Systematic vertical error in UAV-derived topographic models:origins and solutions
01 Apr 2014-pp 3120
TL;DR: In this article, the authors used a simulation approach to demonstrate the effect of camera self-calibration within the processing of SfM-based digital elevation models, and provided practical flight plan solutions that, in the absence of control points, demonstrate a reduction in systematic DEM error by more than two orders of magnitude.
Abstract: Unmanned aerial vehicles (UAVs) equipped with consumer cameras are increasingly being used to produce high resolution digital elevation models (DEMs). However, although such DEMs may achieve centimetric detail, they can also display broad-scale systematic deformation (usually a vertical ‘doming’) that restricts their wider use. This effect can be particularly apparent in DEMs derived by structure-from-motion (SfM) processing, especially when control point data have not been incorporated in the bundle adjustment process. We illustrate that doming error results from a combination of inaccurate description of radial lens distortion and the use of imagery captured in near-parallel viewing directions. With such imagery, enabling camera self-calibration within the processing inherently leads to erroneous radial distortion values and associated DEM error. Using a simulation approach, we illustrate how existing understanding of systematic DEM error in stereo-pairs (from unaccounted radial distortion) up-scales in typical multiple-image blocks of UAV surveys. For image sets with dominantly parallel viewing directions, self-calibrating bundle adjustment (as normally used with images taken using consumer cameras) will not be able to derive radial lens distortion accurately, and will give associated systematic ‘doming’ DEM deformation. In the presence of image measurement noise (at levels characteristic of SfM software), and in the absence of control measurements, our simulations display domed deformation with amplitude of 2 m over horizontal distances of 100 m. We illustrate the sensitivity of this effect to variations in camera angle and flight height. Deformation will be reduced if suitable control points can be included within the bundle adjustment, but residual systematic vertical error may remain, accommodated by the estimated precision of the control measurements. Doming bias can be minimised by the inclusion of inclined images within the image set, for example, images collected during gently banked turns of a fixed-wing UAV or, if camera inclination can be altered, by just a few more oblique images with a rotor-based UAV. We provide practical flight plan solutions that, in the absence of control points, demonstrate a reduction in systematic DEM error by more than two orders of magnitude. DEM generation is subject to this effect whether a traditional photogrammetry or newer structure-from-motion (SfM) processing approach is used, but errors will be typically more pronounced in SfM-based DEMs, for which use of control measurements is often more limited. Although focussed on UAV surveying, our results are also relevant to ground-based image capture for SfM-based modelling.
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Cites methods from "Systematic vertical error in UAV-de..."
...In order to avoid systematic artefacts such as subtle concave distortions 183 (James and Robson, 2014), the photomicrograph grids were captured with the camera in both 184 landscape and portrait orientations (Bemis et al., 2014)....
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Patent•
11 Aug 2020
TL;DR: In this paper, a method and system for developing a flight plan for taking images from an area of interest is disclosed, where a series of trajectories are determined based on a logarithmic spiral curve derived from a range of predetermined basis angles.
Abstract: A method and system for developing a flight plan for taking images from an area of interest is disclosed. A series of trajectories is determined. Each trajectory is determined based on a logarithmic spiral curve derived from a range of predetermined basis angles and selecting a constant tangent angle between a radial line from the location of an image sensor to a target location, and a tangent line to the logarithmic spiral curve at the location of the image sensor. A set of trajectories from the series of trajectories is selected. The selected trajectories are scaled to cover the area of interest. The selected trajectories are transformed to coordinates corresponding to the area of interest. The set of scaled and transformed trajectories are stored as the flight plan for taking images of the area of interest.
References
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TL;DR: In this paper, the authors used the structure-from-motion (SfM) and multi-view-stereo (MVS) algorithms to estimate erosion rates along a 50m-long coastal cliff.
Abstract: Topographic measurements for detailed studies of processes such as erosion or mass movement are usually acquired by expensive laser scanners or rigorous photogrammetry. Here, we test and use an alternative technique based on freely available computer vision software which allows general geoscientists to easily create accurate 3D models from field photographs taken with a consumer-grade camera. The approach integrates structure-from-motion (SfM) and multi-view-stereo (MVS) algorithms and, in contrast to traditional photogrammetry techniques, it requires little expertise and few control measurements, and processing is automated. To assess the precision of the results, we compare SfM-MVS models spanning spatial scales of centimeters (a hand sample) to kilometers (the summit craters of Piton de la Fournaise volcano) with data acquired from laser scanning and formal close-range photogrammetry. The relative precision ratio achieved by SfM-MVS (measurement precision : observation distance) is limited by the straightforward camera calibration model used in the software, but generally exceeds 1:1000 (i.e. centimeter-level precision over measurement distances of 10s of meters). We apply SfM-MVS at an intermediate scale, to determine erosion rates along a ~50-m-long coastal cliff. Seven surveys carried out over a year indicate an average retreat rate of 0.70±0.05 m a-1. Sequential erosion maps (at ~0.05 m grid resolution) highlight the spatio-temporal variability in the retreat, with semivariogram analysis indicating a correlation between volume loss and length scale. Compared with a laser scanner survey of the same site, SfM-MVS produced comparable data and reduced data collection time by ~80%.
859 citations
TL;DR: In this article, the authors show that enabling camera self-calibration as part of the bundle adjustment process inherently leads to erroneous radial distortion estimates and associated digital elevation models (DEMs).
Abstract: High resolution digital elevation models (DEMs) are increasingly produced from photographs acquired with consumer cameras, both from the ground and from unmanned aerial vehicles (UAVs). However, although such DEMs may achieve centimetric detail, they can also display systematic broad-scale error that estricts their wider use. Such errors which, in typical UAV data are expressed as a vertical ‘doming’ of the surface, result from a combination of near-parallel imaging directions and inaccurate correction of radial lens distortion. Using simulations of multi-image networks with near-parallel viewing directions, we show that enabling camera self-calibration as part of the bundle adjustment process inherently leads to erroneous radial distortion estimates and associated DEM error. This effect is relevant whether a traditional photogrammetric or newer structure-from-motion (SfM) approach is used, but errors are expected to be more pronounced in SfM-based DEMs, for which use of control and check point measurements are typically more limited. Systematic DEM error can be significantly reduced by the additional capture and inclusion of oblique images in the image network; we provide practical flight plan solutions for fixed wing or rotor-based UAVs that, in the absence of control points, can reduce DEM error by up to two orders of magnitude. The magnitude of doming error shows a linear relationship with radial distortion and we show how characterisation of this relationship allows an improved distortion estimate and, hence, existing datasets to be optimally reprocessed. Although focussed on UAV surveying, our results are also relevant to ground-based image capture.
656 citations
TL;DR: Recommendations for properties of imaging sensor, data collection and processing of UAV image data to ensure accurate point cloud generation are given.
Abstract: The objective of this investigation was to develop and investigate methods for point cloud generation by image matching using aerial image data collected by quadrocopter type micro unmanned aerial vehicle (UAV) imaging systems. Automatic generation of high-quality, dense point clouds from digital images by image matching is a recent, cutting-edge step forward in digital photogrammetric technology. The major components of the system for point cloud generation are a UAV imaging system, an image data collection process using high image overlaps, and post-processing with image orientation and point cloud generation. Two post-processing approaches were developed: one of the methods is based on Bae Systems’ SOCET SET classical commercial photogrammetric software and another is built using Microsoft®’s Photosynth™ service available in the Internet. Empirical testing was carried out in two test areas. Photosynth processing showed that it is possible to orient the images and generate point clouds fully automatically without any a priori orientation information or interactive work. The photogrammetric processing line provided dense and accurate point clouds that followed the theoretical principles of photogrammetry, but also some artifacts were detected. The point clouds from the Photosynth processing were sparser and noisier, which is to a large extent due to the fact that the method is not optimized for dense point cloud generation. Careful photogrammetric processing with self-calibration is required to achieve the highest accuracy. Our results demonstrate the high performance potential of the approach and that with rigorous processing it is possible to reach results that are consistent with theory. We also point out several further research topics. Based on theoretical and empirical results, we give recommendations for properties of imaging sensor, data collection and processing of UAV image data to ensure accurate point cloud generation.
252 citations
TL;DR: In this paper, the authors investigated the potential of the convergent configuration to minimise the systematic error surfaces, even if the geometrically more complex oblique perspective is used.
Abstract: There are increasing opportunities to use consumer-grade digital cameras, particularly
if accurate spatial data can be captured. Research recently conducted at
Loughborough University identified residual systematic error surfaces or domes discernible
in digital elevation models (DEMs). These systematic effects are often associated
with such cameras and are caused by slightly inaccurate estimated lens
distortion parameters. A methodology that minimises the systematic error surfaces
was therefore developed, using a mildly convergent image configuration in a vertical
perspective. This methodology was tested through simulation and a series of practical
tests. This paper investigates the potential of the convergent configuration to minimise
the error surfaces, even if the geometrically more complex oblique perspective is used.
Initially, simulated data was used to demonstrate that an oblique convergent image
configuration can minimise remaining systematic error surfaces using various imaging
angles. Additionally, practical tests using a laboratory testfield were conducted to
verify results of the simulation. The need to develop a system to measure the topographic
surface of a flooding river provided the opportunity to verify the findings of
the simulation and laboratory test using real data. Results of the simulation process,
the laboratory test and the practical test are reported in this paper and demonstrate
that an oblique convergent image configuration eradicates the systematic error surfaces
which result from inaccurate lens distortion parameters. This approach is significant
because by removing the need for an accurate lens model it effectively improves
the accuracies of digital surface representations derived using consumer-grade digital
cameras. Carefully selected image configurations could therefore provide new opportunities
for improving the quality of photogrammetrically acquired data.
91 citations
TL;DR: In this paper, the authors investigated the relationship between systematic error surfaces or "domes" and inaccurately specified lens distortion parameters, and established a methodology to minimise them using a mildly convergent geometry.
Abstract: The internal geometry of consumer-grade digital cameras is generally considered unstable. Research conducted recently at Loughborough University indicated the potential of these sensors to maintain their internal geometry. It also identified residual systematic error surfaces or “domes”, discernible in digital elevation models (DEMs), caused by slightly inaccurate estimated lens distortion parameters. This paper investigates these systematic error surfaces and establishes a methodology to minimise them. Initially, simulated data was used to ascertain the effect of changing the interior orientation parameters on extracted DEMs, specifically the lens model. Results presented demonstrate the relationship between “domes” and inaccurately specified lens distortion parameters. The stereopair remains important for data extraction in photogrammetry, often using automated DEM extraction software. The photogrammetric normal case is widely used, in which the camera base is parallel to the object plane and the optical axes of the cameras intersect the object plane orthogonally. During simulation, the error surfaces derived from extracted DEMs using the normal case were compared with error surfaces created using a mildly convergent geometry. In contrast to the normal case, the optical camera axes intersect the object plane at the same point. Results of the simulation process clearly demonstrate that a mildly convergent camera configuration eradicates the systematic error surfaces. This result was confirmed through practical tests and demonstrates that mildly convergent imagery effectively improves the accuracies of DEMs derived with this class of sensor.
Resume
On estime qu’en general la geometrie interne des cameras numeriques de qualitecourante est instable. Des etudes recentes menees a l’Universite de Loughborough ont montre que ces capteurs avaient la possibilite de conserver leur geometrie interne. On a egalement pu identifier la cause des erreurs systematiques residuelles provoquant dans les modeles numeriques des altitudes (MNA) des surfaces bombees ou « domes ». Celle-ci est due a de legeres inexactitudes dans l’estimation des parametres de distorsion de l’objectif. On examine dans cet article ces surfaces resultant d’erreurs systematiques et l’on etablit une methodologie permettant de les rendre minimales. On a commence par utiliser des donnees simulees pour s’assurer des effets des variations des parametres d’orientation interne sur les MNA derives, et plus particulierement des effets des variations du modele d’objectif. Les resultats obtenus illustrent bien la relation entre l’imprecision des parametres de distorsion de l’objectif et ces domes. Le couple stereoscopique reste fondamental pour l’extraction de donnees par photogrammetrie, et l’on recourt souvent a des logiciels de production automatique des MNA. C’est la disposition photogrammetrique normale que l’on utilise generalement, dans laquelle la base des cameras est parallele au plan-objet, tandis que les axes optiques des cameras sont perpendiculaires a ce plan-objet. Dans la phase de simulation, on a pu comparer les « domes » d’erreur des MNA issus d’une disposition normale avec ceux issus d’une geometrie a axes legerement convergents. Dans ce dernier cas les axes optiques des cameras se coupent en un meme point du plan-objet, contrairement a la disposition normale. Les resultats obtenus avec cette simulation montrent nettement que l’on peut eradiquer ces bombements surfaciques errones avec une configuration ou les cameras sont legerement convergentes. En effectuant des essais pratiques avec donnees reelles on a eu la confirmation de ces resultats et l’on a vu que la precision des MNA issus de cette categorie de capteurs etait amelioree avec une geometrie a axes legerement convergents.
Zusammenfassung
Die innere Geometrie digitaler Amateurkameras wird allgemein als instabil eingeschatzt. Kurzlich durchgefuhrte Forschungen an der Loughborough University zeigten jedoch das Potential dieser Sensoren ihre innere Geometrie beizubehalten. Die Forschungen identifizierten Oberflachen mit systematischen Fehler oder “Kuppeln”, sichtbar in digitalen Hohenmodellen (DEMs), verursacht durch ungenau berechnete Verzeichnungsparameter. Dieser Artikel untersucht die Oberflachen mit systematischen Fehlern und ermittelt eine Methode, diese zu minimieren. Zunachst wurden simulierte Daten verwendet, um den Effekt von Veranderungen der inneren Orientierungsparameter, speziell der Objektverzeichnung, in digitalen Hohenmodellen zu bestimmen. Vorgelegte Ergebnisse zeigen den eindeutigen Zusammenhang zwischen den “Kuppeln” und den ungenau berechneten Verzeichnungsparametern. Das Stereomodell ist in der Photogrammetrie weiterhin von Bedeutung, weil es oft von Software zur automatisierten Erstellung von Hohenmodellen benutzt wird. Meist wird der photogrammetrische Stereonormalfall verwendet, bei welchem die Kamerabasis parallel zur Objektebene ist und die optischen Achsen der Kameras die Objektebene orthogonal schneiden. In der Simulation wurden die Oberflachen mit Fehlern der Hohenmodelle, extrahiert durch Verwendung des Normalfalls, mit den Oberflachen mit Fehlern der Hohenmodelle, durch Verwendung eines konvergenten Falls, verglichen. Im Gegensatz zum Normalfall schneiden bei konvergenten Aufnahmen die optischen Kameraachsen die Objektebene im gleichen Punkt. Ergebnisse des Simulationsprozesses demonstrieren eindeutig, dass eine konvergente Kamerakonfiguration die Fehler der Oberflachen beseitigt. Dieses Ergebnis wurde durch praktische Tests bestatigt und demonstriert die Bilder die Genauigkeit der Hohenmodelle, dass konvergente mit diesen Sensoren erstellt werden steigern.
Resumen
Por lo general se considera que la geometria interna de las camaras digitales de consumo es inestable. Los resultados de la investigacion realizada recientemente en la Universidad de Loughborough senalan la capacidad de estos sensores para mantener la geometria interna. Tambien identificaron superficies de error sistematico residual o domos, reconocibles en los modelos digitales de elevacion (MDE) (Wackrow et al., 2007), causados por una estimacion ligeramente inexacta de los parametros de distorsion de la lente. Este articulo investiga estas superficies de error sistematico y propone una metodologia para minimizarlas. Inicialmente se usaron datos simulados para determinar el efecto resultante de cambiar los parametros de orientacion interna en los MDE calculados, particularmente el modelo de la lente. Los resultados presentados senalan la existencia de una relacion entre domos y parametros de la lente que han sido especificados de forma inexacta. El estereopar continua siendo importante para la obtencion de datos en la fotogrametria, en muchos casos usando programas de extraccion automatica del MDE. El caso normal en la fotogrametria, utilizado comunmente, es aquel en el que la base de la camara es paralela al plano objeto y los ejes opticos de las camaras intersecan con el plano objeto de forma ortogonal. Las superficies de error del MDE calculado, obtenidas durante la simulacion con el caso normal, se compararon con las superficies de error calculadas usando una geometria ligeramente convergente. A diferencia del caso normal, los ejes opticos de la camara intersecan el plano objeto en el mismo punto. Los resultados de la simulacion demuestran claramente que una configuracion de la camara ligeramente convergente elimina las superficies de error sistematico. Este resultado fue confirmado mediante ensayos practicos y demuestra que las imagenes ligeramente convergentes mejoran de forma efectiva las exactitudes de los MDE calculados con esta clase de sensor.
83 citations