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Mapping without the sun
Zhang, Jixian

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
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