1 Spatial Modelling of the Terrestrial Environment - Georeferencial

Remotely Sensed Topographic Data for River Channel Research 129
Table 6.3 The correct camera calibration parameters as compared to camera parameters
with error simulated under a normal distribution as defined by camera parameter standard
errors obtained from the bundle adjustment
Image 1 Image 2
Correct Simulated Difference Correct Simulated Difference
Xo (m) 283909.26 283909.12 −0.147 283483.46 283483.35 −0.105
Yo (m) 716100.37 716100.33 −0.037 716013.21 716013.13 −0.075
Xo (m) 615.53 615.35 −0.187 615.53 615.53 0.000
omega 0.1970 0.1942 −0.0029 0.2507 0.2464 −0.004
(degrees)
kappa 10.5958 10.5985 0.0026 9.7322 9.7287 −0.0035
(degrees)
phi (degrees) 0.3520 0.3442 −0.0078 0.3988 0.3985 −0.0003
wherever a grid cell fell across a break of slope. Assuming the stereo-matching process
is operating properly, there is an equal probability of the photogrammetric data points being
too high (where the grid cell is predominantly dry) or too low (where the grid cell is
predominantly wet). The results in Table 6.3 suggest that the errors are systematic. The
second hypothesis relates to the operation of the stereo-matching process. Breaks of slope
will have an effect upon the viewing angle of the two images. Using imagery of a similar
scale and breaks of slope associated with a landform of similar relative relief, Lane et al.
(2000) showed that the stereo-correlating algorithm had a tendency to produce erroneous
matches due to dead ground problems. In summary, this demonstrates that determination of
the spatial distribution of error is effective in helping to understand the causes of that error,
and where error is most heavily concentrated. The analysis described in section 6.4.1 could
potentially be improved through a more intelligent approach to error correction, in which
image information content (e.g. water edges) is used to inform the error search process.
However, the finding that errors are greatest at the water edges raises issues of surface
representation, as edge data will be required to capture breaks of slope adequately. The
selective nature of the point removal in section 6.4.1, rather than usinga1mchannel edge
exclusion zone, is clearly preferable.
6.5.2 Causes of the Banding
Initial inspection of the banding suggested that this was probably associated with error in
the triangulation. To assess the extent to which this could be the case, a simple simulation
exercise was undertaken (Figure 6.9(a)). This involved taking a flat DEM, similar in platform
extent to an individual DEM. The associated matrix of object space co-ordinates was then
applied to the collinearity equations used to generate that DEM. This produced a set of
correct image space co-ordinates. The correct image space co-ordinates were then re-applied
to the collinearity equations but with camera positions and orientations perturbed under a
normal distribution according to the SD of each parameter defined during triangulation.
This produces a DEM containing simulated error due to random parameter perturbation.
In addition, it is possible to simulate the effects of matching upon the DEM. We do this by
adding a random perturbation to the image co-ordinates to reflect the non-perfect matching
process. This is defined as having a SD of 1 image pixel.