Spatial Analysis of Bathymetric Data from UAV Photogrammetry and ALS LiDAR: Shallow-Water Depth Estimation and Shoreline Extraction

Abstract

The shoreline and seabed topography are key components of the coastal zone and are essential for hydrographic surveys, shoreline process modelling, and coastal infrastructure management. The development of unmanned aerial vehicles (UAVs) and optoelectronic sensors, such as photogrammetric cameras and airborne laser scanning (ALS) using light detection and ranging (LiDAR) technology, has enabled the acquisition of high-resolution bathymetric data with greater accuracy and efficiency than traditional methods using echo sounders on manned vessels. This article presents a spatial analysis of bathymetric data obtained from UAV photogrammetry and ALS LiDAR, focusing on shallow-water depth estimation and shoreline extraction. The study area is Lake Kłodno, an inland waterbody with moderate ecological status. Aerial imagery from the photogrammetric camera was used to model the lake bottom in shallow areas, while the LiDAR point cloud acquired through ALS was used to determine the shoreline. Spatial analysis of support vector regression (SVR)-based bathymetric data showed effective depth estimation down to 1 m, with a reported standard deviation of 0.11 m and accuracy of 0.22 m at the 95% confidence, as reported in previous studies. However, only 44.5% of 1 × 1 m grid cells met the minimum point density threshold recommended by the National Oceanic and Atmospheric Administration (NOAA) (≥5 pts/m²), while 43.7% contained no data. In contrast, ALS LiDAR provided higher and more consistent shoreline coverage, with an average density of 63.26 pts/m², despite 27.6% of grid cells being empty. The modified shoreline extraction method applied to the ALS data achieved a mean positional accuracy of 1.24 m and 3.36 m at the 95% confidence level. The results show that UAV photogrammetry and ALS laser scanning possess distinct yet complementary strengths, making their combined use beneficial for producing more accurate and reliable maps of shallow waters and shorelines.

1. Introduction

A photographic camera is a device used to capture images, most commonly using digital sensors such as charge-coupled devices (CCD) or complementary metal-oxide-semiconductor (CMOS) sensors [1]. Among photographic cameras, metric or photogrammetric types are specifically designed for mapping and surveying, which ensure high geometric stability and precision [2]. Their primary purpose is to produce central-projection images in which rays in both object and image space remain collinear [3]. In bathymetric monitoring of coastal zones, these cameras are particularly valuable for shallow-water depth estimation from imagery acquired by unmanned aerial vehicles (UAVs). Compared with conventional hydrographic surveys, UAV-based photogrammetry enables the collection of depth data in areas that are otherwise inaccessible [4].

Complementary to cameras, 3D laser scanners employ light detection and ranging (LiDAR) technology to capture high-resolution spatial data. By recording the return signals of emitted laser pulses, they reconstruct the environment as a point cloud, enabling precise measurements of shape and distance [5]. LiDAR systems include airborne laser bathymetry (ALB) [6], airborne laser scanning (ALS) [7], mobile laser scanning (MLS) [8], spaceborne laser scanning [9], terrestrial laser scanning (TLS) [10], and underwater laser scanning [11]. In coastal applications, bathymetric LiDAR provides accurate water-depth measurements, while ALS supports elevation mapping in the terrestrial parts of the coastal zone [12]. However, the high cost of ALB systems continues to limit their widespread adoption, prompting the development of ALS-based shoreline extraction methods.

Traditional bathymetric surveys with echo sounders mounted on manned vessels are often inefficient in shallow or otherwise hard-to-reach waterbodies due to equipment risks, low resolution, and difficulties in mapping transitional areas near the 1 m isobath [13]. To address these limitations, UAVs equipped with photogrammetric cameras and LiDAR systems are increasingly being used, providing high-resolution data suitable for seabed topography and shoreline mapping. Recent studies confirm their potential for improving the accuracy and efficiency of coastal bathymetric measurements. Agrafiotis et al. [14] demonstrated that combining UAV imagery with machine learning, specifically support vector regression (SVR), significantly improves shallow-water depth estimation by correcting refraction effects, reducing the root mean square error (RMSE) to less than 0.5 m. Liu et al. [15] developed the compact integrated water-land survey (CIWS) system, which combines ALS depth points with grayscale photogrammetric images to generate accurate large-scale bathymetric models. Field calibration at Dongjiang Bay (China) achieved a depth accuracy of 0.113 m RMSE, while tests at Miaowan Island confirmed detailed seabed reconstructions. Similarly, Wang et al. [16] evaluated the UAV-mounted Mapper4000U topo-bathymetric LiDAR, which achieved an RMSE of 0.1227 m for water surface elevation and 0.1268 m for seabed depth. Compared with manned ALB systems, the UAV-based system provided higher point cloud density (42 pts/m²) and enabled the detection of submerged objects.

Overall, recent advances demonstrate the potential of UAV-mounted photogrammetric and LiDAR systems to improve the accuracy and efficiency of bathymetric measurements. These studies have shown significant progress in shallow-water depth estimation, seabed modelling, and high-resolution mapping. Nonetheless, important limitations remain. Current approaches vary in spatial coverage and performance under complex coastal conditions, and errors may still occur in anthropogenically modified environments. In addition, comprehensive spatial analyses that separately assess depth estimation and shoreline extraction for different sensor types are still scarce.

To address these gaps, this study analyses UAV-derived bathymetric data collected using photogrammetric cameras and ALS LiDAR. Emphasis is placed on shallow-water depth estimation and shoreline extraction, with parameters such as point cloud density, spatial resolution, and coverage uniformity assessed in relation to the specific characteristics of each sensor type.

The article is organised as follows. The Introduction discusses the significance of UAV-mounted optoelectronic sensors in bathymetric measurements and reviews existing data acquisition methods. The Materials and Methods section describes the use of photogrammetric cameras and ALS scanners, outlines the accuracy assessment, and explains the procedures applied for shallow-water depth estimation and shoreline extraction. The Results section presents spatial analyses from Lake Kłodno, a small inland waterbody, focusing on shallow-water depth estimation and shoreline extraction. The Discussion addresses methodological limitations and potential applications. Finally, the Conclusions summarise the key findings and suggest directions for future research.

2. Materials and Methods

This section presents the equipment and methods used to acquire and analyse bathymetric data, focusing on a photogrammetric camera and ALS, both mounted on UAVs. The following subsections provide detailed descriptions of the data acquisition techniques, processing workflows, and accuracy assessment procedures.

2.1. Photogrammetric Camera

This subsection presents the characteristics of bathymetric data acquired using a photogrammetric camera, evaluates the accuracy of depth estimation, and outlines the method employed to determine the depth of a shallow waterbody.

2.1.1. Data Characteristics

Bathymetric data acquired using a photogrammetric camera takes the form of aerial imagery, which can be processed into digital terrain models (DTMs), orthophotos, and point cloud models. The Structure from motion (SfM) technique plays a key role in this process, enabling the reconstruction of three-dimensional terrain structures from a series of georeferenced red, green, and blue (RGB) images.

The quality and accuracy of the data are significantly influenced by factors such as camera optics, the number and quality of images, lighting conditions, and the geometry of the planned flight. Therefore, a well-prepared photogrammetric flight plan is essential and must take into account key geometric parameters and all necessary technical information [17]:

• Determination of the type of aerial images and their triggering method—depending on the orientation of the photogrammetric camera axis, four types of images are distinguished: vertical, near-vertical, oblique, and highly oblique. The choice depends on the intended use of the photos and the topography. Regarding the triggering method, a commonly used solution is to activate the camera shutter at predefined points in space. Such images are referred to as targeted images. Using a global navigation satellite system/inertial navigation system (GNSS/INS), it is possible to trigger the camera so that the centres of images in adjacent strips, their corresponding stereograms, and triple overlap zones align accurately [18];
• Determination of the ground sampling distance (GSD)—this is a key parameter in flight planning. For high-resolution photogrammetric projects, a GSD of approximately 2–3 cm is typically used [19];
• Determination of UAV flight altitude—photogrammetric surveys conducted with UAVs are generally carried out at altitudes between 70 and 120 m [20];
• Selection of longitudinal and lateral image overlap—for high-resolution photogrammetric projects, it is assumed that longitudinal overlap should be at least 70–90%, and lateral overlap at least 60–80% [21];
• Calculation of the minimum distance between flight profiles—knowing the longitudinal overlap, flight altitude, and selected technical parameters of the camera (sensor size and focal length), the minimum spacing between flight profiles can be calculated [19];
• Determination of UAV flight speed—typical flight speeds for UAV photogrammetric surveys range from 20 to 30 km/h [19].

Proper planning of the flight geometry and consideration of all the aforementioned parameters significantly affect the accuracy of bathymetric data processing. This is particularly important in areas with variable and dynamically changing seabed topography [22].

2.1.2. Measurement Accuracy

Modern photogrammetric cameras enable highly accurate terrain representation, with precision reaching a few centimetres [23]. However, this level of accuracy depends on minimising errors that affect the quality of photogrammetric processing based on aerial imagery. According to Dai et al. [24], the accuracy of a 3D terrain model is influenced primarily by systematic errors related to the camera and by image configuration.

Systematic errors associated with the camera arise from imperfections in photogrammetric equipment. The most common are lens distortion, inaccurate determination of the principal distance, and limitations in image resolution. Lens distortion causes straight lines to bend, particularly near the edges of an image. Errors in the principal distance, often specified as the focal length recorded in the exchangeable image file format (EXIF) metadata, directly affect the accuracy of spatial reconstruction. Both errors can be reduced through proper camera calibration [25]. Image resolution, determined by the focal length and flight altitude, defines the level of detail captured. Higher resolution corresponds to greater potential accuracy of the photogrammetric output [26].

A second group of factors relates to image configuration. Flight altitude is critical, as lower altitudes provide more accurate terrain representation. Shorter baselines between successive images further enhance spatial reconstruction, while greater longitudinal and lateral overlap improves measurement accuracy. Increasing the number of overlapping images covering the same area also enhances overall quality and precision. The geometry of light rays likewise influences reconstruction accuracy: convergence angles close to 90° yield more reliable coordinate estimation, and smaller incidence angles (closer to vertical) minimise distortions and improve geometric fidelity [27].

The accuracy of depth measurement from images largely depends on the algorithm used. In this article, an analysis was conducted of the most commonly used methods for determining waterbody depth, including:

• cBathy—this algorithm analyses wave parameters such as amplitude, frequency, and wave shape over long time series to estimate water depth. Data are recorded using sensors, such as video cameras capturing wave motion, and relationships between wave speed and depth are then established. The accuracy of depth measurements using the cBathy method depends on atmospheric conditions, which can affect the quality of the data captured by the sensors [28];
• Depth Inversion—this method estimates waterbody depth based on the analysis of wave propagation, which results from wind activity, its duration, and gravitational force. Wave parameters are extracted from video imagery, which is transformed into orthorectified images using ground control points (GCPs). The cross-correlation of signal intensity between pixels is then analysed. The Depth Inversion algorithm may be sensitive to changing weather conditions, such as wind, which can affect accuracy [29];
• Radiometric method—this method estimates the depth of shallow waterbodies based on the colour of pixels in aerial images captured by a photogrammetric camera. Water characteristics, such as transparency and seabed topography, influence the accuracy and maximum operational depth of this method. When the contrast between bottom brightness and water transparency is low, depth estimation may become unreliable or impossible. Examples include areas with high levels of optical pollution or significant shadowing. The most favourable conditions for the radiometric method occur in waterbodies with flat bottoms and high transparency [30];
• SVR—this method uses a regression algorithm based on the concept of support vectors to estimate water depth using input data such as SfM point clouds and depth measurements taken at selected locations using a GNSS real-time kinematic (RTK) receiver. Based on these data, a predictive model is developed to estimate depth in areas not covered by direct measurements. One of the main limitations of the SVR method is its computational complexity and high memory requirements, particularly when processing large datasets [14];
• UAV-Derived Bathymetry (UDB)—this method uses algorithms based on multispectral imagery, which offers higher spectral resolution than RGB images by capturing data within specific wavelength ranges of the electromagnetic spectrum. Adverse atmospheric conditions can affect the quality and accuracy of the acquired data [31];
• uBathy—like cBathy, this algorithm analyses wave characteristics. However, unlike cBathy, uBathy is based on principal component analysis (PCA) of the Hilbert transform in the time domain. This process is applied to video imagery to determine the frequency and wavenumber of individual wave components. For each auxiliary video, PCA is performed on the temporal Hilbert transform of grayscale frame intensities. The angular frequency and spatial wavenumber are then calculated for each of the main decomposition modes. The results obtained using uBathy may also be influenced by hydrometeorological conditions such as weather, ocean currents, and sea state [32].

The most commonly used metric for assessing the accuracy of waterbody depth estimation methods is the RMSE. For most of the analysed methods (cBathy, Depth Inversion, uBathy, and UDB), RMSE values were calculated. For the radiometric method, accuracy was expressed as depth difference (DD), while for the SVR method, it was expressed as standard deviation (SD). The results are summarised in

Table 1. Summary of depth estimation accuracy for the cBathy, Depth Inversion, radiometric, SVR, uBathy, and UDB methods.

Method	Location	Depth Range	Depth Error
cBathy	Duck, NC, USA	n/a	0.51 m RMSE
	Agate Beach, OR, USA	0.25–14 m	0.56 m RMSE
Depth Inversion	Suruga Coast, Shizuoka Prefecture, Japan	0.25–8 m	0.33–0.52 m RMSE
Radiometric	Rowy, Poland	0–1.2 m	0.08–0.27 m DD
SVR	Amathouda, Cyprus	0.1–5.57 m	0.11–0.19 m SD
	Agia Napa, Cyprus	0.2–14.8 m	0.45–0.50 m SD
uBathy 1	Victoria Beach, Cádiz, Spain	0–8 m	0.49–0.73 m RMSE (Video 1, tf = 5 s) 0.47–0.59 m RMSE (Video 1, tf = 10 s) 0.38–0.44 m RMSE (Video 2, tf = 0 s) 0.38–0.46 m RMSE (Video 2, tf = 5 s) 0.39–0.43 m RMSE (Video 2, tf = 10 s)
UDB	Tyrrhenian Sea, San Vincenzo, Italy	0–5 m	0.24 m RMSE (Lyzenga) 0.37 m RMSE (Stumpf)
		0–11 m	0.89 m RMSE (Lyzenga) 1.06 m RMSE (Stumpf)

¹, t_f—time constant (in seconds) in the Butterworth filter used to smooth extrinsic camera parameters over time, thereby improving bathymetric estimation.

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Based on the data in Table 1, the cBathy algorithm achieved RMSE values of 0.51 m for Duck, NC, USA, and 0.56 m for Agate Beach, OR, USA. Depth Inversion produced RMSE values between 0.33 m and 0.52 m for the Suruga Coast, Japan. The radiometric method yielded DD values ranging from 0.08 m to 0.27 m for Rowy, Poland. The SVR approach resulted in SD values of 0.11–0.19 m for Amathouda, Cyprus, and 0.45–0.50 m for Agia Napa, Cyprus. For uBathy, RMSE values ranged from 0.38 m to 0.73 m, depending on the video source and the time constant (t_f) used in the Butterworth filter. The UDB method achieved RMSE values of 0.24–0.37 m for depths of 0–5 m and 0.89–1.06 m for depths of 0–11 m, depending on whether the Lyzenga or Stumpf model was applied. Overall, the results indicate that most methods achieve comparable accuracy, with typical RMSE values up to approximately 0.5 m, except in deeper-water applications of the UDB method, where errors can exceed this threshold.

It should be noted that the cBathy, Depth Inversion, and uBathy algorithms rely on video imagery to model wave dispersion. Furthermore, the effectiveness of most methods may be affected by environmental factors such as weather conditions, water transparency, and the presence of optical contaminants.

2.1.3. Depth Estimation Based on UAV Imagery

To analyse the characteristics and accuracy of bathymetric data acquired using a photogrammetric camera mounted on a UAV, several methods for estimating the depth of shallow waterbodies were evaluated. The following algorithms were assessed: cBathy [28], Depth Inversion [29], the radiometric method [30], SVR [14], uBathy [31], and UDB [32].

The comparison was based on three main criteria: the accuracy of depth measurements, hydrometeorological conditions during data acquisition, and the measurement equipment used. RMSE values for the analysed methods were presented earlier in Section 2.1.2 (Table 1). These values indicate that most algorithms achieve a broadly comparable level of depth-measurement precision, making practical considerations decisive in the selection of a suitable method.

Given these practical limitations, several methods were excluded from further analysis. Specifically, the cBathy, Depth Inversion, and uBathy algorithms require the presence of wave activity, as they rely on the analysis of water wave dispersion. Their use also requires the recording of video material. Such conditions are unfavourable for conducting photogrammetric surveys with UAVs, as strong winds may hinder stable and precise positioning. Moreover, wave activity on inland waterbodies is often insufficient for the practical application of these methods. The radiometric method and UDB require the use of multispectral cameras, which were not available during the study.

The SVR algorithm was selected because it processes RGB data from UAVs in an automated mode, includes correction for light refraction at the air-water interface, and can be applied to inland waterbodies regardless of wave activity. The algorithm has been discussed in detail in separate publications [33,34]. Here, it is presented only in a general form to provide context for the spatial analysis. It is based on the SfM technique, in which a three-dimensional point cloud is generated from image data (Figure 1) [35]. In the next step, points located below the water surface are identified and subjected to refraction correction. Based on these points, a linear regression model is developed in a multidimensional space [36], enabling depth estimation across the entire study area.

The choice of the SVR algorithm was further supported by field measurement results, which demonstrated high depth estimation accuracy for depths of up to 1 m in three diverse waterbody areas: a marine waterbody adjacent to the municipal beach in Gdynia, Lake Kłodno [20], and Lake Raduńskie Górne [34]. For model training, GNSS RTK and single-beam echo sounder (SBES) measurements served as reference data. The training dataset comprised 80% of the total sample size, while the remaining 20% was used for validation. During the learning process, the Z-score normalisation algorithm was applied to standardise the input data. In all cases, the depth measurement error, at the 95% confidence level, did not exceed the threshold value of 0.25 m required by the International Hydrographic Organization (IHO) Special Order [37].

2.2. Three-Dimensional Laser Scanner

This subsection describes the characteristics of bathymetric data acquired using a 3D laser scanner, examines the accuracy of shoreline extraction, and outlines the chosen method for determining the shoreline course.

2.2.1. Data Characteristics

LiDAR data acquired through ALS provides complete coverage of the surveyed area with measurement points [38]. The parameters that define the spatial resolution of such data are point spacing and point density. Point spacing refers to the linear distance between successive points in the dataset, while point density indicates the number of points per unit area [39]. Both point spacing and point density are typically reported as average values. Point density is influenced by flight parameters (such as altitude and speed), as well as scanner characteristics, including the pulse-repetition frequency (PRF). Typical systems emit between 10,000 and 500,000 pulses per second [40]. Each pulse can generate one or several returns, depending on the scanned surface. The field of view (FOV) is also important. A wider FOV allows a larger area to be covered in a single flight pass [39].

One advantage of airborne LiDAR is its ability to penetrate vegetation. When the sampling density is sufficiently high, it enables differentiation between returns from tree canopies and the ground surface. Bathymetric laser scanning, on the other hand, enables the recording of points located below the water surface. However, the effectiveness of this measurement depends on environmental conditions, particularly water clarity and the value of the diffuse attenuation coefficient. Under favourable conditions, the depth measurement error does not exceed 0.5 m at the 95% confidence level [41].

During the data processing stage, it is necessary to remove incorrectly recorded points, commonly referred to as noise, which may result from multiple reflections off obstacles or surfaces. Depending on the purpose of the analysis, various filters are applied to classify the points. For example, when creating a DTM, points originating from buildings, trees, and other objects located above the ground surface are eliminated. In the case of shoreline extraction, data preparation requires particular care, as it is essential to filter out points that may interfere with the determination of the land and water boundary, such as echoes from wave surfaces, vegetation, or coastal infrastructure, to achieve the most accurate representation of the actual shoreline.

2.2.2. Measurement Accuracy

A range of shoreline extraction methods can be used to determine the shoreline from ALS data. Several of these are outlined below:

• The method developed by Lee et al. is based on mean-shift segmentation and the integration of LiDAR data, orthophotos, and satellite imagery. In the first step, the method classifies LiDAR points into one of two categories: land or water. To segment the LiDAR point cloud, three filters are applied: the intensity of laser beam reflection from the water surface in the near-infrared (NIR) range, elevation, and RGB colour [42];
• The method developed by Liu et al. is an automatic shoreline extraction technique based on image segmentation using data collected through airborne LiDAR. Initially, the method converts the digital elevation model (DEM), generated from ALS data, into a binary image. The conversion process involves several algorithms, including region grouping and labelling, edge detection of segmented areas, morphological operations, line tracking, and vectorisation. Subsequently, the image is segmented into land and water pixels based on the DEM and a defined tidal datum [43];
• The method developed by Xu et al. is a parametric shoreline extraction technique based on LiDAR point clouds. The first part of the algorithm involves detecting and removing points that belong to the water surface. This is achieved using Euclidean cluster extraction, plane fitting with the random sample consensus (RANSAC) method, and density-distance features of individual points. The second part of the algorithm focuses on identifying potential boundary points and optimising the resulting boundary. For this purpose, the authors proposed a cost function optimisation model [44].

A detailed comparative analysis of the effectiveness of these methods was therefore conducted. However, it should be noted that comparing the points generated by the aforementioned shoreline extraction methods is challenging [12], as the reported accuracies were derived from different datasets. To illustrate the effectiveness of each method, the achieved accuracy levels and the number of datasets used are summarised in

Table 2. Summary of the achieved accuracy levels and the number of datasets used for selected shoreline extraction methods based on LiDAR data from ALS [12].

Authors of the Shoreline Extraction Method	Accuracy Level	Number of Datasets
Lee et al. [42]	1.5 m	4
Liu et al. [43]	4.5 m	1
Xu et al. [44]	1.0 m	5

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Based on Table 2, it can be concluded that the presented shoreline extraction methods meet the minimum accuracy requirements for hydrographic surveys conducted under the IHO Exclusive Order (horizontal position error of 5 m at the 95% confidence level) [37]. It is also worth noting that the methods discussed were tested on various datasets. While Xu et al.’s method was tested on more datasets than those of Lee et al. and Liu et al., its higher reported accuracy is likely attributable not only to the larger dataset, but also to the use of advanced filtering and optimisation techniques, as well as to favourable acquisition conditions of the test datasets, which reduced classification errors. Moreover, the type of waterbody can significantly affect the accuracy of a given shoreline extraction method.

The accuracy of LiDAR data plays a key role in the effectiveness of shoreline extraction methods. High-precision data obtained from laser scanning enables accurate determination of the boundary between land and water. Conversely, LiDAR data affected by noise can introduce errors, which may lead to inaccuracies in the analysis. Therefore, the factors influencing the accuracy of three-dimensional coordinate measurements of terrain points using a 3D laser scanner are presented below [45]:

• Distance measurement uncertainty—this primarily depends on the geometric relationship between the laser rangefinder and the GNSS and INS systems. Measurement error typically ranges from 2 cm to 4 cm; however, with proper calibration of the LiDAR system, an accuracy of approximately 1 cm can be achieved;
• Beam directional angle measurement uncertainty—this depends on the flight altitude and the precision in determining the geometric relationships between the GNSS and INS systems. Notably, this uncertainty increases with altitude;
• Attitude angle measurement uncertainty—this is related to the method used to measure the aircraft’s tilt, installation errors of the inertial measurement unit (IMU), and inaccuracies in determining its orientation within the aircraft’s coordinate system;
• Position coordinate determination uncertainty—the accuracy of GNSS measurements is influenced by factors such as satellite orbit and clock errors, receiver clock errors, signal multipath, satellite constellation geometry, phase ambiguity, and other sources of error. The use of differential GNSS methods allows for coordinate determination accuracy at the centimetre level;
• Time synchronisation error—the laser rangefinder and the GNSS and INS systems record time independently. To ensure consistency, it is necessary to align the measurements to a common time reference, such as the Global Positioning System (GPS) or Coordinated Universal Time (UTC);
• Data interpolation error—this arises from differences in the sampling frequencies of the individual components of the LiDAR system. For instance, laser rangefinders operate at frequencies of up to several hundred kilohertz, while GNSS and INS systems record data at frequencies of several tens to several hundred hertz. Synchronising the data to a single measurement epoch is therefore essential. This error is typically estimated at 3–5 cm.

Considering the uncertainties and measurement errors discussed, laser scanning enables the acquisition of elevation data with an accuracy of up to 0.1 m [46]. The accuracy of determining the three-dimensional coordinates of a terrain point is slightly lower, typically ranging from 0.15 m to 0.25 m [47].

Both bathymetric and airborne LiDAR systems can be used for shoreline determination. However, due to the high costs and limited accuracy of bathymetric measurements, which depend heavily on water clarity, ALS is gaining increasing popularity. LiDAR data collected from airborne platforms, supported by appropriate shoreline extraction algorithms, offer a viable alternative to traditional bathymetric surveys.

2.2.3. Shoreline Extraction Based on LiDAR Data from ALS

To assess the characteristics and accuracy of bathymetric data acquired using a 3D laser scanner mounted on a UAV, an analysis of selected shoreline extraction methods was carried out. Before processing the LiDAR data, a target extraction method was selected based on the following criteria:

• It must be used exclusively for shoreline extraction from a DTM or point cloud;
• The measurement data must originate from ALS;
• It must meet the accuracy requirements for hydrographic surveys as defined by the IHO Exclusive Order.

Based on these criteria, three shoreline extraction methods were selected: Lee et al. [42], Liu et al. [43], and Xu and Xu [48]. Their accuracy is presented in Section 2.2.2 (Table 2), and all methods meet the requirements for hydrographic surveys conducted under the IHO Exclusive Order, which specifies a horizontal accuracy of 5 m at the 95% confidence level [37]. A detailed comparative analysis revealed that the method proposed by Xu et al. achieved the highest accuracy (1 m), outperforming the other methods, which yielded results ranging from 1.5 m to 4.5 m. However, it is important to note that different accuracy metrics are used for shoreline extraction compared to bathymetric measurements, as accurately determining the shoreline can be challenging due to the variability of coastal conditions.

The selection of the method by Xu et al. [44] was further supported by the fact that it is a parametric approach based entirely on the geometric properties of the LiDAR point cloud. An additional advantage of this method is its ability to adjust parameters according to the specific type of waterbody, shoreline characteristics, and measurement conditions (Figure 2).

The method proposed by Xu et al. requires users to adjust its parameters according to the input data, making it a flexible tool suitable for various environmental conditions. However, caution is necessary when applying filters, as not all may be appropriate for a given dataset. For example, in the case of a shoreline with dense vegetation, applying height-based filtering may significantly reduce the number of points, which in turn can decrease the accuracy of the extraction.

In summary, the method proposed by Xu et al. enables accurate shoreline determination. However, its effectiveness largely depends on the appropriate selection of parameters and the quality of the point cloud. Successful application of this method requires experience and a thorough understanding of the specific characteristics of the area being analysed. The comparative analysis of the selected extraction methods, taking into account accuracy levels and the nature of the input data, confirms that both the choice of algorithm and the quality of the data are essential for accurate shoreline mapping.

3. Results

This chapter presents an analysis of bathymetric data acquired using optoelectronic sensors mounted on two UAV platforms. It focuses on shallow-water depth estimation and spatial analysis based on UAV photogrammetry with the SVR method, as well as shoreline extraction and spatial analysis using ALS LiDAR data. The discussion includes data acquisition procedures, processing techniques, spatial coverage, and accuracy assessment for both approaches.

3.1. Shallow-Water Depth Estimation and Spatial Analysis of UAV-Derived Bathymetric Data

The SVR method was applied to estimate shallow-water depth from low-altitude UAV imagery. This approach is effective when high-resolution, high-accuracy data are available. An accurate and precise point cloud can be generated using the SfM technique if high-quality images are captured under favourable lighting and GCPs are properly distributed. UAV flight parameters, such as speed and altitude, also play a critical role in ensuring the quality of the collected data. Before the survey, a photogrammetric control network was designed to ensure accurate georeferencing of the UAV imagery. Ten wooden GCPs (30 × 30 cm) were uniformly distributed across the study area, and their geometric centres were measured with a Trimble R10 GNSS RTK receiver, achieving a georeferencing accuracy of 4.1 cm (SD) [20].

In this study, the SVR method was tested using data acquired on 2–3 June 2022 at Lake Kłodno, an inland waterbody with moderate ecological status. The UAV survey was conducted under calm weather conditions with negligible surface wave activity, which are optimal for applying the SVR method. Because UAV-based bathymetric measurements can be scheduled to avoid periods of strong winds, the influence of waves on the water surface can be minimised, thereby improving depth estimation accuracy. The photogrammetric survey was carried out using a DJI Phantom 4 RTK UAV equipped with a 1-inch, 20-megapixel CMOS sensor. The flight was performed at an altitude of 80 m, with the gimbal angle set to 90° and an image overlap of 80% in both longitudinal and lateral directions. A total of 242 images were captured, resulting in a GSD of 1.5 cm/pixel. Based on these images, an initial UAV-derived point cloud containing 13,448,186 pts was generated using SfM and referenced to the PL-UTM (zone 34N) horizontal coordinate system (Figure 3).

Figure 3 shows that the SfM point cloud does not cover the entire water surface because of the absence of tie points in some areas. In marine waterbodies that lack distinctive surface features, the extent of the generated water surface is likewise expected to be limited.

To optimise the dataset, the SfM point cloud was subsampled to reduce the number of points while preserving key geometric features. This procedure aimed to decrease the data volume without losing essential spatial information. After subsampling, the UAV-derived point cloud contained 5,875,928 points, providing a solid foundation for further analysis. The SVR method was then applied to the shallow-water dataset covering depths between the water surface elevation (160.415 m) and the 1 m isobath (Figure 4). The water surface elevation was determined from averaged height measurements obtained with a Trimble R10 GNSS RTK receiver and referenced to the PL-EVRF2007-NH vertical datum with centimetre-level accuracy.

The point cloud generated using the SVR method demonstrates relatively high spatial coverage in the shallow nearshore zone, particularly down to a depth of 1 m. This indicates that the method can produce accurate bathymetric data under clear, shallow-water conditions with high spatial resolution. Nevertheless, some spatial variability is evident. Certain areas in the northern part of the lake show limited or no data, likely due to reduced bottom visibility, shoreline obstructions such as piers or trees, or unfavourable imaging conditions during data acquisition. Although this study did not include a dedicated depth-accuracy assessment, the SVR-derived data achieved a standard deviation of 0.11 m and an accuracy of 0.22 m at the 95% confidence level. These results suggest that the SVR data likely meet the minimum accuracy requirements for hydrographic surveys conducted in accordance with the IHO Special Order [20].

Building on this, the SVR-derived bathymetric dataset was subjected to spatial analysis focusing on coverage, density, and distribution within a regular grid. A 1 × 1 m grid was generated from the cleaned bathymetric data and clipped to the actual extent of the measurement points. This grid layout allows a clear distinction between surveyed and empty cells, offering an explicit visualisation of spatial coverage and data gaps. These results are an essential step in assessing the quality and completeness of the lake’s bathymetric model (Figure 5).

SVR-derived points are concentrated mainly in the shallow-water zone along the shoreline, particularly in areas where water clarity allowed the bottom to be observed and where image overlap was higher. Gaps in coverage occur in parts of the nearshore zone, primarily between the shoreline and the 0.2–0.3 m isobath, as well as in areas affected by aquatic vegetation blooms or obstructed by piers, moored vessels, and other structures that created shadows and occlusions in the imagery.

Subsequently, point density was classified within the grid cells in accordance with NOAA guidelines, which recommend a minimum density of 5 pts/m² [52]. Based on these guidelines, four density classes were defined: no data (0 pts), low density (1–4 pts), medium density (5–9 pts), and very high density (≥10 pts). Figure 6 shows the spatial distribution of these classes for Lake Kłodno.

In Figure 6, red indicates 9322 grid cells (43.72%) without data, corresponding to the areas described above. Yellow (1–4 pts/m²) represents 2509 cells (11.77%) with low point density, distributed along the shoreline. Areas that meet or exceed the NOAA minimum requirement of 5 pts/m² [52] are shown in light blue (5–9 pts/m²) and dark blue (≥10 pts/m²), comprising a total of 9491 grid cells (44.51%). These are located mainly in the central part of the lake, in areas with high water clarity and along sections with greater image overlap. The spatial distribution of density classes indicates that, despite extensive high-density areas, a substantial part of the lake remains without data. This may affect the completeness and accuracy of the resulting bathymetric model and highlights the need to supplement data in selected areas.

A crucial complement to this analysis is the evaluation of the spatial distribution of data generated using the SVR method. To facilitate comparative studies of bathymetric data collected by different sensors, the point density within individual grid cells was analysed. The evaluation employed the R68 and R95 measures, which are derived by sorting the data from the largest to the smallest values. The R68 measure represents the value exceeded by 68% of the observations, whereas R95 corresponds to the value exceeded by 95%. These measures are advantageous because they do not assume any specific statistical distribution and provide a high level of confidence. Additional statistical measures, including the arithmetic mean, standard deviation, minimum, and maximum values, were also calculated. The analysis revealed an average point density of 26.60 pts/m², with a standard deviation of 39.96 pts. The number of points in a single grid cell ranged from 0 to 195. This wide variation results from the nature of the SVR method, which generates bathymetric data only within a specific depth range. The R68 and R95 values were 113 and 23 pts, respectively. These findings confirm that the SVR-derived data exhibit uneven spatial coverage across the surveyed waterbody. This is further illustrated in Figure 7, which presents a histogram showing the variability in point densities across the grid.

3.2. Shoreline Extraction and Spatial Analysis Using UAV-Derived ALS LiDAR Data

This subsection outlines the process of determining the shoreline using LiDAR data acquired by an ALS system mounted on a UAV, followed by a spatial analysis of the resulting point cloud. A modified shoreline extraction method was applied, based on the approach proposed by Xu et al. and later adapted for airborne LiDAR data by Halicki et al. [53].

LiDAR measurements were conducted on 13 September 2023 over Lake Kłodno. A Velodyne Puck VLP-16 laser scanner, integrated with an SBG Ellipse-D GNSS/INS system, was mounted on an Aurelia X8 Standard LE UAV. The flight was carried out at an altitude of 70 m along two parallel profiles spaced 10 m apart, running parallel to the shoreline. Data acquisition and georeferencing were performed using HYPACK 2024 software. The survey produced a dense LiDAR point cloud containing horizontal and vertical coordinates as well as laser pulse intensity values. The scanned area primarily covered the land part of the lake, which influenced subsequent data processing. In total, 3,374,099 pts were recorded in the PL-UTM (zone 34N) and PL-EVRF2007-NH coordinate systems.

In the initial stage of processing, the point cloud was cleaned by removing duplicate returns and noise (Figure 8). Because of the data’s complexity and irregular distribution, this filtering step was performed manually. Noise removal involved visually identifying and eliminating points that deviated significantly from the surrounding structure or lay outside the area of interest. These included points lacking spatial continuity with adjacent data, points with inconsistent elevation or intensity values, and points originating from floating objects (e.g., moored vessels) or above-water infrastructure (e.g., piers). The objective was to retain only points representing the true shoreline and terrain relief while eliminating artefacts that could compromise the accuracy of subsequent analyses. After cleaning, the spatial distribution of point density was examined to assess overall data quality.

As shown in Figure 8, the ALS LiDAR data provide complete coverage of the nearshore zone of Lake Kłodno. The colour scale indicates elevation values ranging from approximately −7.4 m (lake bottom or water level) to 69.7 m (land elevation). The points are evenly distributed across the surveyed area, which is essential for precise shoreline determination and terrain modelling. The data effectively capture shoreline features and adjacent land objects, enabling detailed spatial analysis.

Following noise removal, the distribution of point density recorded by the Velodyne Puck VLP-16 scanner was analysed. This sensor employs 16 laser beams arranged vertically within a 30° vertical FOV and operates with a vertical angular resolution of 2°. It emits at a wavelength of 903 nm and, at a rotation rate of 600 RPM with a horizontal FOV limited to 90–270°, generates approximately 150,000 measurement points per second. Under these conditions, the average point density was 63.26 points/m², with a standard deviation of 104.38 points/m². The number of LiDAR returns per grid cell ranged from 0 to 1068, with R68 and R95 values of 283 and 52 points, respectively. These results indicate both a high overall density and substantial variability within the dataset.

The cleaned point cloud clearly demonstrates dense coverage of the surveyed coastal zone. However, a considerable part of grid cells (14,719 or 27.63%) contained no data (Figure 9). These empty cells are primarily located along the edges of the scanned area, where the scanner’s effective range decreases due to beam divergence, UAV flight altitude and oblique incidence angles. Additional no-data areas occur in locations with dense vegetation or low surface reflectivity (e.g., water), which reduce valid returns. In contrast, many populated cells exhibit very high point densities: 11,596 cells (21.77%) contain more than 100 pts/m², and over half (52.77%) exceed 10 pts/m². This high spatial resolution provides a robust basis for accurate shoreline determination and detailed analysis of coastal morphology.

Building on the data cleaning and spatial analysis, a modified shoreline extraction method proposed by Xu et al. and later adapted by Halicki et al. was applied (Figure 10) [53]. Since the LiDAR data primarily covered land areas, the step of identifying water areas was omitted. Processing began with density-distance filtering. The UAV trajectory was determined using a minimum height filter set at 70 m. Assuming a shoreline elevation of 0 m, the remaining filter parameters were defined as follows: maximum height 1 m, minimum height −1 m, and maximum density 50 pts within a 1 m radius.

Euclidean cluster extraction was then applied with a tolerance of 0.5 m and a minimum cluster size of 1000 points, allowing smaller clusters to merge into larger groups. These parameter values follow Xu et al. [44], who demonstrated their effectiveness for airborne LiDAR datasets with comparable densities. Edge detection was subsequently performed using the convex hull algorithm to extract boundary points from the filtered dataset. Finally, an additional filtering step based on the average distance from the UAV trajectory was applied twice, and the resulting points were connected into a continuous line. The shoreline derived from ALS LiDAR data for Lake Kłodno is shown in Figure 11.

As shown in Figure 11, many of the extracted shoreline points are located on piers. Because the applied method relies solely on elevation data, points from above-water structures were included as their elevations are similar to the actual shoreline. During the initial filtering stage, the dataset was constrained to ±1 m relative to the assumed shoreline elevation, which resulted in pier points being retained. Furthermore, the use of the convex hull algorithm contributed to the inclusion of these structures in the boundary determination. This limitation underscores that anthropogenic features can reduce the accuracy of shoreline extraction.

For the accuracy assessment, GCPs were measured along the shoreline at approximately 1 m intervals on curves and 5 m intervals on straight sections using a Trimble R10 GNSS RTK receiver. Horizontal coordinates were referenced to the PL-UTM (zone 34N) coordinate system, and vertical coordinates to the PL-EVRF2007-NH vertical datum. Only points with a horizontal accuracy better than 0.10 m were included; those with lower accuracy (e.g., under tree canopies) were excluded. The accuracy of the extracted shoreline was then evaluated by calculating the distances between LiDAR-derived shoreline points and the reference shoreline determined from the GCPs. From these distances, the mean, population SD, and 2.45·SD (corresponding to the 95% confidence level) were computed. The results yielded a mean distance of 1.24 m, an SD of 1.37 m, and a 2.45·SD value of 3.36 m. Despite local inaccuracies caused by piers, these findings confirm that the proposed method meets the minimum requirements for shoreline determination in hydrographic surveys. According to the IHO Exclusive Order, these requirements specify a maximum horizontal position error of 5 m at the 95% confidence level.

4. Discussion

The application of two independent remote sensing methods, UAV photogrammetry (SVR) and airborne laser scanning (ALS LiDAR), demonstrated their complementary potential for mapping shoreline zones and shallow areas of lakes. However, these technologies differ in terrain coverage, data density, and sensitivity to environmental factors such as water transparency, lighting conditions, and the presence of vegetation.

Photogrammetry based on the SfM technique, as applied in the SVR method, showed high accuracy in depth estimation under shallow and optically clear conditions. Although the reported depth measurement error (SD = 0.11 m; 0.22 m at the 95% confidence) originates from another study and was not directly analysed here, these values are consistent with results from other bathymetric studies using photogrammetry [54,55]. The method is particularly effective in environments where hydroacoustic techniques are insufficient, especially in very shallow coastal zones or where vessel access is limited. A significant limitation, however, is the uneven spatial distribution of data: over 43% of grid cells lacked data and only 44.5% met the minimum point density standard recommended by NOAA (≥5 pts/m²). This discontinuity may result from variability in water transparency, surface reflections, and lighting conditions during UAV flights [56]. Furthermore, SfM depends on identifying visible bottom features, which makes it highly sensitive to disturbances caused by aquatic vegetation or bottom sediments [57]. While the ecological characteristics of Lake Kłodno, including moderate turbidity and relatively high transparency, were favourable for UAV-based depth estimation, the method’s effectiveness would decrease in more turbid or dynamic waters. In such environments, stronger light attenuation, scattering, and wave-induced surface distortions occur. Therefore, careful calibration, parameter adaptation, and potentially integration of additional sensor data would be required to ensure reliable results.

ALS LiDAR, in turn, provided high data density and consistency in both terrestrial and coastal zones. The average point density reached 63.26 pts/m², far exceeding values typically used in high-precision terrain and shoreline modelling, where densities usually amount to only a few points per square metre [52]. The use of a modified shoreline extraction algorithm [44] produced results consistent with IHO Exclusive Order requirements. The mean distance from the reference shoreline was 1.24 m, with a 95% confidence interval of 3.36 m. Despite this generally high accuracy, shoreline extraction quality was occasionally constrained by coastal vegetation and overwater infrastructure such as piers. A key limitation of ALS is its inability to distinguish anthropogenic objects from natural features based solely on elevation data. As LiDAR does not capture spectral information, surfaces of similar height, regardless of their actual nature, are often classified as part of the same structure [58]. This can lead to misinterpretation of the land and water boundary in complex coastal environments. Integrating ALS data with high-resolution orthophotos has been shown to improve land cover differentiation and significantly enhance classification accuracy and shoreline mapping [59].

These findings indicate that neither of the analysed methods is sufficient on its own under complex terrain conditions. Integrating them appears to be the most promising approach, as it minimises the limitations of each technique. The literature highlights that combining LiDAR and UAV photogrammetric data, particularly when enriched with RGB or multispectral imagery, yields a significantly improved representation of shorelines and bathymetry in challenging environmental conditions [60,61]. Such a hybrid approach is especially recommended for lakes with highly diverse shorelines and variable water transparency.

5. Conclusions

The analysis demonstrated that the SVR method, when applied to depth modelling in the shallow-water zone of Lake Kłodno, produces highly accurate bathymetric data and meets the IHO Special Order requirements for depth measurement accuracy. However, despite this high level of accuracy, the method is constrained by the uneven spatial distribution of measurement points. Only 44.5% of the 1 × 1 m grid cells met the minimum point density threshold recommended by NOAA (≥5 pts/m²), while 43.7% contained no data. This incomplete spatial coverage indicates that, in practice, the method does not fully comply with the IHO Special Order requirements and may reduce the reliability of the resulting bathymetric map, particularly in areas with complex seabed topography.

Regarding shoreline extraction, the algorithm adapted by Xu et al. for ALS LiDAR data achieved an accuracy level consistent with the IHO Exclusive Order requirements. However, its effectiveness decreased in the presence of coastal infrastructure, such as piers, which were misclassified as shoreline features due to their elevation being similar to that of the surrounding land and water interface. Despite the higher average point density of the ALS data, a substantial number of grid cells along the shoreline remained empty. In contrast, photogrammetric data obtained using the SVR method, although less dense overall, exhibited greater spatial continuity and uniformity, particularly in shallow, well-lit, and unobstructed areas. These findings indicate that, under favourable environmental conditions, UAV photogrammetry can provide more accurate and reliable shoreline determination.

Future research should focus on integrating LiDAR and photogrammetric data, for example by merging point clouds within a unified coordinate system, applying point-level fusion algorithms (combining, for instance, LiDAR-derived elevation and intensity with RGB or multispectral information from photogrammetry), and incorporating these attributes into the dataset to improve land and water boundary classification. Such integration would allow the high spatial resolution of UAV photogrammetry to be combined with the precise elevation information from LiDAR, thereby enhancing shoreline extraction and bathymetric modelling in complex shallow-water environments.