281 
distortion on the model, such as symmetric and asymmetric 
radiation distortion, tangential distortion and affine distortion. 
In the regions with large terrain undulation, it is impossible to 
rectify the image accurately with ordinary low-order 
polynomials, especially in the scanline direction which is 
perpendicular to the flight direction where the error is more 
serious. Therefore, when the orbit parameters of the satellite 
cannot be obtained, RFM can substitute the rigorous bundle 
method. However, RFM requires more GCPs. So it is proposed 
to use the modes of refined second-order RFM according to the 
degree of terrain undulation when the number of GCPs is not 
enough. 
4. EVALUATION RFM 
The general method of checking the validity of 
orthorectification algorithm is: in large scale, using topographic 
maps or other high resolution SPOT or IKONOS orthographic 
images as references, find some GCPs, some of which are used 
to solve the RPC parameters needed by RFM orthographic 
rectification, and the remaining points are used as check points 
(CKPs) of rectified results to determine whether optimized 
RFM has high positioning accuracy on the CKPs. When the 
positioning accuracy of GCPs is high, it is scientific to evaluate 
the validity and accuracy of the algorithm in such way. 
4.1 Beijing-1 Data 
Beijing-1 small satellite panchromatic strip image of Taian, 
Shandong, with resolution 4m, pixel area 6056 X 10920, 
elevation range 50~ 1520m, and imaging time March 31, 
2006( see Figure 3); DEM with 5m resolution of the 
experimental area ( see Figure 4). 
Figure 3. Original image Figure 4. DEM 
4.2 Orthorectification Results 
In the experimental image, 30 obvious objects are chosen as 
GCPs, and another 10 obvious objects as CKPs. As shown in 
Figure 3, GCPs and CKPs are evenly distributed: red points are 
chosen as GCPs, and yellow points are chosen as CKPs. Then, 
compute RPC with GCPs and corresponding DEM, build RFM 
and refined RFM respectively, and generate orthographic 
images with different models respectively. Figure 5 show the 
result of orthorectified image based on refined RFM. 
Figure 5. Orthorectified image based on refined RFM 
The local 1:1 images obtained by cropping the refined RFM 
orthorectified image are shown in Figure 7. It can be seen from 
the figure that the clear outline and edge shadow of the street 
and building have a great stereo effect. While due to the sharp 
height change of the streets and the buildings, the stereo effect 
of the orthographic image has to be further improved by 
eliminating the shadow. 
Figure 6. An enlarged view of Beijing-1 orthorectified image 
4.3 Results Evaluation 
In order to get meaningful results of accuracy evaluation, the 
GCPs set used by model parameter optimization should be 
strictly separated from the CKPs set for accuracy checking. 
Only if independent CKPs non-involved in model parameter 
optimization are used to compute the accuracy indicators can an 
objective conclusion be obtained. The rectified small satellite 
image is usually in a projection rectangular coordinate system. 
To evaluate the image in this coordinate system, the rectified 
image should be compared to high accuracy topographic maps 
or other ground data with accurate geodesic coordinates so as to 
determine the coordinates in the small satellite image of the 
corresponding object point and measure its true coordinates on 
the ground. Then, the positioning accuracy of the orthographic 
image can be computed. Therefore, corresponding CKPs can be 
measured by high accuracy GPS to ensure their independence 
and accuracy, which leads to an objective and valid evaluation. 
In the image of Taian, Shandong orthorectified by RFM, ground 
coordinates of 10 chosen CKPs are measured. The residual 
errors between the traditional first-order RFM orthorectified