Engineering geology
Mapping erosion and deposition

Mapping erosion and deposition in an agricultural landscape: Optimization of UAV image acquisition schemes for SfM-MVS

Introduction

Structure-from-motion (SfM) is a photogrammetric technique used to generate a 3D pointcloud from a collection of overlapping 2D images (Carrivick et al., 2016). The SfM process starts with feature detection, which involves identifying unique features on an image (e.g., using scale-invariant feature transform; Lowe, 2004) and matching homologous features (i.e., keypoints) across overlapping images to generate image correspondences. Given a set of corresponding features, 3D coordinates of matched features (i.e., a sparse pointcloud) can be generated using an iterative bundle adjustment (BA). The BA is a least-squares optimization that simultaneously estimates the 3D positions of a scene and camera poses (Eltner et al., 2016; Triggs et al., 2000). The camera’s intrinsic parameters can be included as an unknown in the BA (i.e., a self-calibrating BA). Following the BA, a multi-view stereo (MVS) algorithm is then used to generate additional points to create a dense pointcloud; the entire workflow is referred to as SfM-MVS (Smith et al., 2016).

The geosciences have been adopting the SfM-MVS workflow to model complex landscapes using images collected from terrestrial (e.g., Stumpf et al., 2015) and airborne platforms (e.g., unmanned aerial vehicles [UAVs]; Meinen and Robinson, 2020). Applications of UAV SfM-MVS include monitoring landslides (e.g., Turner et al., 2015; Lucieer et al., 2014; Niethammer et al., 2012), quantifying soil erosion (e.g., d’Oleire-Oltmanns et al., 2012; Eltner et al., 2013; Peter et al., 2014; Stöcker et al., 2015; Pineux et al., 2017), mapping snow depth (e.g., Nolan et al., 2015; Harder et al., 2016), and monitoring glacial dynamics (e.g., Bash et al., 2018; Immerzeel et al., 2014; Ryan et al., 2015). Study scales range from close-range UAV photography used to generate sub-cm spatial resolutions (e.g., flying height of 8–10 m; Eltner et al., 2013) to high-altitude UAV flights generating decimeter-level spatial resolutions (e.g., flying height of 500 m; d’Oleire-Oltmanns et al., 2012).

Since each study utilizing UAV SfM-MVS differs in its spatial scale and intended application, it can be difficult to infer what the best practices are for UAV survey design in different landscapes. One commonality among UAV SfM-MVS surveys is the method used for camera calibration. Pre-calibration of cameras (e.g., using an independent image set to derive camera intrinsics) is rarely used in most geoscience research and instead a self-calibrating BA is most frequently used. When using a self-calibrating BA, the UAV survey design should reflect this choice; UAV surveys that are composed of exclusively parallel-axis nadir imagery can lead to an incorrect camera model (e.g., incorrect radial distortion terms; Harwin et al., 2015; James and Robson, 2014). If the self-calibration fails to accurately calculate radial distortion terms the resultant 3D model may have a high degree of surface deformation, exhibiting a doming effect (James and Robson, 2014). Despite SfM being most effective with images taken from a variety of locations and perspectives, typical UAV surveys only capture imagery from one perspective (i.e., nadir). The inclusion of oblique imagery and a strong network of ground control points (GCPs) should lead to a more accurate self-calibration.

A cross comparison of accuracy results among existing UAV SfM-MVS surface models in the literature is difficult. Most UAV surveys use nadir-only imagery and do not report the image orientation or incorporate oblique imagery into their survey. Reported accuracies vary widely in horizontal and vertical directions (from centimeters to decimeters) and are difficult to compare due to a lack of standard reporting protocol. For example, literature may report only GCP error metrics (e.g., d’Oleire-Oltmanns et al., 2012), checkpoint error metrics (e.g., Tamminga et al., 2015), comparison with a terrestrial laser scanner (e.g., Eltner et al., 2015), GCP/checkpoint error metrics and evaluation of invariant topography (Lucieer et al., 2014), or GCP error metrics and comparison with LiDAR (Cook, 2017). The lack of standard reporting protocol for SfM-MVS accuracy assessments and unique challenges associated with modelling different landscapes necessitates an independent evaluation of UAV survey designs for different landscapes.

Agricultural landscapes (i.e., croplands and pastures) constitute the dominant land-use on Earth’s surface (i.e., 38%; Foley et al., 2011) but no farm field-scale scale (i.e., >1 ha) accuracy assessments of agricultural SfM-MVS exist; existing UAV surveys are either plot-scale (e.g., Eltner et al., 2013; Stöcker et al., 2015) or have no rigorous accuracy assessment (e.g., d’Oleire-Oltmanns et al., 2012; Peter et al., 2014; Pineux et al., 2017). Agricultural landscapes present a unique challenge for the SfM-MVS workflow due to homogeneous soil textures, vegetation, and minimal variations in topographic relief. To identify the optimal survey design for a self-calibrating BA for agricultural landscapes, we assessed the accuracy of 3D surface reconstructions of a 15.9-hectare field using four different image acquisition schemes: nadir, oblique, and two different combinations of nadir and oblique. We used our 3D surface reconstructions to answer two questions: 1) when using a self-calibrating BA, does the addition of oblique imagery improve the relative accuracy of 3D surface models: a) in the absence of ground control points (GCPs), and b) with a normative distribution of GCPs (i.e., capturing edges and having a comprehensive spatial coverage), and 2) how accurately can sequential UAV surveys detect small-scale erosional processes relative to terrestrial laser scanning? To answer these questions, three field campaigns were conducted over the course of one month. Each campaign consisted of three UAV flights over an agricultural field using parallel-axis flight lines to capture: nadir imagery, west-facing oblique imagery, and east-facing oblique imagery. Ground truth data for accuracy assessments were taken from a network of 27 GCPs.

Study site

Our study site is located in the upper-Nith river basin in southwestern Ontario. The Nith River is a tributary to the Grand River, which flows into the northern basin of Lake Erie, draining an area of 1130 km2. The upper-Nith river basin has a mosaic of land cover comprising 84% agriculture, 6% forest, 6% wetland, and 4% urban cover (Loomer and Cooke, 2011). This predominantly agricultural basin is geologically composed of silty tills with an extensive tile-drainage network (Loomer and Cooke, 2011). The combination of agricultural land use and silty tills along the upper-Nith River contribute a large amount of suspended sediments and phosphorus into the Nith River. Water quality issues are kept in check partly by the Waterloo Moraine in the lower-Nith basin, but the Nith basin is one of the top contributors of sediments to the Grand River (Loomer and Cooke, 2011).

The study site is a 15.9 ha (~40 acre) agricultural field bordering on the south side of the Nith River. The field is a mosaic of landform elements and topographic variation; the southern portion is relatively homogeneous and flat whereas the northern portion is characterized by steep slopes descending into a forested riparian zone (Fig. 1). Subsurface tile drainage was installed prior to the initial survey with soil berms and surface inlets (i.e., catch basins) installed at five locations to prevent overland flow from directly draining into the Nith River.

Fig. 1. Orthomosaic of the study site captured by the UAV (left), a ground control point (GCP) as visualized in the aerial imagery (center), and surface elevation in meters above-sea-level (ASL) (right).

Materials and methods

A FLIR Systems R60 Skyranger UAV was used to collect aerial imagery (Fig. 2a). The R60 Skyranger is a vertical take-off and landing quadcopter weighing 2.8 kg with 40 min flight times. FLIR Systems Mission Control Station (MCS) software is used to automate parallel-axis flight lines across the field. The SR-3SHD payload was used for image acquisitions which acquires 15 MP RGB 4608 × 3288 resolution images (.jpg file format). The SR-3SHD has a 3-axis gimbal that compensates for the yaw, pitch, and roll of the UAV. The payload has a field of view of 46 degrees, 7.5 mm focal length, 6.45 × 4.60 mm sensor, and uses a rolling shutter. The UAV is equipped with a GPS receiver which geotags acquired images.

Fig. 2. (a) Skyranger UAV system with tablet and base station, (b) south-west surface inlet and catch basin (Campaign 1; image facing west), (c) sediment plume approaching the south-east surface inlet and catch basin (Campaign 3; image facing east), (d) ground control point.

A total of 18 ground control points (GCPs; Fig. 1) were distributed across the study site. GCPs were placed to capture the image edges, slopes, and the topographic highs and lows. The GCPs were 12 × 12 in. plywood squares painted fluorescent orange with a distinctive “X” pattern. Each GCP had a small hole in the center where a twelve-inch plastic tent peg was driven into the ground to secure the plywood square to the ground. GCPs were measured using SmartNet’s network Real-time Kinematic Global Navigation Satellite System (RTK-GNSS) with a Leica Viva GS14 and Leica Viva CS15 field controller. The network RTK produced an average accuracy of 0.01 m horizontally and 0.02 m vertically. An additional 9 ground controls were located outside the study area and were used as invariant co-registration control points. These co-registration points were stable features (e.g., painted roadway lines) that were invariant during the study period.

Three field campaigns were conducted on May 7th (Campaign 1), May 17th (Campaign 2), and June 15th (Campaign 3). The study site was tilled on May 12th, which enabled us to compare the field pre and post tillage. Several rainstorms occurred between Campaign 2 and Campaign 3, allowing us to demonstrate the viability of UAV SfM-MVS in detecting small-scale erosional processes. For each field campaign, 18 GCPs were distributed across the field (Fig. 1) and removed after the UAV flights. The 9 co-registration control points were measured once during Campaign 1 and incorporated into each subsequent survey to co-register surface models. Each field campaign consisted of three UAV flights with three different camera orientations: 1) nadir, 2) east-facing oblique, and 3) west-facing oblique. Flights were flown at 90 m above-ground-level and had parallel-axis flight lines with a 70% frontlap and sidelap and a ground-sampling-distance of 0.017 m. The UAV was flown at approximately 4 ms−1. All oblique photos were taken at a 15 degree angle relative to nadir. Flights covered an area of 24 ha to ensure the entire field was captured during each campaign. A Leica Multistation MS50 (a terrestrial laser scanner; TLS) was simultaneously used to scan a small sub-section of the field (indicated in yellow on Fig. 1) to quantify the accuracy of UAV-based surface change-detection.

SfM-MVS surface processing

To determine if the addition of oblique imagery improved the relative accuracy of 3D surface models, we generated four surface models based on four different image sets (Fig. 3): 1) 26 nadir imaging strips [N], 2) 13 east-facing oblique +13 west-facing oblique imaging strips (i.e., convergent imaging scheme [C]), 3) 26 nadir +5 east-facing oblique +5 west-facing oblique imaging strips [NC5], and 4) 26 nadir +26 east-facing oblique +26 west-facing oblique imaging strips [NC26], which comprised all data collected during a single field campaign. The [N] image set had a uniform 70% overlap between images, while the [C], [NC5], and [NC26] image sets had variable levels of image overlap.

Fig. 3. Orientation of camera poses for each image set: (a) 26 nadir imaging strips [N], (b) 13 east-facing oblique +13 west-facing oblique imaging strips [C], (c) 26 nadir +5 east-facing oblique +5 west-facing oblique imaging strips [NC5], (d) 26 nadir +26 east-facing oblique +26 west-facing oblique imaging strips [NC26]. Dotted lines indicate image center.

Pointcloud surface models were created for each of the four image sets using Pix4D (Pix4D SA, Switzerland; Table 1). Image geolocation from the UAV GPS receiver was used to initially locate all the images and to speed up processing time. Overexposed and blurry images were removed before processing. Processing options for each surface were: keypoint image scale of 1, automatic targeted number of keypoints, standard calibration method, and all camera optimizations. Pointcloud densification was conducted using: optimal point density (i.e., computing a 3D point for every 4 pixels), full image scale (i.e., original image size is used to compute additional 3D points), and with 3D points only being generated if they were correctly re-projected in at least 4 images. All GCPs and co-registration points (i.e., 27 GCPs) were used in a self-calibrating BA. If any surface had its average root-mean-square-error exceed 0.010 m for the GCPs, the project was checked for GCP marking error and reprocessed. The data were processed on a Dell Precision Workstation 5810 Tower with Intel Xeon CPU E5-1620 v3 @ 3.5 GHz with quad-core, 64 GB RAM, 8 processors, NVIDIA Quadro K4200 graphics card, and operating on Windows 7 64-bit (Fig. 4).

Table 1. Processing results from four image sets averaged across three campaigns. Camera self-calibration results for Campaign 1 (Px, Py are the [x,y] principal points; R1, R2, R3 are radial distortion coefficients; T1, T2 are tangential distortion coefficients).
Fig. 4. 3D rendering of pointclouds centered on the north-east surface inlet and catch basin: (a) Campaign 1, (b) Campaign 2, and (c) Campaign 3. Illumination conditions were bright for Campaign 2 and 3.

SfM-MVS surface processing for accuracy assessments

To identify the optimal survey design for use with a self-calibrating bundle adjustment (BA), we conducted a total of four tests per field campaign on each image set by incorporating a different number of GCPs in the BA: 1) No GCPs, 2) 13 normative GCPs, 3) 17 normative GCPs, and 4) 21 normative GCPs. For each test, the 9 co-registration points were always used, and supplemented by 4, 8, and 12 of our distributed GCPs respectively. The surfaces generated without GCPs were later georeferenced using all 27 GCPs in CloudCompare (https://www.danielgm.net/cc/) with the align tool using a fixed scale. All GCPs not used in the BA were used as checkpoints to calculate surface error metrics, expressed as absolute vertical and horizontal checkpoint error.

Surface model co-registration procedure for change-detection

Since each pointcloud was processed independently with a unique set of GCPs, small measurement errors (i.e., ±0.02 m vertically) led to vertical misalignments between subsequent pointclouds. To ensure an effective co-registration of surface models we applied an additional alignment technique (for change-detection calculations only). We iteratively edited GCP elevation values (±0.02 m maximum change; i.e., same vertical error as RTK-GNSS) and recreated surface models that minimized change in areas of invariant topography (e.g., roadways, edge of field) and areas that exhibited obvious surface deformation (i.e., doming). As the self-calibration ties the surface model closely to GCPs, it is more logical to edit GCPs within the threshold of their accuracy rather than do a global translation after the surface has been processed. A global translation, while potentially enabling an effective co-registration, can also shift areas of topography that are correctly reconstructed (see Table 2 results). While our approach was both computationally intensive and time consuming, it mitigated deformation in the surface models, allowing for a higher confidence in the accuracy of the change-detection procedures.

Change-detection calculation

Change-detection is most commonly calculated by DEM differencing. While efficient, DEM differencing can only be performed on gridded meshes on a per pixel-basis (i.e., not on pointclouds). Another common technique involves using cloud-to-cloud (C2C) distances, which is a computationally efficient algorithm that calculates the nearest-neighbor distance between point-pairs, but is not always indicative of the true distance between clouds, most notably for low density and noisy clouds. A novel change-detection procedure, the M3C2 algorithm (Lague et al., 2013), offers a more robust change-detection procedure that can be used directly on pointclouds. The M3C2 algorithm calculates a normal vector for each point and fits a cylinder of a specified radius in the direction of the normal vector. Surface change is calculated as the average distance between the two pointclouds in the cylinder, making the M3C2 algorithm less sensitive to surface noise. For a more precise calculation of volumetric change, we used M3C2 distance calculations with vertical normals and a 0.15 m diameter projection.

The M3C2 algorithm was used to compute change-detection results for UAV SfM-MVS surface models between Campaigns 1 and 2, and between Campaigns 2 and 3. To verify the accuracy of our change-detection calculations, UAV-derived change detection results were compared against TLS change-detection results at the north-east surface inlet of our study site.

Results

Surface model accuracy assessments

Four surface models were generated from our four images sets ([N], [C], [NC5], and [NC26]) without using any GCPs in the bundle adjustment (BA). These four surface models had their vertical accuracies assessed by a comparison to the [N] surface model processed with all 27 GCPs for Campaign 1 (Fig. 5). The [N] surface model generated without GCPs had a characteristic surface doming (Fig. 5a) as is commonly seen with nadir-only image sets. The [C] surface model had a complex pattern of error, with error propagating from two radial centers (Fig. 5b). The two other surface models processed without GCPs (i.e., [NC5] and [NC26]) had lower overall surface error thanks to the coupling of nadir and oblique imagery but contained a different distribution of error; both surface models had a “half-pipe” effect (Fig. 5c and d), with negative error towards the east/west edges of the surface and positive error along the centerline of the model.

Fig. 5. Distribution of vertical surface error for each image set processed without GCPs for Campaign 1: (a) 26 nadir imaging strips [N] (RMSE 0.150 m), (b) 13 east-facing oblique +13 west-facing oblique imaging strips [C] (RMSE 0.099 m), (c) 26 nadir +5 east-facing oblique +5 west-facing oblique imaging strips [NC5] (RMSE 0.049 m), (d) 26 nadir +26 east-facing oblique +26 west-facing oblique imaging strips [NC26] (RMSE 0.041 m).

When GCPs were not incorporated into the BA, the [NC26] image set produced the most accurate surface models across all field campaigns (checkpoint error; vertical RMSE: 0.047 m, horizontal RMSE: 0.019 m), with the [NC5] image set following closely behind (vertical RMSE: 0.061 m, horizontal RMSE: 0.025 m). Due to the large amounts of radial doming in the [N] surface models, all [N] surfaces had poor vertical and horizontal accuracies (vertical RMSE: 0.151 m, horizontal RMSE: 0.226 m). While this amount of horizontal inaccuracy was not expected with the [N] image set, the vertical doming was so prominent towards the surface edges of the study site that several checkpoints had very poor alignments. The [C] surface models had significantly better horizontal accuracies than the [N] surface models and better vertical accuracies (vertical RMSE: 0.124 m, horizontal RMSE: 0.037 m).

When GCPs were incorporated into the self-calibrating BA for each field campaign, the coupling of nadir and oblique imagery consistently led to the highest checkpoint accuracy; most notably when a sparse distribution of GCPs were used (Fig. 6). The [N] image set improved by the greatest amount as GCPs were incorporated into the self-calibration (vertical checkpoint RMSE values; no GCPS: 0.151 m, 13 GCPs: 0.052 m, 17 GCPs: 0.040 m, 21 GCPS: 0.028 m). These results contrast with the [NC26] image set which experienced a small improvement and possibly reached a maximum accuracy around 0.028 m (vertical checkpoint RMSE values; no GCPS: 0.047 m, 13 GCPs: 0.029 m, 17 GCPs: 0.029 m, 21 GCPS: 0.028 m). The [N], [NC5], and [NC26] image sets converged towards a similar vertical error metric at 21 GCPs of approximately 0.028 m which is expected based on our RTK-GNSS vertical inaccuracy of ±0.02 m. Horizontal accuracies were very similar between all image sets at 21 GCPs (RMSE range: 0.013 to 0.018 m). The [C] image set had slightly lower horizontal and vertical accuracies for each GCP test due to a large number of outliers.

Fig. 6. Boxplots depicting the absolute vertical [V] and horizontal [H] error of checkpoints across all three field campaigns for all four image sets (i.e., [N], [C], [NC5], and [NC26]). Vertical and horizontal RMSE accuracy metrics at 21 GCPs [V, H]: [N] 0.028 m, 0.017 m, [C] 0.048 m, 0.018 m, [NC5] 0.032 m, 0.016 m, [NC26] 0.028 m, 0.013 m.

Quality of surface model reconstructions

Despite the highly accurate results obtained from the incorporation of oblique imagery into our UAV surveys (most notably the [NC26] image set), the use of oblique imagery proved to be a significant detriment to the generation of certain surface models. The [C] surface models had gaps due to insufficient keypoint matches between image pairs and contained large amounts of vertical noise. Both the [NC5] and [NC26] image sets had poor homologous keypoint matching between oblique and nadir imagery leading to: 1) the pointcloud being processed as 2–3 independent blocks (Campaign 3; [NC26]), 2) migrating vertical error when the nadir image network was tied to the oblique image network at a single image (Campaign 2; [NC5] [NC26]), and 3) a large amount of vertical noise (Campaign 2 & 3; [NC5] [NC26]). These errors were the most pronounced for Campaign 2 when the surface texture and coloration of the field was homogeneous and the lighting conditions were bright (no cloud cover). The Campaign 1 surface model for the [NC5] and [NC26] image sets had excellent matching between nadir and oblique imagery and did not experience keypoint matching issues.

Topographic change-detection: erosion and deposition

The [N] surface model processed with all 27 GCPs was chosen for topographic change-detection of our study site. While we initially wanted to test all four different image sets, this was not possible due to large amounts of vertical noise in the surface models constructed using oblique imagery. Each campaign’s (1–3) [N] surface model underwent our coregistration procedure (i.e., GCP elevations were iteratively edited by ±0.02 m to minimize changes in areas of invariant topography) before change-detection results were calculated. The coregistration procedure significantly reduced surface coregistration error in the southern portion of the study site where the GCP network was sparse.

Between Campaign 1 (May 7th) and Campaign 2 (May 17th) the study site was tilled (May 12th) and one erosive rainstorm occurred on May 15th with a total precipitation amount of 8.4 mm. Change-detection results using the M3C2 algorithm (vertical normal, 0.15 m projection) between Campaign 1 and 2 calculated a mean surface change of +0.010 m. A mean surface change of this magnitude is within our margin of error and indicates that no detectable mean surface-change occurred. Tillage lines, wheel tracks, infilled gullies, and areas where sediment was manually dug out from around the surface inlets are clearly visible in the change-detection map (Fig. 7c, d, e). Surface-change due to tillage and fluvial erosion cannot be differentiated on this change-detection map.

Fig. 7. [N] Surface model M3C2 difference: (a) Campaign 1 to 2 (tillage; mean surface change +0.010 m), (b) Campaign 2 to 3 (erosion; mean surface change −0.020 m), (c, d, e) Campaign 1 to 2 catch basins, and (f, g, h) Campaign 2 to 3 catch basins. Arrows indicate the north-east catch basin used for comparison with terrestrial laser scanner results, whereby black corresponds to difference between Campaign 1 and 2 (a, d) and red corresponds to difference between Campaign 2 and 3 (b, g). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Between Campaign 2 (May 17th) and Campaign 3 (June 15th) three intense precipitation events occurred (i.e., exceeded 5 mm hr−1): May 20th (16 mm), May 31st (19.6 mm), and June 3rd (8.8 mm). The cumulative precipitation between Campaign 2 and 3 totaled 56.4 mm. Our M3C2 change-detection results identified that two major depositional plumes formed in the two northern catch basins (Fig. 7f, g) and several minor depositional plumes formed at the southern catch basins (Fig. 7h). The presence of depositional plumes were validated by field observations (e.g., Fig. 2c) and accuracy assessed against terrestrial laser scanner (TLS) results (Table 2; north-east catch basin). Preferential pathways for flow, ephemeral gullies, and rills (Fig. 2f, g, h) are depicted in our change-detection results leading up to depositional zones. The M3C2 change-detection algorithm calculated a mean surface change of −0.020 m between Campaign 2 and 3, which once again indicates that no detectable amount of sediment was lost from the field (i.e., mean surface-change is still within our margin of error).

To determine how accurately sequential UAV surveys can detect small-scale erosional processes (i.e., change-detection), surface models derived from UAV collected data were compared against data collected from a TLS at each campaign for the north-east catch basin (located in the yellow box in Fig. 1). Between Campaign 1 and 2 sediment was manually removed from the north-east catch basin (Fig. 7d); between Campaign 2 and 3 several erosive rainstorms redistributed sediment across the field with a large depositional plume forming at the north-east catch basin (Fig. 7g). The volumetric change between Campaign 1 and 2, for the north-east catch basin, was ~5% different between [N] (−3.02 m3) and TLS (−2.88 m3) surface models. The difference between UAV and TLS volumetric change quantification widened to ~25% between Campaign 2 and 3. The [N] surface model calculated the volume of the depositional plume at +33.44 m3 and the TLS calculated +26.72 m3. While the [N] surface model over predicted the magnitude of volumetric change, the results are within a 95% confidence interval (using the approach by Lane et al., 2003) for each campaign (i.e. surface change of ±0.040 m). It is important to note that this confidence interval is based on our accuracy assessment with 21 GCPs and 6 checkpoints. The confidence interval is theoretically narrower in areas close to GCPs and confidence in results will decrease as distance from the nearest GCP increases.

The UAV change-detection results of the north-east surface inlet were additionally compared to the TLS dataset using the original [N] surface model (i.e., that underwent no additional coregistration procedure) and the [N] surface models that underwent a global elevation shift of ±0.02 m (i.e., a global coregistration procedure; Table 2). This allowed for a cross-comparison of accuracies with our unique coregistration procedure (i.e., iteratively shifting GCP elevation values by ±0.02 m). Both the global shift and GCP shift resulted in reasonable alignments in areas of invariant topography, but the global shift resulted in decreased accuracies in areas where the surface reconstruction was already accurate (e.g., north-east catch basin; Table 2). The original [N] surface model had poor alignments in the southern portion of the study site where the GCP network was sparse, and minor surface deformation was shown in the change-detection map. Our co-registration procedure (i.e., vertical GCP shift of ±0.02 m before processing) ensured areas with a correct reconstruction were not altered and the shift minimized visible coregistration error in the southern portion of the study site.

Table 2. Volumetric surface change of the north-east catch basin with a 95% confidence interval. Surface change calculated using the M3C2 algorithm for: [TLS] surface models, [N] surface models with a ± 0.02 m GCP elevation shift, original [N] surface models, [N] surface models with a ± 0.02 m global elevation shift.

Discussion

Surface model accuracy

While the use of SfM-MVS for the production of orthomosaics is becoming ubiquitous, the presented methods and results demonstrate the challenges associated with the use of UAV SfM-MVS for 3D surface reconstructions of agricultural landscapes. Our results demonstrate that in the absence of GCPs, the coupling of nadir and oblique imagery led to the highest checkpoint accuracy in both the vertical and horizontal dimensions (e.g., [NC26] checkpoint error; vertical RMSE: 0.047 m, horizontal RMSE: 0.019 m). The addition of oblique imagery eliminated the doming effect of the [N] surface model but both the [NC5] and [NC26] surface models still exhibited some surface deformation (Fig. 5). When GCPs were incorporated into the self-calibrating BA, the [N], [NC5], and [NC26] surface models all converged towards similar vertical (21 GCPs; RMSE 0.028 m to 0.032 m) and horizontal checkpoint accuracies (21 GCPs; RMSE 0.013 m to 0.018 m). All surface models had at least one outlying checkpoint error when 21 GCPs were used in the BA, indicating that a denser GCP network was needed to combat surface deformation for all image sets. While the [NC5] and [NC26] surface models performed well across all checkpoint accuracy assessments, the addition of oblique imagery did not provide any notable advantage over the [N] surface models when 21 GCPs were used in the BA.

The addition of oblique imagery with the [NC26] image set caused a threefold increase in aerial surveying times and a fivefold increase in processing times in Pix4D (Table 1). While other studies recognize the benefits of oblique imagery (e.g., Harwin et al., 2015; James and Robson, 2014), we found that in our agricultural system, with both bare ground and vegetated conditions, that our [C], [NC5], and [NC26] image sets poorly reconstructed the observed 3D surface. Our agricultural study site is a very difficult environment for SfM-MVS due to low amounts of image content (i.e., only dirt; Campaign 1 & 2) and vegetated surfaces (i.e., rows of corn; Campaign 3). Low amounts of image content led to very poor homologous keypoint matches between nadir and oblique image blocks, creating broad-scale vertical noise across surface models. Despite performing well across checkpoint tests, we would not recommend supplementing flight plans with oblique imagery in agricultural landscapes. The benefits of using oblique imaging angles in SfM-MVS is realized in environments where either GCPs cannot be used or when only a sparse distribution of GCPs can be deployed (e.g., when surveying glacial retreat, coastal cliff erosion, or fluvial erosion in complex landscapes); these environments must also have a high amount of image content to facilitate homologous keypoint matching across oblique imagery. For environments that lack image content, using a UAV platform with built-in RTK-GNSS (e.g., DJI Phantom 4 RTK; Matrice 210 RTK V2) is a promising alternative approach for ensuring high quality 3D surface reconstructions.

Across all landscapes, the incorporation of more GCPs into the BA will result in a reduction in surface error, albeit with diminishing returns as more GCPs are used (e.g., Agüera-Vega et al., 2017; James et al., 2017; Sanz-Ablanedo et al., 2018). Based on our findings in agricultural landscapes, when we used 1.3 GCPs per hectare (i.e., 21 GCPs, 6 checkpoints), the [N] image set (0.017 m resolution) had an average vertical RMSE of 0.028 m across three field campaigns with maximum checkpoint vertical errors of 0.056 m, 0.042 m, and 0.042 m. Our final [N] surface models processed with all 27 GCPs contained some surface deformations with similar maximum vertical errors (estimated ±0.04 m), most notably in the southern half of the study site where the GCP network was sparse. This indicates that 1.7 GCPs per hectare (i.e., 27 GCPs) was not entirely sufficient to combat surface doming; a higher density of GCPs (e.g., 2 to 2.5 GCPs per hectare for 0.017 m ground-sampling-distances) is recommended to combat SfM surface deformation in a nadir image acquisition.

Besides an insufficient GCP network, the other two main bottlenecks to UAV SfM-MVS accuracy in our study were RTK-GNSS accuracy (± 0.02 m vertical, ± 0.01 m horizontal) and our ground-sampling-distance. When possible, we would recommend deploying a stable GCP network throughout the study site and on the periphery. Only authors that utilized permanent GCPs throughout their study were able to achieve sub-centimeter accuracy for change-detection (e.g., Eltner et al., 2015). Stable GCPs allow for both a precise co-registration of surface models and remove RTK-GNSS accuracy constraints. For our study, the use of permanent ground controls were only possible outside the study site, which we used as additional GCPs in the BA. Ground sampling-distance was the second bottleneck to our accuracy. While the relationship between ground-sampling-distance and surface model accuracy is difficult to quantify, the quality of surface reconstructions will degrade as the UAV takes images from higher altitudes (Eltner et al., 2016; Smith et al., 2016) or uses sensors with lower spatial resolutions. Pix4D documentation indicates an expected relative vertical accuracy of 1–3 times the ground-sampling-distance, and an in-depth study by James and Robson (2012) found a relative vertical precision of ~1:1000 (measurement precision: observation distance). Based on our maximum vertical errors from checkpoint tests, our vertical accuracy was 3× the ground-sampling-distance and the vertical precision was ~1:2000. Lowering the flying altitude from 90 m to 60 m, to allow for cm-level pixels, could have helped ensure we reached our maximum achievable accuracy. Additional error may have been introduced from our parallel-axis data collection scheme. While it has been shown that using additional flight lines from different directions (i.e., orthogonal flight plans) doesn’t always result in significant improvements in 3D surface reconstructions (e.g., James and Robson, 2014), several SfM software applications (e.g., Pix4D) strongly suggest including orthogonal flight lines for higher quality 3D surface reconstructions. The degree to which our parallel-axis data collection contributed to the observed surface errors is unknown. Other sources of error that are difficult to quantify include error marking the precise center points of GCPs, overexposed imagery, and the use of a rolling shutter.

Agricultural erosion modelling

Agricultural erosion comes with a substantial annual economic cost (e.g., United States $37.6 billion [Uri, 2000]), caused by both on-site and off-site effects. Agricultural erosion is a significant source of excess nitrogen and phosphorus in aquatic ecosystems contributing to eutrophication in freshwater lakes, estuaries and coastal environments (Bennett et al., 2001; Daniel et al., 1998; Foley et al., 2011). On-site redistribution of soil leads to an imbalance of nutrients for plant growth and lower yields. Despite the economic significance of agricultural erosion, spatial and volumetric predictions are mediocre at best (Morgan and Nearing, 2011) and direct measurements of distributed erosion rates are rare.

The most common approach for calculating the magnitude of agricultural soil erosion is employing the use of an erosion model. Researchers will employ either a simple statistical model (e.g., Universal Soil Loss Equation; Wischmeier and Smith, 1978) or a more complex distributed process-based model (e.g., Water Erosion Prediction Project; Flanagan et al., 2001). Newer process-based models allow for both a spatial and volumetric calculation of soil erosion at either the field-scale or watershed-scale by computing runoff and modelling the detachment, transport, and deposition of sediments. Despite large advancements in process-based erosion modelling over the past decades and a new suite of models, these newer process-based distributed models often fail to outperform older statistical models (e.g., Tiwari et al., 2000).

There exists a need to spatially validate both simple statistical models and process-based models at field and catchment scales. However, sources of reliable input data that describe the heterogeneity of the landscape are few and challenging to acquire. Distributed erosion models are typically calibrated and validated to outlet sedigraphs and hydrographs (i.e., data outside the area of interest). However, not all eroded sediment will be converted to sediment yield at a catchment outlet, which is why outlet sedigraphs are a poor proxy for catchment erosion processes (Syvitski et al., 2005; Morgan and Nearing, 2011); sediment redistribution can occur without making its way into the hydrological network. The use of catchment outlet data to calibrate or validate distributed erosion models is not always a valid approach (Morgan and Nearing, 2011). The challenges associated with model calibration and validation can be further exemplified when dealing with process-based models that tend to have an almost infinite number of degrees or freedom leading to issues with spatial equifinality (Morgan and Nearing, 2011). Without field-scale spatial validation data, it has to be assumed that the model is spatially accurate and models the correct process domains (e.g., rill and sheet erosion processes dominate, ephemeral gully erosion is negligible). It must also logically follow that the correct parameter set has been chosen by the modeler (i.e., no issues with equifinality). Given the economic costs associated with agricultural soil erosion and the corresponding ecological impacts, we need to use the type of data presented in this paper to remove our modelling assumptions. Furthermore, spatial predictions of erosion need to be tested at the scale of the decision-maker (i.e., farm field-scale), which is where erosion mitigation strategies take place.

The diachronic analysis of agricultural fields with UAV SfM-MVS is a promising approach that can provide input, calibration, and validation data for erosion models. While sheet erosion and small-scale rill erosion cannot be detected with this approach (change-detection at the 95% confidence interval was >0.040 m), larger process domains such as deep rill and gully erosion can be spatially quantified. It is potentially possible to detect smaller erosional processes by: 1) using stable GCPs, 2) employing a denser GCP network, and 3) increasing the ground-sampling-distance. The methodology in this presented research can also be used a priori to inform models of dominant flow paths and depositional zones, allowing for a more accurate description of the connectivity of the landscape, and can be used to assess the predictive capabilities of erosion models at the field and small-catchment scale.

Conclusions

We presented a comprehensive accuracy assessment of four different UAV survey designs for use with a self-calibrating bundle adjustment in an agricultural landscape. Our findings demonstrate that the coupling of nadir and oblique (15 degree) imagery (i.e., [NC5], [NC26]) improves the relative accuracy of agricultural 3D surface models in the absence of GCPs and with a sparse distribution of GCPs. With a more dense distribution of ground controls (i.e., 21 GCPs), the nadir-only [N] surface model had similar vertical checkpoint error metrics (RMSE 0.028 m) to both the [NC5] (RMSE: 0.032 m) and [NC26] (RMSE: 0.028 m) surface models, and all surface models had similar horizontal checkpoint error metrics (RMSE 0.013 m to 0.018 m). Surfaces generated from image sets that included oblique imagery had poor homologous keypoint matches and were subject to large amounts of systematic noise when feature content on the imagery was low, which is typical in agricultural systems. Processing and survey times were inefficient, costly, and unnecessary with the [NC26] image set given that the [N] image set had similar accuracy metrics with a dense deployment of GCPs. Subsequent [N] surface models were used to reliably identify erosive and depositional processes >0.040 m in depth (i.e., deep rill/gully erosion, and depositional zones). Small-scale erosion processes, such as sheet erosion, are not detectable with the presented UAV SfM-MVS methodology. Relative to a TLS, our sequential UAV surveys over predicted the volumetric change of a sediment plume by 5% and 25% for respective field campaigns. Due to RTK-GNSS accuracy constraints, our results verge on the maximum possible achievable accuracy. In an agricultural landscape, we recommend the use of nadir-only imagery for subsequent UAV surveys with a comprehensive ground control network to combat surface deformation and for use as checkpoints (i.e., 2–2.5 GCPs per hectare when flying at 90 m above-ground-level). Where possible, stable ground controls should be deployed in the study site for surface co-registration and to avoid the accuracy constraints of RTK-GNSS. Caution should be taken when interpreting SfM studies that do not include a comprehensive accuracy assessment of their 3D surface model. Future research should be aimed at the application of UAV SfM-MVS in agricultural settings for studying field-scale erosional patterns, calibrating and validating erosion models, and assessing the hydrologic connectivity of the landscape.

Source: Mapping erosion and deposition in an agricultural landscape: Optimization of UAV image acquisition schemes for SfM-MVS

Authors: Benjamin U.Meinen, Derek T.Robinson

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