A neural network-based water depth inversion method, system, and medium based on virtual control points

Abstract

This invention relates to a neural network-based water depth inversion method, system, and medium based on virtual control points, belonging to the field of water depth inversion technology. The method includes the following steps: S1: multi-source remote sensing data preprocessing; S2: virtual control point construction; S3: spatial-spectral feature fusion and MLP training and prediction; S4: accuracy verification and analysis. This invention addresses the sparsity problem of ICESat-2 data by constructing an adaptive virtual control point (VCP) dataset, enhances the model's adaptability to spatial non-stationarity by fusing spatial-spectral features, and strengthens robustness by employing a multilayer perceptron network with a dropout mechanism. This significantly improves the accuracy and generalization ability of water depth inversion in scenarios without real-world data.

Description

Technical Field

[0001] This invention relates to a neural network-based water depth inversion method, system, and medium based on virtual control points, belonging to the field of water depth inversion technology. Background Technology

[0002] Shallow water depth data is crucial for marine resource development, ship navigation safety, nearshore infrastructure construction, and ecological environment monitoring. Traditional measurement methods mainly include shipborne single-beam and multi-beam sonar systems and airborne lidar systems. While these methods offer high accuracy, they suffer from drawbacks such as high operating costs, low efficiency, and limited coverage, and are difficult to conduct large-scale measurements in remote waters with sovereignty disputes or complex geographical environments. In contrast, Satellite Derived Bathymetry (SDB) technology, with its advantages of high spatiotemporal resolution, wide coverage, and low cost, has become an important means of acquiring shallow water topographic information. Existing SDB models mainly include theoretical analytical models, semi-empirical models, and statistical models. Among them, theoretical analytical models are limited by the acquisition of complex water optical parameters; semi-empirical models (such as the Lyzenga model and the Stumpf model), although widely used, are sensitive to changes in seabed type and aquatic environment; while statistical models can fit the complex nonlinear relationship between water depth and spectrum and are currently one of the most widely used SDB models. Nevertheless, the accuracy and stability of the SDB statistical model are highly dependent on a sufficient number of spatially evenly distributed in-situ measured depth control points. In vast or remote sea areas, the scarcity of measured control points has become a key bottleneck restricting the development of SDB technology.

[0003] Launched in September 2018, NASA's ICESat-2 satellite acquires high-precision, globally available orbital water depth data, making it an ideal source of depth control point (DC) data. Utilizing ICESat-2 data to assist in active-passive fusion inversion of water depth from multispectral imagery has become a research hotspot. However, the training performance of SDB statistical models is highly dependent on the number and spatial distribution of samples. ICESat-2 satellite data exhibits a sparse, banded distribution along its orbit, with significant gaps between orbital regions, and is susceptible to data loss due to cloud cover and aerosol interference. This inherent non-uniform coverage and sample sparsity result in a large spatial sampling bias when used as training samples, making it difficult to train inversion models with good generalization ability and high accuracy. Therefore, overcoming the spatial sparsity limitations of ICESat-2 data and constructing a high-density, high-quality, and spatially balanced training sample set is a pressing technical challenge for current SDB statistical model inversion.

[0004] In existing technologies, some studies have attempted to fuse multispectral imagery and lidar data for water depth inversion. For example, patent application publication number CN118293887A discloses a method for predicting water depth in coastal areas based on multispectral imagery and lidar measurements. This method improves the inversion accuracy to some extent by fusing the two types of data, but it still has the following key limitations:

[0005] The problem of sample sparsity remains unresolved: The depth sounding photons of ICESat-2 are used directly as training samples without expanding the samples to account for their sparse distribution along the track, resulting in a significant decrease in model accuracy in blank areas.

[0006] Spatial feature deficiency: Prediction relies solely on spectral features and does not consider the spatial nonstationarity of water body optical properties (such as changes in optical parameters caused by differences in bottom sediment and suspended matter concentrations in different regions), making it unable to adapt to complex nearshore environments;

[0007] Insufficient sample quality control: The lack of an adaptive strategy to optimize the sample expansion threshold makes it difficult to balance the quantity and quality of samples, which may introduce noisy samples and affect the model accuracy.

[0008] Limited model generalization ability: The random forest model is used, but it does not introduce the nonlinear fitting ability and regularization mechanism of deep learning. It is susceptible to noise interference and has weak adaptability to complex data distributions.

[0009] For example, patent application publication number CN120217826A discloses a method for inverting shallow water depth using both active and passive satellite data. This method extracts virtual control points from ICESat-2 and Sentinel-2 data, calculates preliminary water depth using a multi-band log-ratio model, and then uses an inverse distance weighted algorithm (IDW) to spatially interpolate the residuals of the virtual control points to obtain the inversion result. However, this method cannot effectively fit the nonlinear optical characteristics of complex nearshore waters (such as the non-stationarity of optical parameters caused by suspended sediment and chlorophyll concentration variations). It relies on IDW interpolation to optimize the preliminary results, but the interpolation accuracy is limited by sample density, and it cannot fully utilize spatial information to improve inversion resolution and reliability.

[0010] To address the above problems, this invention proposes a neural network-based method for water depth inversion based on the fusion of spatial spectral features of Virtual Control Points (VCPs). Summary of the Invention

[0011] The purpose of this invention is to propose a neural network-based water depth inversion method, system, and medium based on virtual control points. This invention addresses the data sparsity problem of ICESat-2 by constructing an adaptive virtual control point (VCP) dataset, integrates spatial spectral features to improve the model's adaptability to spatial nonstationarity, and employs a multilayer perceptron network with a dropout mechanism to enhance robustness, thereby significantly improving the accuracy and generalization ability of water depth inversion in scenarios without actual measured data.

[0012] The neural network-based water depth inversion method based on virtual control points described in this invention includes the following steps:

[0013] S1: Multi-source remote sensing data preprocessing:

[0014] Multi-source remote sensing data preprocessing: Denoising and correction of ICESat-2 photon data to obtain seabed signal photons, cloud masking and water body extraction of Sentinel-2 images to obtain cloud-free shallow water images.

[0015] S2: Virtual Control Point Construction:

[0016] S21: Initial control point seed library construction: ICESat-2 photons are converted to Sentinel-2 image coordinate system, and the average value of photon water depth is taken as the true value by pixel as unit. The corresponding spectral reflectance is extracted to form the initial control point ICP seed library.

[0017] S22: Spectral similarity extension: Calculate the spectral distance between the target pixel and the initial control point seed. When the distance is less than or equal to a preset threshold, assign the seed water depth to the target pixel to generate a virtual control point.

[0018] S23: Adaptive Iterative Optimization: Determine the optimal threshold by minimizing the validation set accuracy index, balance the quantity and quality of virtual control points, and expand the initial control point ICP seed library into a high-density virtual control point VCP dataset;

[0019] S3: Spatial-Spectral Feature Fusion and MLP Training Prediction:

[0020] Extract multi-band spectral reflectance and spatial location features from the virtual control point dataset, and construct a joint spatial-spectral feature vector.

[0021] The spatial-spectral joint feature vector is input into a multilayer perceptron (MLP) neural network with a Dropout mechanism for supervised training. Spatial location features are used to constrain the spatial nonstationarity of water body optical properties. Rasterized water depth inversion results with the same resolution as the original image are generated through nonlinear regression.

[0022] S4: Accuracy Verification and Analysis: Extract corresponding grids using measured water depth points, and calculate the overall accuracy and the accuracy of water depth intervals.

[0023] Preferably, in step S1, the ICESat-2 photon data is processed sequentially as follows: separating seabed photons through kernel density estimation, multi-scale quadtree denoising, refraction correction, and tidal correction to obtain seabed signal photons; specifically, it includes the following sub-steps:

[0024] S11: Kernel density estimation (KDE) is used to separate surface photons from seabed photons. The mathematical expression for KDE is:

[0025] ;

[0026] in, Representative at point Estimated density at; It is the total number of sample data points; Represents a single data sample point; It is a kernel function; The bandwidth controls the width of the kernel and directly affects the smoothness of the estimated density. By calculating the KDE density curve, the nearest minimum point below the peak of the sea surface signal is selected as the segmentation threshold. Sea surface photons above this threshold are removed, and the set of seabed photons below this threshold is retained.

[0027] S12: Apply the DBSCAN clustering algorithm to remove discrete background noise, set the search radius and minimum number of contained points, and remove spatially highly discrete background noise.

[0028] S13: Perform multi-scale pre-judgment quadtree segmentation, construct a "track-elevation" two-dimensional plane window along the photon trajectory, recursively perform pre-judgment quadtree segmentation within the window, assign a hierarchical value representing the local density to each photon, and automatically calculate the optimal segmentation threshold within each window using the Otsu's method. This maximizes the inter-class variance between the segmented signal photons and noise photons, adaptively separating high-confidence underwater signal photons. The mathematical expression is as follows:

[0029] ;

[0030] in, Indicates the maximum layer value of photons; This represents the variance between classes.

[0031] Preferably, in step S1, the Sentinel-2 image is sequentially processed with the following steps: radiometric correction, atmospheric correction, cloud masking, and water extraction to obtain a cloudless shallow water image. The water extraction process for the Sentinel-2 image uses the Normalized Difference Water Index (NDWI), which is calculated using the following formula:

[0032] ;

[0033] in, and The optimal threshold is determined by analyzing the NDWI histogram, corresponding to the green band and near-infrared band reflectance of the image, respectively, and a binarized water mask is generated to ensure that subsequent processing is limited to shallow water.

[0034] Preferably, the process of constructing the initial control point ICP seed library in step S21 specifically includes the following sub-steps:

[0035] S211: Convert ICESat-2 photon data to the Sentinel-2 image projection coordinate system and calculate the image cell row and column number corresponding to each photon landing point;

[0036] S212: The average value of the water depth of all photons falling into the same pixel is used as the true value of the water depth of that pixel;

[0037] S213: Extract the spectral reflectance vectors of the blue, green, red, and near-infrared bands corresponding to the pixel, and standardize the spectral vectors to four decimal places to form the "spectral-depth" initial control point ICP seed sequence. ,in, Indicates a certain seed, This indicates the water depth for the seeds.

[0038] Preferably, the process of expanding the virtual control points in step S22 specifically includes the following sub-steps:

[0039] S221: Based on the assumption of optical homogeneity of water bodies, the L1 norm is used as a measure of spectral similarity.

[0040] S222: When the L1 distance between the target pixel and any initial control point seed is less than a preset tolerance threshold, the water depth of the seed is assigned to the target pixel to make it a virtual control point (VCP). The calculation formula is as follows:

[0041] ;

[0042] in, Represents band index, and These represent the target pixel and the seed pixel respectively in the 1st... The reflectivity value of the band;

[0043] S223: By traversing all pixels within the water mask of the entire image, the originally sparse and linearly distributed ICESat-2 samples are expanded into a high-density, area-distributed extended virtual control point (VCP) sample set covering the entire study area.

[0044] Preferably, the adaptive iteration strategy in step S23 specifically includes the following sub-steps:

[0045] S231: Select a series of candidate tolerance thresholds to form a threshold set;

[0046] S232: Generate a corresponding subset of virtual control points for each candidate threshold;

[0047] S233: Using independent ICESat-2 real water depth points that did not participate in the generation of virtual control points as a validation set, a temporary regression model is constructed to calculate the root mean square error between the predicted water depth and the real water depth of each candidate virtual control point VCP subset.

[0048] S234: Select the candidate threshold that minimizes the root mean square error as the optimal spectral matching tolerance threshold.

[0049] Preferably, step S3, which involves spatial spectral feature fusion and MLP training prediction, includes the following sub-steps:

[0050] S31: First, construct the joint feature vector of spatial spectrum, and assign row and column numbers to the feature pixels at spatial locations. Normalization is performed using the following formula:

[0051] ;

[0052] ;

[0053] in, and These represent the column number and row number of the cell, respectively. and These represent the width and height of the image, respectively.

[0054] S32: Combine the normalized spatial feature pixels with the four-band spectral reflectance vector to form a six-dimensional feature vector, and then perform standardization on it using the following formula:

[0055] ;

[0056] in, and These are the mean and standard deviation of the vectors in the training set, respectively. The same vectors are used in subsequent validation, testing, and full-image inversion stages. and Transform the data to prevent leaks.

[0057] Preferably, the multilayer perceptron (MLP) neural network topology in step S3 includes:

[0058] Network structure: Input layer → Fully connected layer → Dropout layer → Fully connected layer → Fully connected layer → Output layer; where the input layer corresponds to the dimension of the joint spatial-spectral feature vector, the fully connected layer uses the ReLU activation function, and the Dropout layer is used to suppress overfitting;

[0059] Training process: Mean squared error is used as the loss function, and the Adam optimizer is used to adjust the network parameters; the Adam optimizer is selected for training, and the mathematical expression for mean squared error is:

[0060] ;

[0061] in, Represents the total number of samples; Representing the The true water depth value of each sample; Representative model for the first The predicted water depth values ​​for each sample are obtained. After training, the optimal model weights are loaded into the network. Spatial spectral features are extracted from all water pixels in the target area and input into the model. Finally, the rasterized water depth inversion results with the same spatial resolution as the original image are output.

[0062] The neural network depth inversion system based on virtual control points described in this invention, applied to the neural network depth inversion method based on virtual control points, includes:

[0063] Data preprocessing module: performs noise reduction and correction on ICESat-2 photon data, and extracts cloud masks and water bodies from Sentinel-2 images;

[0064] Virtual control point construction module: Constructs an initial control point seed library, generates virtual control points through spectral similarity expansion, and performs adaptive threshold optimization;

[0065] Spatial-spectral fusion and neural network inversion module: Extracts joint feature vectors of spatial and spectral data, inputs them into a multilayer perceptron neural network for training, and generates water depth inversion results;

[0066] Accuracy verification module: Calculates the overall accuracy and the accuracy of water depth intervals using measured water depth points.

[0067] The computer-readable storage medium of the present invention stores a computer program, which, when executed by a processor, implements the steps of the neural network-based water depth inversion method based on virtual control points.

[0068] Compared with existing technologies, the neural network-based water depth inversion method, system, and medium of the present invention, based on virtual control points, exhibits the following beneficial effects in terms of technical performance and practical application:

[0069] 1. Sample Construction Dimension: To address the sparsity issue of ICESat-2 data and improve the accuracy of blank areas, existing technologies directly use sparse ICESat-2 bathymetric photons as training samples, failing to address the issue of blank areas distributed along the track. This invention expands sparse linear ICESat-2 samples into a high-density planar VCP dataset through an adaptive virtual control point (VCP) construction strategy (spectral similarity measurement + validation set RMSE minimization threshold optimization), effectively covering blank areas of the study area and significantly improving the inversion accuracy in areas without measured data.

[0070] 2. Feature Fusion Dimension: Adapting to spatial non-stationarity and enhancing adaptability to complex environments.

[0071] Existing technologies rely solely on spectral features, neglecting the spatial non-stationarity and spatial heterogeneity of water body optical properties, and failing to integrate spatial features. This invention fuses pixel spatial location features with spectral features to construct a joint spatial-spectral feature vector, constraining the impact of spatial heterogeneity (such as differences in sediment and changes in suspended matter) on the inversion results. This effectively constrains the spatial non-stationarity of optical parameters in nearshore water bodies (such as estuaries and aquaculture areas). It adapts to complex nearshore environments and enhances the model's adaptability to spatial variations.

[0072] 3. Model optimization dimensions: Enhance nonlinear fitting and noise resistance, and improve result stability.

[0073] Existing technologies employ random forest models, which lack nonlinear fitting capabilities and regularization mechanisms. This invention uses a multilayer perceptron (MLP) network with Dropout regularization to replace the linear model, significantly enhancing nonlinear fitting capabilities. By using mean squared error as the loss function and Adam as the optimizer, the nonlinear fitting ability and noise resistance of the model are enhanced, reducing the risk of overfitting and improving the stability of the results.

[0074] 4. Application Scenario Dimension: Expanding the application scope to scenarios where there is no actual measured data.

[0075] Existing technologies are not optimized for scenarios without actual measurement data and have limited generalization capabilities. This invention, through VCP sample expansion and spatial-spectral fusion, can still achieve high-precision water depth inversion in scenarios such as remote sea areas and vast shallow water areas without in-situ measurement data, providing reliable data support for marine resource development, ship navigation safety, and nearshore ecological monitoring, and has a wider range of applications.

[0076] In summary, this invention overcomes technical bottlenecks through triple optimization of samples, features, and models, significantly improving the accuracy, robustness, and applicability of shallow water depth inversion, and has significant engineering application value. Attached Figure Description

[0077] Figure 1 This is a flowchart of an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram of the VCP extraction process in an embodiment of the present invention; in the figure, (a) represents a schematic diagram of spatial registration between ICESat-2 photons and Sentinel-2 image pixels; (b) represents a schematic diagram of ICP distribution; and (c) represents a schematic diagram of VCP distribution.

[0079] Figure 3 This is a schematic diagram of the multilayer perceptron (MLP) neural network structure in an embodiment of the present invention; in the figure, (a) represents the input layer; (b) represents the hidden layer; and (c) represents the output layer.

[0080] Figure 4 This is a scatter regression analysis plot of the inversion results and measured data in an embodiment of the present invention. Detailed Implementation

[0081] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0082] Example 1:

[0083] like Figure 1 As shown, this embodiment discloses a neural network-based water depth inversion method based on virtual control points, including:

[0084] (1) Data preprocessing: The ICESat-2 photon data were processed sequentially as follows: seabed photons were separated by kernel density estimation, multi-scale quadtree denoising, refraction correction, and tidal correction to obtain high-confidence seabed signal photons; the Sentinel-2 images were processed sequentially as follows: radiometric correction, atmospheric correction, cloud masking, and water extraction to obtain cloudless shallow water images.

[0085] Due to factors such as atmospheric scattering, solar radiation, and instrument noise, ICESat-2 photon data contains a large amount of noise. To address this issue, this embodiment of the invention employs a quadtree denoising algorithm based on multi-scale analysis to extract high-precision ICESat-2 underwater signal photons. First, kernel density estimation (KDE) is performed to separate surface photons from seabed photons, the mathematical expression of which is shown in formula (1):

[0086] (1)

[0087] In the formula, Representative at point Estimated density at; It is the total number of sample data points; Represents a single data sample point; It is a kernel function; in this embodiment, a Gaussian kernel function is used. Bandwidth, the width of the control kernel, directly affects the smoothness of the estimated density. By calculating the KDE density curve, the nearest minimum point below the peak of the sea surface signal is selected as the segmentation threshold. Sea surface photons above this threshold are removed, while the set of seabed photons below this threshold is retained.

[0088] Secondly, a two-stage denoising strategy of "coarse-to-fine" is implemented on the seabed photon point cloud. First, the DBSCAN clustering algorithm is applied, setting the search radius and minimum number of contained points to remove spatially highly discrete background noise. Then, multi-scale pre-judgment quadtree segmentation is performed. This strategy constructs a "track-elevation" two-dimensional planar window along the photon trajectory, recursively performing pre-judgment quadtree segmentation within the window, assigning each photon a hierarchical value representing its local density. Within each window, the Otsu's method (maximum inter-class variance method) is applied to automatically calculate the optimal segmentation threshold. This maximizes the inter-class variance between the segmented signal photons and noise photons, as shown in formula (2):

[0089] (2)

[0090] In the formula, Indicates the maximum layer value of photons; This represents the inter-class variance. This step enables the adaptive separation of high-confidence underwater signal photons.

[0091] After obtaining pure underwater photons, tidal and refraction corrections are required. First, refraction correction is performed based on Snell's law, calculating the refraction angle using the photon incident angle parameter to reposition the horizontal coordinates and vertical elevation of each seabed signal photon, eliminating the refraction effect caused by air entering seawater. Second, tidal correction is performed using high-precision tidal models such as OTPS2 to unify the photon elevation to mean sea level (MSL), thereby obtaining accurate along-track depth control point data.

[0092] While processing the ICESat-2 data, this invention also needs to process Sentinel-2 L2A level multispectral imagery. Although the L2A product has undergone atmospheric correction, it is still necessary to use its QA60 band to construct a cloud mask and remove pixels marked as clouds and cirrus clouds. Subsequently, in order to accurately limit the inversion range, the Normalized Difference Water Index (NDWI) is used for land-water separation, and its calculation formula is shown in formula (3):

[0093] (3)

[0094] In the formula, and These correspond to the green band and near-infrared band reflectance of the image, respectively. The optimal threshold is determined by analyzing the NDWI histogram, and a binarized water mask is generated to ensure that subsequent processing is strictly limited to shallow water.

[0095] (2) Virtual control point construction: The initial control point ICP seed library is constructed by spatiotemporal matching of the preprocessed multi-source remote sensing data. Based on the spectral similarity measurement model and adaptive iteration strategy, the initial control point ICP seed library is expanded into a high-density virtual control point VCP dataset. Figure 2 The VCP extraction process was demonstrated. Figure 2 In the diagram, (a) shows a schematic diagram of spatial registration between ICESat-2 photons and Sentinel-2 image pixels; (b) shows a schematic diagram of ICP distribution; and (c) shows a schematic diagram of VCP distribution. This process aims to solve the problems of scarce measured water depth data and uneven distribution of ICESat-2 data, and to overcome the blindness of traditional interpolation methods.

[0096] First, an initial control point (ICP) seed library is constructed. ICESat-2 photon data is converted to the Sentinel-2 image projection coordinate system, and the row and column numbers of the image pixels corresponding to each photon landing point are calculated. Since ICESat-2 photon footprints are much smaller than Sentinel-2 image pixels, this embodiment aggregates data at the pixel level, calculating the average water depth of all photons falling within the same pixel as the true water depth value for that pixel, and extracting the four-band (blue, green, red, and near-infrared) spectral reflectance vector corresponding to that pixel. To improve seed robustness, the spectral vectors are standardized and retained to four decimal places. These determined "spectral-water depth" sequences constitute the ICP seed sequence. Subsequently, based on the assumption of optical homogeneity of water bodies—that is, water bodies with similar spectral responses within a certain geographical proximity tend to have similar water depths—this invention utilizes the L1 norm (Manhattan distance) as a similarity metric for sample expansion. When any target pixel... With a certain seed The L1 distance between them is less than the preset tolerance threshold. At that time, it is determined that the pixel is "spectrally similar" to the seed, and the water depth of the seed is determined. Assign the target pixel to become a VCP. The calculation formula is shown in formula (4):

[0097] (4)

[0098] In the formula, Represents band index, and These represent the target pixel and the seed pixel respectively in the 1st... The reflectivity value of the band.

[0099] By traversing all pixels within the water mask of the entire image, the originally sparse and linearly distributed ICESat-2 samples were effectively expanded into a high-density, area-distributed VCP sample set covering the entire study area. To ensure the quality of the expanded samples, this invention employs an adaptive iterative optimization strategy based on error analysis: First, a series of candidate tolerance thresholds are selected (e.g., in the range [0.001, 0.003] with a step size of 0.0005), forming a threshold set. Second, for each value in the threshold set... This process generates corresponding VCP subsets. Using a subset of independent ICESat-2 real depth points that were not involved in VCP generation as a validation set, a temporary regression model is constructed to calculate the root mean square error (RMSE) between the predicted and actual depths for each candidate VCP set. Finally, the RMSE of each group is compared, and the model that minimizes the RMSE of the validation set is selected. The value serves as the optimal extension parameter for this study area. Through this strategy, the present invention achieves an optimal balance between sample quantity (coverage) and quality (accuracy), ensuring the physical authenticity of VCP.

[0100] (3) Spatial-spectral feature fusion and MLP training prediction: Extract the multi-band spectral reflectance and spatial location features of the virtual control point VCP dataset, construct a six-dimensional spatial-spectral joint feature vector input to a multilayer perceptron MLP network with Dropout mechanism for supervised training, use geometric spatial location features to constrain the spatial non-stationarity of water body optical properties, and generate water depth inversion results of the target area through nonlinear regression.

[0101] Figure 3 The MLP network structure constructed in this invention is illustrated. In the figure, (a) is the input layer; (b) is the hidden layer; and (c) is the output layer. Traditional SDB models often assume that the "spectrum-depth" mapping relationship is fixed throughout the entire graph, ignoring spatial non-stationarity. To address this issue, this invention endows the model with "spatial awareness" by fusing spatial features. First, a joint spatial-spectral feature vector is constructed. The training samples in this study come from the aforementioned constructed VCP set. Each sample contains six-dimensional input features. and one-dimensional output labels (Water depth). The spectral characteristics are 4-dimensional, i.e. The four-band reflectance was normalized to the range [0, 1] by dividing by 10000 according to the L2A dimension; the spatial feature is 2-dimensional, that is, the row and column number of the pixel in the image. To avoid the dimensional differences of features dominating model training, they are first normalized to [0, 1], as shown in formula (5):

[0102] , (5)

[0103] In the formula, and These represent the column number and row number of the cell, respectively. and These represent the width and height of the image, respectively. Combined into a 6-dimensional feature vector. Subsequently, to enable the model optimizer to converge more efficiently, this study performs standardization (Z-score) on all input features, as shown in Equation (6):

[0104] (6)

[0105] In the formula, and These are the mean and standard deviation of the training set vectors, respectively. The same vectors are used in subsequent validation, testing, and full-image inversion stages. and Transformations are performed to strictly prevent data leakage.

[0106] The MLP network topology constructed in this embodiment is as follows: Input layer (6) → Fully connected layer (32, ReLU) → Dropout layer (p=0.3) → Fully connected layer (16, ReLU) → Fully connected layer (8, ReLU) → Output layer (1, Linear). During training, mean-square error (MSE) is used as the loss function, as shown in formula (7), and the Adam optimizer is selected. In order to improve the generalization ability of the model and prevent overfitting, early stopping and adaptive learning rate strategies are adopted during training.

[0107] (7)

[0108] In the formula, Represents the total number of samples; Representing the The true water depth value of each sample; Representative model for the first The predicted water depth values ​​for each sample are calculated. After training, the optimal model weights are loaded into the network, spatial spectral features are extracted from all water pixels in the target area and input into the model, and finally, a rasterized water depth inversion product with the same spatial resolution as the original image is output.

[0109] (4) Accuracy verification and analysis:

[0110] By extracting corresponding grids from measured water depth points, the accuracy of the water depth inversion results in this embodiment of the invention is verified, and the overall accuracy (Ri) is calculated. 2 Accuracy in terms of RMSE, MAE and water depth ranges (0~5m, 5~10m, 10~15m). Figure 4 The scatter regression analysis results of the inverted water depth results and the corresponding measured water depth data in the embodiments of the present invention are given to intuitively reflect the consistency and overall accuracy level between the inverted results and the measured data.

[0111] (5) Experimental results and comparative analysis:

[0112] To further objectively verify the effectiveness and superiority of the method proposed in this invention, Example 1 and Comparative Example 1 (CN120217826A: Active and Passive Satellite Shallow Water Depth Inversion Method; hereinafter referred to as the Existing Method) were set up to conduct comparative experiments in the same study area, the same hardware environment and the same dataset.

[0113] a. Experimental Environment and Evaluation Indicators

[0114] The experimental hardware environment consisted of an Intel Core i9-10900K CPU, 64GB of RAM, and an NVIDIA GeForce RTX 3090 GPU. The software environment used Python 3.8 and the deep learning framework PyTorch 1.9.

[0115] The evaluation metrics selected are the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²), which are commonly used in the field of water depth inversion. 2 ).

[0116] b. Experiment setup

[0117] Example 1 (Method proposed in this invention): The "spatial-spectral feature fusion + MLP neural network" method of this invention is adopted. The core lies in utilizing the nonlinear mapping capability of MLP to jointly input spatial location features and spectral features to directly predict water depth.

[0118] Comparative Example 1 (Existing Method): The "multi-band log-ratio model + IDW spatial interpolation" method is adopted. This method uses ICESat-2 and Sentinel-2 data to extract virtual control points, uses a multi-band log-ratio model to calculate the preliminary water depth, and then uses the inverse distance weighted algorithm (IDW) to perform spatial interpolation on the residuals of the virtual control points to obtain the inversion result.

[0119] c. Analysis of Experimental Results

[0120] The inversion results of Example 1 and Comparative Example 1 on the same dataset were compared with the measured water depth values. The experimental results are shown in Table 1:

[0121] Table 1. Comparison of accuracy of different methods

[0122]

[0123] d. Results Analysis and Conclusions

[0124] From Table 1 and Figure 4 Analysis shows that Example 1 is significantly better than Comparative Example 1 in all accuracy indicators, with RMSE reduced by approximately 35.9% and R... 2 The accuracy improved by 0.12. This indicates that although Comparative Example 1 compensated for the data gaps to some extent through IDW interpolation, its linear interpolation is inherently difficult to capture the nonlinear spatial variations of water optical properties under complex shallow sea topography. In contrast, this invention, by constructing an MLP neural network, can learn the complex nonlinear mapping relationship between "spectrum-space-water depth". In particular, by directly using pixel coordinates as spatial features in training, it endows the model with the ability to perceive spatial nonstationarity, thereby effectively solving the problem of insufficient accuracy of traditional physical models in complex regions and significantly improving the accuracy and robustness of water depth inversion.

[0125] Example 2:

[0126] The present invention also provides a neural network-based water depth inversion system based on virtual control points for implementing the method of Embodiment 1 above, comprising:

[0127] The data preprocessing module is used to denoise ICESat-2 photon data and perform cloud masking and water extraction on Sentinel-2 images.

[0128] The virtual control point construction module is used to construct an initial control point seed library by spatiotemporal matching of preprocessed multi-source remote sensing data, and expand it into a virtual control point dataset based on a spectral similarity measurement model and an adaptive iterative strategy.

[0129] The spatial-spectral feature fusion and MLP training prediction module is used to extract the joint spatial-spectral feature vector of the virtual control point dataset, input it into the multilayer perceptron network for training, and realize water depth inversion.

[0130] Accuracy Verification and Analysis Module: Extracts corresponding grids from measured water depth points and calculates the overall accuracy and the accuracy of water depth intervals.

[0131] Example 3:

[0132] The present invention also provides a computer-readable storage medium for implementing the method of Embodiment 1 above, storing a computer program, which, when executed by a processor, implements the steps of the neural network water depth inversion method based on virtual control points in Embodiment 1.

[0133] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A neural network-based water depth inversion method based on virtual control points, characterized in that, Includes the following steps: S1: Multi-source remote sensing data preprocessing: Denoising and correction of ICESat-2 photon data to obtain seabed signal photons, cloud masking and water body extraction of Sentinel-2 images to obtain cloudless shallow water images. S2: Virtual Control Point Construction: S21: Initial control point seed library construction: ICESat-2 photons are converted to Sentinel-2 image coordinate system, and the average value of photon water depth is taken as the true value by pixel as unit. The corresponding spectral reflectance is extracted to form the initial control point ICP seed library. S22: Spectral similarity extension: Calculate the spectral distance between the target pixel and the initial control point seed. When the distance is less than or equal to a preset threshold, assign the seed water depth to the target pixel to generate a virtual control point. S23: Adaptive Iterative Optimization: Determine the optimal threshold by minimizing the validation set accuracy index, balance the quantity and quality of virtual control points, and expand the initial control point ICP seed library into a high-density virtual control point VCP dataset; S3: Spatial-Spectral Feature Fusion and MLP Training Prediction: Extract multi-band spectral reflectance and spatial location features from the virtual control point dataset, and construct a joint spatial-spectral feature vector. The spatial-spectral joint feature vector is input into a multilayer perceptron (MLP) neural network with a Dropout mechanism for supervised training. Spatial location features are used to constrain the spatial nonstationarity of water body optical properties. Rasterized water depth inversion results with the same resolution as the original image are generated through nonlinear regression. S4: Accuracy Verification and Analysis: Extract corresponding grids from measured water depth points, and calculate the overall accuracy and the accuracy of water depth intervals; The process of constructing the initial control point ICP seed library in step S21 specifically includes the following sub-steps: S211: Convert ICESat-2 photon data to the Sentinel-2 image projection coordinate system and calculate the image cell row and column number corresponding to each photon landing point; S212: The average value of the water depth of all photons falling into the same pixel is used as the true value of the water depth of that pixel; S213: Extract the spectral reflectance vectors of the blue, green, red, and near-infrared bands corresponding to the pixel, and standardize the spectral reflectance vectors to four decimal places to form the "spectral-depth" initial control point ICP seed sequence. ,in, Indicates a certain seed, Indicates the water depth for the seeds; The process of expanding the virtual control points in step S22 specifically includes the following sub-steps: S221: Based on the assumption of optical homogeneity of water bodies, the L1 norm is used as a measure of spectral similarity. S222: When the L1 distance between the target pixel and any initial control point seed is less than a preset tolerance threshold, the water depth of the seed is assigned to the target pixel to make it a virtual control point (VCP). The calculation formula is as follows: ； in, Represents band index, and These represent the target pixel and the seed pixel respectively in the 1st... The reflectivity value of the band; S223: By traversing all pixels within the water mask of the entire image, the originally sparse and linearly distributed ICESat-2 samples were expanded into a high-density, area-distributed extended virtual control point (VCP) sample set covering the entire study area; The adaptive iteration strategy in step S23 specifically includes the following sub-steps: S231: Select a series of candidate tolerance thresholds to form a threshold set; S232: Generate a corresponding subset of virtual control points for each candidate threshold; S233: Using independent ICESat-2 real water depth points that did not participate in the generation of virtual control points as a validation set, a temporary regression model is constructed to calculate the root mean square error between the predicted water depth and the real water depth of each candidate virtual control point VCP subset. S234: Select the candidate threshold that minimizes the root mean square error as the optimal spectral matching tolerance threshold.

2. The neural network-based water depth inversion method based on virtual control points according to claim 1, characterized in that, Step S1 involves sequentially performing the following steps on the ICESat-2 photon data: separating seabed photons through kernel density estimation, multi-scale quadtree denoising, refraction correction, and tidal correction to obtain seabed signal photons; specifically, it includes the following sub-steps: S11: Kernel density estimation (KDE) is used to separate surface photons from seabed photons. The mathematical expression for KDE is: ； in, Representative at point Estimated density at; It is the total number of sample data points; Represents a single data sample point; It is a kernel function; The bandwidth controls the width of the kernel and directly affects the smoothness of the estimated density. By calculating the KDE density curve, the nearest minimum point below the peak of the sea surface signal is selected as the segmentation threshold. Sea surface photons above this threshold are removed, and the set of seabed photons below this threshold is retained. S12: Apply the DBSCAN clustering algorithm to remove discrete background noise, set the search radius and minimum number of contained points, and remove spatially highly discrete background noise. S13: Perform multi-scale pre-judgment quadtree segmentation, construct a "track-elevation" two-dimensional plane window along the photon trajectory, recursively perform pre-judgment quadtree segmentation within the window, assign a hierarchical value representing the local density to each photon, and automatically calculate the optimal segmentation threshold within each window using the Otsu's method. This maximizes the inter-class variance between the segmented signal photons and noise photons, adaptively separating high-confidence underwater signal photons. The mathematical expression is as follows: ； in, Indicates the maximum layer value of photons; This represents the variance between classes.

3. The neural network-based water depth inversion method based on virtual control points according to claim 1, characterized in that, In step S1, the Sentinel-2 image is sequentially processed with the following steps: radiometric correction, atmospheric correction, cloud masking, and water extraction to obtain a cloudless shallow water image. The water extraction process for the Sentinel-2 image uses the Normalized Water Index (NDWI), calculated using the following formula: ； in, and The optimal threshold is determined by analyzing the NDWI histogram, corresponding to the green band and near-infrared band reflectance of the image, respectively, and a binarized water mask is generated to ensure that subsequent processing is limited to shallow water.

4. The neural network-based water depth inversion method based on virtual control points according to claim 1, characterized in that, The spatial spectral feature fusion and MLP training prediction in step S3 includes the following sub-steps: S31: First, construct the joint feature vector of spatial spectrum, and assign row and column numbers to the feature pixels at spatial locations. Normalization is performed using the following formula: ； ； in, and These represent the column number and row number of the cell, respectively. and These represent the width and height of the image, respectively. S32: Combine the normalized spatial feature pixels with the four-band spectral reflectance vector to form a six-dimensional feature vector, and then perform standardization on it using the following formula: ； in, and These are the mean and standard deviation of the training set vectors, respectively. The feature vector is a six-dimensional vector, and the same one is used in subsequent verification, testing, and full-image inversion stages. and Transform the data to prevent leaks.

5. The neural network-based water depth inversion method based on virtual control points according to claim 4, characterized in that, The multilayer perceptron (MLP) neural network topology in step S3 includes: Network structure: Input layer → Fully connected layer → Dropout layer → Fully connected layer → Fully connected layer → Output layer; where the input layer corresponds to the dimension of the joint spatial-spectral feature vector, the fully connected layer uses the ReLU activation function, and the Dropout layer is used to suppress overfitting; Training process: Mean squared error is used as the loss function, and the Adam optimizer is used to adjust the network parameters; the Adam optimizer is selected for training, and the mathematical expression for mean squared error is: ； in, Represents the total number of samples; Representing the The true water depth value of each sample; Representative model for the first The predicted water depth values ​​for each sample are obtained. After training, the optimal model weights are loaded into the network. Spatial spectral features are extracted from all water pixels in the target area and input into the model. Finally, the rasterized water depth inversion results with the same spatial resolution as the original image are output.

6. A neural network-based water depth inversion system based on virtual control points, applied to the neural network-based water depth inversion method based on virtual control points as described in any one of claims 1-5, characterized in that, include: Data preprocessing module: performs noise reduction and correction on ICESat-2 photon data, and extracts cloud masks and water bodies from Sentinel-2 images; Virtual control point construction module: Constructs an initial control point seed library, generates virtual control points through spectral similarity expansion, and performs adaptive threshold optimization; Spatial-spectral fusion and neural network inversion module: Extracts joint feature vectors of spatial and spectral data, inputs them into a multilayer perceptron neural network for training, and generates water depth inversion results; Accuracy verification module: Calculates the overall accuracy and the accuracy of water depth intervals using measured water depth points.

7. A computer-readable storage medium, characterized in that, The device contains a computer program that, when executed by a processor, implements the steps of the neural network-based water depth inversion method based on virtual control points as described in any one of claims 1 to 5.

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