Rational Polynomial Coefficients Research Articles

The Impact of GCP Chip Distribution on Kompsat-3A RPC Bias Compensation

The vast potential of high-resolution satellite images, including Kompsat-3A, has been demonstrated across diverse applications, such as mapping and disaster monitoring. However, these images can only be utilized as reliable GIS (geographic information system) data when they possess precise geographical information. To achieve this, sensor model information, represented by RPCs (rational polynomial coefficients), requires bias compensation through GCPs (ground control points). Though having a substantial number of well-distributed GCPs across satellite images is ideal, the acquisition process is often restricted due to cost and inaccessibility. The uniform distribution of GCP chips is not guaranteed, necessitating an investigation into the impact of GCP distribution on the bias compensation process, which is the focus of this study. Experiments were meticulously conducted using Kompsat-3A data using dense GCP information. The dense GCP information was automatically generated from aerial orthoimages through a three-step process. Firstly, the GCP chips were extracted from the aerial images, focusing on feature points. Secondly, these chips were projected onto the target Kompsat-3A data to align them accurately. Lastly, precise satellite image coordinates of the chips were obtained through image matching between the chips and the target Kompsat-3A image. The dense GCPs enabled detailed bias analysis that exhibited skewness in most Kompsat-3A data. This necessitates the implementation of an affine model for proper bias compensation over the entire image space. Next, the study delved into the influence of GCP distribution on RPC bias compensation. To this end, each target satellite image space was divided into nine zones, with the dense GCPs assigned accordingly. The accuracy of bias compensation was analyzed across nine experimental cases, ranging from GCPs occupying only one zone to GCPs covering all nine zones. It was observed that GCPs covering at least four or five zones should be utilized for reliable RPC bias compensation of Kompsat-3A, especially when aiming for a high level of accuracy with an RMSE of one pixel. Finally, it was concluded that GCPs covering three zones yielded satisfactory results as a minimum GCP requirement, but this was contingent upon their distribution not following a straight zone pattern.

GPU Acceleration for SAR Satellite Image Ortho-Rectification

Synthetic Aperture Radar (SAR) satellite image ortho-rectification requires pixel-level calculations, which are time-consuming. Moreover, for SAR images with large overlapping areas, the processing time for ortho-rectification increases linearly, significantly reducing the efficiency of SAR satellite image mosaic. This paper thoroughly analyzes two geometric positioning models for SAR images. In order to address the high computation time of pixel-by-pixel ortho-rectification in SAR satellite images, a GPU-accelerated pixel-by-pixel correction method based on a rational polynomial coefficients (RPCs) model is proposed, which improves the efficiency of SAR satellite image ortho-rectification. Furthermore, in order to solve the problem of linearly increasing processing time for the ortho-rectification of multiple SAR images in large overlapping areas, a multi-GPU collaborative acceleration strategy for the ortho-rectification of multiple SAR images in large overlapping areas is proposed, achieving efficient ortho-rectification processing of multiple SAR image data in large overlapping areas. By conducting ortho-rectification experiments on 20 high-resolution SAR images from the Gaofen-3 satellite, the feasibility and efficiency of the multi-GPU collaborative acceleration processing algorithm are verified.

Asymptotic expansions relating to the distribution of the length of longest increasing subsequences

Abstract We study the distribution of the length of longest increasing subsequences in random permutations of n integers as n grows large and establish an asymptotic expansion in powers of $n^{-1/3}$ . Whilst the limit law was already shown by Baik, Deift and Johansson to be the GUE Tracy–Widom distribution F, we find explicit analytic expressions of the first few finite-size correction terms as linear combinations of higher order derivatives of F with rational polynomial coefficients. Our proof replaces Johansson’s de-Poissonization, which is based on monotonicity as a Tauberian condition, by analytic de-Poissonization of Jacquet and Szpankowski, which is based on growth conditions in the complex plane; it is subject to a tameness hypothesis concerning complex zeros of the analytically continued Poissonized length distribution. In a preparatory step an expansion of the hard-to-soft edge transition law of LUE is studied, which is lifted to an expansion of the Poissonized length distribution for large intensities. Finally, expansions of Stirling-type approximations and of the expected value and variance of the length distribution are given.

RELATIVE GEOMETRIC CORRECTION OF MULTIPLE SATELLITE IMAGES BY RIGOROUS BLOCK ADJUSTMENT

Abstract. With the development of satellite imaging technology, many Earth observation satellites have been launched and almost all areas of the Earth are daily covered by satellite images. It is promising to utilize such images in change detection, monitoring, semantic classification, etc. To obtain geometric information on each pixel in images, Rational Polynomial Coefficients (RPCs) of a Rational Functional Model (RFM) are provided with satellite images. However initial RPCs may include geometric errors. Therefore, errors in initial RPCs must be corrected before utilization. In this study, we attempt to perform rigorous block adjustments for refining RFMs of overlapping satellite images without ground control points. Our rigorous block adjustment method operated based on automatically extracted tie-points within overlapping areas. It estimates the optimal adjustment coefficients of RPCs and ground coordinates of tie-points. We achieved relative geometric correction of multiple satellite images by transforming the images based on the estimated adjustment coefficients. As a result, an initial RFM model with an error of around 21.73 pixels was corrected to within 1 pixel, and the reprojection error of check points decreased to 0.87 pixels. We also confirmed that our method showed more accurate results than general image registration methods, such as 2D homography transformation.

ATTENTION-GUIDED COST VOLUME REFINEMENT NETWORK FOR SATELLITE STEREO IMAGE MATCHING

Abstract. In remote sensing, disparity calculation using stereo images is a very necessary task and provides information for estimating the terrain elevation. The fields using disparity of stereo satellite images are used in various fields such as terrain models, autonomous driving using 3D maps, and content development. However, extracting disparity from stereo satellite images is a very difficult task, and inaccurate disparity may be extracted due to complex environments, façade areas of buildings, and texture-less areas. Our proposed method improves feature extraction and 3D aggregation steps based on Gwc-Net using stereo images rectified through RPC (Rational Polynomial Coefficients). To this achieve, we first improve the accuracy of the initial cost volume by extracting important features using the attention module 2D CBAM. In addition, in the aggregation step, we use 3D CBAM to extract important features from the cost volume and use GCE (Correlate-and-Excite) to guide image features to the cost volume to improve disparity. To evaluate the proposed method, the accuracy of disparity is evaluated using RPC-corrected stereo satellite images of DFC2019 data track2 of the US3D dataset. As a result of the experiment, the proposed method exhibited improvement compared to the baseline Gwc-Net.

Preliminary Evaluation of Geometric Positioning Accuracy of C-SAR Images Based on Automatic Corner Reflectors

C-SAR/01 and C-SAR/02 serve as successors to the GF-3 satellite. They are designed to operate in tandem with GF-3, collectively forming a C-band synthetic aperture radar (SAR) satellite constellation. This constellation aims to achieve 1 m resolution imaging with a revisit rate of one day. It can effectively cater to various applications such as marine disaster prevention, monitoring marine dynamic environments, and supporting marine scientific research, disaster mitigation, environmental protection, and agriculture. Geometric correction plays a pivotal role in acquiring highly precise geographic location data for ground targets. The geometric positioning accuracy without control points signifies the SAR satellite’s geometric performance. However, SAR images do not exhibit a straightforward image-point–object-point correspondence, unlike optical images. In this study, we introduce a novel approach employing high-precision automatic trihedral corner reflectors as ground control points (GCPs) to assess the geometric positioning accuracy of SAR images. A series of satellite-ground synchronization experiments was conducted at the Xilinhot SAR satellite calibration and validation site to evaluate the geometric positioning accuracy of different C-SAR image modes. Firstly, we calculated the azimuth and elevation angles of the corner reflectors based on satellite orbit parameters. During satellite transit, these corner reflectors were automatically adjusted to align with the radar-looking direction. We subsequently measured the exact longitude and latitude coordinates of the corner reflector vertex in situ using a high-precision real-time kinematics instrument. Next, we computed the theoretical image coordinates of the corner reflectors using the rational polynomial coefficients (RPC) model. After that, we determined the accurate position of the corner reflector in the Single Look Complex (SLC) SAR image using FFT interpolation and the sliding window method. Finally, we evaluated and validated the geometric positioning accuracy of C-SAR images by comparing the two coordinates. The preliminary results indicate that the positioning accuracy varies based on the satellite, imaging modes, and orbital directions. Nevertheless, for most sample points, the range positioning accuracy was better than 60 m, and the azimuth positioning accuracy was better than 80 m. These findings can serve as a valuable reference for subsequent applications of C-SAR satellites.

Does the Rational Function Model’s Accuracy for GF1 and GF6 WFV Images Satisfy Practical Requirements?

The Gaofen-1 (GF-1) and Gaofen-6 (GF-6) satellites have acquired many GF-1 and GF-6 wide-field-view (WFV) images. These images have been made available for free use globally. The GF-1 WFV (GF-1) and GF-6 WFV (GF-6) images have rational polynomial coefficients (RPCs). In practical applications, RPC corrections of GF-1 and GF-6 images need to be completed using the rational function model (RFM). However, can the accuracy of the rational function model satisfy practical application requirements? To address this issue, a geometric accuracy method was proposed in this paper to evaluate the accuracy of the RFM of GF-1 and GF-6 images. First, RPC corrections were completed using the RFM and refined RFM, respectively. The RFM was constructed using the RPCs and Shuttle Radar Topography Mission (SRTM) 90 m DEM. The RFM was refined via affine transformation based on control points (CPs), which resulted in a refined RFM. Then, an automatic matching method was proposed to complete the automatic matching of GF-1/GF-6 images and reference images, which enabled us to obtain many uniformly distributed CPs. Finally, these CPs were used to evaluate the geometric accuracy of the RFM and refined RFM. The 14th-layer Google images of the corresponding area were used as reference images. In the experiments, the advantages and disadvantages of BRIEF, SIFT, and the proposed method were first compared. Then, the values of the root mean square error (RSME) of 10,561 Chinese, French, and Brazilian GF-1 and GF-6 images were calculated and statistically analyzed, and the local geometric distortions of the GF-1 and GF-6 images were evaluated; these were used to evaluate the accuracy of the RFM. Last, the accuracy of the refined RFM was evaluated using the eight GF-1 and GF-6 images. The experimental results indicate that the accuracy of the RFM for most GF-1 and GF-6 images cannot meet the actual use requirement of being better than 1.0 pixel, the accuracy of the refined RFM for GF-1 images cannot meet practical requirement of being better than 1.0 pixel, and the accuracy of the refined RFM for most GF-6 images meets the practical requirement of being better than 1.0 pixel. However, the RMSE values that meet the requirements are between 0.9 and 1.0, and the geometric accuracy can be further improved.

Improvement and Assessment of Gaofen-3 Spotlight Mode 3-D Localization Accuracy

The spotlight image acquired by the Gaofen-3 satellite has a resolution of 1 m, which has great potential for 3-D localization. However, there have been no public reports on the 3-D localization accuracy evaluation of Gaofen-3 spotlight synthetic aperture radar (SAR) images. Here, three study areas were selected from this perspective, and the SAR spotlight stereo images of the study area were acquired using Gaofen-3. In the case of no ground control points (GCPs), based on the Rational Polynomial Coefficient (RPC) model, these images were used for initial 3-D localization; the plane accuracy was better than 10 m in general, and the elevation accuracy was worse than 37 m in general. Subsequently, the RPC model was optimized using geometric calibration technology, and the 3-D localization accuracy was assessed again. The elevation accuracy was significantly improved, which was generally better than 5 m. The plan accuracy was also improved, and it was generally better than 6 m. It can be seen that Gaofen-3 spotlight stereo images are of good quality, and high plane accuracy can be obtained even without GCPs. Geometric calibration technology improves the 3-D localization accuracy, and the elevation accuracy optimization effect is remarkable. Moreover, the optimization effect of plane accuracy is affected by the properties of stereo-image pairs. The optimization effect of plane accuracy is obvious for asymmetric stereo-image pairs, and the optimization effect of plane accuracy is general for symmetric stereo-image pairs.

GEMVS: a novel approach for automatic 3D reconstruction from uncalibrated multi-view Google Earth images using multi-view stereo and projective to metric 3D homography transformation

ABSTRACT This paper proposes a novel approach for automatic 3D surface reconstruction from uncalibrated and multi-view Google Earth images by using a multi-view stereo method and 3D projective to metric transformation. Without the Rational Polynomial Coefficients, it is impossible to obtain the metric reconstruction of the 3D surface from multi-view satellite images. We solve the uncalibrated multi-view satellite image problem by employing a multi-view stereo vision technique followed by a projective to metric transformation. The virtual pose parameters of the satellite images are obtained by using COLMAP, and the virtual 3D projective reconstruction is done by using EnSoft3D. For projective to metric transformation, we propose to employ 3D homography transformation. Eight 3D correspondence pairs on the viewing frustums between the virtual reference camera and the ideal nadir camera are used to derive a 3D homography matrix. Using the 3D homography matrix, we finally obtain the metric reconstruction of 3D surface up to an unknown height scale in a reference coordinate system of the Google Earth desktop software. Experiments are done in several world locations on Google Earth including building and vegetation areas. Reconstruction error analysis with the Data Fusion Contest 19 dataset is also presented. The average of MAE and RMSE of five tile regions in the dataset are 1.596 m and 2.083 m, respectively.

Radiometric Terrain Correction Method Based on RPC Model for Polarimetric SAR Data

Radiometric terrain correction (RTC) is an important preprocessing step for synthetic aperture radar (SAR) data application in mountainous areas. At present, the RTC processing of SAR depends on the Range Doppler (RD) positioning model. However, the solution of this model has a high threshold for ordinary remote sensing technicians. To solve this problem, we propose an RTC method based on the rational polynomial coefficient (RPC) model, which is widely used in optical remote sensing and is simpler and more practical than the RD model. China’s GF-3 polarimetric SAR data were used to verify the proposed method. The experimental results showed that the RTC method based on RPC is effective and can achieve better correction effects on the premise of reducing the complexity of the algorithm. The correction effect based on the RPC model can be similar to that based on the RD model. The proposed approach can realize the correction of 4~5 dB terrain radiation distortion to a 0.5 dB level.

고해상 위성 스트립 영상의 GCP 칩을 이용한 경제적인 RPCs 보정

CCD (Charged-Coupled Device) 푸쉬부룸 센서에 기반한 대부분의 고해상도 위성은 스트립 모드 촬영을 기본으로 하고 있다. 촬영 방향으로 길게 획득되는 스트립 영상은 궤도 정보를 활용하여 엄밀모델에 기반한 센서모델 처리가 이루어진다. 처리된 데이터는 관리하기 쉬운 단위 영상으로 쪼개져 제공되고 센서모델 또한 사용자가 이용하기에 편리한 RPCs (Rational Polynomial Coefficients)의 형태로 제공된다. 그러나 RPCs 데이터는 오차를 내포하고 있기 때문에, GCPs (Ground Control Points) 등 지상 기준정보를 활용하여 해당 오차를 보정 후 보다 정확한 좌표 정확도를 확보하여야 한다. 최근에는 자동화된 처리를 위해 항공사진이나 기구축 위성영상에 기반한 GCPs 칩 형태의 지상 기준정보가 많이 활용되고 있다. 그러나 이러한 칩은 초기 구축비용이 높고 시간이 지남에 따라 지형이 변화하므로 칩 또한 갱신해야 하는 등 관리에도 비용이 소요된다. 따라서 RPCs 오차 보정 시 필요한 기준 GCP chip의 개수를 적게 활용한다면 보다 경제적인 처리가 가능해질 수 있다. 따라서 본 연구에서는 단위 영상이 아닌 스트립 영상을 RPCs 보정 처리에 활용하여 기준점 수를 줄여보고자 하였다. 즉, 스트립 기반 RPCs 오차 보정과 단위 영상기반 RPCs 보정을 비교·분석하고 그 경제성에 대해 분석하였다. GCPs 칩 개수를 줄여가며 스트립 기반 RPCs 보정을 수행하고 그 영향에 대해 분석하였다. 그 결과 동일한 개수의 GCPs가 활용될 경우 제약조건 도입 시 정확도가 향상되는 것을 확인하였으며, GCPs가 부족한 경우에도 보정이 가능해짐을 확인할 수 있었다.

Resampling Estimation Based RPC Metadata Verification in Satellite Imagery

Recent advances in machine learning and computer vision have made it simple to manipulate a variety of media, including satellite images. Most of the commercially available satellite images go through the process of orthorectification to remove potential distortions due to terrain variations. This orthorectification process typically involves the use of rational polynomial coefficients (RPC) that geometrically remap the pixels in the original image to the rectified image. This paper proposes the first method to verify the authenticity of RPC metadata in an orthorectified satellite image. The steps include calculating the Residual Discrete Fourier Transform (DFT) pattern from the image using a linear predictor based residual spectral analysis and comparing with Expected Residual DFT pattern that is obtained using the RPC metadata associated with the image. If the metadata associated with orthorectified image is correct, then the Residual-DFT pattern (which represents image data) and the Expected-Residual-DFT pattern (which represents metadata) should be similar. We use SSIM (Structural Similarity Index Metric) to quantify the similarity and thereby verify if the data has been tampered or not. Detailed experimental results demonstrate that our method achieves over 97% accuracy in the majority of binary tampering detection tests.

Geometric Quality Improvement Method of Optical Remote Sensing Satellite Images Based on Rational Function Model

The high-precision geometric positioning of optical remote sensing satellites is the prerequisite to determine the application capability of satellite image products. Its positioning accuracy is related to the observation accuracy of each link in the imaging process, including satellite attitude, orbit measurement accuracy, time synchronization accuracy, camera measurement accuracy, and so on. Untimely and inaccurate on-orbit calibration will lead to great geometric positioning errors. To optimize the positioning accuracy of satellite images with the rational function model (RFM) under low positioning accuracy, our paper proposes an improved geometric quality model based on the reorientation of internal and external orientation elements in the RFM model of remote sensing images. By establishing the rational function positioning model, the external orientation model, and the internal orientation model, the original image can be reorientated. Then, we use the improved model to generate uniformly distributed virtual ground control points. By analyzing and verifying the relationship between each rational polynomial coefficient (RPC) and its influence on geometric positioning accuracy, we propose an RPC coefficients optimization method based on image offset correction and positioning dominant coefficients. Finally, we use the small satellite “MN200Sar-1” with low geometric accuracy for experimental verification. The results show that the model can effectively eliminate the errors of internal and external elements in the on-orbit calibration, and the positioning accuracy is improved from one hundred pixels to one pixel. At the same time, the rational polynomial dominant coefficient optimization method can improve geometric positioning accuracy without introducing additional compensation parameters.

Improvement of VHR Satellite Image Geometry with High Resolution Elevation Models

The number of high and very high resolution (VHR) optical satellite sensors, as well as the number of medium resolution satellites is continuously growing. However, not all high-resolution optical satellite imaging cameras have a sufficient and stable calibration in time. Due to their high agility in rotation, a quick change in viewing direction can lead to satellite attitude oscillation, causing image distortions and thus affecting image geometry and geo-positioning accuracy. This paper presents an approach based on re-projection of regularly distributed 3D ground points from object in image space, to detect and estimate the periodic distortions of Pléiades tri-stereo imagery caused by satellite attitude oscillations. For this, a hilly region was selected as a test site. Consequently, we describe a complete processing pipeline for computing the systematic height errors (deformations, waves) of the satellite-based digital elevation model by using a Lidar high resolution terrain model. Ground points with fixed positions, but with two elevations (actual and corrected) are then re-projected to the satellite images with the aid of the Rational Polynomial Coefficients (RPCs) provided with the imagery. Therefore, image corrections (displacements) are determined by computing the differences between the distinct positions of corresponding points in image space. Our experimental results in Allentsteig (Lower Austria) show that the systematic height errors of satellite-based elevation models cannot be compensated with an usual or even high number of Ground Control Points (GCPs) for RPC bias correction, due to insufficiently known image orientations. In comparison to a reference Lidar Digital Terrain Model (DTM), the computed elevation models show undulation effects with a maximum height difference of 0.88 m in along-track direction. With the proposed method, image distortions in-track direction with amplitudes of less than 0.15 pixels were detected. After applying the periodic distortion compensation to all three images, the systematic elevation discrepancies from the derived elevation models were successfully removed and the overall accuracy in open areas improved by 33% in the RMSE. Additionally, we show that a coarser resolution reference elevation model (AW3D30) is not feasible for improving the geometry of the Pléiades tri-stereo satellite imagery.

How to Orient and Orthorectify PRISMA Images and Related Issues

The orientation of satellite images is a necessary operation for the correct geometric use of satellite images whether they are used individually to obtain an orthophoto or as stereocouples to extract three-dimensional information. The orientation allows us to reconstruct the correct position on the ground of the single pixels that form the image, which normally can be performed using certain functions of commercial software customised for each specific satellite. These functions read the metadata parameters provided by the satellite operator and use them to correctly orient the images. Unfortunately, these parameters have not been standardised and various satellites report them according to variable conventions, so new satellites or those that are not widely used cannot be oriented automatically. The PRISMA satellite launched by the Italian Space Agency (ASI) releases free hyperspectral and panchromatic images with metric resolution, but there is not yet a standardised procedure for orienting its images and this limits its usability. This paper reports on the first experimentation of orientation and orthorectification of PRISMA (PRecursore IperSpettrale della Missione Applicativa) images carried out using the three most widely used models, namely the rigorous, the Rational Polynomial Coefficients (RPC) and the Rational Polynomial Functions (RPF) tools. The results obtained by interpreting the parameters and making them suitable for use in standard procedures have made it possible to obtain results with an accuracy equal to the maximum resolution of panchromatic images (5 m), thus making it possible to achieve the highest level of geometric accuracy that can be extracted from the images themselves.

SkySat Data Quality Assessment within the EDAP Framework

Cal/Val activities within the Earthnet Data Assessment Pilot (EDAP) Project of the European Space Agency (ESA) cover several Earth Observation (EO) satellite sensors, including Third-Party Missions (TPMs). As part of the validation studies of very-high-resolution (VHR) sensor data, the geometric and radiometric quality of the images and the mission compliance of the SkySat satellites owned by Planet were evaluated in this study. The SkySat constellation provides optical images with a nominal spatial resolution of 50 cm, and has the capacity for multiple visits of any place on Earth each day. The evaluations performed over several test sites for the purpose of the EDAP Maturity Matrix generation show that the high resolution requirement is fulfilled with high geometric accuracy, although various systematic and random errors could be observed. The 2D and 3D information extracted from SkySat data conform to the quality expectations for the given resolution, although improvements to the vendor-provided rational polynomial coefficients (RPCs) are essential. The results show that the SkySat constellation is compliant with the specifications and the accuracy results are within the ranges claimed by the vendor. The signal-to-noise ratio assessments revealed that the quality is high, but variations occur between the different sensors.

Digital surface model generation from high-resolution satellite stereo imagery based on structural similarity

In this study, we proposed an automatic approach to extract DSMs from VHR satellite imagery. This study aims to apply the histogram of orientated phase congruency (HOPC) descriptor and SIFT-Flow algorithm to match multi-view VHR satellite images densely and extract detailed DSMs competitive with ones generated from Light Detection and Ranging (LiDAR) point clouds. The HOPC descriptor relies on detecting features by calculating the phase congruency model, which allows the image features to be highly robust against illumination changes. Moreover, we developed an automatic algorithm to extract precise and homogenously distributed tie-points and subsequently conduct bias correction of the Rational Polynomial Coefficients (RPC). We tested our proposed algorithm on four WorldViw-3 datasets captured from different viewpoints, and compared the results with the DSMs obtained by the Semi-Global Matching (SGM) algorithm. The experimental results indicated the proficiency of our proposed method in generating accurate and reliable DSMs using VHR satellite data.

Automated RPCs Bias Compensation for KOMPSAT Imagery Using Orthoimage GCP Chips in Korea

High-resolution satellite images, including KOMPSAT, WorldView-3, and Pléiades, are widely used for mapping and environmental monitoring. In particular, satellite images with high spatial resolution should have accurate location information to provide essential spatial information. To this end, most high-resolution satellite images files are provided with rational polynomial coefficients (RPCs) that can be used for the sensor modeling. However, the RPCs have an initial bias. Therefore, most satellite image platforms and researchers match satellite images using ground control points (GCPs) information and perform RPCs bias compensation of images using matching information. In Korea, an image-based GCP chip built using orthographic images is provided for the georegistration of various satellite images. In this manuscript, RPCs bias compensation of KOMPSAT-3A satellite images was performed using GCP chips, and then, the possibility of automation of RPCs bias compensation through GCP chip was analyzed. Image matching such as area-based and edge-based techniques were used, and the results of RPCs bias compensation using GCP chips were analyzed through experiments in various regions. The automated compensation in either area-based or edge-based matching performed well with within 1.5 pixel level of accuracy for test areas with various topographic features. However the forest area was challenging such that new GCP chips with rich feature information were required. In addition, edge-based matching could overcome large seasonal differences including snow cover.

Pursuing 3-D Scene Structures With Optical Satellite Images From Affine Reconstruction to Euclidean Reconstruction

How to use multiple optical satellite images to recover the 3D scene structure is a challenging and important problem in the remote sensing field. Most existing methods in literature have been explored based on the classical RPC (Rational Polynomial Coefficients) camera model which requires at least 39 GCPs (ground control points), however, it is non-trivial to obtain such a large number of GCPs in many real scenes. Addressing this problem, we propose a hierarchical reconstruction framework based on multiple optical satellite images, which needs only 4 GCPs to fully-automated reconstruct the 3D scene structure. The proposed framework is independent from the RPC model and composed of a dense affine reconstruction stage and a followed affine-to-Euclidean upgrading stage: At the dense affine reconstruction stage, a dense affine reconstruction approach is explored for pursuing the 3D affine scene structure without any GCP from input satellite images. Then at the affine-to-Euclidean upgrading stage, the obtained 3D affine structure is upgraded to a Euclidean one with 4 GCPs. Experimental results on two public datasets demonstrate that the proposed method significantly outperforms several state-of-the-art methods in most cases.

Robust Camera Distortion Calibration via Unified RPC Model for Optical Remote Sensing Satellites

On-orbit geometric calibration (GC) is always performed to compensate for geometric distortion from the satellite’s camera. However, the traditional GC method is complex and difficult to apply broadly due to its reliance on a rigorous physical model (RPM), which involves not only complex processing of attitude, orbit, and time, but also the transformation among multiple coordinate systems. Additionally, the RPM is closely related to designs of satellites and cameras, which increases the complexity of the GC, and thus reduces generalizability. This paper proposes a practical and robust GC method to prevent camera distortion based on a standardized rational polynomial coefficient (RPC) model. Through a series of innovations, including stepwise optimization, a priori gross error elimination, the adjustment model with angular resolution, and the correction for the bias field-of-view (FOV) distortion, we were able to achieve robust GC for camera distortion, as well as accurate splicing and registration among segmented images. Method validation using data from the linear-array camera of the ZiYuan3-02 satellite, and the area-array camera of the GaoFen-4 satellite, produced satisfactory results, indicating that our method effectively compensates for systematic geometric distortion such that consistent GC and accuracy comparable with that of traditional RPM-based methods can be obtained.