Virtual Image Generation from the Linear Array Image


Having generated the stereo-virtual images, conventional space intersection may be applied to generate the object space. Since the interior orientation parameters of the virtual image are already established, the mathematical model for the space intersection can be a rigorous collinearity model. However, as stated above, the virtual image has inherited several systematic errors, the most important of which are the neglected attitude parameters of each scan line. These image distortions can be handled via a self calibration collinearity equation. Alternatively, a much simpler approach can also be adopted using a direct linear transformation model which corrects the scale affinities in the image space for the virtual camera:



where L1,…, L11 are the DLT transformation parameters. The DLT model can be further elaborated with the inclusion of the higher terms for the corrections of the higher order distortions.

Evaluation
To evaluate the proposed method and for the purpose of thorough analysis of the influence of the DEM on relief displacements of the push-broom data, a DEM was generated by a known mathematical model. Fig. 5 gives the isometric view of the simulated DEM.

Two stereo push-broom images where also generated in ideal situation, i.e. without scan lines attitude and altitude variations. Based on these data, the following virtual images were generated:

  1. virtual images obtained by a perfect DEM,
  2. virtual images obtained by different approximations of the DEM.
The approximate DEMs were generated by successive smoothing the original DEM leading to the DEMs with 75%, 50%, 25% and 12.5% roughness factors respectively.

Space intersection were then carried out for a dense network of image points on the virtual images and their corresponding mesh on the object space were produced using space intersection by both rigorous and DLT mathematical models. The accuracies were then evaluated on the check points. To have better understanding of the success of the proposed method, a simple DLT space intersection was also carried out on the original linear array data. The results for all datasets are presented in Table 1.

Table 1. accuracy on check points for the stereo-virtual image and the linear array images.


Conclusion
In this paper a study is conducted on the nature of the relief displacements as occurred on the push-broom images. The results of the simulated data presented in Table 1. indicate that relief displacement in linear array images is particularly problematic during the rectification process. The effect of relief displacement can be dramatically reduced by a virtual single-projection image if a DEM of the imaging area is available. In particular it was demonstrated that the available DEM need not be accurate and even a general trend of the DEM can well reduce the effect of relief displacement. This trend can easily be estimated by a surface fitted to the ground control points. The preliminary conclusion to be drawn from this study is that the DLT approach for the space resection and intersection of the linear push-broom images (Almanadili and Novak,…) can be greatly improved by a virtual image which is generated simply using the general trend of the DEM.

These results, however, should be validated by the real data. The following tasks should be the subjects for further investigation:

  • evaluating the relief displacement on the real push-broom images,
  • investigating the influence of the scan line attitude and altitude variation on the accuracy of the generated virtual image,
  • incorporation of a self calibration space resection intersection and/or inclusion of the higher order terms in the DLT model on the stereo-virtual images to reduce the influence of the attitude and altitude variation,
  • investigating the utilization of the satellite ephemeris for the virtual image generation,
  • investigating the possibility of epipolar resampling of virtual images by conventional methods.
References

  • Almanadili and Novak ………….
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