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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
This paper addresses the means to realize this prospect through 
discussion of the results of experimental testing of stereo 
IKONOS Geo imagery in Northern Thailand. The paper reports 
positional accuracy of products generated from IKONOS stereo 
images by applying a bias-correction technique as described 
betow. Result from a second sensor orientation model are also 
shown. 
2. METHODOLOGY 
Obtaining three dimensional coordinates from two dimensional 
images requires that the position and orientation of the images 
in space are known. However, although exterior orientation 
parameters of IKONOS imageries are measured onboard, they 
are withheld. To get around this problem, other mathematical 
models are used instead of a rigorous model. A review of 
replacement sensor models, which are mainly in the form of 
polynomial or ratio-of-polynomial equations, can be found in 
Tao et al (2000) and Tao and Hu (2001). 
Space Imaging supplies rational polynomial coefficients (RPCs) 
for photogrammetric processing by the imagery user. The RPCs 
describe the relationship between the image and object space 
and can be considered as a replacement model for the modified 
collinearity equations which are widely used for line scanner 
imagery. The model for ‘forward’ rational functions for image / 
and ground point / can be given as (Fraser and Hanley, 2003): 
BA 
ST EG, 
BY ZY 
NES 2 
(1) 
where x, yp, = image coordinates 
(X,Y,Z), = corresponding ground coordinates 
Bp 
j = 3" degree polynomial functions 
The absolute accuracy derived from IKONOS stereo pairs 
without ground control points (GCPs) at Reference level is 25m 
(CE90) horizontal and 22m (LE90) vertical (Space Imaging, 
2002). Using RPCs supplied by Space Imaging, Ager (2003) 
measured coordinates on IKONOS stereo pairs over 14 test sites 
in various countries and reported an average of 7.9 m horizontal 
error (CE90) and 7.6 vertical error (LE90). An initial test 
conducted by the authors on a stereo pair of Chiengmai, 
Thailand showed an RMS error of about 7 m. These results are 
far better than the stated specifications from Space Imaging. 
While the accuracy attained is impressive, further improvement 
can be achieved. As shown in Figure 1, the error vectors which 
represent the differences between horizontal coordinates 
obtained from stereo measurement and those accurately 
determined from GPS measurement indicate the presence of 
systematic error. Since the pointing error during stereo 
measurements is much smaller than the resulted systematic 
errors, it means that the supplied RPCs must contain biases. 
Corrections must be applied somewhere along the processing 
line. 
79 
The removal of systematic errors can occur at the end using 
simple 2D transformation to correct the image product. 
Alternatively, the bias correction of RPCs may be done first, 
before the other steps of product generation. The latter approach 
seems more attractive because the correction is carried out at 
the beginning of the mapping process and so the accuracy of all 
intermediate products such as DEM are guaranteed. The bias 
correction technique used in this research is detailed in Fraser 
and Hanley (2003) and will be briefly described below. 
Error vector @ 
| 
10m 
  
Figure 1. Error vectors at check points. 
Under the assumption that RPC biases manifest themselves for 
all practical purposes as image coordinate shifts, a model for 
spatial intersection with bias compensation, which comprises 
one offset parameter per image coordinate, can be derived as 
follows 
ÖX ; 
V j 46 ov; 0 
Y elei I IS à, |^ A u^ 2) 
volo: [mote cms 9o 4 7 Ar =v 
Ay; 
where v, and v, are observational residuals in pixels; 
OX ,,0Y,,0Z, are corrections to approximate values for the 
object point coordinates; Ax, Ay, are image coordinate 
: : à . 0 0 
perturbations or biases that are common to image i; x’, y are 
the image coordinates corresponding to the approximate object 
coordinates; a;;, dj, ..., a»; are partial derivatives of the 
functions in (1) with respect to X, Y and Z; and x, y are the 
measured image coordinates 
Only one GCP is required in solving the bias parameters in (2). 
The process has been carried out via the Barista software 
developed by the photogrammetry research team at the 
University of Melbourne. Bias-corrected RPCs were written 
into another file using the same format as supplied by Space