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Sensor Orientation and Ortho-Rectification of High Resolution Satellite Images:
Review and Application with FORMOSAT-2
Ortho-rectification The last step of the geometric processing is the image ortho-rectification. To rectify the original image into a map image, there are two processing operations:
- Geometric operation The geometric operation requires the mathematical functions of the sensor orientation with the previously-computed unknowns and terrain elevation information, such as a DEM, to create precise ortho-rectified images. But if no DEM is available, different altitude levels can be input for different parts of the image (a kind of ‘rough’ DEM) to minimize this elevation distortion. It is then important to have a quantitative evaluation of the DEM impact on the ortho-rectification process, both in term of elevation accuracy for the positioning accuracy and grid spacing for the level of details: a poor grid spacing when compared to the image spacing could generate artefacts for linear features (wiggly roads or edges). Figures 1 and 2 give the relationship between the DEM accuracy (including interpolation in the grid), the viewing angles with the resulting positioning error on VIR and SAR ortho-images, respectively (Toutin 2003a). One of the advantages of these curves is that they can be used to find any third parameter when the two others are known. It can be useful not only for quantitative evaluation of the ortho-rectification, but to forecast the appropriate input data, DEM or the viewing/look angles, depending of the objectives of the project.  Figure 1. Relationship between the DEM accuracy (in metres) the viewing angle (in degrees) of the VIR image, and the resulting positioning error (in metres) generated on the ortho-image For example (Figure 1), with a QuickBird image acquired with a viewing angle of 27° and having a 5-m accurate DEM, the planimetric error generated on the ortho-image is 3 m. Inversely, if a 2-m final planimetric accuracy for a SPOT5 ortho-image is required and having a 10-m accurate DEM, the SPOT5 image should be acquired with a viewing angle less than 10°. The same error evaluation can be applied to SAR data using the curves of Figure 2.  Figure 2. Relationship between the DEM accuracy (in metres), the look angle (in degrees) of the SAR image, and the resulting positioning error (in metres) generated on the SAR ortho-image. The different boxes at the bottom represent the range of look angles for each RADARSAT beam mode Finally, for any map coordinates (X, Y), with the Z-elevation extracted from a DEM, the original image coordinates (column and line) is computed from the equations of the sensor orientation model. However, the computed image coordinates of the map image coordinates will not directly overlay in the original image; in other word, the column and line computed values will be rarely, if never, integer values. - Radiometric operation To compute the DN to be assigned to the map image cell the radiometric operation uses a resampling kernel applied to original image cells: either the DN of the closest cell (called nearest neighbour resampling) or a specific interpolation or deconvolution algorithm using the DNs of surrounding cells. In the first case, the radiometry of the original image and the image spectral signatures are not altered, but the visual quality of the image is degraded and has a disjointed appearance. A geometric error of up to half pixel is also introduced. In the second case, different interpolation algorithms (bilinear interpolation or sinusoidal function) can be applied. The bilinear interpolation, which weights DNs of four surrounding cells as a function of the cell distance, creates a smoothing in the final image. The piecewise cubic convolution, as being an approximation of the sinusoidal function, which computes 3rd-order polynomial functions using a 4?4 cell window, does not smooth, but enhances and generates some contrast in the map image. The theoretically ideal deconvolution function is the sin(x)/x function using 8 x 8 or 16 x 16 cell window. The finale image is, of course, sharper with more details on features (Figure 3).  Figure 3. Examples of applications of geometric resampling kernels used in the rectification process with a QuickBird image. The sub-images are 350 by 350 pixels with 0.10-m spacing. Letters A, B, C and D refer to different geometric resampling kernels (nearest neighbour, bilinear, cubic convolution, sin(x)/x with 16?16 window), respectively. QuickBird Image © Digital Globe, 2001 These previous functions are geometric resampling kernels, not very well adapted to SAR images. Instead, it is better to use statistical functions based on the characteristics of the radar, such as existing adaptive filters using local statistics. Combining the filtering with the resampling also avoids multiple radiometric processing and transformation, which largely degrades the image content and its interpretation (Figure 4).  Figure 4. Examples of applications of geometric resampling kernels used in the rectification process with RADARSAT-SAR fine mode (F5) image. The sub-images are 600 by 600 pixels with 1.00-m spacing. Letters A, B, C and D refer to different geometric resampling kernels (nearest neighbour, bilinear, cubic convolution, sin(x)/x with 16?16 window), respectively and Letters E and F refer to statistical SAR filters (Enhanced Lee and Gamma), respectively. RADARSAT Images © Canadian Space Agency, 2001 - True ortho-image In urban context, surface heights (mainly buildings and bridges) generate discontinuities, leaning and hidden/shadowed areas. While there are different methods to correct them (Ettarid et al., 2005), the one generally used is (i) to separately generate two ortho-images with a DTM in conjunction with a 3D building model (Amhar et al., 1998) or a digital surface model generated from stereo HR images, and (ii) to merge them. Finally, hidden/shadowed areas can only be eliminated through the superimposition of other true ortho-images acquired from different viewpoint. APPLICATION TO FORMOSAT2 RSI In-track panchromatic stereo-pairs were acquired on a Quebec study site, Canada (47º N, 71º 30’ W) (Figure 5) by the Taiwanese Formosat2 Remote Sensing Instrument (RSI) as a courtesy of the Taiwanese National Space Program Office (NSPO) and SPOT-Image, France (as distributor). Because the CCRS geometric modelling used in the processing already performs the self-calibration of most of internal orientation parameters (principal point displacement, focal length and line-scale variation and CCD line rotation) and because the decentering lens distortion is negligible, only the radial symmetric distortions is additionally addressed. The mathematical functions of these remaining lens distortions are well known (Brown, 1966), and can be computed from the GCP residuals of the sensor orientation when a large number of GCPs regularly distributed in column direction are used (Figure 6).  Figure 5. Forward panchromatic Formosat2 image (24 km by 24 km; 2-m pixel spacing) acquired December 28, 2004 on Quebec, Canada. Formosat2 ? National Space Program Office, Taiwan 2004; Courtesy of SPOT-Image, France  Figure 6. Computation of the radial symmetric distortion for Formosat2 RSI lens by separating random errors (from GCPs) to systematic error (radial distortion) from the GCP residuals: the radius r (in pixel) in x-axis and residual/error (in pixel) in y-axis. In order to verify the impact of self-calibration, sensor orientation, DEM stereo-extraction and ortho-rectification were thus performed on RSI images. The DEM was generated using an area-based image correlation process and compared to 0.2-m accurate lidar data. Because the stereo-pairs and the Lidar data were acquired at different seasons with different planimetric resolutions, the compared elevations do not always exactly correspond to the same ground point and elevation; in fact the height, or a part, of the different surfaces (trees, buildings, etc.) is differently included in the elevation (Figure 8). The Linear Error with 68% level of confidence (LE68) was thus computed for the total overlap area and also for bare soils, where there are no height differences between the two compared ground-point elevations. Table 3. Impact of the self-calibration on sensor orientations for three Formosat2 RSI images with the RMS residuals at GCPs in the image space (x-column and y-row in pixel) and the improvement (in percentage)
Table 3 shows RMS errors of the sensor orientation of three RSI images: large improvements were obtained with the self-calibration, around 50% in the x-direction and more than 25% in the y-direction. Because the panchromatic CCDs are off-centred in y-axis of the focal plane results in radial symmetric distortion in both directions. These 1-2 pixel accurate results are mainly due to the 2-3 m error of the input data, which were not precise enough when compared to RSI sensor resolution (2 m). Even if sub-pixel accuracy could have been achieved, such as the results obtained using CCRS multi-sensor geometric model with other sensors (Toutin, 2003a), these 1.5-pixel accurate results are similar from previous experiments (2 pixels) (Chen et al., 2006). These results demonstrated (i) the range of the radial distortions to be around 1-2 and 0.5 resolutions of the RSI sensor in x-column and y-row directions respectively, and (ii) the necessity to apply lens calibration to achieve (sub-)pixel accuracy for the sensor orientation. Table 4 shows different results during the DEM generation process: improvements when using the self-calibration in the sensor orientation of three RSI images. Less mismatched areas are due to a better sensor orientation for generating the epipolar stereo-images. All elevations errors were also largely decreased with the self-calibration, and the largest improvement was for the bare soils comparison where no height difference occurred between the two compared elevations (stereo and lidar). Consequently without self calibration, the DEM error generated 8-m planimetric error on the ortho-image (Figure 1), which was acquired with 30º viewing angle, while the planimetric error was less than 3 m with self-calibration.
CONCLUDING REMARKS This review on sensor orientation and ortho-rectification of HR images has addressed different key issues: sources and modelling of geometric distortions during the image acquisition; types of delivered image-products; 3D physical end empirical modelling of these distortions and their applicability to the image-products; internal, relative and external sensor orientations; impacts of DEM and resampling kernel on the ortho-rectification. Applications were thus realized with stereo-images acquired on Quebec, Canada by the new Tawainese instrument RSI of Formosat2. Results show that accurate sensor orientation is a requisite to achieve sub-pixel accuracy in the geometric modelling, to stereo-extract 3-4 m accurate DEM and to generate 3-m accurate ortho-image. REFERENCES
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