Using 3D photo-reconstruction methods to estimate ...

Catena 120 (2014) 91–101

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Using 3D photo-reconstruction methods to estimate gully headcut erosion Álvaro Gómez-Gutiérrez a,⁎, Susanne Schnabel a, Fernando Berenguer-Sempere b, Francisco Lavado-Contador a, Judit Rubio-Delgado a a b

GeoEnvironmental Research Group, University of Extremadura, 10071 Cáceres, Spain Technical College, University of Extremadura, 10071 Cáceres, Spain

a r t i c l e

i n f o

Article history: Received 30 May 2013 Received in revised form 28 March 2014 Accepted 8 April 2014 Available online xxxx Keywords: Gully headcut Three dimensional photo-reconstruction (3D-PR) Terrestrial laser scanner (TLS) Point clouds Digital elevation models (DEMs)

a b s t r a c t In this paper, for the first time, three-dimensional photo-reconstruction methods (3D-PR) based on Structure from Motion (SfM) and MultiView-Stereo (MVS) techniques are tested for estimating the volume of gully headcut retreat. The study was carried out using 5 small headcuts in SW Spain: two headcuts located along the channel and 3 lateral-bank headcuts. Firstly, the accuracy of the resulting models was tested using as benchmark a 3D model obtained by means of a Terrestrial Laser Scanner (TLS). Results of this analysis showed centimetre-level accuracies with average distances between the two point clouds for the five headcuts ranging from 0.009 m to 0.025 m. Then, using a Digital Elevation Model of Differences approach (DoDs) the volume of soil loss was estimated for every headcut. Total soil loss ranged from − 0.246 m3 (erosion) to 0.114 m3 (deposition) for a wet period (289 mm) of 54 days in 2013. A different dynamic was observed for the main and lateral-bank headcuts, which showed erosion and deposition, respectively. Additionally, the use of historical photographs was explored with the aim of estimating long or medium-term erosion rates in gully heads. Results of this simulation pointed out to a clear decrease in the accuracy of the model when the photos are not acquired sequentially around the headcut. Finally, some methodological advices about the use of this 3D-PR procedure for monitoring small geomorphological features are presented. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Extension of gully headcuts is usually the main growing mechanism in gullies and therefore headcuts can constitute important sediment sources. Previous studies have highlighted the role of gully headcut activity and their contribution to the overall sediment yield (Oostwoud Wijdenes and Bryan, 1994; Oostwoud Wijdenes et al., 2000). There are numerous techniques for monitoring and quantifying gully erosion: pins (e.g. Chaplot, 2013; Desir and Marín, 2007), poles, micro-topographic profilers (Casalí et al., 2006), total stations (Ehiorobo and Audu, 2012; Gómez-Gutiérrez et al., 2012), LIDAR (Evans and Lindsay, 2010; James et al., 2007), expensive Terrestrial Laser Scanners (known as TLS; Perroy et al., 2010), aerial photographs and photogrammetric techniques (e.g. Gómez Gutiérrez et al., 2009; Ries and Marzolff, 2003; Vandekerckhove et al., 2003), photoreconstruction methods (Castillo et al., 2012) and differential GPS (e. g. Hu et al., 2009). At the same time, measurement methods can be oriented to sample cross-sections spaced at intervals and gully length in order to estimate the eroded volume or to develop a more intensive sampling procedure with the aim of elaborating continuous three⁎ Corresponding author. Tel.: +34 927 257000. E-mail address: [email protected] (Á. Gómez-Gutiérrez).

http://dx.doi.org/10.1016/j.catena.2014.04.004 0341-8162/© 2014 Elsevier B.V. All rights reserved.

dimensional (2.5D–3D) surfaces (i.e. Digital Elevation Models). The bidimensional (2D) approach is usually used to estimate the soil loss caused by rills and ephemeral gullies because these kinds of features are present in the landscape only for a few weeks or months. Some authors have focused their efforts on estimating the accuracy of different techniques and instruments with these 2D approaches (Casalí et al., 2006; Castillo et al., 2012). Casalí et al. (2006) analysed the influence of the distance between cross-sections in rills and ephemeral gullies using a Micro-topographic profiler, showing that distances from 1 to 5 m ensured an error below 10% in the calculation of gully volume, whilst larger distances produced unaffordable errors. For permanent gullies, multi-temporal approaches are common with the purpose of analysing channel dynamics and 3D approaches (using LIDAR, TLS or photogrammetry) are highly recommended. Intensive sampling procedures and data processing with the former methods require expensive equipments, significant expertise and are timeconsuming. Therefore, some researchers are still using 2D approaches with the aim of monitoring permanent gullies (Gómez-Gutiérrez et al., 2012). Recent developments made in tri-dimensional photo-reconstruction techniques (3D-PR), such as the use of Structure from Motion (SfM; Ullman, 1979) and Multiview-Stereo (MVS; Seitz et al., 2006) techniques together, have allowed obtaining high resolution 3D point

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Á. Gómez-Gutiérrez et al. / Catena 120 (2014) 91–101

clouds (Furukawa and Ponce, 2010; Snavely et al., 2006). In order to achieve final point clouds with these techniques, only oblique images (of the feature to be modelled) from consumer un-calibrated and nonmetric cameras are needed. The procedure consists of solving camera model parameters and scene geometry simultaneously, with redundant information coming from oblique conventional images and without the need of using control points during the composition of the model (Snavely et al., 2008). The resulting point cloud needs to be scaled and georeferenced using some control points within the scene but after the composition of the model. The advantages of these techniques over the abovementioned methods have been highlighted in the recent literature as they require little expertise because the processing is almost automatic (James and Robson, 2012), the accuracy is similar to the most accurate methods available today (such as TLS or traditional photogrammetry; Castillo et al., 2012; Chandler and Fryer, 2013; Fonstad et al., 2013; James and Robson, 2012) and by far, these techniques are cheaper and less time-consuming. Undoubtedly, these methods will be widely used during the next years in Geosciences (especially in Geomorphology and Geomorphometry) because, to date, 3D-PR techniques have rarely been used in these disciplines (Niethammer et al., 2011). Currently, the scientific community is exploring and testing the possibilities of these techniques in archaeology (Verhoeven, 2011), palaeontology (Falkingham, 2012), monitoring landslides (Niethammer et al., 2011), glacial landform reconstruction (Westoby et al., 2012), estimating ephemeral gully erosion (Castillo et al., 2012), measuring coastal cliff retreat (James and Robson, 2012) and analysing lava flow processes (James et al., 2012). A general conclusion of these studies is that more work needs to be done in order to analyse the performance of these techniques over a wide range of landforms, processes and scales (e.g. Fonstad et al., 2013; Westoby et al., 2012). Gully erosion is, besides sheetwash, the main soil loss process in rangelands of SW Spain, where valley bottom gullies are typically found in peneplains eroding shallow alluvial sediment fills overlying impervious bedrock. Recent work has demonstrated a high spatial and temporal variability of gully erosion in these areas and the high complexity of the process, with erosion and deposition happening at the same time and in the same cross-section (Gómez Gutiérrez et al., 2009; Gómez-Gutiérrez et al., 2012). For this reason, it is very important to monitor gullies at sufficient frequency and accuracy in order to make reliable estimates of the eroded volume, representing a very expensive and time-consuming work. Due to these difficulties, there is a lack of information about the relationship between channel changes and other environmental variables (Thomas et al., 2004). The main objective of this work is to test the quality and applicability of 3D models generated by means of 3D-PR techniques and free software (123D Catch) in order to quantify geomorphic changes (erosion and deposition) in 5 gully heads. To our knowledge, this is the first experience of using 3D-PR methods based on SfM-MVS techniques to monitor and quantify headcut erosion. Complementary objectives are i) to provide short-term erosion rates produced by 5 headcuts for a wet period spanning from the 8th of February to the 3rd of April 2013, ii) to explore the use of historical photographs with the aim of estimating medium or long-term erosion rates in gully heads and finally iii) to provide some methodological advices about the use of this 3D-PR procedure for monitoring small geomorphological features. 2. Study area Several researches have been conducted in the study area throughout the last years so that the interested reader may find a more detailed description in the literature (Gómez Gutiérrez et al., 2009; GómezGutiérrez et al., 2012; M. Maneta et al., 2008; M.P. Maneta et al., 2008; van Schaik et al., 2008). Summarizing, the field work was carried out in the Parapuños experimental catchment (99.5 ha), located in SW

Spain and representative of rangelands with disperse tree cover (dehesa) forming part of an extensive erosion surface of undulating topography. Climate is Mediterranean with a pronounced dry summer and average annual rainfall of 525 mm, being November and December the rainiest months. The gully is a second order discontinuous channel that drives ephemeral flows and is incised into an alluvial sediment fill of approximately 1.5 m. In the rest of the catchment, soils are very shallow and developed on schists. The channel has a total length of 1000 m with a tributary joining the main branch at 174 m from the basin outlet. Five small headcuts were selected and monitored because of their representativeness in the study area: two headcuts located in the main channel and the tributary and three lateral-bank headcuts situated in the left bank of the main branch. During the last years, a more intense headcut activity has been identified with the extension of the existing main headcuts and the appearance and development of lateral bank-headcuts (Gómez Gutiérrez et al., 2009), justifying the quantification of the process. 3. Methodology The basis of 3D-PR techniques can be found in the recent literature (for an in depth description of SfM techniques see Snavely et al., 2006, 2008), but essentially the procedure consists, in the first place in identifying matching features in different images commonly done by applying the Scale Invariant Feature Transform algorithm (SIFT; Lowe, 2004). Afterwards, the network of features in different images is used to estimate the camera model parameters, i.e. focal length, radial distortion function and camera orientation. Contrary to traditional photogrammetric techniques the geometry of the scene and camera parameters are solved automatically and without control points during the composition of the model. The calculation of camera model parameters and scene geometry is carried out by iterative bundle adjustment with features identified in the overlapped images of the object to be modelled (Snavely et al., 2008). Within the bundle adjustment, feature coordinates are refined using a non-linear least-squares error minimization (Snavely et al., 2008). Finally, by using a few control points it is possible to scale and georeference the point cloud. Nevertheless, point clouds obtained with SfM techniques are not dense enough to produce high quality 3D models, similar to those produced by means of classical photogrammetric techniques (Rosnell and Honkavaara, 2012). Recently, the development of Multi-View Stereo algorithms (MVS; Seitz et al., 2006) has allowed the improvement of point clouds generated with SfM matching techniques increasing the number of points by two or three orders of magnitude (James and Robson, 2012; Westoby et al., 2012). There are several packages of tools, scripts and software available to generate 3D models using photo-reconstruction techniques such as Bundler (Snavely et al., 2006; http://phototour.cs.washington. edu/bundler/), Photosynth (http://photosynth.net/), CMP SfM (Jancosek and Pajdla, 2011; http://ptak.felk.cvut.cz/sfmservice/ websfm.pl?menu=webservice), VisualSFM (Wu, 2013; http:// ccwu.me/vsfm/), ARC3D (Tingdahl and Van Gool, 2011; http:// homes.esat.kuleuven.be/~visit3d/webservice/v2/index.php), Agisoft photoscan (http://www.agisoft.ru/products/photoscan) or 123D Catch (http://www.123dapp.com/catch). In the present paper, 123D Catch software was used because it is free, it is extremely simple to use, it represents an all-to-one solution and, to our knowledge, its suitability has been rarely tested for applications in Geosciences yet. A brief and recent report by Chandler and Fryer (2013) analysed the accuracy of 123D Catch software in order to record an aboriginal cave in Australia evidencing that 3D-PR techniques implemented in 123D Catch software are capable of producing 3D models which are comparable to TLS models (Chandler and Fryer, 2013). Also recently, James et al. (2013) explored the capabilities of 123D Catch in order to quantify surface changes at different scales, concluding that the software was able to produce promising results. In addition, 123D Catch


represents a whole-process automatic solution whilst other software need several routines, packages or scripts to get the final model using SfM and MVS together (such as Photosynth or Bundler). In the present paper, the images used in the photo-reconstruction process were acquired with a SLR camera (Canon 550D) enabling automatic focusing (conventional focal length: 18–55 mm) and exposure. Images were captured following the scheme presented in Fig. 1, because 3D-PR algorithms are designed to work with convergent images. Any part of the feature to be modelled should be represented in at least 3 photographs. The number of photographs taken of the headcuts varied from 41 to 93 (5184 × 3456 pixels) depending on headcut dimensions and complexity. Autodesk team, the company that develops the software, recommends a number of photographs of 50 to 60 spaced from 10 to 60° around the feature to be modelled. Monitoring features directly in the field represents a special challenge because light conditions cannot be controlled as in a laboratory environment. In addition, vegetation and the presence of water in the channel are other important challenges. As result of our experiences and trials, a brief catalogue of recommendations and good practices is presented in Section 4.3. In order to scale and georeference the resulting 3D models, CloudCompare software (http://www.danielgm.net/cc/) was used. This software includes tools to automatically and manually align a 3D model based on a scaled and/or georeferenced model. Manual georeferencing was carried out first, and automatic registration was applied later to refine the matching between the resulting 3D model and the model obtained with a TLS, which was used as benchmark. A Leica C10 Scanstation device was used in order to obtain the benchmark 3D model. A positional error smaller than ±2 mm for every 50 m is expected for measurements made with this equipment. Here, the TLS device was used because the resulting point cloud was also used to test the accuracy of the 3D-PR procedure. However, any other topographic instrument could be used to scale and georeference the model. Even, the 3D model could be scaled with just a few measurements made with a tape in the field and defining a relative coordinate system in

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123D Catch. The transformation between the two coordinate systems (TLS and 3D-PR point clouds) included 3 translations (one per axis: x, y,z), 3 rotations (one per axis: x,y,z) and a scale factor. In order to facilitate the former operations artificial control points were placed in the field, close to the headcut borders (Fig. 1). The Root Mean Square Error (RMSE) obtained during the georeferencing of the point clouds is shown in Table 1. Two sources of error can be identified during the procedure; the first one is the error associated with the georeferencing process and the second one is directly derived from the 3D-PR technique accuracy. Three sources of error in 3D-PR approaches are listed and discussed in James and Robson (2012): 1) the possibility of producing poor feature-position precision, 2) the coarse refinement of the calibration model used and 3) the production of one camera model per every photograph used. According to Goesele et al. (2007), SfMMVS approaches are, in general terms, less accurate than classical photogrammetric methods. James and Robson (2012) provided dimensionless estimations of the quality of SfM-MVS models by means of the relative precision ratio (i.e. precision measurement/observation distance). Figures around 1:1000 were presented in that work. After scaling and georeferencing, a cleaning procedure was carried out in every point cloud in order to delete unnecessarily modelled adjacent features, outliers and erroneous point matches. Finally, in order to compare the number of points, the average spacing and the point density of every point cloud, point clouds were exported to a GIS environment and clipped using a polygon enclosing the headcut and the surrounding area. At this point, there are two possible approaches to estimate 3D-PR technique accuracy; the first is the classic one, which is based on generating 2.5D surfaces (i.e. Digital Elevation Models; DEMs) using the point clouds and comparing the Z values of the resulting surfaces (examples of this procedure are: Castillo et al., 2012; Westoby et al., 2012); the second option is based on comparing directly the distance between the two clouds of points. Both approaches were used in this work, the first one within a GIS environment (ArcGIS 10.0) and the second one using CloudCompare that incorporates tools to

Fig. 1. The 3D-PR techniques work best with a convergent imaging of the headcuts, for example, by following the strategy shown in the image. Note also the position of the control points in the limits of the study area in order to scale and georeference the 3D model later.

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Table 1 Date of each field survey and RMSE obtained using 10 control points during the georeferencing process. Field survey

Date

Headcut 1

Headcut 2

Headcut 3

Headcut 4

Headcut 5

1 2 3 4 5

05/12/2005 08/02/2013 14/03/2013 21/03/2013 03/04/2013

– 0.02 0.01 0.01 0.02

0.05 0.04 0.03 0.01 0.07

– 0.02 0.03 0.00 0.05

– – 0.02 0.01 0.00

– – 0.04 0.01 0.02

calculate the distance between two clouds of points (for details about the method see Girardeau-Montaut et al., 2005). The elaborated DEMs allowed the calculation of the RMSE, the bias and the Pearson's r coefficient. A total of 5 headcuts were surveyed on the same day (21st March 2013) with TLS and photographs in order to estimate the accuracy of 3D-PR techniques. In the abovementioned study by James and Robson (2012) coastal cliff erosion was estimated using seven surveys carried out during a year. To our knowledge, this is the only multi-temporal application of 3D-PR techniques to estimate soil erosion rates or cliff retreat rates and the photographs were collected with the purpose of applying SfM-MVS techniques. Here, we also follow that methodology but with some methodological differences. The first one is focused on using the error estimations in the Digital Elevation Models (DEMs) of Differences (DoD; Wheaton et al., 2010) approach to better constrain the error magnitudes inherent in the eroded volumes determined. Only changes experienced in the Z coordinate above a specific threshold were assumed as soil erosion or deposition. We also explore the possibility of using old photographs of a headcut to produce point clouds based on 3D-PR techniques and therefore to estimate long-term headcut retreat rates and eroded volume. This approach is based on using photographs taken in 21st March 2013 and reducing their resolution and number and imitating the camera pose and the lighting conditions in order to match those in available old photographs for headcut 2 and field survey 1. This field survey was carried out in 5th December 2005 and photographs were taken with a Kodak CX4310 digital camera (2080 × 1544 pixels). After that, 3D models were produced using these photographs and compared with the models obtained with the TLS. The georeferencing process of old photographs was possible due to the existence of control points in the field used in a former research (Gómez-Gutiérrez et al., 2012). Table 1 shows the dates of every field survey and the headcuts monitored. Of special interest are the surveys carried out throughout 2013 when 138.8 mm, 22.6 mm and 128.0 mm of rain were registered in the study area for the time between field surveys 2–3, 3–4 and 4–5 respectively (for a whole description of the instruments used to register rainfall see Gómez-Gutiérrez et al., 2012; M. Maneta et al., 2008). Previous studies in the area revealed the key role of water content of the valley bottom sediments in gully growth (Gómez-Gutiérrez et al., 2012). Erosion records obtained throughout the period 2001–2007 showed that the highest soil losses due to gully erosion took place during wet periods with abundant discharge production. Therefore, although the time between field surveys in 2013 is brief, changes in headcut morphology are expected. Finally, DEMs for every field survey were generated using point clouds and enabling the estimation of volumetric changes. With the purpose of isolating points in the ground surface from vegetation or other features, a minimum Z coordinate grid approach was run (i.e. using a grid, points with the minimum Z coordinate were selected). To do this, the point file information tool implemented in ArcGIS was used to estimate the pixel size which was selected as four times the calculated average spacing of points in the cloud. This selection was made after several trials and ensures that, at least, one of the points belongs to the ground surface. Afterwards, DEMs were elaborated by linearly resampling Triangulated Irregular Network (TIN) models created by Delaunay triangulation within ArcGIS software (Brasington et al., 2000; Westoby et al., 2012) and using the cloud of points previously selected. The assessment of volumetric changes between field surveys

was carried out based on DoD techniques (Wheaton et al., 2010). According to this methodology, a DEM of an initial time (DEM1) is subtracted from another DEM of a final time (DEM2) and the result is a DEM showing the differences between the two surfaces that can be summed with the purpose of quantifying total volumetric change. In order to obtain a more realistic estimation of volumetric change, uncertainties in Z coordinate for every DEM can be included. The sources of uncertainties in DEMs are quite diverse and associated with sampling procedure, topographic complexity, geodetic control, survey point precision, processing methods, interpolation and resolution (Williams, 2012). A deeper description of DoD techniques can be found in Wheaton et al. (2010) and Williams (2012) but basically, changes in DEMs can be considered as a signal (S) to noise ratio (N) (Eq. (1)): S=N ¼ V GC =V E

ð1Þ

where VGC represents variability associated with erosional and depositional processes, whilst VE is variability caused by errors included in the DEMs. Williams (2012) classifies DoD techniques in four classes: minimum level of detection, map probabilistic thresholding, spatial variability of uncertainty based on multivariate analysis and spatial coherence of erosion and deposition. In this paper, a mixed technique based on a minimum level of detection and coherence of erosion and deposition was applied. The error in a DoD (EDoD) can be assumed as the root sum square of errors, being EDEM1 and EDEM2 the errors in DEM1 and 2 respectively (Eq. (2)): 2 2 1=2 : EDoD ¼ ðEDEM1 Þ þ ðEDEM2 Þ

ð2Þ

Minimum level of detection can be considered as a conservative method and has been widely used and accepted (Williams, 2012). In this particular case, the error for a DEM of a specific field survey was assumed to be the error obtained during the georeferencing procedure (RMSEGeo, which depends on the quality of the scene for that field survey; Table 1) plus the average distance between the 3D-PR and TLS point clouds for the field survey carried out in 21st March 2013 (d). The former represents the global accuracy of the method for a specific headcut and can be assumed as invariant during the study period because all the field surveys (excepting field survey 1) were captured using the same scheme (Eq. (3)): EDEM1 ¼ RMSEGeo þ d:

ð3Þ

In addition, some rules were added in order to improve the final estimation of eroded and deposited volume. The outer perimeter of the headcut (i.e. the top of the walls) was digitized using the DEM and a digital hillshade model calculated using the former. In the inner part of this line, erosion as well as deposition were allowed. However, in the outer part, only erosion was accepted as being correct (i.e. collapse of the walls and headcut retreat) and changes meaning deposition in these areas were considered as noise or errors. As an example, for headcut 2 and during the study period 2 only areas experiencing a change in Z coordinate larger than 0.063 m were assumed as real geomorphic changes, because for field survey 1 and field survey 2 RMSEs of 0.04 and 0.03 m were obtained and d was calculated as 0.009. Fig. 2 summarizes the work flow and the methodological steps.


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Fig. 2. Work flow diagram of methods used to estimate headcut eroded volume.*In this work a TLS device was used to scale and georeference the model because the resulting point cloud was also used to test the accuracy of the photo-reconstruction procedure. However, any other topographic instrument could be use at this stage. Even, the model could be scaled with some measurements made with a tape in the field and defining a relative coordinate system in 123D Catch.

Table 2 Summary of the datasets obtained with 3D-PR and TLS techniques for every headcut during the field survey carried out in 21st March 2013, including the Number (N) of photos and points for 3D-PR, the average spacing and the point density. Also included is the average distance (Avg. d) between point clouds calculated using Girardeau-Montaut et al. (2005) method and the standard deviation (Std. dev.) associated with that estimation. The average viewing distance (i.e. camera-to-feature distance) and the relative precision ratio (i.e. the rate between Avg. d and the average viewing distance) are also presented. Finally, statistics related to the GIS approach which was based on elaborating and comparing DEMs (with 3D-PR and TLS techniques) are presented, including the RMSE, the bias or average error and the Pearson's R coefficient (with p b 0.005 for all the cases).

N of photos for 3D-PR N of points 3D-PR TLS Average spacing (m) 3D-PR TLS Point density (pts m−2) 3D-PR TLS Avg. d (m) Std. dev. (m) Avg. viewing distance (m) Relative precision RMSE (m) Bias (m) R

Headcut 1

Headcut 2

Headcut 3

Headcut 4

Headcut 5

93

66

73

41

48

297,151 531,760

771,381 1,830,467

731,704 794,346

901,318 3,181,038

895,559 1,411,288

0.011 0.008

0.009 0.006

0.010 0.009

0.009 0.005

0.009 0.007

7913 13,994 0.025 0.032 9.30 1:372 0.047 −0.019 0.93

17,973 42,648 0.009 0.031 10.50 1:1167 0.091 0.003 0.95

9191 10,016 0.024 0.020 9.70 1:404 0.036 0.019 0.97

13,569 47,598 0.012 0.012 9.50 1:792 0.025 0.006 0.99

17,006 26,800 0.020 0.029 10.00 1:500 0.042 0.007 1.00

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4. Results and discussion 4.1. 3D-PR techniques accuracy The point clouds obtained from 3D-PR method presented a lower number of points than the point clouds sampled by means of the TLS but with comparable magnitude (Table 2). However, the resulting average distances between points were similar due to a more homogeneous cover of points by 3D-PR method. Average point density for 3D-PR method ranged from 7913 to 19,973 points·m−2 which represents enough resolution to develop micro-scale monitoring of processes. Furthermore, point density presented a clear spatial pattern for both techniques. A homogeneous distribution of point density within every headcut resulted from 3D-PR technique as a consequence of the scene being fully encircled during the sampling procedure. The highest point densities were obtained in the inner area of the headcuts and therefore in the most interesting zones (Fig. 3). On the other hand and as expected, TLS sampling resulted in the highest point densities near the TLS location, whilst the lowest point densities were located in the upstream perimeter, far from the TLS location (Fig. 3). Obviously, a more homogeneous spatial distribution of point density could be achieved with more than one station for the TLS instrument; however, the downstream location (Fig. 1) is the only one that ensures no hidden parts in the upstream scarp of the headcut (usually the more dynamic part). In addition, more than one TLS station would result in additional errors and a more time-consuming field survey and office work. The total number of points in every scene, point density and point cloud quality

in 3D-PR methods are a function of the density, sharpness and resolution of the photoset besides the image texture (Westoby et al., 2012). Therefore, it is not possible to control the exact number of points or point density in the resulting point cloud and only some tips or good practices can be used with the aim of obtaining a high quality and dense point cloud. Some of these recommendations are presented in Section 4.3. Regarding the accuracy of the 3D-PR method, the average distances from 3D-PR point cloud to TLS point cloud were always below 0.03 m for the 5 headcuts. In fact, for headcuts 2, 4 and 5 the average distance is around 0.01 m. Fig. 4 presents a 3D view of the spatial distribution of the absolute distances between 3D-PR and TLS point clouds illustrating that most of the points are at a distance b 0.015 m. In addition, no non-linear deformation or distortion was observed in the maps showing the spatial distribution of the distances. Note that larger distances showed in green in the outer part of the scene (Fig. 4C) are the consequence of the area of interest being encircled by the photographs and no systematic errors are present in the headcut or the nearby area. The possibility of non-linear deformation in the point clouds resulting from SfM techniques has been pointed out as a likely weakness (Fonstad et al., 2013; James and Robson, 2012). However, the same authors conclude that their empirical results were promising and the non-linear deformations were minor (Fonstad et al., 2013) or only detectable in 1 out of several scenarios (James and Robson, 2012). Here, gradient maps of distances between point clouds (3D-PR and TLS) were elaborated and visually analysed to corroborate that the 3D-PR model was not affected by non-linear deformations. Headcut 4

Fig. 3. Horizontal point density for headcuts 3 (A) and 5 (B) for TLS point cloud (in the upper part) and 3D-PR (in the lower part). A transparency of 30% was applied to these layers and a hillshade digital model of every headcut was used as base in order to improve visualization of headcut morphology. The position of the TLS instrument can be clearly depicted in the upper maps. Finally, flow direction is indicated by arrows.


97

A

B

C

Fig. 4. 3D view of headcut 4 DEM (A), point cloud obtained with 3D-PR method (B) and distances between the 3D-PR and TLS point clouds calculated using the cloud to cloud distances (C) proposed by Girardeau-Montaut et al. (2005). Note that the outer parts of the scene present larger distances as a consequence of the area of interest being fully encircled by the photographs and no systematic errors are shown in the area of interest (i.e. within the headcut).

(represented in Figs. 4 and 5) is a good example of complexity because it shows two lobes and two pronounced steps being the highest distances (excluding the perimeter zone in green) between the point clouds (0.110 m) in the base of the scarp of the left bank lobe where visibility is restricted and the photo-reconstruction is limited to a few photos. In this case, the combination of aerial and ground photo-datasets could be a good option in order to minimize the hidden areas in complex landforms. Recently, some authors have reported similar

accuracies, highlighting the applicability of 3D-PR techniques with the aim of monitoring earth surface processes at micro-scale (Castillo et al., 2012; James and Robson, 2012). In this line, Castillo et al. (2012) found larger differences between DEMs generated by 3D-PR and TLS around the gully rims and most of the study area (a 7 m reach of an ephemeral gully) presented distances b0.03 m. However, Castillo et al.'s (2012) approach was based on comparing the derived DEMs (2.5D), here, distances between the two point clouds were estimated

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Fig. 5. DoD for headcut 4 and periods 3 and 4. Headcut retreat upstream was not observed throughout these periods and the values of the DoDs are presented only for the area within the headcut in order to facilitate the interpretation of the map. In the rest of the figure, grey values correspond with a hillshade of the area that was used as base map. Fig. 4 presented a 3D view of this headcut. Note that erosion is represented by negative values whilst deposition is represented by positive values. Soil loss is concentrated in discontinuities and near the walls whilst accumulation happened in the bottom of the headcut. Note the clear relation between cattle paths and headcut location.

with a 3D approach which is highly recommended because the elaboration of DEMs entail additional errors. These kinds of comparisons based on a 3D frame against GIS based approaches (2.5D) are more reliable for 3D datasets but have been rarely used to test 3D-PR techniques. A recent exception is the work by Koutsoudis et al. (2014) where the cloud-tomesh distance function offered by CloudCompare software was used to quantify the accuracy of a 3D-PR model of a monument in Greece. James and Quinton (2014) have also used this 3D approach recently, in this case, to test the accuracy of a hand-held mobile laser scanner. James and Robson (2012) obtained metre-level accuracies comparing SfM-MVS results with classical photogrammetry at hillside-scale. In the same work but at a different scale, authors presented millimetrelevel accuracies for a cliff face when compared SfM-MVS with TLS. James and Robson (2012) provided relative precision ratios of 1:950– 1500 and 1:1000–1800 for the coastal cliff and the volcanic craters respectively. In general terms, lower relative precision rates were obtained here with figures ranging from 1:372 to 1167. In this line, it seems logical that the accuracy will be, in some sense, not only associated with image characteristics but also with landform complexity that determinates visibility. This hypothesis is also supported by the results of Westoby et al. (2012) who compared DEMs obtained by means of 3DPR techniques and TLS for Constitution Hill in Wales. Westoby et al. (2012) found that the largest differences between both DEMs were located in areas of steeply sloping relief. In addition to the 3D calculation of distances between point clouds, in the present research, DoDs were obtained using 3D-PR and TLS point clouds for the same date (21/03/ 2013). Then, the relationship between DoDs values and some topographical variables (slope gradient, roughness and curvature) was explored. No statistically significant relationship was obtained, pointing to a more complex relationship. In fact, the 3D approach based on cloud to cloud distances showed that differences in z coordinate are mainly related with visibility from camera locations (i.e. areas with low visibility presented higher cloud to cloud distances; Fig. 4). Summarizing, the few works published in which 3D-PR techniques are used agree that they are suitable for monitoring gemorphological processes at detailed scales producing similar accuracies to TLS

equipments. Results presented here support that in the case of permanent headcut monitoring centimetre-level accuracies can be expected using a similar sampling procedure and data processing. Furthermore, no evidences of systematic errors were found analysing bias and the spatial distribution of distances between 3D-PR and TLS point clouds. Additional advantages of the procedure presented here are related with: a) the cost of the study because just a conventional camera, a computer and an internet connection are needed to run the procedure and b) the processing time, as for every field survey used throughout this work just 30 h were needed to get the final point cloud for the 5 headcuts (including field work, image processing, point cloud filtering, georeferencing and scaling) and using a conventional computer (i5 processor, 2.8 Ghz and 4 GB of RAM memory). 4.2. Gully erosion dynamics Soil losses estimated for the whole study period were highly variable. Table 3 shows the eroded-deposited volume estimated for every headcut and period by means of the DoD approach. A clear incision dynamic was monitored in the main headcut of the channel (headcut 1) and the tributary (headcut 2) with soil losses of − 0.061 m 3 and − 0.246 m 3 , respectively. Lateral headcuts (i.e. headcuts 3, 4 and 5) showed figures of − 0.008 m 3 , 0.114 m 3 and 0.020 m 3 . The aggradation in headcuts 4 and 5 during this shortterm study period is related with the input of sediments originated from sheetwash along the hillslopes, as previously observed in the study area by Gómez-Gutiérrez et al. (2012). Incision periods on the main headcuts of the channel have been also characterized previously by Gómez-Gutiérrez et al. (2012) as periods where the hydrological behaviour of the catchment was governed by high soil moisture content of the valley bottom sediments that originated the production of saturation overland flow as a consequence of abundant rainfall. In fact, February 2013 as well as April 2013 were humid, registering average rainfall of 289.4 mm. Total net erosion was estimated for periods 1, 2 and 3 whilst net deposition was calculated for the last period.


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Table 3 Estimated eroded volume by means of DoD technique (negative values for erosion and positive values for deposition-aggradation) for every headcut throughout the study periods and soil erosion rates. Note that not all the headcuts were monitored for all the periods and that the eroded volume estimated for period 1 is based in the use of the old photographs.

From To Duration (y) Rainfall (mm) Headcut 1 Eroded volume (m3) Rate (m3·y−1) Headcut 2 Eroded volume (m3) Rate (m3·y−1) Headcut 3 Eroded volume (m3) Rate (m3·y−1) Headcut 4 Eroded volume (m3) Rate (m3·y−1) Headcut 5 Eroded volume (m3) Rate (m3·y−1) Total (m3) a

Period 1

Period 2

Period 3

Period 4

Total

05/12/2005 08/02/2013 7.150 –

08/02/2013 14/03/2013 0.090 138.8

14/03/2013 21/03/2013 0.022 22.6

21/03/2013 03/04/2013 0.038 128.03

289.43

–

0.021 0.232

–0.037 −1.688

–0.045 −1.173

–0.061

−0.904 −0.126

−0.116 −1.283

−0.077 −3.513

−0.053 −1.382

−1.15 –0.246a

–

−0.118 −1.305

0.017 0.776

0.093 2.425

−0.008

–

–

0.063 2.874

0.051 1.329

0.114

–

– −0.213

0.086 2.242 0.132

0.020

−0.904

−0.066 −3.011 −0.100

Total eroded volume for the period from 8th February 2013 to 3rd April 2013.

Regarding the observed processes, headcut wall retreat was only registered in headcut 2 whilst geomorphic changes in the rest of the headcuts were associated with erosion and deposition in the base of the scarps or in the bottom of the headcuts. In contrast, the erosion of lateral-bank headcuts (headcuts 3, 4 and 5) does not seem to be related with water saturation of the valley bottom. According to field observations, the location, genesis and dynamic of these headcuts are strongly linked with cattle paths crossing the channel (Fig. 5). Paths are important features because they concentrate and direct overland flow from the hillslopes to the main channel. In addition, animals provoke mechanical erosion of the soil. Livestock density has been described as a crucial factor in the development of gullying processes in the study area (Gómez Gutiérrez et al., 2009). The lateral headcuts 3, 4 and 5 possibly are operating as sinks for sediments eroded at hillslopes by sheetwash. Headcut 4 is a good example to explain the spatial pattern of erosion and deposition in lateral-bank headcuts where erosion happens near the walls or along discontinuities in the bed of the headcut and deposition is registered in central areas in the bottom of the headcut (Fig. 5). Although the lateral-bank headcuts experienced net accumulation during the short-term study period from 8th February to 3rd April analysed here (or little erosion in the case of headcut 3), they are features of very recent growth and development. In fact, in 2002 they did not exist as proven by a detailed mapping of the channel that was carried out by means of high-resolution aerial photographs and field work. Details about the mapping procedure can be found in Gómez Gutiérrez et al. (2009). In order to quantify the eroded volume in headcuts 3, 4 and 5, for a medium-term study period, their location was translated to the detailed map of the channel in 2002 and the surface of the bank at that time was modelled. The procedure consisted in mapping headcuts borders in the DEMs generated for field survey 4. Later, using the borders of every headcut, points within them were deleted and TINs were elaborated with the points located in the borders. The final step consisted in calculating the volume within the TIN assumed as the surface in 2002 and the DEM (field survey 4). Using this procedure, the estimated total volume was − 0.581 m 3 , − 0.498 m 3 and − 4.68 m 3 , which results in annual losses of at least − 0.054 m 3 ·y − 1 , − 0.046 m 3 ·y − 1 and − 0.435 m 3 ·y − 1 for headcuts 3, 4 and 5, respectively. These values besides the increase of the number of lateral headcuts in the channel (n = 22) give an idea about the magnitude of the process and the quick degradation of the valley bottom that is taking

place in the catchment. In 2006, 16 headcuts were identified (Gómez Gutiérrez et al., 2009) as compared with 22 headcuts recognized throughout the field work carried out for this research (2013). The simulation carried out imitating the survey of 2005 resulted in an average distance between TLS and 3D-PR point clouds of 0.018 m with a standard deviation of 0.023, for headcut 2 as compared to 0.009 m obtained for the point cloud generated with all the photographs, convergent geometry and higher resolution. In addition, the reconstructed surface was obviously smaller because only points corresponding to features represented in 3 out of the 6 photographs were modelled. Unsurprisingly, these results illustrate a clear decrease in the accuracy of the point cloud when the convergent geometry is not preserved. However, the global accuracy of the model is still enough to estimate the volume of sediment eroded in the headcut at medium-term temporal scales. According to the RMSEs for field surveys 1 and 2 and the calculated average distances, a minimum level of detection of 0.084 m was considered and an eroded volume of −0.904 m3 was estimated for headcut 2 for the period from December 2005 to February 2013. This soil loss means an average rate of −0.126 m3·y−1 which seems to be credible, taking into account that an annual rate of −4.17 m3·y−1 was measured with classic topographical techniques for the whole channel during the period from December 2001 to June 2007 (Gómez-Gutiérrez et al., 2012). 4.3. Methodological considerations As it was said previously, monitoring features directly in the field represents an important challenge and some methodological considerations of our experiences and trials can be outlined. The number of photographs and spacing between them will depend basically on feature dimensions and the distance from the camera to the object, but essentially, any part of the object should be present in, at least 3 photographs, and redundancy is highly recommended. Theoretically, the more resolution the photographs have the larger amount of points will be obtained in the final model. However, due to the performance of 123D Catch software, which sends the images for processing into the cloud and gives the model back to the user, Autodesk staff recommends photographs with not very high resolutions (i.e. resolutions of 3–4 Mp). Furthermore, if a series of photographs of the same object are taken with similar resolutions but with different lighting, the resulting models will present different amounts of points. In fact, throughout this work two other headcuts were monitored but their results had to be rejected because they were located under tree cover where lighting conditions

100


are highly variable and volatile. For these cases, authors suggest trying the field survey to be carried out at night and with artificial lighting or under diffuse illumination (i.e. cloudy conditions) as was proposed by James and Robson (2012). In addition, the use of photographs obtained by means of High Dynamic Range techniques as input for 3D-PR should be explored in the future. For the purpose of monitoring channels, the presence of water represents an important impediment because reflective, glossy or transparent objects are not reconstructed in a reliable way. Therefore channels with permanent flow cannot be completely monitored with 3D-PR methods, and supplementary techniques for submerged areas will be necessary. Finally, vegetation seems to be another important problem due to several issues as it has been previously experienced by other authors (e. g. Westoby et al., 2012). In this case, the authors propose a very intensive photo capture in order to ensure that, even in the case of a dense vegetation cover, enough points are located in the ground surface. Finally, the highest inaccuracies of the resulting 3D models are associated to hidden or low visibility areas. With the purpose of minimizing these inaccuracies in complex landforms such as gullies, the combination of aerial and ground photodatasets is highly recommended. Recently, it has been hypothesized by Fonstad et al. (2013) that the combination of ground-based and close-range aerial images will probably result in a better reconstruction of the topographical surface. However, there is no research published about the use of ground-based and aerial images all together.

5. Conclusions In this paper, a new methodology was applied and tested with the aim of estimating soil loss for 5 small headcuts in a permanent gully. The method consisted of using 3D-PR models obtained by 123D Catch software which is based on the SfM and MVS dense reconstruction algorithms. The models generated by the 3D-PR method presented high and homogeneous point densities allowing the reconstruction of small features. A 3D approach was used to test the accuracy of the point clouds generated by 3D-PR method using point clouds obtained by means of a TLS as benchmark. Results of the analysis showed centimetre-level accuracies, which indicate that 3D-PR techniques used here are suitable for monitoring geomorphological processes at detailed spatial scales producing similar accuracies to TLS equipments. In addition, no nonlinear deformations or other systematic errors were observed in the area of interest (i.e. the centre of the scene and the modelled feature). Additional advantages of this methodology were corroborated throughout the research; low cost, short processing time and low expertise requirements. Afterwards, a DoDs procedure was used with the aim of estimating soil loss in gully heads during a wet period (with a total rainfall of 289.43 mm in 54 days) in 2013. A clear incision dynamic was registered in the main headcut of the channel and the tributary whilst lateral-bank headcuts presented a more chaotic behaviour. At the same time, the use of historical photographs for 3D-PR with the purpose of estimating medium or long-term erosion rates in gully heads was explored. Results showed a clear decrease in the accuracy of the model when the convergent geometry was not preserved, however, the global accuracy obtained for the model was still enough to estimate headcut eroded volume at medium-term temporal scale.

Acknowledgements This research was financed by the Spanish Ministry of Economics and Competitiveness through project CGL2011-23361 and the Government of Extremadura (FEDER, file number GR10071). We also would like to extend our thanks to M.R. James, one anonymous reviewer and the editor of the paper who provided valuable comments and constructive reviews.

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