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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
Figure 2 is exaggerated 50 times for better visualization. From 
Figure 2, it can be seen that the dominant errors are systematic 
and exist mainly in the north-east direction. The RMS errors for 
both QuickBird panchromatic and multispectral pairs are shown 
in Table 3. For similar results using IKONOS data, refer to Di et 
al. (2002). 
  
       
  
    
os 
(b)Q 
a, i 5 
uickBird image 
Figure 1. Distribution of GCPs (red triangles) 
and CKPs (green circles) 
  
  
  
Image Type X y Z 
Etrors in panchromatie | a gaom |; &738m<|>12.667m 
pair (meter) 
Errors in multispectral |. S94]. 7,498m-| 32296m 
  
  
  
  
  
pair (meter) 
  
Table 3. Differences (RMS) computed from GCPs 
and RFC-derived ground points 
691 
  
The errors were exaggerated 50 times. 
  
  
  
Figure 2. Differences between the RFC-derived and GPS- 
surveryed ground coordinates of GCP points (panchromatic 
QuickBird stereo images) 
ACCURACY IMPROVEMENT 
In general, there are two ways to improve the accuracy of RFC- 
derived ground coordinates (Di et al., 20032; Li et al., 2003). The 
first is to refine the RFCs based on a large number of GCPs (more 
than 39 GCPs are required for the third-order RF). This method is 
theoretically applicable, but not practical where large numbers of 
such GCPs are not available. The second approach refines the 
ground coordinates calculated from the RFs using a polynomial 
correction in either the image space or object space. This method 
requires significantly fewer GCPs than the first approach, and has 
the advantages of simplicity and efficiency. A number of 
publications have reported results using variations of this 
approach (Grodecki and Dial, 2003; Di et al., 2003b). 
In this research, four models are evaluated for their ability to 
improve accuracies in both the object space and image space: 1) 
translation, 2) scale and translation, 3) affine, and 4) a second- 
order polynomial (Table 4). For each model in object space, RF- 
based triangulation (Di et al., 2001; 2003a) is applied to calculate 
the ground coordinates (X, Y, Z). Since the correct coordinates 
(C, Y', Z) of the GCPs are known, three equations can be 
established in accordance with the model equations in Table 4. 
Using all available GCPs (usually more than the minimum 
number required), over-determined equation systems can be set 
up to compute the optimal estimates of the transformation 
parameters by a least-squares adjustment. The transformation 
parameters can be used to compute the improved coordinates of 
other points. CKPs are used to assess the appropriateness of the 
models. The root mean square error (RMSE) of each model is 
calculated based on differences between RF-derived and known 
coordinates of the CKPs. 
In object space, the translation model adds a shift vector (ao, bo, co; 
to the ground coordinates (X, Y, Z) computed from the RFCs tc