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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The numerator and denominator in formula (1) are in third 
polynomial in general: 
p(X, Y, Z) = ao + ajX + a 2 Y + a 3 Z + a 4 XY + a 5 XZ + aeYZ + 
a 7 X 2 + a 8 Y 2 + a 9 Z 2 + a 10 XYZ+ a u X 3 + a 12 XY 2 + a 13 XZ 2 + a 14 X 2 Y 
+ a 15 Y 3 + a 16 YZ 2 + a 17 X 2 Z + a 18 Y 2 Z + a 19 Z 3 
So there are 20 coefficients in formula (4) and 80 in formula (4) 
which are called RPCs 
2.2 RFM Stereo Orientation 
RFM could express the transformation relation of image 
coordinate and corresponding 3-dimension space coordinates. 
So we could calculate the space coordinate of corresponding 
image points using the two RFMs of the left and right image, 
vice versa we could calculate image coordinate of stereo pair 
using RFMs and 3-dimension coordinate(Tao 2001). (Fig. 1) 
r,. C) 
O O 
1—ts? V. 
J" X) 
Figure 1. Stereo-model construction based on RFM model 
Generally the RPCs provided by C ARTOS AT-1 is calculated 
using satellite ephemeris, attitude coefficient and rigid sensor 
model, but not using ground control point. The accuracy of 
RPCs is restricted by ephemeris, attitude data and is low. 
Ground control points is used to improve the accuracy of RPCs. 
For a single image, an affine transformation in image 
coordination system is used to correct the system error and 
improve the accuracy of RFM. 
L' = ao + afS + a 2 L 
S' = b 0 + bpS + b 2 L (5) 
Where, (L, S) and (L', S') are image coordinate before and after 
correction independently; 
aO, al, a2 and bO, bl, b2 are the coefficients of affine 
transformation. 
At least 3 points are required in affine transformation. 
For stereo model using RFM, we could improve the accuracy of 
RFM both in image coordinate system and spatial coordinate 
system. Firstly, we calculate the model coordinate using RFM 
of the stereo pair; then transform the model coordinate to 
ground coordinate using linear 3-dimension transformation. 
Finally using ground control points to improve RFM stereo 
orientation accuracy. 
~x r 
Af 
~X~ 
r 
= 
Y B 
+ ÀR 
Y 
Z' 
f~F 
(4) 
Z 
(6) 
Where (X,Y,Z) is the model coordinate of RFM, 
(X G J a ,Z G ) is the ground coordinate of origin point , 
(X',Y\?) is the corrected spatial coordinate, R is the 
rotarion matrix of <tA H, K, and >is the scaling coefficient. 
Obviously the transformation has 7 independent coefficient, 
X G > Y g ^ Z g , i), il, K andA.. So at least 2 planimetrie and 3 
height control points are needed in coefficient calculation. And 
4 planimetrie and height points in the comer of the model or 
more evenly distributed control points are used in coefficient 
calculation. 
3. EXPERIMENT AND ANALYSIS 
3.1 Experiment Data 
In this paper, a stereo pair of Beijing (city and hilly area) 
together with 16 control points were used to evaluate the 
geometric accuracy of the CARTOSAT-1 stereo mapping. The 
accuracy of ground coordinates of these control points 
measured from in-situ GPS is in centimeters, and the accuracy 
of image coordinates measured by JX4 DPS is sub-pixel. The 
distribution of the GCPs see figure 2. 
Figure 2. GCPs Distribution 
3.2 Experiment Schemes 
With different numbers and distributions (different in 
planimetry and height) of control points we tested the accuracy 
of CARTOSAT-1 stereo mapping. And we produced 
topographic map(fig. 3), DEM(fig.4) and ortho-image(fig. 5) 
using JX4 DPS according to the survey specification of 
national 1:50,000 topographic maps.