UBathy (v2.0): A Software to Obtain the Bathymetry from Video Imagery

Citation: Simarro, G.; Calvete, D. UBathy (v2.0): A Software to Obtain the Bathymetry from Video Imagery. Remote Sens. 2022,14, 6139. https://doi.org/10.3390/rs14236139 Academic Editors: Panagiotis Agrafiotis, Gema Casal, Gottfried Mandlburger, Karantzalos Konstantinos and Dimitrios Skarlatos Received: 11 November 2022 Accepted: 26 November 2022 Published: 3 December 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). remote sensing Technical Note UBathy (v2.0): A Software to Obtain the Bathymetry from Video Imagery Gonzalo Simarro 1,*,† and Daniel Calvete 2,† 1Marine Sciences Institute, CSIC, Passeig Maritim de la Barceloneta 37-49, 08003 Barcelona, Spain 2Department of Physics, Polytechnic University of Catalonia–BarcelonaTech, Jordi Girona 1-3, 08034 Barcelona, Spain *Correspondence: simarr[email protected] † These authors contributed equally to this work. Abstract: UBathy is an open source software developed for bathymetry estimation from video images. The proposed scheme is based on extracting the wave modes from videos of the nearshore surface wave propagation. These videos can be formed either from raw camera images, which must have been previously calibrated, or from georeferenced planviews. For each wave mode extracted from the videos, the wave frequency and the spatially dependent wavenumbers are obtained. The frequencies and wavenumbers from different videos are used to estimate the bathymetry by adjusting the dispersion relationship for linear surface water waves. The bathymetry at different times can further be weighted and aggregated using the Kalman filter. The new software is suitable for Argustype video monitoring stations and for moving cameras mounted on drones or satellites, and it is meant for users familiar with coastal image processing and suitable for non-experienced users. The software and an application example are available on the GitHub platform. Keywords: bathymetry; video monitoring; remote sensing; beach; nearshore; coastal zone; signal decomposition 1. Introduction Coastal zone management and research requires knowing the bathymetry and its changes [ 1 , 2 ]. Bathymetry has an immediate interest in decision making processes and, further, bathymetric timeseries allow to understand morphodynamic processes and to validate models which, in turn, are helpful to predict future changes and to analyze the impact of potential human actions [ 3 , 4 ]. Managers and scientists (marine geologists, coastal modelers, etc.), with different levels of technical background, are faced with the need for bathymetry, preferably with high frequency and at a low cost. The development of accurate, affordable and easy-to-use technologies can benefit all of them. Techniques for direct bathymetry measurements such as bottom-contacting vehicles [ 5 ], swath-sounding sonar systems [ 6 ] or bathymetric LIDAR [ 7 ], produce very high quality bathymetry due to their high resolution. However, they are economically expensive and time-consuming techniques. Hence, they are only used at most a few times a year for a given site, except for very specific field campaigns. In the highly dynamic nearshore area, sporadic campaigns are important to obtain a rough estimate of the characteristics or the current state of the beach, but are of minor value to study its dynamics at the event scale. The main alternative techniques to those listed above use sequential observations of the sea surface to infer the bathymetry from how it affects sea wave characteristics. These sequences of observations, which may come from satellite imagery [ 8 ], fixed coastal video monitoring stations [ 9 ], drones [ 10 ] or radars [ 11 ], are used to analyze the water wave propagation from which to infer the bathymetry. The methods are all based on the linear dispersion relationship, which relates the wave period and the wavelength (or, equivalently, the wave celerity) to the local water depth. In the nearshore zone, specific schemes have Remote Sens. 2022,14, 6139. https://doi.org/10.3390/rs14236139 https://www.mdpi.com/journal/remotesensing Remote Sens. 2022,14, 6139 2 of 18 been developed to deal with non-monochromatic wave propagation in shallow waters, namely: cBathy [ 9 ], UBathy [ 12 ] and COCOs [ 13 ]. These algorithms, initially developed for videos obtained from fixed video monitoring systems (“Argus-like”, [ 14 ]), use videos of planviews (projections of the raw images into the mean water level plane) of around 10 min at 2 Hz and can also be applied to videos from radar [ 15 ] and drones [ 16 ]. The software proposed in this paper belongs to this category of schemes. The cBathy algorithm [ 9 ] starts by transforming the time history of the intensity of each pixel into the frequency domain. To obtain the local water depth at a given point, cBathy considers a neighborhood and obtains the wave spatial pattern and the wave period through frequency-domain empirical orthogonal functions of the cross spectral matrices. The dispersion relationship then allows them to obtain estimates of the depth for each dominant frequency and, also, a weighted average of them. A Kalman time filter over the results of the available videos is required to obtain the bathymetry for successive dates (Figure 1A). The excellent results of cBathy clearly show the capability of using frequency and wavenumber values extracted from videos to estimate the bathymetry from the dispersion relationship when it is combined with a Kalman filter. The algorithm has recently been updated [ 17 ] to include, for instance, an adaptive scheme to determine the optimum size for the mentioned neighborhood, and it is available as open source Matlab toolbox. The original UBathy algorithm [ 12 ] first splits the video in time to obtain sub-videos that are analyzed individually. The Hilbert transform of each sub-video is decomposed in space and time using empirical orthogonal functions (EOF). For the subsequent analysis, the modes whose temporal behavior is periodic are considered. For each of these modes, the wavenumber field is obtained locally fitting a plane to the phase of the spatial component of the mode. Finally, once all the sub-videos have been analyzed, the local depth is obtained by fitting the dispersion relationship to the set of pairs of wavenumbers and periods found at each point. The results with this algorithm show that the global analysis performed in the mode decomposition, while filtering the different wave constituents in the videos, allows a good extraction of wave numbers and periods and an improvement in the bathymetric estimation. COCOs algorithm [ 13 ] splits the video in time and, for each sub-video, performs a space-time decomposition of the Hilbert transform of the signal, similar to UBathy. In this case, however, a dynamic mode decomposition (DMD) [ 18 ] is applied. This decomposition does not force orthogonality of the space components of the modes and ensures periodicity time-wise. The wavenumbers are obtained from the space components of the modes using in this case a two-dimensional fast fourier transform (2D-FFT) in a neighborhood whose size is obtained adaptively, and analyzing the wave celerity. By adjusting the Dopplershifted linear dispersion relationship, a bathymetry and an associated current field are obtained for each sub-video. The estimation of the bathymetry is finally performed by applying a Kalman filtering to the resulting bathymetry of consecutive sub-videos and stopping the process once the convergence of the solution is found (Figure 1B). The COCOs results support the benefits of a global analysis of the wave modes as well as the capability of the Kalman filter for aggregating the bathymetry results within the video. This algorithm is available as open source Matlab toolbox. The aim of this work is to present an improved version of the UBathy algorithm, including details of its open source software toolbox. The improvements include the application of robust principal component analysis (RPCA) [ 19 ] and DMD algorithms within the mode decomposition step, the use of adaptive neighborhoods for wavenumber and local water depth estimation, the outlier exclusion through the use of RANdom SAmple Consensus approach (RANSAC) [ 20 ] and, finally, the bathymetry aggregation through Kalman filtering. The work is complemented with the software, developed to be used by coastal community members not necessarily with programming expertise and, as developed in Python, with no additional licensing costs of proprietary tools. As new features, the software allows to obtain the bathymetry from video images covering different Remote Sens. 2022,14, 6139 3 of 18 areas (with or without overlapping) and captured at different times. This allows large areas to be covered and avoids problems of camera synchronization. In addition, the videos can be based on calibrated raw images or georeferenced planviews (Figure 1C), allowing the use of multiple image sources (fixed stations, drones, satellites, etc.). The theoretical background and the main code characteristics are presented in Section 2. To illustrate the performance of UBathy, Section 3presents and discusses the results for different videos obtained from a video monitoring station, including also some recommendations of use. The paper ends in Section 4with some conclusions. Figure 1. Basic characteristics in regard data input and use of Kalman filter for cBathy ( A ), COCOs (B) and the proposed improved version of UBathy (C). 2. Methods and Software Description UBathy has been developed to estimate the coastal bathymetry from the propagation of nearshore water waves as observed in video images. The main features of the software and the methodology are listed below. Software characteristics. UBathy is an open source software developed in (also open source) Python3 and available at GitHub platform. It runs on any platform with a standard installation of Python3.9 (i.e., with “The Python Standard Library”) and OpenCV, NumPy, SciPy and matplotlib modules. The code is complemented with an example case so that any user can fully execute it. A guided example is included to run on Jupyter Notebook to facilitate its use to non-experienced users. The software is suitable for users who are familiar with coastal image processing. Videos sources. A novel aspect of UBathy is that allows to directly process videos of raw camera images in addition to usual planview videos. In the first case (raw images), the videos can be acquired typically from fixed video monitoring stations (“Argus” type, [ 14 ]) but also from new CoastSnap stations [ 21 ]. For their processing, only the calibration of the camera is needed, without any further post-processing, together with the position of the mean water level at the time of the recording. Videos of planviews can normally come from fixed video monitoring stations or from the processing of drone flights. For planview videos it is necessary to know their georeference and the position of the mean water level. Mode decomposition. The extraction of the wave modes and corresponding wave periods is performed by global analysis of the images. The software allows, at user’s request, to decompose the videos in time (wave periods) and space (wave phase) using EOF, following [ 12 ], or DMD [ 13 ]. In addition, the user can also reduce the signal noise of the videos by applying an RPCA [19]. The wavenumber estimation uses local adjustments of the wave phase. Remote Sens. 2022,14, 6139 4 of 18 Bathymetry estimation. The bathymetry is obtained by fitting the surface waves dispersion relationship with the wavenumbers and frequencies of the different modes, taking into account the different mean water levels. Another novel aspect of this software is the flexibility to obtain the bathymetry by assembling videos that: (1) cover different parts of the coastal area, (2) do not need to be recorded synchronously and with the same sea level and, (3) are made of different types of images (planviews and raw images). In addition to the bathymetry obtained from the above analysis, a Kalman filter is used to obtain the bathymetry at a given time by accumulating the results obtained up to that time. The execution of the UBathy software is performed through the following steps: Step 0: Video and data setup. The video frames, data for image georeferencing and mean water level during the recording of the videos are provided. Step 1: Generation of meshes. Generation of the spatial meshes to express the mode decomposition, the wavenumbers and the bathymetry. Step 2: Mode decomposition. The wave is decomposed into different modes, with the corresponding wave period and spatial phase. Step 3: Wavenumber computation. The spatial phase of each mode is analyzed to extract the wavenumbers in the spatial domain. Step 4: Bathymetry estimation. Estimation of the bathymetry from the set of periods and wavenumbers of different videos. Step 5: Kalman filtering. Determination of the bathymetry evolution by time filtering the bathymetry results obtained from videos at different times. Thereafter, Section 2.1 details the methodology and theoretical background for each of the different steps and Section 2.2 describes the software execution procedure, including the data structure, inputs and outputs. 2.1. Methodological Background 2.1.1. Generation of Meshes For each video, the mesh where to obtain the modes (“M-mesh”) depends on whether the video is made of planview or raw (oblique) images. If it is made of planviews, the mesh are those xy -points of the planview which fall within the domain where the bathymetry is to be estimated (Figure 2A). When the video is made of raw images, the mesh is build as a set of xy -points within the bathymetry domain so that: (1) they correspond to integer-valued pixels of the raw images, so as to avoid later interpolations, and, (2) they resemble, as far as possible, a uniform equilateral triangle mesh of given resolution δM , so as to avoid over-weighting the areas of the raw image where the pixel footprint in space is higher (Figure 2B). For each video, the mesh where to obtain the wavenumber k (the “K-mesh”) is made of the xy -points of a uniform equilateral triangle mesh of resolution δK that fall both within the bathymetry domain and the xy -domain of the image, whether it is planview (Figure 2C) or raw (Figure 2D). Finally, the mesh for the bathymetry (“B-mesh”) are the xy -points of a uniform equilateral triangle mesh of resolution δB within the bathymetry domain (Figure 3). This mesh is independent of the videos. Remote Sens. 2022,14, 6139 5 of 18 Figure 2. Meshes for modes ( top ) and wavenumbers ( bottom ) for videos made up of planviews ( A , C ) and raw images ( B , D ). The bathymetry domain is shown in blue; planview ( A , C ) or camera ( B , D ) domains are shown in red. Figure 3. Mesh for the bathymetry. The bathymetry domain is shown in blue. 2.1.2. Mode Decomposition Following Simarro et al. [12] , each video is first cut to obtain, every time step ∆t (equal or higher than the time step between frames), a set of sub-videos of durations w1 , w2 , ...(Figure 4). The signal in each sub-video is decomposed in space and time to estimate the wavenumbers and periods of the dominant wave components. Previously, the RPCA algorithm by [ 19 ] can be applied, with IM iterations, to remove noise from the signal. Further, the time Hilbert transform of the signal must be done before the mode decomposition to obtain a natural retrieval of phases [ 12 ]. Since the Hilbert transform generates overshoots at both ends of the time domain, the sub-videos are first increased at both ends with the expected maximum period ( Tmax , which is the maximum affection zone of the overshoots) and, once Hilbert-transformed, cropped back to wi(Figure 5). Two different space-time mode decompositions are allowed for the Hilbert-transformed sub-videos: EOF [ 12 ] and DMD [ 13 , 22 ]. If EOF is applied, the modes that are considered for further analysis are those explaining a percentage of the total variance above a critical value ( vE∼ 2.5%), having a proper temporal periodic behavior ( σω/ω⩽ 0.15, following the notation in the original work) and with the period within a range [Tmin,Tmax] . If DMD is applied, the rank for the dimension reduction embedded in DMD must be provided ( rD∼ 6) and the modes considered for further analysis are all those with a period in the range [Tmin,Tmax] . Either using EOF or DMD, the results for each sub-video is a set of Remote Sens. 2022,14, 6139 6 of 18 modes. Each mode has a wave period and its complex-valued spatial component, given in the M-mesh, which can be represented by an amplitude and a phase (Figure 6). Figure 4. Sub-video generation from a video; the time step between frames is 1 fps (fps = frames per second). Figure 5. RPCA + Hilbert transform of the sub-videos. Figure 6. Spatial phase of two modes obtained for videos of planviews ( A ) and raw images ( B ). The white circle (A) represents the size of the neighborhood to estimate the wavenumber. 2.1.3. Wavenumber Computation For the modes obtained in the above decomposition, the wave wavenumbers, k , are computed using their period and spatial phase, which represents the phase of the wave (Figure 6). This step can be performed in different ways ([ 13 ] and references therein): from the phase gradient, performing spatial 2D-FFTs or, recalling the complex nature of the modes, through particle image velocimetry techniques (cross-correlation). A modification of the approach by Simarro et al. [12], based on computing the phase gradient, is considered here. For each of the modes, the wavenumber k at each point P of the K-mesh is obtained by adjusting the phase locally to a plane. To achieve this, the phase values of the points of the M-mesh that are in a neighborhood of a given radius RK around point P are used (e.g., the points within the white circle in Figure 6A for the black dot). The values of RK are detailed below in this subsection. The phase values at these points are shifted to be centered around zero to avoid phase jumps at ±π (following the “phase fitting” method at Simarro et al. [12] ) and then approximated with a plane kxx+kyy+α0 , where kx , ky and α0 are free coefficients. To remove the noise and the outliers in the phases, evident in some areas of Figure 6, a RANSAC approach [ 20 ] is applied maximizing the number of points with fitting errors below 0.25rad ≈15◦. The wavenumber is then k=qk2 x+k2 y. Remote Sens. 2022,14, 6139 7 of 18 Once the wavenumbers k of a mode of frequency ω have been computed, a first selection is performed using the parameter γ=ω2/(gk) , in which those with γ> 1.2 are discarded (gaps in Figure 7A,B). This parameter is also used to introduce two additional parameters that will be used later, in the estimation of the bathymetry, to evaluate the quality of the computed wavenumbers. For any point P of the K-mesh, the mean, µγ and standard deviation, σγ , of γ (Figure 7C,D), are computed with the values in a neighborhood of P of radius 0.5λ, with λ=2π/kthe estimated wavelength at P. Regarding the radius RK , used to determine the neighborhood in which the phase is fitted to a plane, it has to be taken into account that very small neighborhoods make the results more sensitive to noise but large neighborhoods are likely to contain jumps of the phase. Given these limitations, it is convenient to use an RK that is, at most, of the order of one-half wavelength of the local wave. However, it is not known a priori since it depends on the wave period and the local (unknown) depth. In order to circumvent this problem, neighborhoods adapted to the different wave modes and depths are chosen. As the frequency ω of a wave mode is known, the wavelengths corresponding to a set of depths in the range in which the bathymetry will be estimated are used; dmin and dmax , respectively, are the minimum and maximum obtainable depths; nK equispaced intermediate depths are defined in this range (see Figure 8, where nK=3) dj=dmin +j(dmax −dmin) nK,j=1, . . . , nK. (1) For each depth dj , the wavelength λj= 2 π/kj is obtained from the dispersion relationship ω2=gkjtanh (kjdj) and the radius of the neighborhood is computed as RK,j=cKλj , where cK is a factor of the wavelength that must be around 0.5. Consequently, the values of k , γ , µγ and σγ will be obtained for each RK,j , assuming that larger radius will work better in deeper regions and vice versa. This approach follows a similar philosophy of adaptivity proposed by Gawehn et al. [13], Holman and Bergsma [17]. Figure 7. Wavenumber k ( A ), γ ( B ), µγ ( C ) and σγ ( D ) obtained from the spatial phases and period in Figure 6A, taking RKthe radius of the white circle in the same figure. Remote Sens. 2022,14, 6139 8 of 18 Figure 8. Depths djand wavelengths λjfor RK,j. 2.1.4. Bathymetry Estimation The outcome of computing wavenumbers for all RK ’s of all modes of all sub-videos of all the videos from which a bathymetry will be computed, is a (very large, in general) set of tuples {x,y,ω,k,µγ,σγ,zs} , with zs the surface elevation, at each point of the K-meshes — recall that γ=ω2/(gk) is also provided. For the computation of the bathymetry, the tuples with the most reliable values of kare selected by requiring that |γ−µγ|⩽eB,σγ⩽eB, (2) where eB∼0.075 is a critical error (Table 1). To estimate the bed elevation zb at a point P in the B-mesh, those tuples in a neighborhood of radius RB , which is discussed below, are used. First, an error is computed for a given depth zbof each j-th tuple as εj(zb) = γ−γ0=ω2 gk −ω2 gk0, with k0=k0(ω,zs,zb) the wavenumber obtained by solving ω2=gk0tanh (k0(zs−zb) ) . Above, most j sub-indexes are avoided for readability (e.g., in ω , k and zs ). The dispersion relationship is solved using an improved version of the explicit approximation by Simarro and Orfila [23] . Following a RANSAC-like approach, a first approximation of zb is found by maximizing the amount of tuples that satisfy |εj|<eB (Figure 9A) for zb ’s in the range corresponding to the given range of depths. In a second step, for the J tuples satisfying |εj|<eB(around 350 in Figure 9A), zbis obtained by minimizing (Figure 9B) ε(zb) = v u u t 1 J J ∑ j=1 ε2 j(zb). Following the same strategy as for the wavenumber, once zb has been estimated at all possible points in the B-mesh, the quality of zb in a point P is assessed through the standard deviation, σzb , of the values of zb in a neighborhood of radius RB around P. This radius RB , also employed to select the tuples for the estimation of the bathymetry, is computed by scaling a characteristic local wavelength, LB , as RB=cBLB , where cB∼ 0.2 is a dimensionless coefficient and, at each point P of the B-mesh, LB is the average of wavelengths obtained at the point closest to P of the K-mesh. Figure 9. Estimation of zbfrom tuples (ω,k,zs): RANSAC discard (A) and optimization (B). Remote Sens. 2022,14, 6139 9 of 18 2.1.5. Kalman Filtering The result of the previous steps is a set of bathymetries zb and (self) errors σzb obtained at different times tj (i.e., zb,j and σzb,j ) in points of a unique B-mesh. Following [ 9 ] the Kalman filter is applied in time at each spatial point. The filtered bathymetry is initialized at time t0as zKal b,0 =zb,0 , and, to update the bathymetry from time tj−1to time tj, it is zKal b,j=zKal b,j−1+Kj(zb,j−zKal b,j−1), (3) where Kj is the “Kalman gain”. The Kalman gain, together with other useful variables, is obtained as Kj=p p+σ2 zb,j ,p=Pj−1+Q2(tj−tj−1)2,Pj= (1−Kj)p. (4) Above, Pj , that is initialized as P0= 0, is the a posteriori variance of the error: its square root, a length, gives a measure of the quality of the Kalman filtered bathymetry. Moreover, Q , with units of velocity, is the expected natural variability of the bed, e.g., 0.1 ms. The value of Q could depend, in general, on the wave conditions and on the bathymetry itself, but it is considered constant. 2.2. Software Implementation This section briefly describes the structure and software workflow of UBathy. A detailed description of the file structure, format of the files, software workflow and an application example can be found at https://github.com/Ulises-ICM-UPC/UBathy (accessed on 10 November 2022), site to be updated if any future changes or developments take place. The code and the data used in this paper are hosted permanently on Zenodo at https://doi.org/10.5281/zenodo.7360216 [24], see Appendix A. 2.2.1. Video and Data Setup The user must provide the video frames from which the software will estimate the bathymetry. These frames, uniformly distributed in time, must be either in image format (PNG or JPEG) or in a container format (AVI, MPEG or QT) from which images of each frame are extracted. For each video, the camera calibration file must be supplied in the case that frames are raw camera images, or a file where the image is georeferenced in the case of planviews. At https://github.com/Ulises-ICM-UPC (accessed on 10 November 2022) the reader can find codes for camera calibration and planview generation from drones. For each video, a file with the mean water level has to be included. In addition to the videos and these files, the user has to provide a file with the spatial coordinates of the boundary of the domain in which the bathymetry is to be estimated ( xy_boundary.txt ), a file with the list of videos that compose the different bathymetry results ( videos4dates.json ) and a main file of parameters ( parameters.json ) where the values of the parameters described in Section 2.1, and few other introduced here, are assigned. The equivalence between the parameters of the previous section and the name of the parameters in the parameters.json file is detailed in the Table 1. It is also possible to provide ground truth bathymetry that can be used to evaluate the results obtained with UBathy. 2.2.2. Generation of Meshes The meshes for mode decomposition and wavenumber computation, which are specific to each video, and the mesh for bathymetry estimation, common to all videos, are generated from the mesh resolutions set in parameters.json , the domain defined in xy_boundary.txt and the spatial region covered by the images as described in Section 2.1.1. These meshes are stored in a temporary scratch folder in NPZ format (a compressed for- Remote Sens. 2022,14, 6139 16 of 18 Figure 14. Bathymetry ( top , ( A , B )) and errors ( bottom , ( C , D )) for cropped (160 s) videos without using Kalman (left, (A,C)) and using Kalman filter starting 7 days before (right, (B,D)) . Table 4. Influence of Kalman filtering using cropped (160 s) and full (600 s) videos. Videos of 160 s Videos of 600 s Case Points Bias m RMSE m Points Bias m RMSE m no Kalman 4119 −0.18 0.39 4429 −0.09 0.22 1 day 4346 −0.15 0.33 4469 −0.13 0.24 2 days 4364 −0.20 0.33 4477 −0.17 0.27 3 days 4394 −0.15 0.28 4480 −0.14 0.24 4 days 4394 −0.15 0.28 4480 −0.14 0.24 5 days 4412 −0.15 0.28 4488 −0.13 0.23 6 days 4419 −0.17 0.29 4493 −0.15 0.28 7 days 4419 −0.17 0.29 4493 −0.16 0.29 4. Conclusions The UBathy open source toolbox, presented in this paper, estimates nearshore bathymetry from videos of calibrated raw images and georeferenced planviews. The videos may be obtained from Argus-type video monitoring stations or from moving cameras, such as drones or satellites. The software is appropriate for users who are familiar with coastal image processing. The paper discusses in detail the specific methodology of the UBathy algorithm and describes the use of the software. The algorithm incorporates advances over the last decade in nearshore bathymetric estimation from videos. The inversion method is based on [ 12 ] as well as it incorporates contributions from [ 9 ] (e.g., Kalman filter) and [ 13 ] (e.g., DMD and adaptive neighborhoods). In addition, further improvements of UBathy are presented, such as the algorithm for determining the bathymetry from the period and wavenumber of multiple wave modes which can come from multiple videos, the application of RPCA to reduce the noise in the videos or the use of RANSAC to reduce outliers. The toolbox is flexible, allowing the estimation of bathymetry by assembling videos recorded at different times, at different sea levels and covering different areas. Extraction of wave modes can be made either with EOF or DMD. The bathymetry estimated at different times can be aggregated using a Kalman filter. The paper illustrates with an example the use of the toolbox and its capability to estimate the bathymetry with a quality that is roughly Remote Sens. 2022,14, 6139 17 of 18 similar to that of a bathymetric survey. The software is suitable for non-experienced users and the application example is available on the GitHub platform. Author Contributions: Conceptualization, G.S. and D.C.; methodology, G.S. and D.C.; software, G.S. and D.C.; validation, G.S. and D.C.; formal analysis, G.S. and D.C.; investigation, G.S. and D.C.; data curation, G.S. and D.C.; writing—original draft preparation, G.S. and D.C.; writing— review and editing, G.S. and D.C.; visualization, G.S. and D.C.; project administration, G.S. and D.C.; funding acquisition, G.S. and D.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Research funded by Ministerio de Ciencia e Innovación and European Regional Development Fund grant number PID2021-124272OB-C21 and PID2021124272OB-C22 and MCIN/AEI/10.13039/501100011033. Data Availability Statement: The current version of model and input data are available: https: //doi.org/10.5281/zenodo.7360216 under CC BY 4.0 license. Acknowledgments: The authors would like to thank the Ajuntament de Castelldefels for allowing the installation of the video cameras, to Puertos del Estado of the Spanish Government for providing date of the tidal gauge in the harbor of Barcelona and to the Autoritat Portuària de Barcelona for the bathymetric survey of the study site. Conflicts of Interest: The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript: EOF Empirical orthogonal functions DMD Dynamic mode decomposition FFT Fast Fourier transform RANSAC Random sample consensus approach RPCA Robust principal component algorithm Appendix A. Software Source Code Software name: UBathy Developers: Gonzalo Simarro, Daniel Calvete Contact address: [email protected] Cost: free License: Creative Commons Attribution 4.0 International Availability: https://doi.org/10.5281/zenodo.7360216 Year first available: 2022 New developments: https://github.com/Ulises-ICM-UPC/UBathy (accessed on 10 November 2022) Hardware requirements: PC, server. System requirements: Windows, Linux, Mac. Program language: Python (3.9) Dependencies: OpenCV, NumPy, SciPy and matplotlib modules. Program size: 100 KB Documentation: README in GitHub repository and example in an editable Jupyter Notebook. References 1. Davidson, M.; Van Koningsveld, M.; de Kruif, A.; Rawson, J.; Holman, R.; Lamberti, A.; Medina, R.; Kroon, A.; Aarninkhof, S. The CoastView project: Developing video-derived Coastal State Indicators in support of coastal zone management. Coast. Eng. 2007,54, 463–475. [CrossRef] 2. 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[CrossRef] 25. de Swart, R.; Ribas, F.; Simarro, G.; Guillén, J.; Calvete, D. The role of bathymetry and directional wave conditions on observed crescentic bar dynamics. Earth Surf. Process. Landforms 2021,46, 3252–3270. [CrossRef] 26. Ribas, F.; Simarro, G.; Arriaga, J.; Luque, P. Automatic shoreline detection from video images by combining information from different methods. Remote Sens. 2020,12, 3717. [CrossRef] 27. Simarro, G.; Bryan, K.; Guedes, R.; Sancho, A.; Guillen, J.; Coco, G. On the use of variance images for runup and shoreline detection. Coast. Eng. 2015,99, 136–147. [CrossRef] 28. Simarro, G.; Ribas, F.; Álvarez, A.; Guillén, J.; Chic, O.; Orfila, A. ULISES: An open source code for extrinsic calibrations and planview generations in coastal video monitoring systems. J. Coast. Res. 2017,33, 1217–1227. [CrossRef]