A Knowledge-Based Search Strategy for Optimally Structuring the Terrain Dependent Rational Function Models

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 correct representation of the topography of terrain is an important requirement to generate photogrammetric products such as orthoimages and maps from high-resolution (HR) or very high-resolution (VHR) satellite datasets. The refining of the digital elevation model (DEM) for the generation of an orthoimage is a vital step with a direct effect on the final accuracy achieved in the orthoimages. The refined DEM has potential applications in various domains of earth sciences such as geomorphological analysis, flood inundation mapping, hydrological analysis, large-scale mapping in an urban environment, etc., impacting the resulting output accuracy. Manual editing is done in the presented study for the automatically generated DEM from IKONOS data consequent to the satellite triangulation with a root mean square error (RMSE) of 0.46, using the rational function model (RFM) and an optimal number of ground control points (GCPs). The RFM includes the rational polynomial coefficients (RPCs) to build the relation between image space and ground space. The automatically generated DEM initially represents the digital surface model (DSM), which is used to generate a digital terrain model (DTM) in this study for improving orthoimages for an area of approximately 100 km2. DSM frequently has errors due to mass points in hanging (floating) or digging, which need correction while generating DTM. The DTM assists in the removal of the geometric effects (errors) of ground relief present in the DEM (i.e., DSM here) while generating the orthoimages and thus improves the quality of orthoimages, especially in areas such as Dehradun that have highly undulating terrain with a large number of natural drainages. The difference image of reference, i.e., edited IKONOS DEM (now representing DTM) and automatically generated IKONOS DEM, i.e., DSM, has a mean difference of 1.421 m. The difference DEM (dDEM) for the reference IKONOS DEM and generated Cartosat-1 DEM at a 10 m posting interval (referred to as Carto10 DEM) results in a mean difference of 8.74 m.

Georeferenced archival aerial images are key elements for the study of landscape evolution in the scope of territorial planning and management. The georeferencing process proceeds by applying to photographs advanced digital photogrammetric techniques integrated along with a set of ground truths termed ground control points (GCPs). At the end of that stage, the accuracy of the final orthomosaic is assessed by means of root mean square error (RMSE) computation. If the value of that index is deemed to be unsatisfactory, the process is re-run after increasing the GCP number. Unfortunately, the search for GCPs is a costly operation, even when it is visually carried out from recent digital images. Therefore, an open issue is that of achieving the desired accuracy of the orthomosaic with a minimal number of GCPs. The present paper proposes a geostatistically-based methodology that involves performing the spatialization of the GCP errors obtained from a first gross version of the georeferenced orthomosaic in order to produce an error map. Then, the placement of a small number of new GCPs within the sub-areas characterized by the highest local errors enables a finer georeferencing to be achieved. The proposed methodology was applied to 67 historical photographs taken on a geo-morphologically complex study area, located in Southern Italy, which covers a total surface of approximately 55,000 ha. The case study showed that 75 GCPs were sufficient to garner an orthomosaic with coordinate errors below the chosen threshold of 10 m. The study results were compared with similar works on georeferenced images and demonstrated better performance for achieving a final orthomosaic with the same RMSE at a lower information rate expressed in terms of nGCPs/km2.

Ground control points (GCPs) are used in the process of indirectly georeferencing Unmanned Aerial Systems (UAS) images. A minimum of three ground control points (GCPs) is required but increasing the number of GCPs will lead to higher accuracy of the final results. The aim of this study is to provide the answer to the question of how many ground control points are necessary in order to derive high precision results. To obtain the results, an area of about 1 ha was photographed with a low-cost UAS, namely, the DJI Phantom 3 Standard at two different heights, 28 m and 35 m above ground, the camera being oriented in a nadiral position, and 50 ground control points were measured using a total station. In the first and the second scenario, the UAS images were processed using the Pix4D Mapper Pro software and 3DF Zephyr, respectively, by performing a full bundle adjustment process with the number being gradually increased from three GCPs to 40. The third test was made with 3DF Zephyr Pro software using a free-network approach in the bundle adjustment. Also, the point clouds and the mesh surfaces derived automatically after using the minimum and the optimum number of GCPs, respectively, were compared with a terrestrial laser scanner (TLS) point cloud. The results expressed a clear overview of the number of GCPs needed for the indirect georeferencing process with minimum influence on the final results.

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.

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.

A rational function model (RFM) can be used directly to convert the relationships between image coordinates and object space coordinates without using any physical imaging parameters (such as satellite position and attitude). Thus, RFMs facilitate versatility and high security during geometric processing of optical satellite imagery. Increasingly, RFMs are offered to users as the basic geolocation model for further geometric processing by imagery vendors. However, imagery vendors might perform inadequate in-orbit geometric calibrations, or the calibrated geometric parameters might not be updated in a timely manner. Thus, the RFMs may suffer from high distortion due mainly to interior errors (such as lens distortion). Using the radiometric correction products of Ziyuan1-02C panchromatic and multispectral sensor as examples, the present study addresses the compensation of systematic errors in RFMs. An undistorted RFM can be generated after calibrating the interior error compensation model once, before high-accuracy registration between the panchromatic imagery and multispectral imagery can be achieved using the undistorted RFM. Experimental evaluations based on the positioning accuracy using a few ground control points (GCPs) with an undistorted RFM matched the accuracy of the GCPs. In addition, our approach greatly improves the accuracy of registration (which surpasses 0.7 panchromatic pixels) between panchromatic and multispectral imagery.

Recently, photogrammetric products produced using Unmanned Aerial Vehicles (UAVs) are frequently preferred for disaster management, geological, and meteorological studies, urban studies and military purposes. Obtaining products with UAV photogrammetry provides a significant advantage over ground-based methods in terms of speed and cost. At the same time, the accuracy of the products produced is of particular importance. In this study, the effects of the number of Ground Control Points (GCPs) and GCP network design on accuracy were investigated. In this direction, 12 GCPs with homogeneous distribution in the study area were established and their locations were determined by GNSS measurements. Then, scenarios with different number of GCPs and different network designs were created, and the accuracy of these points were evaluated. As a result, it has been concluded that 5 GCPs homogeneously distributed in the field is sufficient for the products at high accuracy (≤ 10 cm) required in geomatics applications, increasing the number of the GCPs will not benefit the accuracy of the project and this process is disadvantageous in terms of increasing the cost along with the speed.

Aim. Determination of the elements of external spatial orientation of the surveying systems at the moment of image acquisition is the fundamental task in photogrammetry. Principally, this problem is solving in two ways. The first way is direct positioning and measuring of directions of camera optical axis in the geodetic space with the help of GNSS/INS equipment. The second way is the analytical solution of the problem using a set of reference information (often such information is a set of ground control points whose geodetic positions are known with sufficient accuracy and which are reliably recognised on aerial images of the photogrammetric block). The authors consider the task of providing reference and control information using the second approach, which has a number of advantages in terms of reliability and accuracy of determining the unknown image exterior orientation parameters. It is proposed to obtain additional images of ground control points by the method of their auxiliary aerial photography using an unmanned aerial vehicle (UAV) on a larger scale compared to the scale of the images of the photogrammetric block. The aim of the presented work is the implementation of the method of creating reference points and experimental confirmation of its effectiveness for photogrammetric processing. Methods and results. For the entire realization of the potential of the analytical way to determine the elements of external orientation of images, it is necessary to have a certain number of ground control points (GCP) and to keep the defined scheme of their location on the photogrammetric block. As the main source of input data authors use UAV aerial images of the terrain, which are obtained separately from the block of aerial survey, and have a better geometric resolution and which clearly depict the control reference points. Application of such auxiliary images gives the possibility of automated transferring of the position of ground control point into images of the main photogrammetric block. In our interpretation, these images of ground control points and their surroundings on the ground are called "control reference images". The basis of the work is to develop a method for obtaining the auxiliary control reference images and transferring of position of GCP depicted on them into aerial or space images of terrain by means of computer stereo matching. To achieve this goal, we have developed a processing method for the creation of control reference images of aerial image or a series of auxiliary multi-scale aerial images obtained by a drone from different heights above the reference point. The operator identifies and measures the GCP once on the auxiliary aerial image of the highest resolution. Then there is an automatic stereo matching of the control reference image in the whole series of auxiliary images in succession with a decrease in the resolution and, ultimately, directly with the aerial images of photogrammetric block. On this stage there are no recognition/cursor targeting by the human operator, and therefore there are no discrepancies, errors or mistakes related to it. In addition, if to apply fairly large size of control reference images, the proposed method can be used on a low-texture terrain, and therefore deal in many cases without the physical marking of points measured by GNSS method. And this is a way to simplify and reduce the cost of photogrammetric technology. The action of the developed method has been verified experimentally to provide the control reference information of the block of archival aerial images of the low-texture terrain. The results of the experimental approbation of the proposed method give grounds to assert that the method makes it possible to perform geodetic reference of photogrammetric projects more efficiently due to the refusal of the physical marking of the area before aerial survey. The proposed method can also be used to obtain the information for checking the quality of photogrammetric survey for provision of check points. The authors argue that the use of additional equipment - UAV of semi-professional class to obtain control reference images is economically feasible. Scientific novelty and practical relevance. The results of approbation of the "control reference image" method with obtaining stereo pairs of aerial images with vertical placement of the base are presented for the first time. There was implemented the study of the properties of such stereo pairs of aerial images to obtain images of reference points. The effectiveness of including reference images in the main block of the digital aerial triangulation network created on UAV’s images is shown.

Abstract. The Tian-Hui 1 (TH-1) is the first stereo mapping transmission satellite in China, and the primary mission goal of the satellite is for topographic mapping at 1:50,000 scale without Ground Control Points (GCPs). 1st, 2nd and 3rd satellite of TH-1 was launched on August 24, 2010, May 6, 2012 and October 26, 2015. In TH-1 satellite, many payloads are put on a small satellite platform, which has a low cost. The optical camera of TH-1 includes Line-Matrix CCD (LMCCD) camera, high resolution camera and multispectral camera with 60 km ground swath width. To get high geometric accuracy without GCPs, the on-orbit calibration camera parameters and the Equivalent Frame Photo (EFP) Multi-functional bundle adjustment are proposed and realized in ground image processing of TH-1. In order to evaluate the location accuracy of TH-1, some testing fields are established. All GCPs of testing fields are measured by GPS. The GCPs are not participated the EFP Multi-functional bundle adjustment, and are only as Check Points (CPs) to evaluate the location accuracy. The evaluation of 1st satellite is shown: the horizontal accuracy is 10.3 m (RMSE) and the vertical accuracy is 5.7 m (RMSE) without GCPs, which can satisfy for topographic mapping at 1:50,000 scale. The overviews of TH-1 satellite are described in this paper: First, the system overview is introduced, including mission and optical camera of TH-1. Then, the on-orbit calibration camera parameters using LMCCD image and the EFP Multi-functional bundle adjustment are presented. Finally, the location performance is analysed without GCPs and with different number of GCPs. In addition, the products of TH-1 are introduced.

Abstract. Utilizing ground control points (GCPs) to georeference photogrammetry-based point cloud data is a common practice in unmanned aerial system (UAS) mapping. Direct georeferencing or integrated sensor orientation (ISO) can be used to obtain georeferenced point clouds from UAS without relying heavily on GCPs. However, the accuracy of the point cloud may be impacted by the accuracy of the trajectory solution obtained by GNSS. To improve point cloud accuracy, post-processing kinematic (PPK) solutions can be applied to the UAS trajectory, which may provide higher accuracy than low-accuracy trajectory solutions and minimize the reliance on GCPs. This study compares the accuracy and precision of two different point clouds generated using different methods. One point cloud was generated using traditional photogrammetric methods with low accuracy Global Navigation Satellite System (GNSS) observations from the UAS and GCPs that have an average accuracy of one to two centimeters, while the other was generated using PPK trajectory solution for the UAS’s trajectory with two software: open-source Emlid Studio and the widely used Inertial Explorer. The use of PPK techniques in UAS mapping may have several potential benefits over traditional methods. By correcting the errors in the UAS's trajectory, a user may only need to depend on fewer ground control points, which can reduce the time and cost associated with fieldwork. This is particularly useful in areas that are difficult to access or have limited ground control point options, such as in urban or forested areas. To evaluate performance, a GNSS receiver is used to obtain measurements on checkpoints, which are used to assess the accuracies of the point clouds. In our experiments, the accuracy of the point clouds generated using PPK trajectory solution with high accuracy GCPs was found to be higher than those generated with low accuracy GNSS observations while aided with high accuracy ground control points. While the use of PPK with GCPs is generally expected to provide more accurate and reliable data than low-accuracy GNSS observations even after adjusting with GCPs, the number and distribution of GCPs can still significantly impact overall accuracy. Therefore, careful consideration of the number of GCPs and their placement is essential to achieve the desired level of efficiency and effectiveness in UAS mapping.

UAV기반 멀티센서 시스템을 통해 취득된 영상의 지오레퍼런싱 정확도는 사용된 GPS/INS 시스템의 성능뿐만 아니라 카메라와 GPS/INS 시스템간의 상호관계를 나타내는 탑재변수의 정확도에 의해 영향을 받는다. 따라서 멀티센서 시스템 개발에 있어서 탑재변수의 정확한 추정은 필수적이다. 현재 우리는 재난/재해와 같은 긴급 상황에 대한 빠른 대응을 위해 실시간으로 대상지역을 감시할 수 있는 저고도 UAV기반의 실시간 공중자료획득 시스템을 개발하고 있다. 본 연구는 현재 개발 중인 시스템의 탑재변수 추정을 위한 시스템 캘리브레이션 방법론을 제안한다. 또한 실제 시스템의 제원을 이용한 시뮬레이션 데이터를 이용하여 정확하고 효율적인 캘리브레이션을 위한 효과적인 비행경로 및 지상기준점의 필요 개수를 도출하였다. 실험 결과, 총 6개의 스트립으로 구성된 비행경로를 따라 획득된 데이터와 5점 이상의 지상기준점 정보를 이용하면 제안된 방법론을 통해 정확한 탑재변수의 추정이 가능함을 확인할 수 있었다. 향후에는 제안된 방법론을 이용하여 개발된 시스템의 탑재변수를 추정하고 이를 이용하여 획득된 센서 데이터의 지오레퍼런싱 정확도 평가를 수행할 예정이다. The geo-referencing accuracy of the images acquired by a UAV based multi-sensor system is affected by the accuracy of the mounting parameters involving the relationship between a camera and a GPS/INS system as well as the performance of a GPS/INS system. Therefore, the estimation of the accurate mounting parameters of a multi-sensor system is important. Currently, we are developing a low altitude multi-sensor system based on a UAV, which can monitor target areas in real time for rapid responses for emergency situations such as natural disasters and accidents. In this study, we suggest a system calibration method for the estimation of the mounting parameters of a multi-sensor system like our system. We also generate simulation data with the sensor specifications of our system, and derive an effective flight configuration and the number of ground control points for accurate and efficient system calibration by applying the proposed method to the simulated data. The experimental results indicate that the proposed method can estimate accurate mounting parameters using over five ground control points and flight configuration composed of six strips. In the near future, we plan to estimate mounting parameters of our system using the proposed method and evaluate the geo-referencing accuracy of the acquired sensory data.

Structure-from-Motion (SfM) photogrammetry is increasingly employed in geomorphological applications for change detection, but repeatability and reproducibility of this methodology are still insufficiently documented. This work aims to evaluate the influence of different survey acquisition and processing conditions, including the camera used for image collection, the number of Ground Control Points (GCPs) employed during Bundle Adjustment, GCP coordinate precision and Unmanned Aerial Vehicle flight mode. The investigation was carried out over three fluvial study areas characterized by distinct morphology, performing multiple flights consecutively and assessing possible differences among the resulting 3D models. We evaluated both residuals on check points and discrepancies between dense point clouds. Analyzing these metrics, we noticed high repeatability (Root Mean Square of signed cloud-to-cloud distances less than 2.1 cm) for surveys carried out under the same conditions. By varying the camera used, instead, contrasting results were obtained that appear to depend on the study site characteristics. In particular, lower reproducibility was highlighted for the surveys involving an area characterized by flat topography and homogeneous texturing. Moreover, this study confirms the importance of the number of GCPs entering in the processing workflow, with different impact depending on the camera used for the survey.

This research demonstrates the potential and evaluates the conditions of experiment of SPOT image path and bloc adjustment using a 3D physical model for geometric correction of multi-source images developed at the Canada Centre for Remote Sensing. In a first step, image paths are automatically generated with the images acquired from the same orbit. Results with 11 panchromatic and 6 multiband SPOT images show that the same accuracy can be obtained with large image blocks as with a single image using a limited number of ground control points (GCPs) and tie points in all image overlaps. When the viewing angle differences of adjacent images or paths are less than 30°, the elevation should be added to these tie points, because the intersection geometry is too weak. When the viewing angle differences of adjacent images or paths are less than 6°, the final accuracy of the block can be reduced by a factor of six, and GCPs have to be added on these images to recover the initial block accuracy.

With increasing demands in real-time or near real-time remotely sensed imagery applications in such as military deployments, quick response to terrorist attacks and disaster rescue, the on-board geometric calibration problem has attracted the attention of many scientists in recent years. This paper presents an on-board geometric calibration method for linear CCD sensor arrays using FPGA chips. The proposed method mainly consists of four modules—Input Data, Coefficient Calculation, Adjustment Computation and Comparison—in which the parallel computations for building the observation equations and least squares adjustment, are implemented using FPGA chips, for which a decomposed matrix inversion method is presented. A Xilinx Virtex-7 FPGA VC707 chip is selected and the MOMS-2P data used for inflight geometric calibration from DLR (Köln, Germany), are employed for validation and analysis. The experimental results demonstrated that: (1) When the widths of floating-point data from 44-bit to 64-bit are adopted, the FPGA resources, including the utilizations of FF, LUT, memory LUT, I/O and DSP48, are consumed at a fast increasing rate; thus, a 50-bit data width is recommended for FPGA-based geometric calibration. (2) Increasing number of ground control points (GCPs) does not significantly consume the FPGA resources, six GCPs is therefore recommended for geometric calibration. (3) The FPGA-based geometric calibration can reach approximately 24 times faster speed than the PC-based one does. (4) The accuracy from the proposed FPGA-based method is almost similar to the one from the inflight calibration if the calibration model and GCPs number are the same.