Ocean Dynamics

, Volume 61, Issue 10, pp 1521–1540

Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal

Authors

    • Faculdade de Ciências do Mar e do AmbienteUniversidade do Algarve
    • Forschungszentrum Küste
  • Pedro Manuel Ferreira
    • Centre of Intelligent SystemsUniversidade do Algarve
  • Luis Pedro Almeida
    • Faculdade de Ciências do Mar e do AmbienteUniversidade do Algarve
  • Guillaume Dodet
    • Faculty of Science, LATTEX, IDLUniversity of Lisbon
    • LNEC Estuaries and Coastal Zones DivisionNational Laboratory of Civil Engineering
  • Fotis Psaros
    • Department of Marine ScienceUniversity of the Aegean
  • Umberto Andriolo
    • Dipartimento di Scienze della Terra, Facoltà di IngegneriaUniversità di Ferrara
  • Rui Taborda
    • Faculty of Science, LATTEX, IDLUniversity of Lisbon
  • Ana Nobre Silva
    • Faculty of Science, LATTEX, IDLUniversity of Lisbon
  • Antonio Ruano
    • Centre of Intelligent SystemsUniversidade do Algarve
  • Óscar Manuel Ferreira
    • Faculdade de Ciências do Mar e do AmbienteUniversidade do Algarve
Article

DOI: 10.1007/s10236-011-0440-5

Cite this article as:
Vousdoukas, M.I., Ferreira, P.M., Almeida, L.P. et al. Ocean Dynamics (2011) 61: 1521. doi:10.1007/s10236-011-0440-5
Part of the following topical collections:
  1. Topical Collection on Multiparametric observation and analysis of the Sea

Abstract

This study discusses site-specific system optimization efforts related to the capability of a coastal video station to monitor intertidal topography. The system consists of two video cameras connected to a PC, and is operating at the meso-tidal, reflective Faro Beach (Algarve coast, S. Portugal). Measurements from the period February 4, 2009 to May 30, 2010 are discussed in this study. Shoreline detection was based on the processing of variance images, considering pixel intensity thresholds for feature extraction, provided by a specially trained artificial neural network (ANN). The obtained shoreline data return rate was 83%, with an average horizontal cross-shore root mean square error (RMSE) of 1.06 m. Several empirical parameterizations and ANN models were tested to estimate the elevations of shoreline contours, using wave and tidal data. Using a manually validated shoreline set, the lowest RMSE (0.18 m) for the vertical elevation was obtained using an ANN while empirical parameterizations based on the tidal elevation and wave run-up height resulted in an RMSE of 0.26 m. These errors were reduced to 0.22 m after applying 3-D data filtering and interpolation of the topographic information generated for each tidal cycle. Average beach-face slope tan(β) RMSE were around 0.02. Tests for a 5-month period of fully automated operation applying the ANN model resulted in an optimal, average, vertical elevation RMSE of 0.22 m, obtained using a one tidal cycle time window and a time-varying beach-face slope. The findings indicate that the use of an ANN in such systems has considerable potential, especially for sites where long-term field data allow efficient training.

Keywords

Video monitoringCoastal morphodynamicsArtificial neural networksCoastal erosionNearshoreRemote sensing

1 Introduction

The use of video methods for coastal monitoring has increased during the last three decades, with related studies covering a wide range of topics including coastal morphology (Aarninkhof and Holman 1999), swash processes (Stockdon et al. 2006; Vousdoukas M.I., Wziatek D., Almeida L.P. (submitted after minor revision). Coastal vulnerability assessment based on video wave run-up observations at a meso-tidal, steep-sloped beach. Ocean Dynamics), nearshore bar morphology (e.g. Ruessink et al. 2000; van Enckevort and Ruessink 2003a, b), longshore currents (Chickadel et al. 2003), and surf zone bathymetry (e.g. van Dongeren et al. 2008; Catálan and Haller 2008; Aarninkhof and Ruessink 2004). Optical methods allow non-intrusive, continuous measurements at temporal and spatial scales and resolutions for which in situ data collection would demand much greater inputs of personnel, equipment, and costs than are generally available.

One of the primary products of video monitoring stations is time-averaged surf zone imagery (TIMEX), created by averaging a series of snapshots collected from a stationary field of view. Image intensity patterns along TIMEX images have been shown to express time-averaged, energy dissipation rates of a breaking, random wave field (e.g. Lippmann and Holman 1989). Greyscale variance imagery (SIGMA) is another important product of such systems, representing the standard deviation of pixel intensities along the image frame for a given acquisition period. For both types of image, temporal windows between 5 and 30 min are used (e.g. Plant and Holman 1997).

Images are projected from distorted, pixel dimensions to real-world, geographical coordinates, in order to provide quantitative information (Lippmann and Holman 1989; Hartley and Zisserman 2006). Specialized image processing algorithms are applied to identify coastal features of interest such as the horizontal position of the shoreline (e.g. Holman and Stanley 2007; Plant et al. 2007). Plant and Holman (1997) presented an approach for automatic shoreline extraction, based on the identification of the shoreline intensity maximum (SLIM) position, along cross-shore pixel intensity transects. The method has been improved in subsequent studies (e.g. Madsen and Plant 2001) while other approaches have also emerged to classify image sections as surf/swash zone and subaerial beach. The pixel intensity clustering (PIC) method is based on hue–saturation–value (HSV) colour pixel intensity differences (Aarninkhof et al. 2003) while artificial neural network (ANN) classifiers have also been used (Kingston 2003).

Monoscopic-view coastal imaging systems can only resolve the two horizontal dimensions of shoreline position (xsrl and ysrl), and hence, additional information is required to estimate the shoreline elevation zsrl. The latter can be expressed in terms of the instant hydrodynamic conditions from Eq. 1 (e.g. Aarninkhof et al. 2003; Plant and Holman 1997):
$$ {z_{\text{srl}}} = {z_0} + {\eta_{\text{s}}} + {z_{\text{correction}}} $$
(1)
where z0 is the tide- and wind-induced offshore water level without the contribution of gravity waves, ηs is the wave set-up, and zcorrection is an additional correction term, estimated differently depending on the shoreline extraction approach followed. The wave set-up ηs can be estimated using standard empirical equations (e.g. Holland et al. 1995; Holman and Sallenger 1985), or using wave propagation numerical models (e.g. Aarninkhof et al. 2003). zcorrection can be related to the depth of the waves breaking near the shore (e.g. Plant and Holman 1997; Madsen and Plant 2001) or to a certain exceedence value of the maximum swash height associated with wave-induced waterline oscillations (e.g. Aarninkhof et al. 2003). Hence, zcorrection can be expressed as a function of wave parameters such as the significant wave height Hs, the deep water wavelength Lo, the peak wave period Tp, and the Iribarren number ξ (e.g. Battjes 1974), defined as:
$$ \xi = \frac{{{\beta_{\text{s}}}}}{{{{\left( {{H_{\text{o}}}/{L_{\text{o}}}} \right)}^{{1/2}}}}} $$
(2)
where βs is the beach slope, which for this study was considered as the foreshore slope and will be represented as the tangent of the slope hereinafter.

Images are acquired every hour and the extracted shorelines result in several ‘contour lines’ during each tidal cycle, allowing a daily estimation of the intertidal beach topography (e.g. Aarninkhof et al. 2003; Madsen and Plant 2001). It should be noted that the shoreline contour elevations are obtained from wave transformation calculations, which are related to beach morphology and thus to intertidal topography. As a result of this complexity, the intertidal beach slope (Eq. 2), being a parameter usually considered for estimations of both swash elevation and wave set-up (e.g. Stockdon et al. 2006), is also one of the main products of such video systems.

Furthermore, due to the application of monoscopic view, the horizontal geographical position of an image feature is directly related to its elevation, according to the following equations (e.g. see Wolf 1974):
$$ {x_2} = {x_1} + \sqrt {{{{({x_1} - {x_c})}^2} + {{({y_1} - {y_c})}^2}}} \frac{{{z_2} - {z_1}}}{{{z_2} - {z_c}}}\cos \left( \alpha \right) $$
(3)
$$ {y_2} = {y_1} + \sqrt {{{{({x_1} - {x_c})}^2} + {{({y_1} - {y_c})}^2}}} \frac{{{z_2} - {z_1}}}{{{z_2} - {z_c}}}\sin \left( \alpha \right) $$
(4)
where indexes 1 and 2 correspond to the feature’s horizontal coordinates for elevations z1 and z2, respectively, index c denotes the camera position coordinates, and α is an angle defined by:
$$ \tan \left( \alpha \right) = \frac{{{y_1} - {y_c}}}{{{x_1} - {x_c}}} $$
(5)

Equations 35 imply that the horizontal position of the shoreline is also related to its elevation, while the estimation of both carry certain degrees of errors (Aarninkhof et al. 2003; Plant and Holman 1997).

In light of the above discussion, and despite the use of video systems for daily intertidal topography monitoring at various coastal sites (e.g. Holman and Stanley 2007; Smith and Bryan 2007; Pearre and Puleo 2009), their complex operation still raises points for further research. Although image geo-rectification errors can be accurately estimated and usually lie within acceptable limits, the variety of intra-annual environmental, hydrodynamic, and morphological conditions make robust automatic shoreline detection a difficult task and a topic for investigation (Plant et al. 2007), including issues of data quality control and filtering (e.g. Madsen and Plant 2001). As described above, coupling the extracted horizontal shoreline positions with elevation values carries a particular degree of uncertainty and justifies an additional data filtering component, in order to allow fully automated mapping of the intertidal topography (e.g. Madsen and Plant 2001; Uunk et al. 2010; Harley et al. 2006).

All the above imply that setting-up and calibrating a newly installed coastal video system is a challenging and in many aspects a site-specific process. As a result, researchers working in different geographic locations have modified existing, or developed new, shoreline extraction and data quality control methods, in an effort to cope with regional and temporal variations in the remotely sensed environment (Madsen and Plant 2001; Plant et al. 2007; Uunk et al. 2010; Pearre and Puleo 2009). Against the foregoing background, the present contribution aims to: (1) describe a coastal video monitoring system operating at the meso-tidal, reflective Faro Beach (Algarve coast, S. Portugal) and (2) present efforts to produce robust intertidal topography measurements, emphasizing site-specific system optimization using ANNs, and performance and stability under different operating modes.

2 The study area

Faro Beach (Praia de Faro) is located along the central and eastern parts of the Ancão Peninsula (Fig. 1a), in the westernmost sector of the Ria Formosa barrier island system (Algarve, S. Portugal). In the central part of the peninsula, the dune ridge has been almost completely overtaken by urban development, and some of the ocean front has been artificially stabilised with sea walls (Ferreira et al. 2006). These structures are often overwashed during equinoctial spring tides or under storm conditions. The central and western parts of Faro Beach show a long-term erosion trend, whereas the eastern sector is accreting and vegetated foredune development is evident (Ferreira et al. 2006).
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig1_HTML.gif
Fig. 1

a Map of Algarve (S. Portugal) showing the locations of the study area, the Huelva tidal gauge, the Infinity pressure transducer and the IH buoy. b Map of the study area including topo-bathymetric LIDAR data, showing the location and field of view of the cameras, as well as the area monitored with RTK-DGPS surveys. The cameras are also shown in the inset photo

Tides in the area are semi-diurnal, with average ranges of 2.8 m for spring tides and 1.3 m for neap tides, although a maximum range of 3.5 m can be reached. Wave climate in the area is moderate to high, with an average annual significant offshore wave height Hs = 0.92 m and average peak period Tp = 8.2 s (Ferreira et al. 2009; Almeida et al. 2011a,b). For the majority of the time (71%), the waves approach from the W-SW, while for 23% of the time they come from an E-SE direction (Costa et al. 2001). Faro Beach is a ‘reflective’ beach (classification according to Wright and Short 1984) with beach-face slopes typically over 10% and varying from 6% to 15%, and a tendency to decrease eastwards, where a ‘low tide terrace’ beach state is found. Beach sediments are medium to very coarse sands (classification according to Folk 1980) with d50 ∼ 0.5 mm and d90 ∼ 2 mm.

3 Materials and methods

3.1 Wave and tidal data

Wave data are available from a wave buoy deployed offshore Faro Beach by the Portuguese Hydrographic Institute (IH; www.hidrografico.pt) while tidal data are provided by the Huelva tide gauge (www.puertos.es, Fig. 1a). In addition, an Infinity pressure transducer (Infinity PT) was deployed for four periods of 2.5 months during 2008–2010 at a location ∼1 km offshore Faro Beach (∼15 m depth, Fig. 1b). Pressure measurements were obtained for the first 15 min of each hour, and hourly bursts were processed applying pressure attenuation correction. Zero-crossing values were obtained (e.g. Tucker and Pitt 2001), along with wave spectra and statistical wave parameters including significant wave height and peak wave period. Although Infinity PT measurements are considered to be the most reliable source of wave and tidal data, the measurements are interrupted and non-directional and do not cover the entire monitoring period.

Tidal measurements from the Huelva gauge have been found to closely represent the conditions in Faro Beach (see Fig. 2a) and have been used for the periods when the Infinity PT was not operating. Periods with data from both sources were used for estimating and correcting time lags using cross correlation, and a linear fit correction was also applied. Post-fit root mean square error (RMSE) was estimated to be around 0.09 m.
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig2_HTML.gif
Fig. 2

Validation of the Huelva tidal gauge measurements (a) and the modelled significant wave height (b) and peak period (c) against the Infinity PT measurements for the period from 01/11/2009 to 10/01/2010

The IH buoy measurements are almost continuous, with gaps occurring sporadically. As a result, continuous offshore wave data were provided by a nesting chain of three wave model grids, starting from a large-scale model covering the whole North Atlantic and ending with a fine resolution model at the study site.

The third generation spectral wave model Wave Watch III (WW3; Tolman 2002) was implemented for the North Atlantic (Dodet et al. 2010) with a 0.5° resolution and forced with 6-h wind fields from the NCEP/NCAR Reanalysis wind fields (Kalnay et al. 1996) to generate hourly spectral outputs along the boundary of a finer grid covering the Gulf of Cadiz. This intermediate WW3 model has a 0.05° resolution and extends from 10.0° to 6.0° W in longitude and from 34.0° to 39.0° N in latitude. Spectral grid and wind forcing are the same as the ones used in the North Atlantic model of Dodet et al. (2010).

Hourly spectral outputs were generated to force the local (Faro Beach) SWAN model, running at a 500-m resolution, 40 × 20-km rectangle grid, situated offshore Faro Beach. The large-scale model has already been calibrated and validated (Dodet et al. 2010) and further comparisons were made between outputs of the local SWAN model and the Infinity PT measurements, to validate the nesting strategy. These comparisons resulted in statistical errors, calculated for the period March 2009 to February 2010, as follows: bias = −0.08 m, RMSE = 0.21 m, and normalized RMSE = 26.7%, with the normalized RMSE decreasing to 18.4% if only those wave heights greater than 1 m were considered (see also Fig. 2). Model data from the nearest grid point to the IH buoy location were used for the present study.

3.2 Topographic and bathymetric data

Topographic data were collected using an RTK GPS and accuracy is estimated to be in the range of 5 cm for both vertical and horizontal dimensions. Bathymetric data were collected using two RTK GPSs and an eco-sounder for bed-levelling, for which estimated horizontal and vertical accuracies are around 1 and 0.20 m, respectively, for vertical levelling. Forty topographic surveys took place during the monitoring period (September 2009 to April 2010), mainly during spring tides, as well as before and after storm events. Post-storm bathymetric data were also collected. From each survey’s measurements topographic grids were generated and were rotated so that the x- and y-axes corresponded to cross-shore and longshore dimensions, respectively. The rotation angle was 39° anti-clockwise, around the origin of the new coordinate system corresponding to (x0, y0) = (12,255, −295,575) in Datum 73 (EPSG:27493).

3.3 The video monitoring station

Two Mobotix M22, 3.1 megapixel (2,048 × 1,536 resolution), Internet Protocol (IP) cameras were installed on a metallic structure, placed on the roof of a restaurant in Faro Beach, and connected to a PC (Fig. 1b). The elevation of the centre of view (COV) is around 20 m above mean sea level (MSL). The image acquisition took place at 1 Hz, at hourly 10-min bursts, during daylight. After each 10-min image acquisition set, the system was scheduled to run processing scripts which generate the ‘primary products’, i.e. snapshot images, time-averaged (TIMEX) images, variance (SIGMA) images, and timestack images (e.g. Holman and Stanley 2007). In this study, SIGMA images represent the sum of the absolute pixel intensity differences between consecutive images and can be considered as ‘accumulated motion images’. In a similar fashion to variance SIGMA, high values are related to high wave-breaking activity and swash activity. For consistency with standard coastal video monitoring terminology, ‘accumulated motion images’ are referred to as ‘SIGMA’ hereinafter.

The system was set-up to monitor a coastal stretch measuring 500 m alongshore (Fig. 1b), with image processing and FTP transfer operations being scheduled during inactive acquisition intervals. A sophisticated database structure was developed to cope with the amount and variety of data resulting from the system’s different operations. Image filename conventions were developed to indicate acquisition date and time (GMT time zone), camera IP, and image type (e.g. snapshot and TIMEX), facilitating archiving and further processing. Different libraries were established for the wave and tidal data, as well as for the camera geometries, including information for camera calibration, ground control points, and manually and automatically defined geometry solutions (see Section 3.4), all indexed according to camera IP and MATLAB serial date.

The system has been operating since February 4, 2009, although it has been interrupted during the summer season (June–September) when beaches are busy due to tourism-related activities, making video monitoring unfeasible for various social reasons (such as beach-users complaining for the presence of the cameras). Measurements from the period February 4, 2009 to May 30, 2010 are discussed in this study.

3.4 Camera geometry

3.4.1 Image geo-rectification

Most camera lenses impose a certain amount of distortion on the acquired scenery, the correction of which (camera calibration) is fundamental to the precise transformation from image to metric coordinates. The camera’s intrinsic parameters can be expressed in mathematical terms through the K matrix:
$$ K = \left( {\begin{array}{*{20}{c}} \alpha & 0 & {{u_0}} \\ 0 & \beta & {{v_0}} \\ 0 & 0 & 1 \\ \end{array} } \right) $$
(6)
where α, β correspond to the focal length measured in u and v pixel units, respectively, uo and vo correspond to the image centre (called also principal point, e.g. see Heikkilä and Silvén 1997). In the present application, the K matrix was estimated using the Camera Calibration toolbox of Bouguet (Bouguet 2007) on 15–20 images of an A3 size checkerboard, obtained from various view angles and from each camera.
Assuming the pinhole camera model and using homogenous coordinates, the transformation from metric system coordinates (X, Y, Z) to undistorted image coordinates (U, V) and vice-versa is performed through the 3 × 4 perspective transformation matrix P (Hartley and Zisserman 2006):
$$ P\left[ \begin{gathered} X \hfill \\ Y \hfill \\ Z \hfill \\ 1 \hfill \\ \end{gathered} \right]{ = \left[ \begin{gathered} U \hfill \\ V \hfill \\ 1 \hfill \\ \end{gathered} \right]} $$
(7)
P matrix can be decomposed as:
$$ P = {\text{KR}}\left[ {I| - C} \right] $$
(8)
where K is the camera calibration matrix expressed by Eq. 6, I is the identity matrix, and C and R are the translation and rotation matrices of the camera’s COV, respectively (Hartley and Zisserman 2006).
The C translation matrix accounts for the location of the camera COV in the coordinate reference system used, and can be represented as:
$$ C = \left[ \begin{gathered} {X_{\text{cam}}} \hfill \\ {Y_{\text{cam}}} \hfill \\ {Z_{\text{cam}}} \hfill \\ \end{gathered} \right] $$
(9)

The R matrix expresses the effective orientation of the COV and is defined by three angles COV-pan, COV-tilt, and COV-roll relative to the Cartesian system of coordinates.

For undistorted images, the perspective transformation matrix P is a function of the camera angles and coordinates and can be estimated using an iterative procedure on the basis of a farm of ground control points (GCPs; e.g. Vousdoukas et al. 2009; Vousdoukas at al. 2011; Plant and Holman 1997). Real-world GCP positions were obtained through RTK-DGPS surveys while image coordinates were identified manually by the user. The system defined by Eqs. 69 has six unknowns and each GCP point results in two equations; while in the present case over ten GCPs were used, producing an over-specified system to which an iterative solver was applied to find the optimal camera angle and position values (Lagarias et al. 1998). The definition of the GCP and all the necessary procedures to estimate the perspective transformation matrix P took place during system installation and have since been repeated every 6 months.

Pixel footprints are the projections of each pixel in geographical coordinates and their dimensions express the horizontal resolution of the image space, which ranges from 0.10 m to infinity, depending on the distance from the COV. The selected monitoring area was such that that maximum alongshore pixel footprint was 1 m, since the alongshore footprint is more sensitive to the distance from the camera than is the cross-shore footprint. Plan-view images were generated with a horizontal resolution of 0.25 m, projected considering a horizontal plane with elevation equal to the instant sea level z0.

3.4.2 Camera displacement correction

An automatic camera geometry procedure was applied on a hourly basis to cope with camera movement (due to either thermal expansion or mechanical factors), which has been shown to introduce significant geo-rectification errors in similar systems (e.g. Holman and Stanley 2007; Pearre and Puleo 2009). Correction of the perspective transformation matrix P was based on common image features between images of unknown and manually defined camera geometry; following a procedure defined by the following steps (see also Vousdoukas et al. 2011):
  1. 1.

    A speed-up robust features (SURF) keypoints identifier algorithm (Bay et al. 2008) was applied to one of the snapshot images obtained during the day and for which the manual camera geometry P0 was estimated (see GCPs and perspective transformation matrix P estimation; Section 3.4.1). This image was referred to as F0.

     
  2. 2.

    All F0 keypoints were indexed and those found at sea and beach locations were separated and excluded, leaving only those that corresponded to fixed objects (deliberately included) in the field of view (FOV), with image coordinates \( U_0^{\text{ik}} \) and \( V_0^{\text{ik}} \); where ik is the keypoint index. Note that this manual procedure took place only for F0.

     
  3. 3.

    For each day, the keypoints identifier algorithms was applied to ten images from each hourly set, equally distributed in time \( F_{\text{is}}^{\text{ii}} \); where is corresponds to an index number unique for every set, counting from the system’s initiation and ii is the image number.

     
  4. 4.

    Keypoints pair matches between F0 and each image \( F_{\text{is}}^{\text{ii}} \) were extracted using the SURF algorithm and outliers were filtered using a RANSAC algorithm implementation (Fischler and Bolles 1981), followed by a least squares fit approach (Huber 1981).

     
  5. 5.
    Mean keypoint image coordinates \( U_{\text{is}}^{\text{ik}} \) and \( V_{\text{is}}^{\text{ik}} \)were estimated for each set:
    $$ \left[ {U_{\text{is}}^{\text{ik}},V_{\text{is}}^{\text{ik}}} \right] = \left[ {\frac{{\sum\limits_{{{\text{is}} = 1}}^{\text{ni}} {U_{{{\text{is,ii}}}}^{\text{ik}}} }}{\text{ni}},\frac{{\sum\limits_{{{\text{is}} = 1}}^{\text{ni}} {V_{{{\text{iis,ii}}}}^{\text{ik}}} }}{\text{ni}}} \right] $$
    (10)
    where ni is the number of daily image sets (ni = 10 in the present case).
     
  6. 6.

    For each hourly set, step 5 produced a set of image points with coordinates \( U_{\text{is}}^{\text{ik}} \) and \( V_{\text{is}}^{\text{ik}} \), coupled with frame F0 features with coordinates \( U_{\text{is}}^{\text{ik}} \) and \( V_0^{\text{ik}} \)image coordinates. Since the latter can be converted in real-world coordinates through the projection matrix P0, they were used as GCPs to update the camera geometry, following the procedure described in Section 3.4.1.

     
  7. 7.

    Steps 3–6 were repeated to apply the above correction for every set. If the number of keypoint pairs resulting from step 4 was less than ten, the latest updated geometry was considered.

     

3.5 Shoreline detection

The shoreline detection procedure followed was based on the SIGMA images and consisted of the following steps:
  1. 1.

    Sections of the SIGMA image outside a pre-defined region of interest (ROI) were masked to reduce computational loads and prevent ‘noise’ from sections irrelevant to coastal processes (e.g. parking, roads, and lights), or the adjacent sea beyond the surf zone. The seaward ROI boundary was defined from long-term topographic data from Faro Beach and was defined to always include the swash zone.

     
  2. 2.

    A baseline value was subtracted from the masked SIGMA image to enhance the sections related to wave-induced detected motion. The baseline value was equal to the mean value of pre-defined image sections not impacted by waves.

     
  3. 3.

    The SIGMA image, having been masked and adjusted for baseline value, was geo-rectified in a rotated, metric coordinate system, such that the x and y dimensions expressed longshore and cross-shore distance respectively (see Section 3.2).

     
  4. 4.
    The maximum intensity value was estimated from each vertical (cross-shore) pixel array and the extracted alongshore maxima vector was smoothed by an iterative low-pass filter and used to normalize image pixel intensities:
    $$ I_{{i,j}}^{\text{norm}} = \frac{{{I_{{i,j}}}}}{{{I_{{\max, j}}}}} $$
    (11)
    where I is the pixel intensity, and i = 1/M and j = 1/N indicate horizontal and vertical pixel dimensions, respectively, of an image with M × N pixels. Imax,j corresponds to the smoothed alongshore pixel intensity maxima vector.
     
  5. 5.

    High intensity features were extracted according to a threshold exceedence criterion Ithr and resulted in bodies (patches) for which the area and geometric centre in pixel dimensions were estimated. The feature with the highest area was always selected for shoreline extraction and the rest of the image sections were masked. The second largest feature was also considered (not masked) if (a) its area was <20% smaller than the one of the largest feature and (b) its geometric centre was found further onshore.

     
  6. 6.

    The shoreline was defined as the unmasked area’s onshore border.

     
The above approach is robust given that the intensity threshold Ithr applied in step 5 is properly defined. Extensive testing showed that for the reflective Faro Beach a value of ∼0.2 was effective for most cases, but was found to be too low for certain images. Mild wave conditions, combined with good visibility and clean camera lenses, resulted in a SIGMA image with a single narrow white band stretching alongshore (e.g. Fig. 3a), which tended to be wider as the wave forcing increased. The normalized pixel intensity histograms in such cases were characterized by a dominant peak at low intensity values (I < 0.1), with the threshold found at values slightly higher than the peak (Fig. 3a). More energetic conditions resulted in wider surf and swash zones, enhancing the higher intensity histogram frequencies and generating additional peaks. In such cases, the threshold was usually found along the saddle point between the first two peaks (e.g. Fig. 3c). Finally, several images were characterized by noise due to rain, sea spray, haze, or dirty camera lenses, which made the pixel intensity distribution peaks less distinctive.
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig3_HTML.gif
Fig. 3

Examples of different cases of SIGMA images, extracted shorelines (continuous lines) and the corresponding pixel intensity histograms. Vertical dashed lines on the histograms indicate the optimal thresholds for: a mild conditions and one feature; b visible nearshore bar; c, d noisy images obtained during intense wave and low visibility conditions

A graphic user interface (GUI) shoreline extraction tool was developed, applying the procedure described in steps 1–6 and allowing the user to inspect the detected shoreline and change the pixel intensity threshold, as well as to apply manual corrections and flag bad quality images when necessary. The above manual image processing is standard for achieving the optimal accuracy from coastal video imagery (see ‘Introduction’ in Uunk et al. 2010).

Given that a standard ROI was considered, the only input parameter for the shoreline detection model was the pixel intensity threshold Ithr, which has been shown to be related to the pixel intensity histograms. As a result, to further enhance data return rates, a data-driven automated procedure was developed for image classification and shoreline extraction threshold assessment. Analysis of the pixel intensity histograms showed that they were usually characterized by the presence of one or two peaks, which are often ‘bell shaped’. Thus, the amount of information related to each image was reduced by applying iterative fittings, so as to represent the histogram as a function of the sum of a 2nd-order polynomial and two Gaussian functions:
$$ n(I) = {p_1} + {p_2}\,I + {p_3}\,{I^2} + {g_1}\exp \left( { - {{\left( {\frac{{I - {g_2}}}{{{g_3}}}} \right)}^2}} \right) + {k_1}\exp \left( { - {{\left( {\frac{{I - {k_2}}}{{{k_3}}}} \right)}^2}} \right) $$
(12)
where n is the histogram frequency, p1–3 are coefficients to parameterize the quadratic function and gj and kj the Gaussian parameters (j ∼ [1 2 3], for amplitude, centre, and width, respectively), and I expresses normalized pixel intensities (equivalent to Eq. 11, but notations were omitted to maintain simplicity).

An iterative solver was applied to each image histogram (Lagarias et al. 1998) to estimate the p, k, and g parameters in Eq. 12, with initial values for p2 and p3 being zero, and p1 being equal to the mean histogram frequency value. The initial values of g3 and k3 were set to 0.1 and the values of the two highest discrete histogram frequency peaks were used for the amplitudes g1 and k1, along with the corresponding normalized pixel intensities, defining the initial guesses for the centres g2 and k2.

The pixel intensity space was discretized in 30 segments to give an equal number of threshold values which were used as inputs to the shoreline detection procedure (step 5, above), applied in a bootstrap manner. An optimal threshold value was defined for each image, after evaluating the extracted shorelines against the manual ones (see previous paragraph), based on the RMSE of the alongshore cross-shore shoreline position. Only cases for which the RMSE was ≤1 m were accepted, and for each image the ‘optimal’ threshold value, corresponded to the shoreline with the minimum RMSE. This resulted in a 1,803 × 1 vector of ‘target’ threshold values for an equal number of images, which was used to train a three-layer multilayer perceptron ANN, using as input variables the p, g, and k parameters, as well as the four histogram statistical moments. A two-step delay was applied between the ANN output and its inputs, meaning that the thresholds for the two previous images were also considered as inputs.

The ANN was trained by the Levenberg–Marquardt algorithm (Marquardt 1963) using a modified training criterion for error minimization (Ferreira et al. 2002; Ruano et al. 2002), in order to estimate the parameters describing the non-linear function between the inputs and the optimal threshold. Two training tests were performed using two different layer topologies (a) [10 40 1] and (b) [10 50 1], with numbers referring to the number of neurons in the input, hidden, and output layers, respectively. Seventy per cent of the data were being used for training and 30% for generalization testing, considering a 6-h time step. One hundred training trials were performed for each network topology using randomly selected initial parameters. From these trials, the best ANN was chosen by comparing the results obtained in the training and generalization datasets.

3.6 Shoreline contour elevation

For this particular study, the elevation of the extracted shoreline contours was related to the offshore wave and tidal measurements according to Eq. 13, which differs slightly from Eq. 1:
$$ {z_{\text{srl}}} = {c_1} \cdot {z_0} + {c_2} \cdot {R_2} + {c_3} $$
(13)
where the offshore water level z0 is obtained by adding the tidal elevation to the mean sea level (MSL = 2 m according to the present coordinate system), R2 is the 2% exceedence run-up height value, and c1–3 are empirical coefficients. Several empirical parameterizations proposed in the literature (Hunt 1959; Stockdon et al. 2006; Holman 1986; Douglas 1992) were tested for R2 estimation.

Shoreline elevation models were generated using ground truth topographic data from ∼40 RTK-DGPS surveys and ∼400 video shoreline contours (February 2009 to May 2010), extracted during the corresponding tidal cycle of each survey. Surface grids were generated from the RTK-DGPS survey data and zsrl values were estimated after interpolation of the shoreline’s horizontal positions. In order to avoid bias by shoreline outliers (i.e., in the far field of each image), only shoreline data within a distance of 300 m alongshore from the video station were considered. This series of operations as described generated a set of ∼20,000 points for which all the input and output parameters of Eq. 13 were known, allowing best-fit estimates to be made of the empirical coefficients c1–3 through an iterative solver (Lagarias et al. 1998).

Two versions of Eq. 13 were considered for the above calculations: (1) with ηsrl being related only to the sea level (i.e. c2 = 0, equation solved for c1 and c3), and (2) with ηsrl being related to both the sea level and wave run-up height. The beach-face slope βs for this study was estimated considering the profile sections with 1 m ≤ z ≤ 5 m (MSL = 2 m), unless the tide did not recede sufficiently to expose a 1-m elevation, in which case the minimum measured elevation in the surveyed area was used as the lower limit. All beach-face slope βs values correspond to tan(βs), omitted to maintain simplicity. All parameterizations were tested considering both alongshore-varying (i.e. the exact beach-face slope and elevation from the topographic grid) and alongshore-averaged beach-face slopes and zsrl values. These combinations of fitting parameters and input values resulted in a total of 36 tested cases, which are referred to as Fit-1 hereinafter (see also Table 2).

Shoreline horizontal positions were extracted from images geo-rectified using a reference level equal to the offshore sea level z0, although this elevation can be different to that estimated by Eq. 13, i.e. zsrl ≠ z0. This implies that according to the monoscopic-view theory, once the elevation difference will be applied to Eqs. 34, the xsrl and ysrl positions will be corrected. As a result, the ground truth zsrl values will be obtained after interpolation from different locations of the topographic grid. However, this will mean that the Fit-1 procedure has to be repeated considering the new ground truth zsrl elevation values, implying a non-linear problem. As a result, the fitting of Eq. 13 was nested in another iterative procedure, in which: (a) xsrl and ysrl were corrected according to the updated zsrl, using Eqs. 3 and 4; (b) Fit-1 estimations took place; and (c) steps (a) and (b) recurred until a convergence criterion was satisfied. The 36 cases tested during Fit-1 were considered, with the Fit-1 parameters being used as initial values. This second group of tests is hereinafter referred to as Fit-2.

In addition, an ANN was also trained to produce zsrl elevation values using as inputs the sea level z0, wave parameters (Hs, Tp, and Lo), and the intertidal beach slope (βs), as well as the result of the optimal parameterization (which in the event, as reported further below, was case P3 from Fit-1). The present ANN should not be confused to the one used for shoreline extraction; in this case radial-basis-function ANNs (Moody and Darken 1989) were employed, also trained using the Levenberg–Marquardt algorithm and the modified training criterion (Ferreira and Ruano 2000). Two basis functions were tested: Gaussian and inverse multiquadric. The dataset was composed of approximately 20,000 input–output patterns, of which one half was used for training purposes and the other for generalization testing. The ANN’s initial parameters were randomly selected and iteratively optimized by the training algorithm, using the ‘early stopping’ technique (i.e. stopping when the error criterion computed using the generalization data set ceases to decrease between iterations). An exhaustive search was conducted to find an appropriate number of neurons for each of the basis functions considered, by varying their number from eight to 24. For each of these cases, 20 training trials were executed due to the random nature of the parameter initialization procedure. One model was then selected on the basis of the trade-off between the error criterion taken independently from the training and generalization data sets, and the maximum absolute error found. The used model consisted of 16 neurons employing Gaussian basis functions.

The above procedure is hereinafter referred to as Fit-ANN and does not include an xsrl and ysrl correction according to zsrl, as the ANN model estimates a best-fit zsrl solution for the initial horizontal shoreline positions corresponding to elevations z0. In case the absolute difference between the zsrl elevations estimated by the ANN model and the input initial zsrl estimation (see previous paragraph) exceeded a threshold value, the ANN estimate was discarded. The threshold for the present case was set equal to 0.7 m. However, it should be noted that exceeding this threshold is a rare event corresponding to cases where the ANN produces higher errors that are seen as outliers. This is common in ‘real-world’ applications of ANNs and is attributed to incomplete coverage of input–output space in training data and to the high dimension of the network parameters vector (for a detailed discussion, see Sjöberg and Ljung 1994).

3.7 Automated intertidal topography mapping

The procedure described in the previous section aimed to evaluate different approaches for shoreline elevation estimation and was based on the manual shoreline set. Selected approaches based on the performance of those tests were used for additional testing, in order to evaluate the system’s performance during unsupervised operation, when automatic shoreline detection errors are also an acting factor. Additional errors can be related to inaccuracies on the updated intertidal topography, which will affect the beach-face slope βs and thus also the ensuing calculations when βs is used as an input for zsrl estimation.

Several ‘contour lines’ were considered for each tidal cycle to estimate the intertidal beach topography and to update a digital elevation model (DEM) of the study area. The ‘time window’ defining the data considered varied from one to several tidal cycles (Uunk et al. 2010). Surface grids were generated from the 3D scattered points after applying an iterative procedure to identify and extract outliers, which is described in the Appendix (see also Fig. 4).
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig4_HTML.gif
Fig. 4

Example of the procedure for estimating the updated intertidal topography from the extracted shoreline contours (a colours indicate vertical elevation in m for all three panels). Spurious points are removed (bred dots) through iterative filtering and the final DEM is produced after space-scale smoothing (ddashed lines indicate area covered by the shoreline contours). The produced DEM after direct gridding of the initial contours is shown for comparison (c)

To test the possible system set-ups (e.g. zsrl estimation approach, time window size), several ‘virtual system deployments’ were performed, initiated with a DEM obtained from a LIDAR survey topography of the area. The testing period covered five months (December 1st, 2009 to May 1st, 2010) and automatic shoreline detection took place using the best extraction approach for threshold estimation (which in the event was ANN2, as described further below). Intertidal topography measurements were validated against data from 22 topographic surveys that took place during the same period. For each survey grid, both the vertical RMSE along the updated DEM section and the alongshore-averaged slope deviations were measured and used as performance indicators. Different cases were tested with intertidal topography being estimated for time windows of 1, 2, or 3 days. In addition, for comparative purposes, tests using the manual shoreline set were made.

4 Results

4.1 Camera movement correction

Feature positions were shown to vary for 0–4 pixels around a mean value and, in most cases, keypoint displacement was around 1 pixel (see Fig. 5 for an example of recorded feature motion). The SURF algorithm can identify features with dimensions of several pixels and in that case their position is equal to their centroid and can also include decimal points. A daily motion pattern can be discerned from the data, most likely related to changes in the geometry of the camera due to thermal expansion, with the amplitude of the displacement varying with time. Some more intense geometry change events are observed (e.g. see December 25 in Fig. 5), which usually coincide with storm and strong wind conditions.
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig5_HTML.gif
Fig. 5

Example of the estimated displacement of an image feature in image coordinates U, V, during the period 3/12/2009 to 2/5/2010. Values express differences (in pixels) from the initial image feature positions

4.2 Shoreline detection

The shoreline detection algorithm was tested on the ∼2,200 manually processed images and threshold definition approaches were evaluated using as output quality criteria the data return rates and the RMSE, compared with manual results. The data return rates were estimated considering as ‘data’ those images for which more than 50% of the extracted shoreline belonged to the ROI. For each of the ‘accepted’ shorelines, RMSE values of the cross-shore position were estimated, as well as the mean RMSE for all images.

Applying a constant threshold value of Ithr = 0.2 resulted in data return rates of 42% and an average cross-shore position RMSE of 1.9 m (see Table 1). Results after using the two pixel intensity threshold estimation ANN models were rather similar (Fig. 6) and improved the data return rates to 63% and 65%, with RMSE of ∼1.67 and 1.65 m for ANN1 and ANN2, respectively. Most of the rogue shorelines were obtained from images acquired after 4:00 p.m., when the reflection of the sun on the sea made the water-sand boundary less distinct. As a result, data return rates increased significantly after excluding those images and the best value obtained was 83% (ANN2, Table 1), with RMSE = 1.06 m.
Table 1

Shoreline detection results (data return rates and RMSE) for different approaches for determining the pixel intensity threshold

Threshold definition

System topology

All images

Images before 5:00 p.m.

Data return rate (%)

Average RMSE (m)

Data return rate (%)

Average RMSE (m)

Ithreshold = 0.2

42

1.9

65

1.35

ANN1

(10 40 1)

63

1.67

81

1.08

ANN2

(10 50 1)

65

1.65

83

1.06

https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig6_HTML.gif
Fig. 6

Cumulative distributions of RMSE of the cross-shore shoreline positions after automatic shoreline detection using ANN1 (solid line) and ANN2 (dashed line) derived pixel intensity thresholds. Only those shorelines found inside the ROI were processed and RMSE values were based on the manually extracted shorelines (a). RMSEs were also estimated considering de-trended cross-shore shoreline positions to indicate shape similarities (b)

Additional RMSEs were estimated considering de-trended cross-shore shoreline positions to focus on shape similarities (low RMSE values) between the manually and automatically extracted shorelines. The values obtained from ANN1 and ANN2 were very similar (Fig. 6b) and the errors were smaller, which suggest that the shorelines obtained from the two ANN models were of similar shape but slightly shifted in the cross-shore direction. The errors also indicate that the automatically extracted shorelines are also of similar shape to the manual ones.

4.3 Shoreline contour elevations

The topographic surveys provided information regarding the beach-face slope βs, which was found to vary between 5.1% and 14.4%, with an average value of ∼10.3%, without data for summer season conditions. Several proposed parameterizations were tested against the field data (e.g. see, Sunamura 1984; US Army Corps of Engineers 2002 and references therein), using averaged wave conditions for different time windows before the survey (between 0.5 and 5 days). Alongshore variable or averaged βs values were considered; however no statistically significant correlations were produced, with Pearson’s coefficient values r being consistently at <0.3 (95% confidence intervals). The best results were observed for Eq. 14, which had an RMSE of ∼0.031; this however was higher than that obtained using the average slope (RMSE, ∼0.024).
$$ {\beta_{\text{s}}} = 0.56 \cdot {\left( {\frac{{{H_{\text{b}}}}}{{{g^{{1/2}}}{T_{\text{p}}}}}} \right)^{{ - 0.5}}}d_{{50}}^{{1/4}} - 0.215 $$
(14)
where d50 is the mean grain size = 0.5 mm and Hb is the breaking wave height, estimated by applying a wave propagation model based on the energetic approach (Vousdoukas et al. 2005). A robust βs parameterization could provide an accurate estimate to be used for the R2 estimations in Eq. 13 (see also Eq. 2), when necessary. However, given the results obtained, a constant value βs = 10.3% was used as an estimated beach-face slope value in most cases.
Iterative estimation of the empirical coefficients of Eq. 13 according to the dataset and all the parameterizations described in Section 3.5 resulted in several cases, which were evaluated on the basis of the estimated RMSE (Table 2). Post-fit RMSE values ranged from 0.26 to 0.43 m and were similar to the cases to which the iterative xsrl and ysrl perspective correction according to zsrl values (Fit-2, 0.30 m < RMSE < 0.41 m) was applied. Fit-2 resulted in higher errors compared with Fit-1, except for the cases P1, P8, and P9, and the optimal performance was achieved without applying the correction. Using a constant beach-face slope appeared to have only a minor effect on the accuracy while longshore averaging of the zsrl values extracted from the RTK-DGPS surveys data resulted in slightly reduced RMSEs. Parameterization P3, based on Holman (1986) (Table 2), produced marginally better results among the tested theoretical formulations; while the minimum RMSE = 0.18 m was obtained by the ANN model, considering a constant slope and longshore averaged zsrl values.
Table 2

RMSE from the zsrl parameterization results for all tested cases (best values highlighted)

Parameter

Fit-1 RMSE (m)

Fit-2-RMSE (m)

βs= f(x)

tan(βs) = 10.3%

βs= f(x)

tan(βs) = 10.3%

\( {z_{{{\text{srl}},x}}} \)

\( \overline {{z_{{{\text{srl}},x}}}} \)

\( {z_{{{\text{srl}},x}}} \)

\( \overline {{z_{{{\text{srl}},x}}}} \)

\( {z_{{{\text{srl}},x}}} \)

\( \overline {{z_{{{\text{srl}},x}}}} \)

\( {z_{{{\text{srl}},x}}} \)

\( \overline {{z_{{{\text{srl}},x}}}} \)

P1

zsrl= c1zo+ c2

0.43

0.42

  

0.41

0.40

  

P2

zsrl= c1zo+ c2Hoξ + c3

0.28

0.26

0.28

0.26

0.30

0.30

0.30

0.30

P3

zsrl= c1zo+ c2Hoξ + c3Ho+ c4

0.26

0.26

0.26

0.26

0.31

0.31

0.30

0.30

P4

zsrl= c1zo+ c2(βHoLo)0.5+ c3

0.28

0.26

0.28

0.26

0.30

0.30

0.30

0.30

P5

zsrl= c1zo+ c2Ho(Ho/Lo)−0.5+ c3

0.27

0.27

0.27

0.27

0.30

0.30

0.30

0.30

P6

zsrl= c1zo+ c2(HoLo)0.5+ c3

0.27

0.27

0.27

0.27

0.30

0.30

0.30

0.30

P7

zsrl= c1zo+ c2βHo+ c3

0.27

0.27

0.27

0.27

0.30

0.30

0.30

0.30

P8

zsrl= c1zo+ c2(Ho/Lo)0.5+ c3

0.35

0.33

0.35

0.33

0.31

0.31

0.31

0.31

P9

zsrl= c1zo+ c2β(Ho/Lo)0.5+ c3β(HoLo)0.5+ c4

0.33

0.30

0.33

0.30

0.30

0.30

0.30

0.30

P10

Fit-ANN

0.19

0.18

0.19

0.18

    

Key: βs= f(x) use of alongshore-varying beach-face slope extracted from topographic surveys, \( {z_{{{\text{srl}},x}}} \) and \( \overline {{z_{{{\text{srl}},x}}}} \) alongshore-varying or averaged shoreline contour elevation, respectively, ci constants

Among the tested cases, four are used for further comparisons in Section 4.4 (see also Fig.7 and Table 3 for information on performance and fitting coefficients):
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig7_HTML.gif
Fig. 7

Results of the parameterizations for the shoreline contours elevation zsrl (see also Eq. 13) considering only the tidal elevation z0 (a), z0 along with a modified Holman (1986) equation (b), z0 along with (HoLo)0.5 (c) and an ANN model (d)

Table 3

The four optimum parameterization results for the shoreline contour elevation zsrl (see also Eq. 13) and the corresponding mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and maximum error (in m)

Equation

Fitting coefficients

MAE

RMSE

MSE

Max

E1

\( {z_{\text{srl}}} = {c_1}{z_{\text{o}}} + {c_2} \)

c1 = 1.02; c2 = 1.11

0.286

0.351

0.149

1.2

E2

\( {z_{\text{srl}}} = {c_1}{z_{\text{o}}} + {c_2}{H_{\text{o}}}\xi + {c_3}{H_{\text{o}}} + {c_4} \)

c1 = 1.04; c2 = 0.28; c3 = 0.17; c4 = 0.40

0.193

0.260

0.082

0.99

E3

\( {z_{\text{srl}}} = {c_1}{z_{\text{o}}} + {c_2}{\left( {{H_{\text{o}}}{L_{\text{o}}}} \right)^{{0.5}}} + {c_3} \)

c1 = 1.04; c2 = 0.04; c3 = 0.52

0.205

0.272

0.089

0.94

E4

\( {\text{Fit}} - {\text{ANN}} \)

-

0.123

0.171

0.039

0.89

  1. E1:

    P1, Fit-2: for simplicity reasons, since it requires only tidal data.

     
  2. E2:

    P3, Fit-1: best case from existing parameterizations.

     
  3. E3:

    P6, Fit-1: best case from parameterizations not using the beach-face slope as input.

     
  4. E4:

    P10, Fit-ANN: best case overall.

     

4.4 Operational performance

Further testing took place to evaluate the system’s performance in unsupervised operation when the following factors are included: (a) automatic shoreline detection (it should be noted that that the results presented in Tables 2 and 3 were obtained from the ‘manual shoreline set’) and (b) the beach-face slope as a time-varying variable (in some cases). Four different approaches to estimate the shoreline contour elevation were tested, as reported in Table 4. Elevation RMSEs were estimated for the ‘remotely’ updated area, as well as for alongshore-averaged slope deviations (Table 4 and Fig. 8), using field measurements from 22 topographic surveys. Approach E2 was tested twice, once using the beach-face slope from the updated topography and once using a constant value.
Table 4

RMSE values obtained from the system’s 5 months unsupervised operation under different settings (for further information on the first column see Table 3

Case

Manual set one tidal cycle

Unsupervised operation

One tidal cycle

2 days

3 days

Min (m)

Max (m)

Mean (m)

βs

Min (m)

Max (m)

Mean (m)

βs

Min (m)

Max (m)

Mean (m)

βs

Min (m)

Max (m)

Mean (m)

βs

E1

0.11

0.71

0.38

0.03

0.22

0.98

0.46

0.03

0.16

0.75

0.44

0.03

0.19

0.72

0.43

0.03

E2

0.09

0.48

0.22

0.02

0.14

0.63

0.28

0.02

0.15

0.56

0.25

0.02

0.17

0.53

0.28

0.02

E2SLU

0.10

0.54

0.26

0.02

0.15

0.68

0.31

0.02

0.13

0.56

0.28

0.02

0.15

0.52

0.28

0.02

E3

0.09

0.50

0.25

0.01

0.13

0.66

0.30

0.02

0.13

0.55

0.26

0.02

0.16

0.54

0.28

0.02

E4

0.04

0.65

0.18

0.01

0.05

0.67

0.22

0.01

0.08

0.56

0.24

0.02

0.13

0.510

0.28

0.02

Subscript SLU indicates using a constantly updated beach-face slope βs). The mean absolute error of the βs is also shown

Min, max, and mean minimum, maximum, and average values of all the RMSE values obtained during the testing period, against data from 22 topographic surveys.

https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig8_HTML.gif
Fig. 8

A 5-month period of unsupervised operation system performance validated against 22 topographic surveys: significant wave height (left axis, circles) and peak wave period (right axis, crosses) (a), RMSE (b), and maximum absolute error (c) of the elevation, as well as absolute error of the beach-face slope (d). E1 and E4 correspond to different system set-ups (see Table 3 for more information) and the x-axis is in days (note that the x-space is not linear). Subscripts indicate the width of the time window in days (1, 2, and 3 days) and ‘man’ stands for manual shoreline set

Average, minimum, and maximum RMSE using the manual dataset resulted in lower values compared with unsupervised operation (Table 4). Cases E2 and E4 produced the best results for the tests with the manually extracted shorelines (mean RMSE, 0.22 and 0.18 m, respectively). Errors from one tidal cycle window unsupervised operation showed an increase of greater than 10% for most cases, and extending the time window to 2 days reduced the errors overall. Longer time windows suppressed the maximum observed error, but increased the minimum and average errors (Table 4). Cases during which updated beach-face slope values were considered resulted in increased error values overall. Moreover, performance considering only the tidal elevation (E1) was poorer for all the cases, with average RMSE values being almost double those of the other cases. The best performance under unsupervised operation (average RMSE = 0.22 m) was obtained by E4, applying a one tidal cycle window (Table 4). The second-best results were produced by applying a 2-days window and E2 with a constant slope. Also, mean absolute beach-face slope errors were higher at ∼0.03, ranging from 0.01 to 0.02 for the other cases. Video-extracted topography was characterized by smaller slope values, compared with the ones measured at the field.

An overview of the system’s performance for four selected cases is provided in Fig. 8: (1) E4manual as the approach with the best results, (2) E41 day, with the best unsupervised operation performance, (3) E12 days, the best case for tide only, and (4) E42 days, corresponding to the optimal unsupervised mode case using empirical formulations (and not an ANN model). The maximum absolute errors for each survey (Fig. 8), not to be confused with the maximum RMSE during the tested period reported in Table 4, ranged from ∼0.3 to ∼1.3 m. The alongshore-averaged beach-face slope deviations (Fig. 8) reached 0.05.

5 Discussion

5.1 Shoreline detection

The automatic shoreline extraction data return rates of this study (83%) are satisfactory (e.g. see Table 5 in Plant et al. 2007 for a comparison of different methods). However, some of the tested images were used for the training of the ANN threshold estimation model, which implies that data return rates may change if the method is applied to new images. The shoreline extraction performance is more likely to be affected if the pixels intensity histograms of some of the additional images are different from those used for training. Similarly, the trained ANN models may not provide accurate results if any of the camera settings, model, or the study site change.

The RMSE histograms (Fig. 6) showed that the accepted shorelines (inside the ROI) were very close to the ‘manual shorelines set,’ as also shown by the small average RMSE values (Table 1). However the shoreline is an ambiguous feature, and the ‘manual set’ also carries some uncertainties. Previous studies have showed that the feature identified as ‘shoreline’ varies among different methods (see also Introduction), e.g. SLIM may lie at submerged positions (Madsen and Plant 2001), while PIC extracted shorelines are shifted onshore because their elevations include a certain exceedence value of the maximum swash height (Aarninkhof et al. 2003). This is also the case for this investigation, since the zsrl parameterization results indicate swash contributions to the zsrl values, as well as a tidal correction (e.g., see c1 > 1; Fig.7). The tidal correction implies that weaker wave dissipation during high tides can result in increased run-up elevations and a shoreward shifted ‘shoreline position’.

The onshore shift of the extracted shorelines can be explained by the fact that the method tracks the shoreline starting from the dune then seawards. Moreover, SIGMA images tend to highlight the boundaries of high dissipation areas, rather than the central parts indicated in TIMEX images. The reason is that high values along the SIGMA images indicate change, while in TIMEX such values represent persistence of bright colours, i.e. foam and breaking rollers. At the swash zone, the first SIGMA intensity peak close to the coast is usually linked to consequent swash motions and constant colour variations from bright swash to darker dry/wet sand, driving abrupt intensity changes. Moreover, the presently extracted shoreline feature lies shoreward of the first cross-shore SIGMA intensity peak and is likely strongly related to the wave run-up height. As a result, the extracted shoreline feature is expected to migrate onshore under intense wave conditions, while SLIM position has been shown to follow the opposite pattern (Madsen and Plant 2001).

One of the disadvantages of the approach followed in the study is that the shoreline can lie anywhere along the increasing section of the cross-shore pixel intensity transect, depending on the pixel intensity threshold value. However, colour based methods are expected to suffer from a similar uncertainty, since colour pixel intensity classification along the swash zone may fluctuate slightly with varying light and hydrodynamic conditions. However, the results indicate that this uncertainty is not significant, since the ‘active’ (positively sloped) section is narrow and the ANN threshold estimation approach performs well. Moreover, errors are partially smoothed-out during interpolation of the high number of extracted points. Given all the above, and the fact that the shoreline position xsrl and ysrl is also related to the elevation zsrl through Eqs. 3 and 4, the discussion to follow in Section 5.2 is focused on the performance analysis of the remotely sensed intertidal topography, and its comparison with the surveyed topography, in particular with respect to the vertical errors.

An advantage of the use of SIGMA images is that since they detect motion, they are less sensitive to variations in visibility and luminosity variations in the remotely sensed environment. Even though considering colour information may allow additional selection criteria, the results obtained can be more sensitive to poor image quality, which may alter the image features’ colour and texture. Rain, sea spray, and dirty lenses can also affect the shoreline extraction approach used here, but mostly under very low visibility conditions. Lens condition, poor visibility, along with sun reflection at certain times of the day, were the main causes of rogue extracted shorelines. However, the data return rates and errors were satisfactory, given the number of processed images considered (>2,000) and the fact that they were acquired mainly during winter conditions.

Significant care was taken to maintain and clean the camera lenses during the station’s operation, and it is likely that inferior maintenance efforts would have lowered data return rates. Also, for a significant proportion of the time, the reflective Faro Beach is characterized by an absence of nearshore bars, resulting in a dominant wave breaking and dissipation feature found near the shoreline and allowing the use of a constant ROI. Thus, it is likely that Faro Beach is more favourable for the shoreline detection model used compared with a mildly sloped coast, where dissipation patterns would be more dispersed along the field of view and less prominent at the shoreline limit (Aarninkhof et al. 2003).

5.2 Operational performance

The RMSEs discussed in Section 4.3 (see also Table 2) were based on all the local intertidal topography estimations when field data were available; while the values discussed in Section 4.4 (see also Table 4) represent the average of all the daily RMSEs obtained from the comparisons with topographic grids. Moreover, RMSEs in Table 2 were based on all the available topographic data during the station’s operation, while Table 4 refers to a smaller period for which unsupervised operation was tested (see Section 3.7). Even though the two parameters are not directly comparable, the values from the grid comparisons (Table 4, Section 4.4) are expected to be lower, due to the interpolation and 3-D data filtering operations as discussed in Section 3.7.

The effect of data filtering could be discerned by the trend towards lower RMSE values in Table 4, for the manual set, compared with the ones in Table 3. For example, case E2 decreases from an RMSE of 0.26 (Table 3) to 0.23 m (Table 4), with both tests considering the beach-face slope as a constant parameter. The latter has the advantage that the results for each tidal cycle are independent of the previous results, preventing ‘echoing’ of rogue estimations; which could be the case for E2slu and E4. Such rogue estimations, apart from being caused by poor shoreline detection, could be related to intense wave conditions, during which the uncertainty in wave run-up height estimation is higher.

Performance using the manual shoreline set was superior to automatic extraction and supervised shoreline extraction is a valid option when optimal accuracy is required (see introduction in Uunk et al. 2010). For a total of 2,500 images (∼1 year of data), no more than 12 processing hours are required, an acceptable value given the temporal data coverage. On the other hand, unsupervised operation performance was only slightly inferior and the results indicate an RMSE below 0.10 m for certain tidal cycles, and mean beach-face slope errors around 0.01–0.02 (Fig. 8). The above results lie in the same range as previous findings, including either supervised (e.g. Plant and Holman 1997; Aarninkhof et al. 2003) or autonomous operation (Madsen and Plant 2001; Uunk et al. 2010). However, direct comparison is not straight-forward since the evaluation criteria and the temporal and spatial coverage of measurements discussed in the literature varies substantially.

Several approaches to estimate the shoreline elevation zsrl exist in the literature, including empirical ones as used in this study, as well as ‘process-based’ methods that involve applying 1-D (Aarninkhof et al. 2003) or 2-D hydrodynamic models (Siegle et al. 2007). While the latter could potentially have the advantage of being non-site specific, we consider an empirical approach based on field data more suitable for Faro Beach and potentially for other similar sites. The main reason for this is that data-driven efforts can compensate for inaccuracies related to the hydrodynamic data and even geo-rectification errors. The estimated RMSE of ∼0.09 m (Fig. 2a) for the tidal measurements was in the same order of magnitude as the final intertidal topography errors; while certain errors were also introduced by the use of wave model results for offshore wave conditions (Fig. 2b). Finally, storm surge elevation is a parameter that has not been accurately estimated, but is rather partially expressed by the empirical zsrl parameterizations, and is also likely to contribute to errors.

Empirical parameterizations were found to successfully correct some of the above-mentioned inaccuracies in the system’s input data. Moreover, the improved performance from the application of ANN models (Table 3) implies that they likely resolve existing non-linear interactions between the input parameters; like the effect of offshore wave parameters on water level, water level on wave run-up height, etc. ANNs appear to describe the cumulative effect of such interactions better than the other parameterizations, as also indicated by the zsrl error values.

The input variables used for the ANN training represent a multi-dimensional space, therefore sufficient input–output data coverage is crucial for the performance of the final ANN model. During the first ANN implementation efforts, mean RMSE values exceeding 1 m were observed for certain tidal cycles, indicating that the training dataset did not fully cover the year-long occurrence of various beach states and hydrodynamic conditions. This implies that although the ANN model produced accurate zsrl estimations, it also generated outliers that affected the overall accuracy. The above issue was dealt with by replacing the ANN-zsrl estimates with those from equation E2 (Table 3), when their absolute difference exceeded 0.7 m (see also Section 3.6). However, further data acquisition, and ANN re-training is expected to result in significant improvements, provided the new dataset will cover input–output regions that are not sufficiently covered at present.

Apart from the discussed uncertainties in the wave and tide input data, the specific case of Faro Beach is a very dynamic, reflective beach, which may undergo cross-shore changes in elevation of several metres, even during moderate wave conditions and especially when SW and SE waves interchange (Ciavola et al. 1997). Such factors make separation of data errors from actual change more difficult, and do not allow the use of longer time windows which could enhance robustness in less dynamic settings (Uunk et al. 2010). Moreover, the settlement of Faro Beach experiences frequent electric power outages during thunderstorms, resulting in data gaps, especially during the winter. As a result, applying short 1- or 2-day time windows proved to be robust, while considering longer windows proved less accurate given the rapidly responding beach.

The effect of applying xsrl and ysrl corrections when the zsrl values are different from the image geo-rectification plane elevation has been little discussed in the related literature, despite the fact that it is an important theoretical aspect of the system’s concept and operation. The results show that applying the correction may improve the system’s performance in some cases, while for other cases errors are higher. One of the disadvantages of applying the correction is that independent artefacts in the estimation of the shoreline contour horizontal and vertical coordinates interact and can result in rogue values for both parameters. The xsrl and ysrl values detected from the image express, with a particular degree of uncertainty, the position of the MSL and can be used as an independent system product (e.g. see, Pearre and Puleo 2009). Then again, the zsrl estimates carry particular errors which, along with the sharp angle of view (see also Eqs. 3 and 4), may lead to rogue xsrl and ysrl corrections, and reduce accuracy.

The preceding discussion implies that the estimated xsrl, ysrl, and zsrl are approximations, with their precision affected by factors such as: (1) the geo-rectification errors related to camera geometry uncertainties and the pixel footprint; (2) the fact that the extracted shoreline feature probably includes a range of elevations while the image is geo-rectified on a horizontal plane and, thus, the extracted xsrl and ysrl values are distorted to an extent (see Eqs. 3 and 4); (3) monoscopic vision, which implies that surface irregularities (e.g. cuspate features) are distorted and may introduce 3-D geo-location errors and even ‘shadow’ features. These factors also justify the improvement of accuracy of the parameterizations (Table 3) resulting from alongshore zsrl averaging, which was also the case when using a constant beach-face slope value. The distortion of alongshore irregularities is also shown in Fig. 9, in which the errors follow a rhythmical pattern in that direction, implying that the cuspate features are not well resolved by the video-extracted topography.
https://static-content.springer.com/image/art%3A10.1007%2Fs10236-011-0440-5/MediaObjects/10236_2011_440_Fig9_HTML.gif
Fig. 9

Comparison of topographic grids generated from field surveys data (a) and from video intertidal topography measurements (b). Most of the vertical elevation errors (c) are related to alongshore variability, which appears to be distorted on the remote sensed grid. All values are in m

5.3 Camera movement

The application of the camera geometry correction procedure showed that using manual geometry solutions for periods of several months may result in errors typically around 1–2 pixels and up to 4 pixels. Apparently, the related geo-location errors are more important for locations distant from the cameras, where pixel footprints are higher and horizontal uncertainties can reach 4 m. Image homography matrix estimation is a fundamental computer vision problem, and the procedure followed for automatic geometry correction was based on robust, optimized algorithms, with processing times ranging between 3–10 s per image. Estimated accuracy after the correction is below 0.5 pixels and the correction also improves the vertical position significantly, given that Faro Beach is reflective and steeply sloping.

The applied camera geometry correction takes into account fluctuations with a minimum temporal scale of 1 h but does not consider high frequency camera oscillations, e.g. those due to wind turbulence. In such a case, we assume that the 10-min image averaging compensates for such camera behaviour and blur is expected on the image, although this in general was rare. Given that the increase computational effort required to apply the high frequency correction is substantial and the expected impact of such oscillations on the overall accuracy is low; geometry corrections for such time scales were not applied. However, there is no limitation on such an extension of the approach followed, which appears to efficiently correct geometry changes due to thermal expansion, shown to be reduced on cloudier days. While drifting was observed for certain periods, no persistent camera angle changes were observed (jumps), in contrast to other studies (Holman and Stanley 2007; Pearre and Puleo 2009).

6 Conclusions

This paper has reported efforts to assess and enhance the intertidal topography monitoring capacity of a coastal video station, including a specially developed shoreline detection approach and empirical parameterizations to estimate the shoreline contour elevation.

Shoreline detection based on processing of SIGMA images, and using a specially trained ANN for pixel intensity threshold estimation, resulted in data return rates of 83%, with an average horizontal cross-shore RMSE of 1.06 m.

Considering a manually validated shoreline set, an optimal RMSE of 0.18 m for the vertical elevation was obtained using an ANN while empirical parameterizations based on the tidal elevation and the wave run-up height resulted in an RSME of 0.26 m. This error was reduced to 0.22 m after applying 3-D data filtering and interpolation. Beach-face slope errors were around 0.02.

Tests for a 5-month period of fully automated operation applying the ANN model resulted in an optimal average RMSE of 0.22 m, obtained using a one tidal cycle time window and a time-varying beach-face slope.

Applying horizontal positioning corrections according to differences between the estimated and projected shoreline elevations improved the performance in some cases, but was not found to be an overall significant factor.

The findings of the study indicate that the use of ANNs in similar video systems has much potential, especially for sites where long-term field data exist, allowing efficient training.

Acknowledgments

The authors gratefully acknowledge the European Community Seventh Framework Programme funding under the research project MICORE (grant agreement no. 202798). We are indebted to the Restaurant ‘Paquete’ for allowing us to deploy the cameras on their rooftop and for supplying electric power and space for our equipment.

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© Springer-Verlag 2011