2. SENSOR ORIENTATION AND ORTHO-RECTIFICATION Whatever the geometric models and its associated mathematical functions used, the method is more and less the same, and can be summarized in three processing steps:
With VIR-HR images, different types of image data with different levels of pre-processing can be obtained, but the different image providers unfortunately use a range of terminology to denominate the same type of image data. Table 2 gives the terminology of the different pre-processed products for some HR images. Table 2. Terminology of the different pre-processed products for some HR images
The raw level-1A images with only normalization and calibration of the detectors without any geometric correction are satellite-track oriented. For radar the equivalent is the slant range images. In addition, full metadata related to sensor, platform and image are provided. These level-1A images being the best and most preferred level were largely processed using physical models and achieved sub-pixel accurate results with all sensor types (Toutin, 2004). With empirical models, relatively bad results were achieved with QuickBird Basic images using 3D polynomial functions (Noguchi et al., 2004) but better results using RFM with QuickBird (Robertson, 2003) and Formosat (Chen et al., 2006), while Wolniewicz (2004) found better results using a physical model than RFM with QuickBird Basic images. Vendor-supplied RFM is also available with Cartosat and will be evaluated, as well as physical models, during the Cartosat-1 Scientific Assessment Program co-organized by ISPRS and ISRO. Finally, no RFM is supplied with SPOT-5 or RADARSAT-2/TerraSAR data due their inability to model high-frequency distortions inherent to raw images with large FOV (Madani, 1999). The georeferenced level-1B images corrected for systematic distortions due to the sensor, the platform and the Earth rotation and curvature are satellite-track oriented. For radar the equivalent is the ground range images. Generally, few metadata related to sensor and satellite are provided and some are related to 1B or slant-to-ground processing. Since they have been systematically corrected and georeferenced, the ‘level 1B’ images just retain the terrain elevation distortion, in addition to a rotation-translation related to the map reference system. A 3D 1st order polynomial model with two Z-elevation parameters could thus be efficient depending of the requested final accuracy but RFM supplied with QuickBird Standard data achieved also good results (Robertson, 2003). The map-oriented level-2A/B images are corrected for the same distortions as geo-referenced images are North oriented while ground control points (GCPs) were used more accurate positioning of 2B images. Generally, very few metadata related to sensor and satellite are provided; most of metadata are related to the 2A/B processing and the ellipsoid/map characteristics. Since these images only retain the elevation distortion a 3D 1st-order polynomial model with Z-elevation parameters in both axes can thus be efficient, even for SAR data, depending of the requested final accuracy (Ahn et al. 2001, Fraser et al. 2002, Vassilopoulou et al. 2002) but 3D 4th-order polynomial functions (Kersten et al. 2000, Vassilopoulou et al. 2002) without improvements. However, vendor-supplied RFM (Grodecki 2001) were also evaluated (Fraser et al. 2002, Tao and Hu 2002) using also GCPs either to remove bias (Fraser et al. 2002) or to improve the original RF parameters (Lee et al. 2002). Only few results were published in high relief terrain using 3D polynomial functions (Kersten et al. 2000, Vassilopoulou et al. 2002). Most of these experiments and results with pixel accuracy or better were achieved with very accurate cartographic data (0.10 m) in an academic environment where errors and processing are well controlled. On the other hand, operational studies obtained larger errors of few pixels (Davis and Wang 2001, Kristóf et al. 2002, Kim and Muller 2002, Tao and Hu 2002; Di et al., 2003). Finally although level-2 images are no more in their original geometry, physical models can be still approximated and developed for using basic information of the metadata (Toutin, 2003a) and has been proven to achieve better results than RFM in operational environments (Wolniewicz, 2004). 2.2. Sensor orientation Depending of the type of images and the final requested accuracy, the sensor orientation should include the internal orientation (principal point displacement, focal length variation, radial symmetric and decentering lens distortions, line scale variation, line rotation) and the external orientation (position, attitude, line of sight), as well as the relative orientation when more than one image is processed. In some cases, the sensor does not need an internal orientation because the parameters have been determined with well-controlled test-range imagery (Grodecki and Dial, 2003) or because they have already been corrected, such as for level-1B and 2. In other cases, some of the parameters and their impact are negligible in relation to the sensor resolution and the final accuracy. The sensor orientation can be performed step by step or integrated into a combined modelling. In fact, it is better to consider the total geometry of viewing (platform + sensor + Earth + map) in the sensor orientation, because some of their distortions are correlated and have the same type of impact on the ground. It is theoretically more precise to compute one ‘combined’ parameter only than each component of this ‘combined’ parameter, separately, avoiding also over-parameterization and correlation between terms. Some examples of ‘combined’ parameters include:
When more than one image is processed, a spatio-triangulation, generally a block bundle adjustment, can be performed to reduce the number of GCPs. All model parameters of each image/strip are determined by a common least-squares adjustment so that the individual models are properly tied in and the entire block is optimally oriented in relation to the GCPs. With the spatio-triangulation process, the same number of GCPs is theoretically needed to adjust a single image, an image strip or a block. However, some tie points (TPs) between the adjacent images have to be used to link the images and/or strips. This process has been successfully applied using either physical models (Toutin, 2003b) or empirical models (Grodecki and Dial, 2003, Fraser et al. 2002). They thus prevent the adjustment from diverging and they also filter the input errors. Since there are always redundant observations to reduce the input error propagation in the geometric models a least-square adjustment is generally used. When the mathematical equations are non-linear, which is the case for physical and 2nd and higher order empirical models, some means of linearization (series expansions or Taylor’s series) must be used. A set of approximate values for the unknown parameters in the equations must be thus initialized:
2.3. 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:
2.3.1. 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 |