Abstract
Since few years ago it has been generally accepted without any dispute that the 3D affine transformation applied to high-resolution satellite imageries (HRSI), produces results as accurate as those obtained by the RPCs derived from rigorous photogrammetric model. However, as the higher order terms are absent in the affine transformation, the degree of success of this model obviously hinges upon the geometric nature of the imagery to be geo-rectified. In authors view, there are a latent confusion and misunderstanding in the minds of the photogrammetric practitioners as regards the potential of the 3D affine transformation as a replacement model for the geometric correction of the HRSI. The main intention of this paper is, therefore, to analyse the 3D affine transformation by concentrating more on its limitations. To obtain deeper insight into the nature of the 3D affine model, it is applied to images with larger field of view as well as the images of highly mountainous terrains. The geo-coding success of the affine model is then evaluated by comparing the object coordinates of a dense cloud of homologous points derived by the affine model with the object coordinates of the same points obtained by the standard terrain-independent rational functions. Extensive tests conducted over excessively mountainous as well as the hilly terrains indicate that there are clear distortion trends in the residual ground coordinates that cannot be fully absorbed into the 3D affine coefficients. The sources of these non-linear trends such as the satellite attitude and position variations, the terrain relief, the earth curvature and their impact on the final accuracy are analysed using the scatter patterns of the residual errors.
Highlights
In recent years, the major trends in sensor orientation and geo-positioning solutions for high resolution satellite imageries have been dominantly confined to the fitting rational function coefficients to the rigorous photogrammetric collinearity equations (Tao et al, 2001; Dial and Grodecki, 2005; Grodecki, 2001)
Regarding the fact that the fitted RPCs to the rigorous photogrammetric model are effectively as precise as the rigorous model, one can consider the virtual ground coordinate points (VGCPs) derived by the terrain-independent rational function, practically equivalent to the points generated by the rigorous model itself
This stage is carried out based on the RPC intersection formulation given by Equation 3
Summary
The major trends in sensor orientation and geo-positioning solutions for high resolution satellite imageries have been dominantly confined to the fitting rational function coefficients to the rigorous photogrammetric collinearity equations (Tao et al, 2001; Dial and Grodecki, 2005; Grodecki, 2001) This approach proved to be accurate, flexible and easy to implement and the main stream photogrammetric software developers did not hesitate to tailor the RPC-based 3D ground reconstruction into their systems. To be able to determine the rate of success of the affine transformation, it is of crucial importance not to rely solely on RMSE’s and the min/max of the residual errors The reason for this is that, depending on the number and distribution of the GCPs and bearing in mind the fact that the error patterns may be symmetrical; the resulted accuracy figures could be misleading. These are followed by detailed examination of the significance of these nonlinear terms using several tests carried out on Cartosat-1 toolkit stereo imageries
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