The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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4.4 Parameter Correlation 5. INDEPENDENT ASSESSMENT 
Considering again case 3, the largest correlation coefficients 
existed between the perspective centre co-ordinates (PCCs) and 
the principal distance (maximum magnitude: 0.83) and between 
the PCCs and the rangefinder offset (0.67). The maximum 
correlation magnitude between the rotation angles co and <j) and 
the principal point was quite favourable at 0.63, though it 
should be recalled that the 10 model did not include decentring 
distortion terms, which were found to be insignificant. The only 
noteworthy correlation between the 10 parameters was 0.71 
between c and do- For the rest of the range APs the maximum 
correlation with any other parameter (EO or IO) was 0.20. 
Addition of the empirical terms in case 4 changed the situation, 
with maximum coefficients of 0.90 between e 2 and en, and 0.64 
between do and e 4 . In both cases 3 and 4, though, all APs were 
statistically significant in terms of the ratio of the estimate to 
the standard deviation. 
4.5 Scale Error Estimation 
Addition of the scale error, d l5 to the case 3 adjustment did not 
significantly change the residual RMS measures. A high 
correlation of 0.86 existed with do but, interestingly and 
encouragingly, the correlation with c was only 0.44. These 
could be reduced by increasing the depth variation in the target 
field. Though statistically significant, d t was excluded from the 
final AP models due to its lack of impact on the other 
performance measures. What this demonstrates is that the scale 
error parameter can be successfully estimated by including 
easily-measured spatial distance observations in the self 
calibration adjustment, though it is conceded that a large 
number (33) were used in this experiment. 
4.6 Lens Distortion Modelling Results 
The estimated radial lens distortion profile, 8r, of the SR-3000 
is plotted in Figure 8. Though the amount of distortion is quite 
high, -205 pm at the maximum observed radial distance of 4.55 
mm, this represents only about 5 pixels due to the 40 pm pixel 
size. The corresponding Ict error envelope is not perceivable 
since the estimated standard deviation of ki was almost two 
orders of magnitude (76 times) smaller than k] itself. The higher 
order terms of the radial lens distortion model were found to be 
insignificant. 
5.1 Accuracy Assessment 
To assess the accuracy improvement gained by the different IO 
model cases, the object space co-ordinates of the surveyed 
points were compared with those determined from the LRC. A 
rigid body transformation of the LRC-determined co-ordinates 
onto the surveyed co-ordinates was required for each of the 6 
independent images. The overall RMSs of co-ordinate 
differences calculated from the total available set of 188 points 
are given in Table 3. The case 2 IO set yields improvement in 
only one dimension (X) and the accuracy actually degrades 
slightly in Y and Z. Clearly there is considerable improvement 
realised by using the physical AP model (case 3). In case 4 
there is more overall improvement in Z relative to case 3, but 
there also was a slight degradation in X, which may be due to 
over-parameterisation with the empirical terms. 
Case 
RMS 
% improvement 
X 
(mm) 
Y 
(mm) 
Z 
(mm) 
X 
Y 
Z 
1 
47 
57 
70 
- 
- 
- 
2 
42 
63 
74 
11 
-11 
-7 
3 
31 
14 
43 
34 
75 
37 
4 
35 
15 
36 
27 
74 
48 
Table 3. RMS of check point differences and % improvements. 
-500 . -500 
Y (mm) X (mm) 
a) 
Y (mm) 
b) 
Figure 9. Uncorrected and corrected planar target data, a) 
Figure 8. Estimated radial lens distortion profile. Isometric view b) side view