International Archives of the Photogrammetry, Remote Sensing and Spot Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
  
  
Ec Ewer of GCP collected with topographic map: the 
road intersection. 
QuickBird © 2002 and Courtesy DigitalGlobe. 
  
  
Figure 3. 
  
  
Example of GCP collcsted with hand- held GPS: the 
pole defined with its shadow. Even the shadow of 
the power line is visible on the snow. 
QuickBird © 2002 and Courtesy DigitalGlobe. 
ao ces eve tu 
1 
REA nca 
igure 4. 
Example of GCP collected win DGPS: the while 
stop line at the road intersection. 
QuickBird © 2002 and Courtesy DigitalGlobe. 
838 
3. EXPERIMENT AND RESULTS 
3.1 Experiment 
The experiment deals with the computation of the parameters of 
CCRS 3D physical model using the four sets of GCPs. In the 
model computation, each GCP contributes to two observation 
equations: an equation in X and an equation in Y. The 
observation equations are used to establish the error equations 
for GCPs, which are weighted as a function of the accuracy of 
the image and cartographic data. The normal equations are then 
derived and resolved with the unknowns computed. In addition, 
conditions or constraints on osculatory orbital parameters are 
added in the adjustment to take into account the knowledge and 
the accuracy of the ephemeris. They thus prevent the 
adjustment from diverging and they also filter the input errors. 
Since there are always redundant observations to reduce the 
input error Pe. in the geometric models a least-square 
adjustment is used. Since the mathematical equations of the 3D 
physical model are non-linear, some means of linearization 
(series expansions) were used. A set of approximate values for 
the unknown parameters in the equations are thus initialized 
from the osculatory and sensor parameters. More information 
on least-squares methods applied to geomatic data can be 
obtained in Mikhail (1976). The results of this processing are: 
° the parameter values for the 3D geometric model; 
* the residuals in X and Y directions for each GCP and 
their root mean square (RMS) residuals; 
e. the errors and bias in X and Y directions for each 
independent check point (ICP) and their RMS errors; 
° the computed cartographic coordinates for each point. 
In the four tests, GCPs were spread at the border of the image to 
avoid extrapolation in planimetry, and cover the full elevation 
range of the terrain (lowest and highest elevations) to avoid 
extrapolation in altimetry. When more GCPs than the 
minimum theoretically required are used, the GCP residuals 
reflect the modelling accuracy. Additionally, the GCPs 
collected by the DGPS were also used as ICPs to obtain an 
unbiased validation of the collection methods’ modelling 
accuracy. 
3.2 Results 
Table 1 gives for each collection method, the GCP accuracy, 
the number of GCPs and ICPs, the root mean square (RMS) 
residuals and errors (in metres) of the least-square adjustment 
computation for the GCPs and ICPs, respectively. GCP RMS 
residuals reflect modelling and GCP accuracy, while ICP RMS 
errors reflect restitution accuracy, which includes feature 
extraction error and thus are a good estimation of the final 
positioning accuracy of planimetric features. However, the final 
internal accuracy of the modelling of the 3D modelling will be 
better than these RMS errors. Consequently, it is thus normal 
and “safe” to obtain residuals from the least-squares adjustment 
in the same order of magnitude as the predominant GCP error. 
Table 1 shows that RMS residuals/errors were generally in the 
same order of magnitude as the input data error, which is, 
depending of each collection method, a combination of image 
pointing error, X-Y planimetric error and propagation of Z-error 
as a function of the viewing angle. The analysis of the general 
results demonstrates that the 3D physical model is stable and 
robust over the entire stereo-images without generating local 
ten uae V- o £^ FP 
pouce seite milit e rper