The Characterization of Ground Control Point Distribution Patterns for the Performance Assessment of Camera Models
3.Camera Models
The camera models can be categorized by the degree of assumptions and approximations. They are ranged from a fully abstract model such as the polynomial warping technique to a fully physical model which is too complex and practically impossible to be implemented analytically due to random variations of some physical parameters. The examples of assumptions are :
- Satellite orbit is circular or straight line in the scale of a scene
- Earth is flat, spherical or ellipsoidal
- Camera focal length or scan-line length are fixed
- Attitude of the satellite is fixed or a linear function of time, and so on
It is common sense that the camera model which is closer to a fully physical model shows better performance on accuracy and robustness using smaller number of GCPs. Inter-parameter dependency and improperly assigned degree of freedom for parameters to be adjusted can however cause the divergence, oscillation or incorrect convergence of the parameter adjustment.
In this paper, we tested two camera models which are close to a full physical model. One is developed and published by Shin and Lee (Shin & Lee 1997, shin et al, 1998). It is based on Cartesian coordinate transformation from image coordinate to map coordinate and vice versa. This technique converts the raw image coordinates (column, row) to the ground coordinates (map projection) by modeling CCD alignment on focal plane, sensor scanning geometry, satellite orbit and attitude geometry, and Earth shape and rotation. The coordinate transform is performed by using a vector projection technique with axes rotation. The residual error sources after this systematic modeling are :
- Satellite position (along-track, across-track, radial)
- Satellite velocity (along-track,across-track, radial)
- Satellite attitude (pitch, roll, yaw)
These nine error source parameters described above are estimated by a non-linear extended Kalman filter. The GCPs (measurements) are applied recursively (one by one) to the Kalman filter and the nine parameters are inversely estimated resulting in an accurate camera model. Since the error range and GCP accuracy information is fed into the initial Kalmna filter covariance matrix, this technique can achieve accurate geometric correction by using a couple of
GCPs (shin & Lee 1998).
The other model was developed by Toution (Toution 1983, 1995). The mathematical equation of the model is similar to the photogrammetric equation such as collinearity and coplanarity conditions. This model was integrated into a commercial photogrammetry and satellite image processing software, PCITM. PCI v.62 OrthoEngine software was used for the experiments.
4.Experiments
A SPOT-PAN image was selected as a test image. A total number of 22 GCPs (road crossings) were carefully selected from the test image and their image coordinates were determined with a sub-pixel precision. The ground truth data were collected by field measurements by using a differential GPS receiver giving a meter's accuracy (see Figure 2). The 22 GCPs were sorted according to each distribution pattern described in Section 2. The each ordered GCPs was applied to set the camera model and the rest were used as check points for the independent accuracy assessment.
Figure 2. Test image : SPOT-PAN, viewing angle = -4.7deg.©CNES
Figure 3 shows results of the Shin & Lee's model. As described in Section 2, COV)L2S, ALG_E2C resulted in the fastest convergence to the final accuracy of about 10m (1 pixel). In this case, Shin & Lee's model can achieve the accuracy by using only 3~5 GCPs. Figure 4 shows the results of the PCI camera model. It shows that the PCI camera model requires than ten GCPs to achieve the final model accuracy.
Figure 3: Performance of Shin & Lee's model
Figure 4: Performance of PCI model
