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.