Automated extraction of free surface fluctuations using ...

Automated extraction of free surface fluctuations using SfM-MVS photogrammetry EDGAR FERREIRA, PhD student, School of Civil and Building Engineering, Loughborough University, Loughborough, UK Email: [email protected] (author for correspondence) JIM CHANDLER, Professor, School of Civil and Building Engineering, Loughborough University, Loughborough, UK Email: [email protected] RENE WACKROW, Lecturer, School of Civil and Building Engineering, Loughborough University, Loughborough, UK Email: [email protected] KOJI SHIONO, Professor, School of Civil and Building Engineering, Loughborough University, Loughborough, UK Email: [email protected]

Automated extraction of free surface fluctuations using SfM-MVS photogrammetry ABSTRACT This paper describes a spatial measurement technique to measure the free surface of natural fluid flows in laboratory applications. This effective solution is based on “Structure-from- Motion/Multi-view Stereo” (SfM-MVS) photogrammetry and is capable of reconstructing water surface morphology, both at an instant and with a high spatial resolution. The efficiency and accuracy of the method is dependent upon the acquisition of high quality imagery (i.e. sharply focussed, no motion blur) with appropriate multi-frame camera coverage and configuration, and data processing must utilise appropriate camera calibration data. The potential of the technique for developing hydraulic understanding is demonstrated using two contrasting approaches. First, the water surface behind a living vegetation element is analysed along a single transect. Second, the full three-dimensional characteristics of the captured water surfaces are examined using statistical methods which demonstrate surface dissimilarity between vegetated and non-vegetated cases. The technique is transferable to real-world field sites.

Keywords: Eco-hydraulics; free surface measurement; laboratory studies; SfM-MVS photogrammetry 1

Introduction

The need for accurate water depth readings has always been a basic requirement in river engineering practice. Consequently, a wide range of approaches aiming to gauge water surface elevations in-situ or in the laboratory have been applied traditionally, ranging from rudimentary techniques involving graduated cables or rods, to more sophisticated methods such as ground penetrating radar or ultrasonic sounders (Bridge & Demicco, 2008). In more recent times, researchers working on fluvial hydraulics have extended these measurements, notably in terms of potential applications and spatial description. For example: Han & Endreny (2013) investigated intra-meander hyporheic fluxes based on head loss measurements determined with a point gauge; Biron et al. (2002), analysed the water surface topography at an asymmetrical confluence by means of a total station; Cochard & Ancey (2008), employed an image projection approach to trace the free surface associated to a dambreak; Felder & Chanson (2012), studied the free surface profiles over broad-crested weirs using sidewall photography; Dabiri & Gharib (2001), proposed a system combining the free surface gradient detector technique with digital particle image velocimetry to synchronously appraise the free surface distortion and the underlying turbulence in a free shear facility; Nichols et al. (2013), fabricated an acoustic wave probe to monitor the free surface over a fixed gravel bed flume; Tsubaki & Fujita (2005), explored a stereoscopic method to

reproduce the free surface spawned over an asymmetric trench; and, Fujita et al. (2011), obtained the water surface profile induced by hemisphere particles by applying an image processing protocol to laser light sheet based binary images. Common practice in fluvial hydraulics research is still however typically characterised by a sparse water elevation or topography (depending whether datum coincides or not with the bed) spatial resolution (see e.g. Zhao et al., 2014). Hence, the work described in this paper provides water surface descriptions at a very high spatial resolution and at an instant through the application of Structure-from-Motion/Multi-view Stereo (SfM-MVS) photogrammetry. As the term implies, SfM-MVS photogrammetry has its roots in a well-established spatial measurement method known as photogrammetry. Many excellent introductory texts explain the basic principles of photogrammetry. Among others, Fryer et al. (2007) provides a useful textbook which includes a chapter on earth science applications, comprehending for example a flume bed evolution study (Chandler et al., 2007), and Luhmann et al. (2006) offers a more extensive source of reference of photogrammetry science. Strictly, the phrase “Structurefrom-Motion” evolved from the machine vision community, specifically for tracking points across sequences of images occupied from different positions (see e.g. Spetsakis & Aloimonos, 1991). SfM-MVS implements mathematical models developed many years ago in photogrammetry, including: coplanarity and collinearity, and particularly the self-calibrating bundle adjustment (Kenefick et al., 1972). The SfM-MVS approach has been explained by a range of authors (e.g. James & Robson, 2012; Micheletti et al., 2015; Smith et al, 2015), but in essence it involves acquiring digital photographs from a number of positions relative to the object of interest. A scale invariant feature transform identifies distinctive features appearing upon multiple images and establishes the spatial relationships between the original camera positions in an arbitrary and unscaled coordinated system. A self-calibrating bundle adjustment is then used to calibrate the cameras used and derive a sparse set of coordinates to represent the object. This is then intensified using MVS (Multi-View Stereo) techniques, to generate a very high resolution point cloud, which is colour-coded using the original image data. External geometric constraints can be then optionally applied, to transform the 3-D data to a desired coordinate system. Despite the unanimous agreement on the significance of free surface activity regarding, e.g., gas transfer mechanisms (Tsubaki & Fujita, 2005), or as an “echo” of the spatial/time development of the flow (Cobelli et al., 2009), few studies, of which Cochard & Ancey (2008), Dabiri & Gharib (2001) and Tsubaki & Fujita (2005) are notable examples, have quantified the spatial variation of free surface elevation at large spatial scales (i.e. in the threedimensional space) and at a single instant in time. The methodological development reported in this paper provides a way of quantifying free surface heterogeneities produced by

vegetation elements at large space scales, with a high spatial resolution and instantaneously. The approach exploits the ability of three synchronised cameras to freeze motion, combined with SfM-MVS photogrammetry to create a 3-D representation of the water surface. Besides the obvious advantages over one and two-dimensional sensors, the technology introduced in this paper improves certain aspects and overcomes some limitations of past work. Major advances regarding the pioneering study by Tsubaki & Fujita (2005) can be summarized in three points. First, cameras pose and scene geometry are here automatically ascertained due to the high number of conjugate points measured, due the superior performance of the scale invariant feature transform algorithm. Second, linear and non-linear errors arising due to inadequate ground control or limitations with kernel based approaches (Tsubaki & Fujita (2005) use a cross-correlation technique) are suppressed, enhancing the reliability of derived data (Fonstad et al., 2013). Third, the need to stain the water with a colourant or project a pattern to the free surface is obviated, making the workflow presented in this paper practicable for field application. Finally, contrary to Dabiri & Gharib (2001), SfM-MVS photogrammetry is able to cope with small and steep free surface slopes, and with competitive data acquisition and processing times, since expensive phase unwrapping algorithms are avoided (Cochard & Ancey, 2008). The paper is organized as follows: the experimental set-up is described; then, results are presented and further processed using two complementary approaches, before some conclusions are finally drawn. 2 2.1

Materials and Methods The flume setup

Experiments were conducted in a 5.24 m long and 91.5 cm wide straight open-channel flume in the Sir Frank Gibb Civil and Building Laboratories of Loughborough University. Water was supplied to the test area by means of an upstream tank with plastic tube bundles for straightening the incoming flow. Previous experiments have shown that close to the inlet, the spanwise and vertical time-averaged velocity components were much lower than the magnitude of the principal velocity component, thus indicating that entrance effects were reduced by this apparatus. At the outlet, a manually operated tail gate was manipulated to fix the desired water depth. Although our goal was to develop a method to remotely measure free surface heterogeneities in vegetated flows, it was considered pertinent to capture imagery both with and without vegetation for comparative purposes. The discharge and the tail gate level were kept constant across these two tests (some branches of the vegetation were pruned to make the vegetation height coincident with the water depth). For the latter, a localized hole was created on a smooth bed for vegetation insertion, with the vegetation being placed at

approximately 2.9 m from the flume inlet and at its centreline, i.e., free surface readings were taken in the second half of the flume length. The chosen species, a conifer tree (Fig. 1a), was used while fresh and exhibited a static mode of reconfiguration under stressed conditions (Albayrak et al., 2014). Our work included the measurement of flow discharge Q, specimen frontal projected area (in dry conditions) Ap and wet mass wmass, and the free surface fluctuations (Section 3). The values obtained were: Q = 0.133 m3s-1, Ap = 0.053 ± 0.003 m2 and wmass = 65 ± 2 gr. As free surface irregularities were minor in our experiments, and the flume bed gradient was rather small (0.0014), the SfM-MVS data was not de-trended in this work.

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(b) 1

2 3

5

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Figure 1 (a) Conifer tree (upstream view), (b) schematic of the experimental apparatus including a projector screen (1), three cameras (2), external lighting (3), seeding particles (4) and photogrammetric control targets (5)

2.2

Imaging

A multi-camera system comprising three Nikon D80 digital SLR cameras, each equipped with a 24 mm fixed focus lens, was used for water surface measurement. Cameras were mounted on a foam pad fastened to a wood stand (positioned two meters above the free surface, each camera separated by 23 cm, Fig. 1b). Image synchronization is critical when measuring dynamic entities as asynchronism may cause the surface model extraction algorithm to fail. Synchronisation of up to 1/1000 of a second was ensured by adapting an existing electronically controlled triggering box to accommodate a third D80 camera. Image matching can only be successful if some visible surface texture is captured, which is challenging in naturally dark laboratory conditions, and particularly involving a rapidly moving and dynamic

water surface. For our experimental arrangement appropriate texture was created using artificial “seeds” (Section 2.3), necessitating the following exposure settings for the 3 cameras: manual mode, aperture f-2.8, shutter speed 1/400 second and ISO 1600. It is now fully recognized that consumer grade digital cameras are adequate for accurate photogrammetric measurement, provided camera calibration is considered (Chandler et al., 2005). Hence, similarly to Wackrow et al. (2015), calibration data was obtained offline and for each individual camera. Additionally, external lighting sources had to be used to provide appropriate illumination necessary to capture sharp imagery free of motion blur. Direct light generated numerous specular reflections which compromised matching strategies. Therefore, indirect and more diffuse illumination was achieved by directing the light sources to a projector screen (Fig. 1b) located above the flume. 2.3

Seeding material and control

Scene reconstruction requires adding floating marks or “seeds” to the free surface and the selection of a suitable material was challenging. Although in practice they worked as flow tracers, these particles were here solely used to provide suitable image texture to guarantee SfM-MVS effectiveness. Following Weitbrecht et al. (2002) and Chandler et al. (2008), the guiding criteria for selection were: density, diameter, durability and cost. The authors identified 1 mm cork particles (http://www.ccmoore.com/). Preliminary tests revealed that these particles indeed float, are well perceived by the cameras at the prescribed object to camera distance, offer a good contrast with the free surface and can be reused after drying (typically within a few days if no artificial drying is used). Seeds were spread manually with the aid of a wood container with two (superimposed and mismatched) metal sieves in the bottom. By this way, we could adjust the “dispenser effective diameter” and were able to seed the water at a rate compatible with the free surface velocity. The particles were collected near the tail gate via a small floating wooden bar, which guided the floating particles to a collecting net. Photogrammetric control was established to define a local scaled coordinate system, but also provided the opportunity to assess the accuracy of the experimental layout. Ringed Automatically Detected (RAD) coded targets (PhotoModeler Scanner, 2014) were printed at a diameter of 7 mm and coordinated using professional survey grade instrumentation, a Trimble M3 Total Station (Trimble, 2016) (Fig. 1b). 2.4

Quality control tests

2.4.1 General remarks While evaluating the quality of spatial data it is important to distinguish three components, notably precision, accuracy and reliability, and relate these elements to random, systematic

and gross error sources, respectively (Cooper, 1998). Random errors are unavoidable, are subject to change and can be estimated by statistics. Systematic errors arise from inexact functional models and improperly calibrated equipment. Finally, gross errors are genuine mistakes or “blunders”, but can be normally isolated if there are redundant data to provide checks. Ideally, these three aspects are assessed by precision, accuracy and reliability metrics. This section presents some simple test cases that give an insight into the magnitude of these descriptors for the present arrangement. 2.4.2 Measurement precision Measures of precision can be estimated by assessing the covariance matrix. This is a biproduct of the internal bundle adjustment used to determine the position and orientation of the cameras, conjugate points appearing in the images and implements a least-squares estimation procedure (Cooper, 1998). These values are uniquely dependent on “endogenous factors” such as image geometry, the precision of the image coordinates and the number of images that each point appears upon. Such precision estimates can be directly retrieved from PhotoModeler

Scanner

(64

bit)

(PhotoModeler

Scanner,

2014).

Conventional

photogrammetric practice suggests that “control” or “reference” points should be widely and uniformly distributed around the periphery of the “volume of interest” (i.e. over the area covered by the images) to improve point positioning accuracy (Luhmann et al., 2006). This was difficult to achieve in our flume study (e.g. it being impracticable to distribute markers beneath the water surface). Therefore, linear targeted arrays were located on either side of the flume, plus four extra targets just above the water surface (due to the drawing perspective, two of these four extra targets are omitted in Fig. 1b). The merit of this configuration was initially gauged by simulating the water surface through an array of photogrammetric targets placed on a flat board, temporarily placed at approximately the same plane as the expected water surface. This allowed two examinations to be conducted. First, the spatial variation of precisions of point coordinates distributed across the water surface could be estimated and summarised (below). In addition, a comparison between the estimated positions and an assumed plane allowed accuracies to be estimated (Section 2.4.3). Three images of the planar board were processed using PhotoModeler. This demonstrated that point precision for a conjugate point located close to the water surface was ±0.8 mm, ±0.8 mm and ±1.2 mm in the x (longitudinal), y (lateral) and z (vertical) directions, respectively. The lower precision in the vertical direction arises from the fact that cameras were confined to a single zone above the free surface. The hypothetical adoption of additional cameras located at varying heights would improve such precisions, by creating stronger image geometry.

2.4.3 Measurement accuracy Accuracies can only be assessed by comparing estimated data with some form of external truth or accepted standard (Cooper, 1998). In this work, accuracy was evaluated by three methods, with the first and second involving the board mentioned above. Previous work (Chandler et al., 2005; Wackrow & Chandler, 2008) has shown that this provides a rigorous way to assess accuracy and identifying unresolved systematic errors in the measurement process. Typically these are manifest by an error surface or “dome”, which arise due to minor inaccuracies in the parameters used to model lens distortion derived during camera calibration (Chandler et al., 2005; Wackrow & Chandler, 2008; Wackrow et al., 2015; Smith et al., 2015). By assuming board planarity and ignoring surface irregularities, it was possible to estimate discrepancies from this plane surface, with the mean error being found to be 1.1 mm (standard deviation of ±1.4mm). Complementary to this, four of these RAD targets were surveyed directly using the Trimble M3 Total Station and their coordinates compared against PhotoModeler estimates. Likewise, average height differences of 1.1 mm were determined. The third test was executed in the course of the vegetated trial reported in Section 3, and involved a single surface estimate by reading a “survey staff strip” (using Image, Fig. 3b) placed towards the side of the flume, an approach used by Schneider et al. (2012). This allowed us to confirm a general agreement between the SfM-MVS measurement system and the water depth marker (difference of 2 mm). Although slightly higher than the expected precision, there were no cork particles located exactly adjacent to the depth marker and some interpolation was necessary. Due to the analysis performed in Section 3, this accuracy (and precision, see above) were considered appropriate for the present context. However, it should be stated that future studies focussing on other hydraulic processes may well be more demanding in terms of the required accuracy and precision. 2.4.4 Measurement reliability Cooper & Cross (1988) defined reliability as a “measure of the ease with which outliers may be detected” and proposed a broadly accepted indicator (the τ factor), which is difficult to quantify when studying dynamic surfaces (such as a free surface). In the spirit of Cooper & Cross (1988), the authors of the present work consider that visualization is a valuable tool that can replace numerical metrics when ascertaining reliability. As pointed out by Wood & Fisher (1993) “it (visualisation) can easily convey the significance of data uncertainty”. Accordingly, reliability was appraised by manually agitating still water that was seeded with cork particles. Application of SfM-MVS photogrammetry produced a convincing free surface representation that is free of noise. This can be visualised as a traditional figure (Fig. 2) or video (http://geomaticsjc.lboro.ac.uk/ven/WaveSurface-Control.gif).

Figure 2 Surface model representation illustrating a complex but convincing waveforms 3

Results

Digital photogrammetry systems incorporate a series of user definable strategy parameters which, when inappropriately assigned, deteriorate the efficiency of image correlation algorithms and, consequently, the quality of the surface representation. The number of the strategy parameters varies with the choice of system and parameter selection is dependent upon the illumination and texture captured in the imagery (Gooch & Chandler, 2000; Lane et al., 2004). Therefore, the writers carried out a simple test to guide parameter selection, which proved straightforward in this case. A small rectangular plastic water storage tank (1.0 x 0.5m) was filled with water and seeded with cork particles, under similar seeding and lighting conditions as the main flume. Images were gathered and processed, using the default strategy parameters currently recommended by the PhotoModeler SfM-MVS software. A patch consisting of 55734 elevations was arbitrarily picked from the surface model and its standard deviation (σ) computed. The calculated value (±0.5 mm) suggested that the main feature of this surface (i.e. horizontal planarity) was being accurately detected, thus validating the use of the default strategy parameters in our main tests. Figure 3 shows original imagery captured for both the un-vegetated (Fig. 3a) and vegetated (Fig. 3b) flows. Figure 3c is a visualisation of the dense colour-coded point cloud representing the vegetated case. It should be emphasized that this surface representation was created in less than 5 minutes on a personal computer with an Intel Core i7-3770 3.4 GHz processor and 8 GB of RAM. Prior to the analysis described below, points of the free surface lying outside our region of interest (before x = 0 where the conifer tree was eventually positioned) were removed and dubious point

elevations were filtered using a semiautomatic local variance based filter inspired by Lane et al. (2004). Based on an iterative process, a conservative filter threshold was set so that only free surface points were preserved. At the end of this stage, 122604 (over an area of approximately 1.5 m2) and 151383 (over an area of approximately 1.6 m2) free surface points were retained for the reference flow (no conifer tree) and perturbed flow (with the conifer tree), respectively. This high number of points ensured the representativeness of the studied water surfaces, a sine qua non condition for the analysis performed in Sections 3.1 and 3.2.

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(b)

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Figure 3 Free surface (a) reference flow (no vegetation), (b) perturbed (vegetated) flow, and (c) 3D colour-coded point cloud of the vegetated flow (Note: white dots are PhotoModeler “smart points”)

To portray the spatial variability of the water surface, two sampling formats were tried: (1) a single transect in the middle of the flume containing 825 points taken at 2 mm intervals (Fig.

4 and Section 3.1, only applied to the vegetated perturbed case) and (2) considering the full 3D coordinates derived (Section 3.2). The major advantage of the second approach is the provision of three-dimensional empirical information, thus enabling researchers to embrace the concept of the random-field approach (see e.g. Coleman et al., 2011) to study the free surface shape/structure and ultimately, its signature on different flow zones (Sukhodolov & Sukhodolova, 2014). Thus far, this view has been limited to the analysis of flow-bed interactions through the use of spectra, structure functions and statistics. We advocate that SfM-MVS photogrammetry is a promising solution to extend this approach to the free surface. In this study, eminently focused on the methodological traits of SfM-MVS photogrammetry, we start by considered two specific snapshots from a broader dataset to better illustrate some outputs that can be derived from SfM-MVS photogrammetry. Hence, for the first time, we will look at the following basic questions: What type of wave is induced by these flexible vegetation elements? Are the water heights normally distributed in this case?

Figure 4 Surface model (vegetated case): vegetation location (green circle) and the considered free surface profile (blue) 3.1

Longitudinal free surface variation

Figure 4 provides a plan view representation of the captured water surface with variations in grey representing absolute elevation above the flume bed (White: 0.295 m and Black: 0.280 m), illustrating an elevation range of approximately 13 mm. During the vegetated trial, small scale free surface disturbances were originally detected on the wake of the vegetation, with these disturbances being progressively dissipated downstream (Fig. 4). Hence, it was attempted, in a first instance, to fit a damping wave equation to the profile data (i.e. along the

blue line in Fig.4) through a non-linear regression. Any real water wave is the manifestation of many waves. However, it would have some practical significance if the waves past the conifer tree could be described by a simple analytical form (which will only eventually occur if sine-like wave modes prevail). At a fixed time, a damped sinusoidal wave is given by the product of a decaying exponential signal and a pure sine wave: z = e-bxAcos(kx + φ), where b is a damping coefficient, A is the wave amplitude, k is the wave number, φ is the phase and z and x have the same meaning as before. Figure 5 compares the measured water surface profile with the damping equation. Overall, and excluding the first few centimetres immediately after the conifer tree, two main regions can be distinguished. Before x ≈ 0.75 m, the water depth (initially) increases and the damping wave equation consistently underestimates the wave peaks; after this instance, the measured water wave is well described by the damping equation.

Figure 5 Comparison of the downstream profile and the damping equation assuming b = 0.518, A = -0.005 m, k = 44.407 m-1 and φ= -69.932 rad

3.2

Towards a continuum approach

Further statistical analysis utilised filtered water surface elevation points extracted immediately downstream of the conifer tree until x ≈ 0.23 m. This approach used all elevation points within this area, rather than just points extracted in a downstream sectional plane. As the inner flow region was not measured, this area was delineated from visual inspection as a tentative way to isolate possible side wall effects. This area is therefore assumed to be mainly affected by the wake of the conifer tree.

As expected, the first moment (μ) and the standard deviation (σ) of the water depth slightly increased from the non-vegetated reference flow (μ = 0.284 m and σ = 0.001 m) to the vegetated perturbed flow (μ = 0.289 m and σ = 0.002 m). It is unlikely to retrieve a pure normal distribution from experimental data and Totton & White (2011) review distinct methods to judge data normality. However, Montgomery & Runger (2003) state that normality tests are fruitless when extensive datasets (as in our case) are exploited. An alternative is to generate normal probability plots to examine water elevation distributions, as shown by Nichols & Shepherd (2012). Basically, this approach involves plotting the experimental observations zi (i =1:n with n being the total number of samples ) versus the standardized normal scores (SNS) (Fig. 6a).

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Figure 6 (a) Normal probability plots (linear regression lines represented as solid lines), and (b) density distribution of the vegetated flow water elevations. The number of bins was set based on Freedman-Diaconis rule (Freedman & Diaconis, 1981)

Figure 6a suggests that free surface fluctuations are non-normally distributed in the vicinity of flexible isolated (or highly sparse) vegetation elements. Note that in the non-vegetated reference flow case, the vast majority of points lie in a straight line (i.e. water heights are normal distributed), whereas in the vegetated perturbed flow this tendency is more difficult to discern. This fact is reinforced in Fig. 6b, where it seems apparent that a logistic distribution works better than a normal one. This departure from normality has also previously been observed on steep ocean waves (Srokosz & Longuet-Higgins, 1986). At present we are acquiring more data and in a follow-up study intend to more systematically characterize these free surface fluctuations and their potential link with vegetation properties. The existence of such a connection can have ground-breaking implications for the development of quantitative theories in fluvial hydraulics and ecology.

4

Conclusions

This work has presented a method to yield high resolution representations of dynamic water surfaces using SfM-MVS photogrammetry. A description of the method was accompanied by an examination of the quality of extracted data, suggesting accuracies of 1-2 mm can be achieved. Furthermore, two distinct analyses have demonstrated how a dense numerical description of high resolution surface morphology, captured at an instant, can answer fundamental questions linked to the nature of the free surface. The authors believe that SfMMVS photogrammetry may open new avenues for researchers working on free surface dynamics/structure, especially for those trying to infer subsurface properties from the free surface pattern (Brocchini & Peregrine, 2001). In summary, this work is seen as an important step to improve our understanding of flow-free surface interactions, a necessity recently claimed by Sukhodolov (2015). Limited progress in this area is perhaps a manifestation of technological constraints, specifically an inability to adequately measure free surface topography. SfM-MVS photogrammetry can achieve this but can perhaps also allow progress in other domains, the validation of computational models being one obvious example. Due to the innovative character of this work, future applications will increase the cumulative experience with SfM-MVS photogrammetry and dictate eventual operational and methodological refinements (e.g. increasing the sampling rate beyond the 3 Hz current achievable, among others) needed in laboratory and field conditions. In general, SfM-MVS photogrammetry is anticipated to be similarly applicable to other free surface formats, for example above rough beds or at confluences. The objective of each study should dictate the quality of data required. By quantifying the required precision, appropriate survey design can identify the optimum geometry, defined by the camera to object distance and focal length (i.e. scale), relative position and number/type of synchronised cameras. This is clearly dependent upon the availability of synchronised cameras/lenses and site constraints but can be achieved before any images are acquired or measurements taken, through network simulation methods. During application, some form of simple accuracy check should be included, although this can be difficult to achieve. Recent preliminary work conducted by the authors (results not shown here), indicates that SfM-MVS photogrammetry is also viable in field environments and that under certain circumstances, e.g. in white water flows, flow traceability is “naturally supplied” by the free surface features. Acknowledgements Authors would like to thank the assistance of Mr. Nick Rodgers during the experiments. The first author would also like to thank Dr. Dave Coates, Dr. Emiliano Renzi and Dr. Maureen McIver from Loughborough University for the useful inputs while writing this work.

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