Mitigating systematic error in topographic models derived from UAV and ground‐based image networks

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 restricts 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 characterization 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. © 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

3‐D uncertainty‐based topographic change detection with structure‐from‐motion photogrammetry: precision maps for ground control and directly georeferenced surveys

Structure‐from‐motion (SfM) photogrammetry is revolutionising the collection of detailed topographic data, but insight into geomorphological processes is currently restricted by our limited understanding of SfM survey uncertainties. Here, we present an approach that, for the first time, specifically accounts for the spatially variable precision inherent to photo‐based surveys, and enables confidence‐bounded quantification of 3D topographic change. The method uses novel 3D precision maps that describe the 3D photogrammetric and georeferencing uncertainty, and determines change through an adapted state‐of‐the‐art fully 3D point‐cloud comparison (M3C2), which is particularly valuable for complex topography. We introduce this method by: (1) using simulated UAV surveys, processed in photogrammetric software, to illustrate the spatial variability of precision and the relative influences of photogrammetric (e.g. image network geometry, tie point quality) and georeferencing (e.g. control measurement) considerations; (2) we then present a new Monte Carlo procedure for deriving this information using standard SfM software and integrate it into confidence‐bounded change detection; before (3) demonstrating geomorphological application in which we use benchmark TLS data for validation and then estimate sediment budgets through differencing annual SfM surveys of an eroding badland. We show how 3D precision maps enable more probable erosion patterns to be identified than existing analyses, and how a similar overall survey precision could have been achieved with direct survey georeferencing for camera position data with precision half as good as the GCPs'. Where precision is limited by weak georeferencing (e.g. camera positions with multi‐metre precision, such as from a consumer UAV), then overall survey precision can scale as n^‐½ of the control precision (n = number of images). Our method also provides variance–covariance information for all parameters. Thus, we now open the door for SfM practitioners to use the comprehensive analyses that have underpinned rigorous photogrammetric approaches over the last half‐century. Copyright © 2017 John Wiley & Sons, Ltd.     

Using structure‐from‐motion to create glacier DEMs and orthoimagery from historical terrestrial and oblique aerial imagery

Increased resolution and availability of remote sensing products, and advancements in small‐scale aerial drone systems, allows observations of glacial changes at unprecedented levels of detail. Software developments, such as structure‐from‐motion (SfM), now allow users an easy and efficient method to generate three‐dimensional (3D) models and orthoimages from aerial or terrestrial datasets. While these advancements show promise for current and future glacier monitoring, many regions still suffer a lack of observations from earlier time periods. We report on the use of SfM to extract spatial information from various historic imagery sources. We focus on three geographic regions, the European Alps, high Arctic Norway and the Nepal Himalayas. We used terrestrial field photographs from 1896, high oblique aerial photographs from 1936 and aerial handheld photographs from 1978 to generate digital elevation models (DEMs) and orthophotos of the Rhone glacier, Brøggerhalvøya and the lower Khumbu glacier, respectively. Our analysis shows that applying SfM to historic imagery can generate high quality models using only ground control points. Limited camera/orientation information was largely reproduced using self‐calibrated model data. Using these data, we calculated mean ground sampling distances across each site which demonstrates the high potential resolution of resulting models. Vertical errors for our models are ±5.4 m, ±5.2 m and ±3.3 m. Differencing shows similar patterns of thinning at lower Rhone (European Alps) and Brøggerhalvøya (Norway) glaciers, which have mean thinning rates of 0.31 m a^?1 (1896–2010) to 0.86 m a^?1 (1936–2010) respectively. On these clean ice glaciers thinning is highest in the terminus region and decreasing up‐glacier. In contrast to these glaciers, uneven topography, exposed ice‐cliffs and debris cover on the Khumbu glacier create a highly variable spatial distribution of thinning. The mean thinning rate for the Khumbu study area was found to be 0.54 ± 0.9 m a^?1 (1978–2015). Copyright © 2017 John Wiley & Sons, Ltd.     

The significance of rock structure,lithology and pre‐glacial deep weathering for the shape of intermediate‐scale glacial erosional landforms

The main landforms within the glacially scoured Precambrian rocks of the Swedish west coast are closely connected to the principal structural pattern and have lately been explained as mainly a result of etch processes, probably during the Mesozoic and with a possible second period of etching during the Neogene. To explore the effect of multiple glacial erosion on the rock surfaces, an island with two different lithologies and with striae from different directions was selected for a detailed study, focusing on the shape of roches moutonnées. Air‐photo interpretation of bedrock lineaments and roches moutonnées combined with detailed field mapping and striae measurements are used to interpret the structural and lithological control on the resulting shape. The study reveals a significant difference in shape between roches moutonnées in augen‐granite and orthogneiss. Low elongated and streamlined roches moutonnées occur in the gneiss area, striated by a Late Weichselian ice flow from the NE. This ice flow is subparallel with both the local dominant trend of topographically well‐expressed joints and the schistosity of the gneiss. Frequently, there are no signs of quarrying on the lee‐sides of the gneiss roches moutonnées and hence they resemble the shape of whalebacks, or ruwares, as typically associated with the exposed basal weathering surface found in tropical areas. The granite roches moutonnées were formed by an older ice flow from the ESE, which closely followed the etched WNW–ESE joint system of the granite. Late Weichselian ice flow from the NE caused only minor changes of the landforms. On the contrary, marks of the early ESE ice flow are poorly preserved in the gneiss area, where it probably never had any large effect as the flow was perpendicular to both schistosity and structures and, accordingly, also to the pre‐glacial relief. The study demonstrates that coincidence between ice flow direction and pre‐glacially etched structures is most likely to determine the effects of glacial erosion. Copyright © 2002 John Wiley & Sons, Ltd.     

Using visibility analysis to improve point density and processing time of SfM-MVS techniques for 3D reconstruction of landforms

Image network geometry, including the number and orientation of images, impacts the error, coverage, and processing time of 3D terrain mapping performed using structure-from-motion and multiview-stereo (SfM-MVS). Few studies have quantified trade-offs in error and processing time or ways to optimize image acquisition in diverse topographic conditions. Here, we determine suitable camera locations for image acquisition by minimizing the occlusion produced by topography. Viewshed analysis is used to select the suitable images, which requires a preliminary digital elevation model (DEM), potential camera locations, and sensor parameters. One aerial and two ground-based image collections were used to analyse differences between SfM-MVS models produced using: (1) all available images (ALL); (2) images selected using conventional methods (CON); and (3) images selected using the viewshed analysis (VIEW). The resulting models were compared with benchmark point clouds acquired by a terrestrial laser scanner (TLS) and TLS-derived DEMs. The VIEW datasets produced denser point clouds (28–32% more points) and DEMs with up to 66% reduction in error compared with CON datasets due to reduction of gaps in the DEM. VIEW datasets reduced processing time by 37–76% compared with ALL, with no reduction in coverage or increase in error. DEMs produced with ALL and VIEW datasets had similar slope and roughness, while slight differences that may be locally important were observed for the CON dataset. The new method helps optimize SfM-MVS image collection strategies that significantly reduce the number of images required with minimal loss in coverage or accuracy over complex surfaces. © 2020 John Wiley & Sons, Ltd.     

Paired 10Be sampling of polished bedrock and erratic boulders to improve dating of glacial landforms: an example from the Western Alps

Cosmogenic nuclide dating of glacial landforms may lead to ambiguous results for ice retreat histories. The persistence of significant cosmogenic concentrations inherited from previous exposure may increase the apparent exposure ages for polished bedrocks affected by limited erosion under ice and for erratic boulders transported by glaciers and previously exposed in high-altitude rock walls. In contrast, transient burying by moraines, sediments and snow decreases the apparent exposure age. We propose a new sampling strategy, applied to four sites distributed in the Arc and Arve valleys in the Western Alps, to better constrain the factors that can bias exposure ages associated with glacial processes. We used the terrestrial cosmogenic nuclide ¹⁰Be (TCN) to estimate the exposure time from paired sampling of depth profiles in polished bedrock and on overlying erratic boulders. For a given sampling site, the exposure ages for both the polished bedrock and boulder are expected to be the same. However, in six cases out of seven, boulders had significantly higher ¹⁰Be surface concentrations than those of the associated polished surfaces. In present and past glacial processes, the ¹⁰Be distribution with depth for boulders and bedrocks implies the presence of an inheritance concentration of ¹⁰Be. Our study suggests that ¹⁰Be concentrations in erratic boulders and in polished bedrocks provide maximum and minimum exposure ages of the glacial retreat, respectively. © 2019 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd     

An automatic approach for rill network extraction to measure rill erosion by terrestrial and low‐cost unmanned aerial vehicle photogrammetry

For an erosion event (October 2016) occurred at the Sparacia experimental area (Southern Italy), both terrestrial and low‐altitude aerial surveys were carried out by consumer grade camera and quadcopter (low‐cost unmanned aerial vehicle [UAV]) to measure rill erosion on two plots with steepness of 22% and 26%. Applying the structure from motion (SfM) technique, the three‐dimensional digital terrain models (3D‐DTMs) and the quasi three‐dimensional models (2.5D‐digital elevation model [DEM]) were obtained by the two surveys. Furthermore, 3D‐DTM and DEM were built using the available aerial photographs (166) and adding 40 terrestrial photographs. For the first time, the convergence index was applied to high‐resolution rill data for extracting the rill network, and a subsequent separation into contributing and non‐contributing rills was carried out. The comparison among the three surveys (terrestrial, UAV, and UAV + terrestrial) was developed using two morphometric parameters of the rill network (drainage density and drainage frequency). Moreover, using as reference the weight of sediment stored on the tanks located downstream of the plots, the reliability of soil loss measurement by 3D models was tested. For both contributing and non‐contributing rills, the morphometric parameters were higher for the terrestrial than for UAV and UAV + terrestrial surveys. For both plots, SfM always provided reliable soil loss measurements, which were affected by errors ranging from ?8% to 13%. Although the applied technique used a low‐cost UAV and a consumer grade camera, the obtained results demonstrated that a reliable estimate of rill erosion can be obtained in an area of interest.     

Testing the use of an image‐based technique to measure gully erosion at Sparacia experimental area

The first part of this investigation was aimed at testing the use of a three‐dimensional (3D) digital terrain model and a quasi‐tridimensional (2.5D) digital elevation model obtained by a large series of oblique images of eroded channels taken from consumer un‐calibrated and non‐metric cameras. For two closed earth channels having a different sinuosity, the ground measurement of some cross sections by a profilometer (P) was carried out and their real volume was also measured. The comparison among the three methods (3D, 2.5D, and P) pointed out that a limited underestimation of the total volume always occurs and that the 3D method is characterized by the minimum difference between measured and real volume. For this reason, 3D model can be used as benchmark. In the subsequent part of the investigation, the three ground measurement methods were applied for surveying of an ephemeral gully (EG) channel at the Sparacia area. The morphological and hydraulic variable values of the 24 surveyed cross sections determined by both 2.5D model and profilometer were compared. This comparison showed that the estimate error is generally less than ±10%. The EG measurements carried out by the three methods supported the applicability both of the empirical relationship between EG length and its eroded volume and the theoretical dimensionless relationship among the morphological variables describing the channelized erosion process. Finally, it was demonstrated that the effect of the distance interval on the EG volume measurement by 3D and 2.5D models is negligible for the investigated EG.     

Cost‐effective non‐metric photogrammetry from consumer‐grade sUAS: implications for direct georeferencing of structure from motion photogrammetry

The declining costs of small Unmanned Aerial Systems (sUAS), in combination with Structure‐from‐Motion (SfM) photogrammetry have triggered renewed interest in image‐based topography reconstruction. However, the potential uptake of sUAS‐based topography is limited by the need for ground control acquired with expensive survey equipment. Direct georeferencing (DG) is a workflow that obviates ground control and uses only the camera positions to georeference the SfM results. However, the absence of ground control poses significant challenges in terms of the data quality of the final geospatial outputs. Notably, it is generally accepted that ground control is required to georeference, refine the camera calibration parameters, and remove any artefacts of optical distortion from the topographic model. Here, we present an examination of DG carried out with low‐cost consumer‐grade sUAS. We begin with a study of surface deformations resulting from systematic perturbations of the radial lens distortion parameters. We then test a number of flight patterns and develop a novel error quantification method to assess the outcomes. Our perturbation analysis shows that there exists families of predictable equifinal solutions of K₁‐K₂ which minimize doming in the output model. The equifinal solutions can be expressed as K₂ = f (K₁) and they have been observed for both the DJI Inspire 1 and Phantom 3 sUAS platforms. This equifinality relationship can be used as an external reliability check of the self‐calibration and allow a DG workflow to produce topography exempt of non‐affine deformations and with random errors of 0.1% of the flying height, linear offsets below 10 m and off‐vertical tilts below 1°. Whilst not yet of survey‐grade quality, these results demonstrate that low‐cost sUAS are capable of producing reliable topography products without recourse to expensive survey equipment and we argue that direct georeferencing and low‐cost sUAS could transform survey practices in both academic and commercial disciplines. Copyright © 2016 John Wiley & Sons, Ltd.     

Use of terrestrial photogrammetry based on structure‐from‐motion for mass balance estimation of a small glacier in the Italian alps

Different high‐resolution techniques can be employed to obtain information about the three‐dimensional (3D) surface of glaciers. This is typically carried out using efficient, but also expensive and logistically demanding, light detection and ranging (LiDAR) technologies, such as airborne scanners and terrestrial laser scanners. Recent technological improvements in the field of image analysis and computer vision have prompted the development of a low‐cost photogrammetric approach, which is referred to as ‘structure‐from‐motion’ (SfM). Combined with dense image‐matching algorithms, this method has become competitive for the production of high‐quality 3D models. However, several issues typical of this approach should be considered for application in glacial environments. In particular, the surface morphology, the different substrata, the occurrence of sharp contrast from solar shadows and the variable distance from the camera positions can negatively affect the image texture, and reduce the possibility of obtaining a reliable point cloud from the images. The objective of this study is to test the structure‐from‐motion multi view stereo (SfM‐MVS) approach in a small debris‐covered glacier located in the eastern Italian Alps, using a consumer‐grade reflex camera and the computer vision‐based software PhotoScan. The quality of the 3D models produced by the SfM‐MVS process was assessed via the comparison with digital terrain models obtained from terrestrial laser scanning (TLS) surveys that were performed at the same epochs. The effect of different terrain gradients and different substrata (debris, snow and firn) was also evaluated in terms of the accuracy of the reconstruction by SfM‐MVS versus TLS. Our results show that the quality of this new photogrammetric approach is similar to the quality of TLS and that point cloud densities are comparable or even higher compared with TLS. However, special care should be taken while planning the SfM survey geometry, to optimize the 3D model quality and spatial coverage. Copyright © 2015 John Wiley & Sons, Ltd.     

Bank erosion in agricultural drainage networks: new challenges from structure‐from‐motion photogrammetry for post‐event analysis

Drainage channels are an integral part of agricultural landscapes, and their impact on catchment hydrology is strongly recognized. In cultivated and urbanized floodplains, channels have always played a key role in flood protection, land reclamation, and irrigation. Bank erosion is a critical issue in channels. Neglecting this process, especially during flood events, can result in underestimation of the risk in flood‐prone areas. The main aim of this work is to consider a low‐cost methodology for the analysis of bank erosion in agricultural drainage networks, and in particular for the estimation of the volumes of eroded and deposited material. A case study located in the Veneto floodplain was selected. The research is based on high‐resolution topographic data obtained by an emerging low‐cost photogrammetric method (structure‐from‐motion or SfM), and results are compared to terrestrial laser scanning (TLS) data. For the SfM analysis, extensive photosets were obtained using two standalone reflex digital cameras and an iPhone5® built‐in camera. Three digital elevation models (DEMs) were extracted at the resolution of 0.1 m using SfM and were compared with the ones derived by TLS. Using the different DEMs, the eroded areas were then identified using a feature extraction technique based on the topographic parameter Roughness Index (RI). DEMs derived from SfM were effective for both detecting erosion areas and estimating quantitatively the deposition and erosion volumes. Our results underlined how smartphones with high‐resolution built‐in cameras can be competitive instruments for obtaining suitable data for topography analysis and Earth surface monitoring. This methodology could be potentially very useful for farmers and/or technicians for post‐event field surveys to support flood risk management. Copyright © 2015 John Wiley & Sons, Ltd.     

The transition from Alboran to Algerian basins (Western Mediterranean Sea): Chronostratigraphy,deep crustal structure and tectonic evolution at the rear of a narrow slab rollback system

The eastern Alboran basin and its transition to the Algerian basin is a key area in the Mediterranean realm where controversial kinematic and geodynamical models are proposed. Models imply striking differences regarding the nature of the crust, the prevalence of brittle faulting and ductile shear, the origin of magmatism, the style of Miocene deformation and the driving mechanisms of the Alboran plate kinematics. Combining a new chronostratigraphic chart of the Alboran and Algerian basins based on the Habibas (HBB-1) core drill, deep seismic sections striking WSW-ENE and SSE-NNW, and potential field data, we re-assess the tectonic evolution that controlled the sedimentation and basement deformation of the westernmost limit of the Algerian basin and its transition with the Alboran domain. A WSW-directed extensional tectonic phase has shaped a stretched continental crust with typical tilted blocks along ∼100 km from Burdigalian to Tortonian times, which is assumed to result from the WSW-directed migration of the Alboran block driven by a narrow slab rollback. In the Algerian basin, this event was followed by the emplacement of an oceanic-type crust. Potential field signatures of the deep basin as well as geometrical correlations with onland outcrops of inner zones suggest a minimum WSW-directed displacement of the Alboran terrane of ∼200 km. At the southern foot of the Algerian basin, the continent-ocean transition is sharp and may result from the westward propagation of a slab tear at depth, forming two segments of STEP (Subduction-Transform Edge Propagator) margins. Our results support models of intense shear tractions at the base of an overriding plate governed by slab rollback-induced mantle flow. Finally, Messinian salt tectonics affected overlying deposits until today. A late Tortonian to Quaternary dominantly transpressive tectonic episode linked to the Africa-Iberia convergence post-dates previous events, deforming the whole margin.