1 Spatial Modelling of the Terrestrial Environment - Georeferencial

Remotely Sensed Topographic Data for River Channel Research 131
Table 6.4 The effects of introduction of tie points upon the average standard deviation of
exposure stations. Figures in brackets give the change in parameter due to tie point addition
with respect to the no tie point case
Mean exposure Mean exposure Mean exposure
station residual station residual station residual
Standard deviation standard deviation standard deviation standard deviation
Photogrammetric block of unit weight X (m) Y (m) Z (m)
No tie points
Waimakariri— Feb 0.55 ±0.088 ±0.084 ±0.061
1999
Waimakariri— March 0.98 ±0.097 ±0.102 ±0.081
1999
Waimakariri— Feb 0.89 ±0.110 ±0.119 ±0.052
2000
With tie points
Waimakariri— Feb 1.04(+0.490) ±0.082(–0.006) ±0.088(0.004) ±0.061(0.000)
1999
Waimakariri— March 1.13(+0.150) ±0.071(−0.026) ±0.076(-0.026) ±0.059(−0.022)
1999
Waimakariri— Feb 0.94(+0.050) ±0.080(−0.030) ±0.091(−0.028) ±0.045(−0.007)
2000
Figure 6.9(b) demonstrates two important characteristics. First, systematic error is evident
in the dataset. This is significant with an elevation range of 0.50 m. With two DEMs,
and banding in the same direction, the total banding could be as much as 1 m, and commensurate
with the scale of banding shown in Figures 6.2(b) and 6.3. This suggests that a major
cause of the banding that is commonly observed in studies of low relief surfaces when
DEMs are stitched together (e.g. Stojic et al., 1998) could be the propagation of random
error in camera positions and orientations into locally systematic error in the DEM. The
banding is only about 0.13% of the flying height and likely to be a problem when the feature
of interest has relief of the same order as the banding.
The main problem with banding is how to deal with it. The predominant cause of banding
was thought to be the propagation of errors in camera position and orientation into the
derived DEM surfaces. This implies that improvement in the precision of camera position
and orientation should result in less error in the DEM surface. There was no additional
ground control available. However, it was possible to add additional tie points into the
bundle adjustment used to determine camera position and orientations. Tie points are based
upon the principle that the co-location of a point of unknown object space co-ordinates upon
n images results in the creation of 2n equations to determine 3 unknowns. Thus, it introduces
2n-3 units of redundancy for each point, which can be used to improve the precision of
camera positions and orientations. This has appeal because it addresses the hypothesized
root causes of the surface error. Thus, points that could be visually identified on both
overlapping images were used as tie points (e.g. Stojic et al., 1998; Chandler et al., 2001).
This was performed in a systematic manner, by adding additional rows of tie-points between
existing rows of ground control points. In total, 94, 113 and 88 tie-points were added to the
February 1999, March 1999 and February 2000 Waimakariri blocks, respectively.
In photogrammetric terms, addition of tie-points appears to have two main effects. First,
those SD values that were especially high are reduced to more acceptable, albeit still large,
values (Table 6.4). This is especially the case in z, and this reflects a problem common to