Sensor Orientation and Ortho-Rectification of High Resolution Satellite Images:
Review and Application with FORMOSAT-2
HR data acquisition and their pre-processing
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
| SPOT5 | Cartosat1 | Formosat2 | OrbView3 | IKONOS-II | QuickBird3 | Radarsat2 |
|---|
| 0A | | | | | | Signal data |
| 1A | Standard OrthoKit Basic stereo | 1A | Basic | | Basic | Single look complex |
| 1B | | | | | Standard | Ground range |
| 2A | Standardgeoref | 2 | | Geo Standard | | Map |
| 2B | | | | Reference Pro | | Precision Map |
| 3 | Ortho Product | | Ortho | Precision
PrecisionPlus | Ortho DG DOQQ | Ortho |
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).
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:
- the ‘orientation’ of the image is a combination of the CCD line rotation, the platform heading due to orbital inclination, the yaw of the platform, the convergence of the meridian;
- the ‘scale factor’ in along-track direction is a combination of the line scale and focal length variations, the velocity, the altitude and the pitch of the platform, the detection signal time of the sensor, the component of the Earth rotation in the along-track direction; and
- the ‘levelling angle’ in the across-track direction is a combination of the principal point displacement, the platform roll, the viewing angle, the orientation of the sensor, the Earth curvature; etc.
Whatever the pre-processing level of data, the geometric model used and the method used for the sensor orientation, some GCPs (1-10) have to be acquired for computing or refining the different orientations parameters of the mathematical functions. GCP cartographic co-ordinates should be obtained from differential global positioning system (GPS) to insure the best results. If the accuracy of cartographic sources (maps, ortho-photos, etc.) is worse, the number of GCPs should be increased depending also of the final expected accuracy. These GCPs can also be used for the internal sensor orientation in a self-calibration.
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:
- to zero for the empirical models, because they do not reflect the image acquisition geometry; or
- from the osculatory orbital/flight and sensor parameters of each image for the physical models.
More information on least-squares methods applied to geomatics data can be obtained in Mikhail (1976) and Wong (1980). The results of this processing step are:
- the parameter values for the sensor orientation of each image;
- the residuals in X and Y directions (and Z if more than one image is processed) for each GCP/ETP/TP and their root mean square (RMS) residuals;
- the errors and bias in X and Y directions (and Z if more than one image is processed) for each ICP if any, and their RMS errors; and
- the computed cartographic coordinates for each point, including ETPs and TPs.
When more GCPs than the minimum theoretically required are used, the GCP residuals reflect the modelling accuracy, while the ICP rms errors reflect the final accuracy taking into account ICP accuracy. As mentioned previously, this final accuracy is mainly dependent on the geometric model and the number of GCPs used versus their cartographic and image co-ordinates. When ICPs are not accurate, their errors are included in the computed rms errors; consequently, the final internal accuracy of the modelling will be better than these rms errors.