The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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Figure 3: Sample of RADARSAT-2 GCPs Distribution in 
Image Coordinate System 
First, the geographic latitude and longitude of GCPs are 
projected onto a planar map coordinate system. In our case, we 
use Polar Stereographic (PS) projection for high arctic region 
and Lambert Conformal Conic (LCC) for the rest of Canada. 
Then, a global polynomial transformation Equation (2) between 
the image coordinates (pixel/line) and the projected map 
coordinates is determined through the least square regression. 
Figure 4: GCPs Geographic Distribution 
Figure 5: Total Errors for a 2nd Order Global Polynomial 
Transformation (RMS: 0.96 Pixel) 
In most cast, a perfect fit for all GCPs would require an 
unnecessarily high order of transformation. Instead of 
increasing the order, the user has option to tolerate a certain 
amount of error. When the transformation coefficients of the 
global polynomial transformation equation (1) and its the 
inverse transformation (10) are calculated, the inverse 
transformation (10) is used to retransform the reference 
coordinates of the GCPs back to the source coordinate system. 
Unless the order of transformation allows for a perfect fit, there 
is some discrepancy between the source coordinates and the 
retransformed reference coordinates. The Figure 5 displays the 
discrepancies at all GCP locations for the example in Figure 3. 
It clearly shows that the errors along the image edges are larger 
than the centre of the image. 
The Root Mean Square (RMS) error is the average distance 
between the input source location of all GCPs and their 
retransformed locations. They can be estimated based on 
equation (8) and (9). The discrepancies shown in Figure 5 are 
enlarged for presentation purpose. The actual values are 
estimated as below. 
ò x = 0.66, <T v =0.70 and <T,=0.96 (11) 
The estimated total RMS error is 0.96 pixel, which is smaller 
than 1 pixel. This indicates that a second order global 
transformation polynomial is good enough for our ice and oil 
spill monitoring applications. The geoIocationGrid tie points 
(GCPs) provided in product.xml will be used to automatically 
geo-correct the RADARSAT-2 images. The diagram in Figure 
6 shows the automated data processing flow.