data
30
2
20
1.5
10
1
0
0.5
5
10
15
20
25
5
10
15
20
25
number of pose pairs used in calibration
number of pose pairs used in calibration
Fig. 8.5 Calibration errors for the QR, Tsai-Lenz, and Dual Quaternion algorithms when using
laser scanner data. The algorithms used n ¼ 5 ;; 25 poses to compute the calibration matrices
which were then tested on 25 other poses, showing the mean translational (left) and rotational
errors (right)
methods strongly outperform the algorithms by Tsai and Lenz and the Dual
Quaternion method: The improvement in median error is around 80 %. The
rotation errors are similar for all calibration methods with their median values
ranging from 0 : 81 to 0 : 95 . One thing, however, is interesting: Preconditioning
the QR24 algorithm massively decreases translational accuracy while only slightly
reducing rotational errors.
In general, given the laser scanner's accuracy of approximately 0.5 mm and the
average accuracy of the ICP matching of 1.1 mm, a median translational cali-
bration error of 1.3-1.4 mm is convincing.
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