4-2-3
7 CALIBRATION RESULTS
Figure 5. Image location accuracy assessed using the subpixel
shift method. Standard deviation=0.04 pixel
5 DISTORTION MODEL
The parameters to be calibrated include the camera exterior
orientation parameters with respect to the telescope of the
theodolite, the camera interior orientation parameters, and the
parameters in the error function model below:
Sx = A■ y + x(K/ + K 2 r 4 + K/) + P x (r 2 + 2x 2 )+ P 2 (2xy)
Sy = B-y + y(K t r 2 + K 2 r 4 + K/) + P x (2 xy) + P 2 (r 2 + 2/)
where ^ and B are the affine deformation parameters, Ks the
radial lens distortion parameters and Ps the decentring lens
distortion parameters (Brown 1971).
6 WARM-UP EFFECT AND STABILITY TEST
The camera and a target were set stable. A frame of image was
captured and the target image in it were located every 5 minutes
from switch-on. The x and y co-ordinates are graphed against
time as in Fig. This shows that the warm-up period is about 1
hours and after that the x and y stay stable to 0.04 and 0.02 pixel
respectively.
In order to minimise the warm-up effect, the camera was always
switched on at least two hours before the experiments.
Calibration were carried out at five identifiable focal length
settings. These focal length settings are coded which represent
nominal focal lengths of 5.4 (minimum), 10.8, 16.2, 21.6, 43.2
(maximum) mm respectively. The calibrated values and the root
mean squared residuals (RMS) for image co-ordinates are shown
in Table 1.
Table 1. Calibration Results
Focal Settings (mm)
Parameters
5.4
10.8
16.2
21.6
43.2
X() mm
-0.39
-1.66
-3.46
-2.47
9.23
Y() mm
28.96
28.30
20.91
9.98
-9.22
Z() mm
55.32
55.52
57.31
56.89
61.04
CO
1.57376
1.57364
1.57458
1.57653
1.55807
.45041
0.77979
-1.11973
-1.33119
1.05899
K
-2.01235
2.34151
-0.44200
-0.23107
-2.62046
X0
312.01
312.86
314.08
315.82
347.95
yo
413.19
412.55
418.86
423.52
454.18
c
901.91
1048.07
1240.01
1490.79
3112.96
Ki lo-u
0.316
0.187
0.155
0.106
0.041
K2 10-21
-0.305
-0.215
-0.588
-0.360
-0.059
K3 10-21
-1.03
-0.671
0.957
0.480
0.322
P] io- 9
-0.649
-1.88
-1.83
-1.92
-0.332
P2l0- 9
-0.132
0.398
-1.01
-1.18
0.123
A 10- 6
-0.997
3.17
4.87
0.947
3.80
B 10-4
-0.344
-0.336
-0.369
-0.306
-0.305
RMSx
0.086
0.078
0.091
0.121
0.144
RMSy
0.081
0.082
0.084
0.127
0.236
RMS
0.084
0.080
0.088
0.124
0.190
In order to
assess the
effect of
lens distortion, RMSs from
calibrations using no lens distortion parameters, using radial lens
distortion parameters only and using both radial and decentering
lens distortion paramters are shown in row 1 through to row 3 of
Table 2 respectively. It is quite evident that the radial lens
distortion is very significant at all focal settings. The shorter the
focal length, the greater the radial lens distortion. It ranges from
0.2 at maximum zoom to 1.6 pixels at minimum zoom.
Comparatively, the decentering lens distortion is less significant,
only showing a 0.02 pixel improvement. It is, however, worth
considering. 8
Table 2. Significance of lens distortion parameters
Focal Settings (mm)
5.4
10.8
16.2
21.6
43.2
No lens parameters
1.748
0.963
0.556
0.400
0.416
Radial lens par.
0.094
0.119
0.122
0.154
0.268
Radial+Decentering
0.090
0.086
0.094
0.133
0.266
8 REPEATABILITY OF CALIBRATED VALUES
8.1 Repeatability of the whole parameter set
The calibrated parameter values for each focal setting should
remain valid to certain accuracy whenever the lens returns to this
focal setting after zooming in or out. Repeatability here refers to
this accuracy. In order to assess this repeatability, data were
collected again for each calibrated focal setting in the same
manner as for calibration but on the next day and after sufficient
