Systematic Error Compensation Based on a Rational Function Model for Ziyuan1-02C

The Rational Polynomial Coefficients model (RPC) can be used directly to convert image coordinates and object space coordinates without using any satellite physical parameters such as position and attitude. Thus, RPCs are widely accepted by the industry. Based on the RPC model, the present study evaluates the accuracy of different evaluation methods for multi-source China's high-resolution satellite panchromatic images in Hebei Gu-yuan area. The accuracy is evaluated by the Mean Square Error evaluation method and the Circular Error evaluation method. And two methods are compared to get a better accuracy conclusion. The four scene images of this experiment are from Ziyuan-3, Gaofen-1A, Gaofen-1B, and Gaofen-1D satellites. Based on the coordinates of the ground point measured by GPS-RTK, the image coordinates and the artificial image point measurement are subtracted from the object coordinates according to the RPC model, and the results are statistically and accurately analyzed. Experiments show that the accuracy of ZY3-2 satellite imagery is higher than other satellites without ground control point (which surpasses 16.66 panchromatic pixels in the Circular Error evaluation method). Its sensor products have smaller exterior errors. The accuracy of GF-1D satellite imagery is higher than other satellites with ground control point (which surpasses 5.36 panchromatic pixels in the Circular Error evaluation method). It has smaller interior errors in sensor products. In addition, it has significant systematic errors.

Evaluation of Rational Function Model for High-Resolution KOMPSAT-5 SAR Imagery with Different Sizes of Virtual Grid and Reference Coordinate Systems

The volume of data generated by earth observation satellites has increased tremendously over the last few decades and will increase further in the coming decade thanks in particular to the launch of nanosatellites constellations. These data should open new avenues for Earth surface monitoring due to highly improved spectral, spatial and temporal resolution. Many applications depend, however, on the accuracy of the image geometric model. The geometry of optical images, whether acquired from pushbroom or frame systems, is now commonly represented using a Rational Function Model (RFM). While the formalism has become standard, the procedures used to generate these models and their accuracies are diverse. As a result, the RFM models delivered with commercial data are commonly not accurate enough for 3-D extraction, subpixel registration or ground deformation measurements. In this study, we present a methodology for RFM optimization and demonstrate its potential for 3D reconstruction using tri-stereo and multi-date Cubesat images provided by SkySat and PlanetScope, respectively. We use SkySat data over the Morenci Mine, Arizona, which is the largest copper mine in the United States. The re-projection error after the RFM refinement is 0.42 pix without using ground control points (GCPs). Comparison of our Digital Elevation Model (DEM with ~3 m GSD) with a reference DEM obtained from an airborne LiDAR survey (with ~1 m GSD) over stable areas yields a standard deviation of the elevation differences of ~3.9 m. The comparison of the two DEMs allows detecting and measuring the topographic changes due to the mine activity (excavation and stockpiles). We assess the potential of PlanetScope data, using multi-date DOVE-C images from the Shisper glacier, located in the Karakoram (Pakistan), which is known for its recent surge. We extracted DEMs in 2017 and 2019 before and after the surge. The re-projection error after the RFM refinement is 0.38 pix without using GCPs. The accuracy of our DEMs (with ~9 m GSD) is evaluated through comparison with the SRTM DEM (GSD ~30 m) and with a DEM (GSD ~2 m) calculated from Geoeye-1 (GE-1) and World-View-2 (WV-2) stereo images. The standard deviation of the elevation differences in stable areas between the PlanetScope DEM and SRTM is ~12 m, and ~7 m with the GE-1&WV-2 DEM. The mass transfer due to the surge is clearly revealed from a comparison of the 2017 and 2019 DEMs. The study demonstrates that, with the proposed scheme for RFM optimization, times series of DEM extracted from SkySat and PlanetScope images can be used to measure topographic changes due to mining activities or ice flow, and could also be used to monitor geomorphic processes such as landslides, or coastal erosion for example.

Digital surface models (DSMs) extracted from high-resolution Radarsat-2 stereo-images using different geometric modeling (deterministic, new hybrid, and empirical) are evaluated. The 3-D deterministic models are Toutin's and hybrid Toutin's models (TM and HTM) developed at the Canada Centre for Remote Sensing, and the empirical model is the rational function model (RFM). TM is computed with one and eight ground control points (GCPs), HTM without GCP and RFM supplied by MacDonald, Dettwiler and Associates Ltd. is postprocessed with 3-9 GCPs depending of degrees of 2-D polynomial functions. The DSMs are then generated and compared to 0.2-m accurate lidar elevation data. Because DSMs included the height of land covers, elevation linear errors with 68% and 90% confidence level (LE68 and LE90) are computed and compared over bare surfaces only. LE90 results are: TM with eight GCPs achieves the best results (6.3 m), then HTM with no GCP (7 m), TM with one GCP (8.6 m), and finally RFM the worst (9.7 m) whatever the polynomial degree and GCP number. HTM is the only modeling not using any GCP, which offers a strong advantage in operational environments.

The imagery vendors of the most advanced remote sensing satellites usually only provide the coefficients of rational function model (RFM) to replace the sensor model and the precise imaging parameters (orbit parameter, attitude parameter, and so on). So, the rigorous imaging model was limited to use in the geometric correction of remote sensing image. The RFM method could obtain a better correction performance in most cases. However, when the image contains few numbers or uneven distribution of ground control points (GCPs), such as infrared image, the RFM method could not obtain the expected performance. Therefore, a geometric correction method for linear pushbroom infrared imagery using compressive sampling (CS) is proposed. The core idea of the proposed method is to use the equivalent bias angles to approximate the influence of the errors (thermal distortion, optical distortion, assembly error, satellite orbit errors, attitude errors, and so on) in the imaging process and adopt the CS method to recover the equivalent bias angle signals. Most of the data are processed scene by scene with enough GCPs for each scene in conventional methods. This restriction is broken by using the sparsity of equivalent bias angle signals in the proposed method. The infrared images from the Hyperion of EO-1 are used as experiment data, and the results of experiments demonstrate the feasibility and superior performance of proposed method.

Identifying the optimal structure of terrain dependent Rational Function Models (RFMs) not only decreases the number of Ground Control Points (GCPs) required, but also increases the accuracy of the model, by reducing the multi-collinearity of Rational Polynomials Coefficients (RPCs) and avoiding the ill-posed problem. Global optimization algorithms such as Genetic Algorithm (GA), evaluate the different combinations of parameters effectively. Therefore, they have a high ability to detect the optimal structure of RFMs. However, one drawback of these algorithms is their high computation cost. This article proposes a knowledge-based search strategy to overcome this deficiency. The backbone of the proposed method relies on the technical knowledge about the geometric condition of image at the time of acquisition, as well as the effect of external factors such as terrain relief on the image. This method was evaluated on four different datasets, including a SPOT-1A, a SPOT-1B, an IKONOS-Geo image, and a GeoEye-Geo imagery, using various number of GCPs. Experimental results demonstrate the efficiency of the proposed method to achieve a sub-pixel accuracy using few GCPs (only 4–6 points) in all datasets. The results also indicate that the proposed method improves the computation speed by 140 times when comparing with GA.

The object-to-image transformation of high-resolution satellite images often involves a rational functional model (RFM). Traditionally, RFM uses point features to obtain the transformation coefficients. Since control lines offer greater flexibility than control points, this study proposes a new RFM approach based on linear features. The proposed methods include direct RFM and bias-compensated RFM using control lines. The former obtains the rational polynomial coefficients (RPCs) directly from control lines, whereas the latter uses sensor-orientated RPCs and control lines to determine compensated coefficients. The line-based RFMs include vector and parametric line representations. The experiments in this study analysed the effects of line number, orientation, and length using simulation and real data. The real data combined three-dimensional building models and high-resolution satellite images, such as IKONOS and QuickBird images. Experimental results show that the proposed algorithms can achieve pixel-level accuracy.

Georeferencing of high resolution satellite images using sensor-dependent Rational Function Model (RFM) is a common approach in the remote sensing community since the turn of the millennium. In the case of mono image evaluation, the georeferencing is performed using the ground control points (GCPs), and the image-wide georeferencing accuracy is estimated at the independent check points (ICPs). Nevertheless, such an accuracy assessment approach has some disadvantages and must be overcomed by a proper method as suggested by the figure condition analysis (FCA). Considering various bias compensation methods, the FCA is adopted to RFM and a case study is performed on three high resolution satellite images (HRSIs), IKONOS Geo, QuickBird OrthoReady Standard and OrbView-3 Basic, covering undulating and mountainous Zonguldak test site. The results demonstrate that a bias compensation is required for all images, and IKONOS has the highest accuracy both at GCPs and figure condition points (FCPs) where OrbView-3 has the lowest accuracy. The innovative characteristics of FCA and further research issues are also discussed.

Digital Elevation Model (DEM) generated by bistatic Synthetic Aperture Radar Interferometry (InSAR) usually has systematic plane and elevation errors. However, the DEM adjustment method based on the function model can only correct systematic elevation error, affecting the plane accuracy of DEM mosaic products. Given this issue, this paper proposes a three-dimensional InSAR-DEM block adjustment method based on general models with a separate adjustment strategy, that is, first correct vertical error using the adjustment method based on the function model and then correct horizontal error using the method based on Rational Function Model (RFM) after compensating for elevation errors. In order to extract the Tie Points (TPs) and Ground Control Points (GCPs) used in adjustment, we propose a Normalized Correlation Coefficient matching method based on Complex Slope Maps (NCC-CSM). We conduct experiments using 29 TanDEM-X Co-registered Single look Slant range Complex (CoSSC) data. The accuracies of adjustment results are verified using ICESat-2 ATL08 data and selected GCPs, respectively. The adjustment experiments show that the elevation accuracy of InSAR-DEM is improved from 1.70 m to 1.35 m, the absolute and relative plane accuracies are improved by 5.58 m and 11.53 m, respectively, and the horizontal and vertical geometric discontinuity in the overlapping area disappear. The matching experiments of TPs and GCPs show that the proposed NCC-CSM method is superior to the traditional NCC method based on DEM (NCC-DEM), especially in flat areas.

Nowadays, numerous earth-observation data are obtained from different kinds of platforms, in which data from synthetic aperture radar (SAR) sensors and optical sensors account for the vast majority. They have been widely used in different fields such as 3 dimensional (3D) geo-information reconstruction, object recognition and others. Researchers have investigated the suitability of the rational function model (RFM) for 3D geo-information production with stereo SAR-optical images. Compared with optical remote sensing data, parameters of the RFM for satellite SAR images are not provided to users in most cases, which increases the workload of users applying the SAR-optical stereo geolocation based on RFM. Moreover, the fitting accuracy of RFM to the Range Doppler (RD) model, which is considered as the rigorous sensor model for SAR imagery, do not always meet the requirements. Therefore, a new RD-RFM stereo geolocation model by integrating the RD model of SAR images with the RFM of optical images are proposed for 3D geo-information reconstruction with SAR-optical stereo image pairs. Experiments are conducted based on dataset from Gaofen-3 (GF-3) SAR satellite and Gaofen-2 (GF-2) optical satellite covering urban and mountainous areas in Xinyi City and Dengfeng City, Henan Province, China, respectively. Results indicated that our proposed model can achieve the best performance with different terrain and different convergence angle of stereo SAR-optical image pairs. Compared with the traditional stereo geolocation model based on the RFM for both SAR and optical data, our proposed model is more concise and efficient for the production of 3D geo-information with stereo SAR-optical image pairs, and it's easy to be implemented for users.

With the increasing demand for high-resolution remote sensing images for mapping and monitoring the Earth’s environment, geometric positioning accuracy improvement plays a significant role in the image preprocessing step. Based on the statistical learning theory, we propose a new method to improve the geometric positioning accuracy without ground control points (GCPs). Multi-temporal images from the ZY-3 satellite are tested and the bias-compensated rational function model (RFM) is applied as the block adjustment model in our experiment. An easy and stable weight strategy and the fast iterative shrinkage-thresholding (FIST) algorithm which is widely used in the field of compressive sensing are improved and utilized to define the normal equation matrix and solve it. Then, the residual errors after traditional block adjustment are acquired and tested with the newly proposed inherent error compensation model based on statistical learning theory. The final results indicate that the geometric positioning accuracy of ZY-3 satellite imagery can be improved greatly with our proposed method.

Abstract. ZiYuan-3 (ZY-3) mapping satellite is the first civilian high-resolution stereo mapping satellite of China. The satellite’s objective is oriented towards plotting 1:50,000 and 1:25,000 topographic maps. This article proposes ZY-3 mapping satellite Rigorous Image Geometry Model and Rational Function Model (RFM). In addition, this paper utilizes the image of the ZY-3 satellite with the region of flatlands, hills and mountains for the block adjustment experiment. Different ground control points are selected and the accuracy is validated by check points, and the some Digital Surface Model (DSM), Digital Orthophoto Map (DOM) are generated and the accuracy is also validated by check points. The experiment reveals that the planar accuracy of DOM and vertical accuracy of DSM are better than 3m and 2 m, respectively. The experiment demonstrates the effectiveness of ZY-3 mapping satellite image geometry model.

Due to its large area Large Scale Topographic Mapping (LSTM) for Indonesia requires acceleration strategies that must be innovative enough to take into account the production efficiency. Satellite-based technologies are still a preferable choice especially in conjunction with the security clearance and weather. Standards for the Very High-Resolution Satellite Imagery (VHRS) utilization are essential, especially in a situation where there are so many available sensors and processing methods implemented. Hence, the selection of a proper geometric correction method is fundamental in order to utilize the VHRS imagery as one source of geospatial data especially for LSTM production and updating purposes. For CSRT geometric correction, an orthorectification process is required, where this process requires input data from the Ground Control Point (TKT) and the Digital Elevation Model (DEM). Therefore, the Least Square Adjustment (LSA) method is implemented to be able to include 8-9 GCPs per-scene (orbital and sensor parameters) and the DEM with a maximum resolution 4 times of the VHRS imagery’s Ground Sampling Distance (GSD) in the process of producing VHRS orthoimages. In addition, the role of orbital and sensor parameters is also essential for the geometric correction because its relation to the Direct Georeferencing (DG) of each pixel by Rigorous Sensor Model (RSM) approach. However, in the situation where the reliable orbital and sensor parameters are not available, the Rational Function Model (RFM) can be used as an alternative solution for the geometric correction of VHRS imagery. This paper discusses the VHRS utilization with a comprehensive approach that can be implemented in a local coordinate system i.e. the Indonesian Geospatial Reference System for the production of the reliable VHRS imageries.

Abstract. Positioning accuracy is a key indicator that restricts the accuracy of satellite image mapping. Laser altimetry acquires surface height in decimeters or higher accuracy, providing high-accuracy topographic information for satellite photogrammetry. This study proposes a four-step high-accuracy positioning method called laser altimetry data-guided stereo images positioning (LGSP): photon outlier removal, digital surface model (DSM) generation by a variant of the tube-shape semi-global matching (tSGM), fast point cloud alignment, and DSM and rational function model (RFM) refining. First, outliers of the laser altimetry data are filtered out via confidence selection and open access DSM constraints. Second, the DSM around high-accuracy photons is generated via the variant of tSGM. Third, fast point cloud alignment is performed to align the DSM with laser altimetry data. Finally, we propose a high-resolution stereo model refinement method based on alignment parameters. Experiments on two satellite stereo datasets with different loads, resolutions, and topographies show that LGSP improved the planimetry accuracy of satellite stereo images after adding laser altimetry data. What’s more, LGSP significantly improved the height accuracy of satellite images. Specifically, LGSP reduced the height errors from the original 5.99 m to 1.00 m for the Ziyuan-3 stereo dataset and from the original 20.39 m to 0.83 m for the Gaofen-7 stereo dataset, and slightly outperformed bundle adjustment in which four ground control points were deployed around the four corners of the stereo images. RFM refining based on alignment parameters has been made publicly available at https://mega.nz/file/EFQASJ6A#BKjoupHVshylQR4wCxGd9BDtg08bhy-_aY-c_rHnl-0.

This study evaluates a methodology for using IKONOS stereo imagery to determine the height and position of buildings in dense residential areas. The method was tested on three selected sites in an area of 8.5 km long by 7 km wide and covered by two overlapping (97% overlap) IKONOS images. The images were oriented using rational function models in addition to ground control points. Buildings were identified using an algorithm that utilized the Digital Surface Model (DSM) extracted from the images in addition to the image spectral properties. A digital terrain model was used with the DSM created from the IKONOS stereo imagery to compute building heights. Positional accuracy and building heights were evaluated using corner coordinates extracted from topographic maps and surveyed building heights. The results showed that the average building detection percentage for the test area was 82.6% with an average missing factor of 0.16. When the image rational polynomial coefficients were used to build the image model, results showed a horizontal accuracy of 2.42 and 2.39 m Root Mean Square Error (RMSE) for the easting and northing coordinates, respectively. When ground control points were used, the results improved to the sub-meter level. Differences between building heights extracted from the image model and the corresponding heights obtained through traditional ground surveying had a RMSE of 1.05 m.