Photon Counting LiDAR Denoising Method Based on Improved DENCLUE

Abstract

Photon counting lidar denoising method based on improved DENCLUE, including selecting a research area and obtaining a global positioning point cloud data set of the research area; excluding noise points far from the sea surface; data segmentation: dividing the data set into four quadrants, calculating the number of point cloud data in each quadrant, if it is less than the noise point threshold, it is recorded as a noise point; if it is between the noise point threshold and the minimum clustering size, the point cloud in this quadrant can be subjected to improved DENCLUE clustering processing; if it is greater than the preset minimum clustering size, the quadrant is divided again until the previous two situations are met; using improved DENCLUE for denoising is to use the simulated annealing algorithm to determine the density core. This method has less dependence on parameters and has significant effects in the denoising of ICESat-2 data, providing an effective new method for shallow sea remote sensing water depth detection.

Description

Technical Field

[0001] The present invention relates to a photon counting lidar data denoising method based on improved DENCLUE, belonging to the technical field of lidar, especially the technical field of lidar data processing. Background Art

[0002] The shallow sea area, as a key base for global fisheries and a convergence area for numerous economic activities, including fisheries, maritime transportation, tourism, and recreational activities, plays a crucial role in the economic development of coastal areas. Precise, high-resolution, and continuous bathymetric surveys are recognized as key elements for coastal area management and are also of great importance for the protection and management of coral reefs. Since the first demonstration of the technology of airborne green-wavelength lidar for bathymetry in 1969, bathymetric lidar technology has become an indispensable tool for nearshore water area surveying and mapping.

[0003] With the continuous progress of water color remote sensing technology, retrieving nearshore shallow water depth information using hyperspectral satellite image data has become a widely applied technology. Lidar data has attracted much attention due to its high application value in the marine field, especially in applications such as shallow sea bathymetry and coral reef management. The ICESat-2 lidar satellite launched by the National Aeronautics and Space Administration (NASA) in September 2018 has shown significant application potential in the field of shallow sea bathymetry. Combining ICESat-2 and hyperspectral image data to retrieve nearshore water depth has become a hot research direction in the field of water color remote sensing. However, ICESat-2 data is affected by factors such as the atmosphere and the sea surface, and there are a large number of noisy data, which poses challenges to the accuracy and usability of the data and also limits its application in precise oceanography research. Therefore, how to effectively retain the sea surface point cloud and seabed point cloud data in ICESat-2 while removing the noisy points has become a crucial topic in this field.

[0004] Current spatial clustering methods, such as Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Ordering points to identify the clustering structure (OPTICS), perform well in denoising ICESat-2 data and have been widely used. Zhong et al. proposed a two-step denoising method combining the DBSCAN clustering algorithm and a two-dimensional window filter. First, the DBSCAN algorithm is used for preliminary denoising, and then the two-dimensional window filter is applied to further denoise the preprocessed underwater photon data. Gao et al. proposed an improved differential, regression, and Gaussian adaptive nearest neighbor filtering method to improve the denoising performance of photon cloud data by combining large-scale and small-scale search radii, effectively distinguishing signal photons and noise photons. Zhu et al. proposed an OPTICS algorithm with elliptical search and distinguished signal point clouds from noise by the maximum inter-class variance, achieving good denoising results for point cloud data in forest areas. Yin et al. proposed an adaptive OPTICS algorithm, which effectively improved the denoising accuracy of ICESat-2 laser photon data through rough denoising by histogram threshold and fine denoising by combining K-nearest neighbor and DBSCAN. Tang et al. proposed an innovative multi-level adaptive denoising algorithm. This algorithm first uses the OPTICS algorithm for preliminary denoising to eliminate randomly distributed noise photons; subsequently, according to the slope change of the forest terrain, the size of the elliptical search domain is automatically adjusted to perform refined denoising. Liu et al. proposed an adaptive clustering and kernel density estimation method, which adapts to the distribution characteristics of photons in ICESat-2 data by determining input parameters (the semi-major axis and semi-minor axis of the horizontal elliptical neighborhood, and the minimum number of points), and then uses the core distance and reachable distance values to determine the classification threshold to distinguish signal photons and noise photons. Zheng et al. proposed a filtering method combining density and distance, which removes low-density noise through an adaptive elliptical filter and then uses a distance-based filter to eliminate high-density noise clusters, thereby extracting pure seabed signal photons from ICESat-2 data.

[0005] Currently, the main spatial clustering denoising methods for lidar data such as ICESat-2 are the DBSCAN and OPTICS algorithms. However, the denoising effects of these two clustering methods depend on the selection of parameters, and different parameters produce different denoising effects. The DENCLUE algorithm does not depend on algorithm parameter settings and has shown sufficient accuracy and robustness in point cloud classification. In this invention, the traditional DENCLUE algorithm is improved, and the improved DENCLUE algorithm is applied to the denoising of ICESat-2 lidar data, effectively improving the denoising accuracy. Summary of the Invention

[0006] The object of the present invention is to provide a denoising method for photon counting lidar based on improved DENCLUE to overcome the deficiencies of the prior art.

[0007] The denoising method for photon counting lidar based on improved DENCLUE is characterized by including the following steps:

[0008] 1) Select a research area and obtain the global positioning point cloud data set of this research area;

[0009] 2) Exclude noise points far from the sea surface:

[0010] Directly identify the sea surface through the method of height frequency statistics, and classify the point cloud data within 5 meters above and 50 meters below the sea surface as noise point clouds;

[0011] 3) Data segmentation:

[0012] For the denoised data set, first determine the four upper, lower, left, and right boundaries of the data in the along-track distance and height, calculate the center point, divide the data set into four quadrants, and calculate the number of point cloud data in each quadrant;

[0013] If the number of point clouds in a certain quadrant is less than the preset noise point threshold noise_number, then mark all the point clouds in this quadrant as noise points;

[0014] If the number of point clouds in the quadrant is between noise_number and min_number, then the point clouds in this quadrant can be processed by improved DENCLUE clustering;

[0015] If the number of point clouds in a certain quadrant is greater than the preset minimum clustering size min_number, then divide this quadrant again to form four smaller quadrants, and repeat the statistics of the number of point cloud data in each quadrant until the previous two situations are met;

[0016] 4) Use improved DENCLUE for denoising:

[0017] Improved DENCLUE uses the simulated annealing algorithm to determine the density core.

[0018] In step 3), min_number is calculated by dividing the total number of data points in the point cloud by the maximum distance of the point cloud along the track direction, and the closest multiple of 5 is taken as the result, and this value does not exceed 50; while noise_number is half of min_number, and the closest multiple of 5 is also taken, and its maximum value is also limited within 50.

[0019] In step 4), for each data pointp i =( x i , y i ), the kernel density estimation is used to calculate its local density, and the Gaussian kernel function is adopted for the kernel density estimation. The formula is as follows:

[0020] (1)

[0021] Wherein, p j =( x j , y j ) are other points in the dataset, h is the bandwidth parameter; n is the total number of point clouds in the dataset;

[0022] After calculating the kernel density of each point, the simulated annealing algorithm is used to find the density attractor, and based on this, a new density estimate ρ is calculated; the simulated annealing algorithm accepts or rejects a new solution according to the Metropolis criterion in Formula 2 to find the global optimal solution or a solution close to the global optimal solution; wherein, Δρ is the energy difference - here it is the change in density, and T is the temperature parameter of simulated annealing; according to the Metropolis criterion, the calculated result of the probability P(accept) is between [0,1], indicating the probability of accepting a new solution; if P(accept)>0.5, that is, close to 1, the new solution is accepted; if P(accept)≤0.5, that is, close to 0, the new solution is rejected;

[0023] (2)

[0024] For each pair of density attractors p i and p j , by calculating the Euclidean distance between them and comparing it with the sum of their respective radii to determine whether they are adjacent; when the distance between two attractors does not exceed the sum of their radii, an edge is drawn between the corresponding nodes in the graph, symbolically connecting these two adjacent attractors; this process ultimately constructs a graph, where the nodes represent density attractors and the edges map the adjacency between them; as the construction of the graph is completed, further in-depth analysis is carried out to identify and define clusters.

[0025] The potential clusters are revealed by identifying each connected component in the graph, and each connected component may correspond to a cluster. Within each connected component, the center of the cluster is determined by finding the point with the highest density, and all points within this component are regarded as members of the same cluster.​​​​

[0026] In step 4), for ICESat-2 ATL03 data, the bandwidth h is automatically calculated by multiplying the standard deviation of the selected point cloud by 0.2.

[0027] The DENCLUE (Density Clustering) used in the present invention is an advanced clustering algorithm that relies on kernel density estimation to identify the clustering structure in the data. This algorithm defines clustering as the local maximum of the probability density function and assigns data points through a method called "hill climbing", so that all data points tending to the same local maximum are grouped into the same cluster. Unger et al. combined the core idea of the DENCLUE method through an improved DBSCAN algorithm to effectively extract geometric patterns such as traffic lanes from LIDAR point clouds. Experimental results show that this method is superior to existing clustering techniques in terms of accuracy and robustness.

[0028] The present invention proposes an improved DENCLUE algorithm that is less dependent on parameters and exhibits superior denoising performance when dealing with complex data sets. This method first performs frequency statistics on the data to identify and eliminate data in areas far from signal points; subsequently, the remaining data is partitioned to lay the foundation for the application of the simulated annealing algorithm, which replaces the traditional hill climbing method for denoising the partitioned data. By denoising and refraction correction of ICESat-2 data and performing accuracy comparison analysis with in-situ observed water depth data, the results show that the correlation coefficient between the denoised ICESat-2 data and the in-situ data exceeds 0.9, and the average relative error is less than 1%. These results indicate that the improved DENCLUE algorithm proposed by the present invention has a significant effect on denoising ICESat-2 data and provides an effective new method for shallow sea remote sensing bathymetry. Brief Description of the Drawings

[0029] Figure 1 It is a schematic diagram of ATL03 data of the Great Barrier Reef 1.

[0030] Figure 2 It is a schematic diagram of ATL03 data of the Great Barrier Reef 2.

[0031] Figure 3 It is a schematic diagram of ATL03 data of Ganquan Island.

[0032] Figure 4 It is a schematic diagram of ATL03 data of Oahu Island.

[0033] Figure 5 It is the flow chart of the improved DENCLUE algorithm.

[0034] Figure 6Schematic diagram of the data chunking method of the DENCLUE algorithm of the present invention.

[0035] Figure 7 It is a comparison chart of the denoising results of the Great Barrier Reef 1. Among them, (a) is the denoising result of the DENCLUE algorithm for the Great Barrier Reef 1, (b) is the denoising result of the DBSCAN algorithm for the Great Barrier Reef 1, and (c) is the classification result based on confidence for the Great Barrier Reef 1.

[0036] Figure 8 It is a comparison chart of the denoising results of the Great Barrier Reef 2. Among them, (a) is the denoising result of the DENCLUE algorithm for the Great Barrier Reef 2, (b) is the denoising result of the DBSCAN algorithm for the Great Barrier Reef 2, and (c) is the classification result based on confidence for the Great Barrier Reef 2.

[0037] Figure 9 It is a comparison chart of the denoising results of Ganquan Island. Among them, (a) is the denoising result of the DENCLUE algorithm for Ganquan Island, (b) is the denoising result of the DBSCAN algorithm for Ganquan Island, and (c) is the classification result based on confidence for Ganquan Island.

[0038] Figure 10 It is a comparison chart of the denoising results of Oahu Island. Among them, (a) is the denoising result of the DENCLUE algorithm for Oahu Island, (b) is the denoising result of the DBSCAN algorithm for Oahu Island, and (c) is the classification result based on confidence for Oahu Island.

[0039] Figure 11 Comparison chart of the accuracy analysis of the in-situ measured water depth. Among them, (a) is the accuracy evaluation result of the Great Barrier Reef 1, (b) is the accuracy evaluation result of Ganquan Island, and (c) is the accuracy evaluation result of Oahu Island. Detailed implementation manners

[0040] The following takes ICESat-2 data as an example to better illustrate the technical solution of the present invention.

[0041] 1. ICESat-2 data

[0042] The ICESat-2 satellite was launched by NASA on September 15, 2018, and completes an orbital cycle every 91 days, covering the latitude range from 88°N to 88°S globally. It is equipped with an advanced topographic laser altimeter system that uses photon counting technology to emit low-energy 532 nm blue-green light pulses at a frequency of 10 kHz. In addition, the pulse width of ATLAS is only 1.5 ns, the center spacing of the footprints is about 0.7 m, and the coverage area of each footprint reaches 17 m. The ATLAS system simultaneously emits three pairs of laser pulses, and the center spacing between adjacent pairs of laser pulses is 3.3 km. In each pair of laser pulses, there is a strong pulse and a weak pulse, the center spacing between them is 90 m, and the energy ratio is about 4:1.

[0043] Currently, ICESat-2 provides four levels of data products, including Level-1, Level-2, Level-3A, and Level-3B. These products combine raw telemetry data with highly processed products, providing researchers with a rich information resource. In particular, the Level-2 product, namely the ATL03 global positioning point cloud data set, details the point cloud data information, including latitude, longitude, and altitude, providing valuable data resources for high-precision measurement of the Earth's surface topography. This data can be downloaded from the NASA website at the link: https: / / search.earthdata.nasa.gov / search.

[0044] 2. Study Area

[0045] To ensure the reliability of the algorithms proposed in this study, the selection of the study area considered the following key factors: water depth conditions, terrain undulation, degree of human activity interference, and data acquisition time. Based on these criteria, this study finally selected Ganquan Island, the Great Barrier Reef, and Oahu as the experimental study areas. Specifically, the water depth in Area 1 of the Great Barrier Reef does not exceed 5 meters, the terrain is relatively flat, and it is basically not affected by human activities; the water depth in Area 2 of the Great Barrier Reef is less than 10 meters, the terrain has slight undulations, and the impact of human activities is small; the water depth of Ganquan Island does not exceed 15 meters, the terrain has obvious undulations, and it is less affected by human activities; the maximum water depth of Oahu can reach 20 meters, the terrain has significant undulations, and it is greatly affected by human activities. In addition, to evaluate the impact of data acquisition time on the results, this study specifically selected ATL03 data at different times:

[0046] Great Barrier Reef 1: ATL03_20230630070939_01542008_006_02.h5, as Figure 1 shown;

[0047] Great Barrier Reef 2: ATL03_20230408111340_02761908_006_02.h5, as Figure 2 shown;

[0048] Ganquan Island: ATL03_20220317202009_13071401_006_01.h5, as Figure 3 shown;

[0049] Oahu: ATL03_20230630154820_01602001_006_02.h5, as Figure 4 shown;

[0050] The specific trajectory distributions of the four groups of data are also as Figures 1-4 shown.

[0051] 3. In-situ Observation Data

[0052] In this study, in-situ bathymetry data was used for validation. Digital elevation model data of the Great Barrier Reef, lidar data of Waikiki Island and Ganquan Island, and multibeam bathymetry data of Wuzhizhou Island were obtained. The assessment data of the Great Barrier Reef in Australia is a high-resolution digital elevation model developed by Geoscience Australia, with a resolution of 30 meters. This dataset is based on years of ocean mapping and integrates shipborne multibeam and single-beam echo sounding data, airborne lidar bathymetry data, and satellite-derived bathymetry data collected from 2010 to 2020. Its elevation is based on the WGS-84 coordinate system. The Ganquan Island data is a synthetic product of lidar bathymetry data and multibeam bathymetry data. Among them, the lidar bathymetry data was obtained by the airborne Optech Aquarius bathymetry system at a flight altitude of approximately 300 m; the multibeam bathymetry data was obtained by the R2SONIC2024 shallow-water multibeam system, and the integrated bathymetry accuracy of the dataset is approximately 35 cm. The assessment data of Waikiki Island in the Hawaiian Islands comes from the shallow-water depth information obtained by Optech in 2013 using airborne lidar technology. This lidar system operates in the blue-green band at 532 nm, with a root mean square error of 0.3 m.

[0053] 4. Improved DENCLUE Denoising

[0054] 4.1 Overall Process

[0055] The point cloud data of the single-photon lidar system carried by the ICESat-2 satellite in the ocean area contains a large amount of noise data. The DENCLUE algorithm can adapt to complex data distribution structures and is particularly suitable for complex datasets where the natural data distribution may consist of multiple different density regions. This is especially important when dealing with datasets with non-uniform distributions, while DBSCAN and OPTICS may perform poorly on such datasets. Moreover, the DENCLUE algorithm is less sensitive to parameters, making it easier to adjust and use in practical applications. The DBSCAN algorithm is very sensitive to parameter selection, and although the OPTICS algorithm provides a method that does not require presetting the number of clusters, there are still certain difficulties in parameter selection. Therefore, in this invention, the DENCLUE algorithm is used to denoise ICESat-2. However, during the day, atmospheric scattering causes a particularly large number of noise points above the sea surface points, and it is difficult for spatial clustering to remove such noise. Therefore, the idea of frequency statistics and block classification is added to improve the accuracy of the DENCLUE clustering algorithm. After data partitioning, the original DENCLUE algorithm has difficulty completely removing the noise points near the seabed signal point cloud. Therefore, the DBSCAN algorithm is added to remove the noise point cloud that is difficult to remove around the signal point cloud to achieve the purpose of precise denoising. The overall process is as followsFigure 5 as shown

[0056] 4.2 Data Partitioning

[0057] The ICESat-2 ATL03 data contains a large amount of noise data, which is usually located in areas far from the sea surface and the seabed. At the same time, the amount of sea surface signal point cloud data is huge, and the sea surface undulation generally does not exceed 5 meters. The underwater detection ability of ICESat-2 usually does not exceed 50 meters. Therefore, the sea surface can be directly identified by the method of altitude frequency statistics, and the point cloud data within 5 meters above and 50 meters below the sea surface can be directly classified as noise point cloud.

[0058] After excluding the noise points far from the sea surface, the distribution of the remaining noise points shows a certain regularity. However, the effect of using the DENCLUE clustering algorithm to denoise these data is not ideal. In view of this, the present invention proposes a new method of data partitioning. By splitting the data, the signal point cloud in a small area shows an obvious structured distribution, so as to more effectively identify and remove noise points (as Figure 6 shown). The present invention first determines the four boundaries of up, down, left, and right of the data in the along-track distance and height, calculates the center point therefrom, and divides the data set into four quadrants. Then, the algorithm calculates the number of point cloud data in each quadrant. If the number of data in a certain quadrant is less than the preset noise point threshold (noise_number), then all the point clouds in that quadrant are marked as noise points. If the number of data is greater than the preset minimum clustering size (min_number), then the quadrant is divided again to form four smaller quadrants, and the number of point clouds in each quadrant is repeatedly counted. If the number of data in the quadrant is between noise_number and min_number, then the point clouds in that quadrant can be processed by the DENCLUE clustering. In this algorithm, min_number is calculated by dividing the total number of data points in the point cloud by the maximum distance of the point cloud along the track direction, and the closest multiple of 5 is taken as the result, but this value does not exceed 50. And noise_number is half of min_number, and the closest multiple of 5 is also taken, and its maximum value is also limited within 50. Such a setting aims to provide a dynamically adjustable threshold for the clustering algorithm to adapt to point cloud data of different scales and distributions.

[0059] 4.3 Improved DENCLUE

[0060] Since the present invention performs partitioning processing on data, in order to better process and adapt to the partitioning processing method, the present invention improves the DENCLUE algorithm to make it more adaptable to the data results of partitioning processing. Originally, the DENCLUE algorithm used the hill-climbing method to determine the density core, and the improved DENCLUE uses the simulated annealing algorithm to determine the density core. The simulated annealing algorithm helps the algorithm jump out of the local optimal solution, increases the possibility of finding the global optimal solution, and can effectively avoid falling into the local optimal solution.

[0061] For each data point p[i](xi, yi), kernel density estimation is used to calculate its local density. The kernel density estimation uses a Gaussian kernel function, and the formula is as follows:

[0062] (1)

[0063] where p[j](x j , y j ) are other points in the dataset, and h is the bandwidth parameter. For ICESat-2 ATL03 data, the bandwidth h is automatically calculated by multiplying the standard deviation of the selected point cloud by 0.2.

[0064] After calculating the kernel density of each point, we use the simulated annealing algorithm to find the density attractor and calculate the new density estimate ρ accordingly. The simulated annealing algorithm accepts or rejects new solutions according to the Metropolis criterion (Formula 2) to find the global optimal solution or a solution close to the global optimal solution. Among them, Δρ is the energy difference (here it is the change in density), and T is the temperature parameter of simulated annealing.

[0065] (2)

[0066] For each pair of density attractors p[i] and p[j], by calculating the Euclidean distance between them and comparing it with the sum of their respective radii to determine whether they are adjacent. When the distance between two attractors does not exceed the sum of their radii, draw an edge between the corresponding nodes in the graph to symbolically connect these two adjacent attractors. This process finally constructs a graph, where the nodes represent density attractors, and the edges map their adjacency.

[0067] With the construction of the graph completed, further in-depth analysis is carried out to identify and define clusters. The potential clusters are revealed by identifying each connected component in the graph, and each connected component may correspond to a cluster. Within each connected component, the center of the cluster is determined by finding the point with the highest density, and all points within this component are regarded as members of the same cluster.

[0068] 5. Precision Evaluation Method

[0069] In the present invention, the ICESat-2 data after denoising and refraction correction in three study areas are compared and analyzed with in-situ sounding data to evaluate the effect of data processing. The mean absolute error (MAE), root mean square error (RMSE), mean relative error (MRE), and coefficient of determination ( r 2 ) are calculated according to formulas (3) to (6).

[0070] , (3)

[0071] , (4)

[0072] , (5)

[0073] , (6)

[0074] where is the data inverted by ICESat-2; data, and n is the total number of point clouds.

[0075] where a is the data inverted by ICESat-2; b data, and n is the total number of point clouds.

[0076] 6. Denoising Results and Accuracy Evaluation

[0077] 6.1 Denoising Results

[0078] To verify the effectiveness of the present denoising method, the denoising results based on the improved DENCLUE are compared and analyzed with the denoising results of the DBSCAN algorithm and the classification results based on confidence. The results are as Figures 7-10As shown in the figure. The DENCLUE algorithm demonstrates its unique advantages. In the denoising results of the Great Barrier Reef 1, the signal points (red points) show a trend of gradually decreasing from about 50 meters to about 40 meters in elevation, forming a relatively obvious continuous banded distribution, while the noise points (black points) are more scattered and mainly distributed on both sides of the signal points. In the denoising results of the Great Barrier Reef 2, the signal points are mainly concentrated in the elevation range of about 50 meters, showing a relatively flat distribution, and the noise points are evenly distributed in elevation but with a small number. In the denoising results of Oahu, the DENCLUE algorithm also retains continuous seabed signal points, similar to the denoising results of the DBSCAN denoising algorithm. In the denoising results of Oahu, the signal points are distributed from 0 meters to about 50 meters in elevation, which is relatively flat as a whole, and the noise points are widely distributed in elevation but with a small number. Through these analyses, it can be seen that the DENCLUE algorithm can accurately identify and extract signal points, effectively remove noise interference, and retain the core features of the data when dealing with scenarios where the distribution of signal points is relatively continuous and has obvious characteristics. The performance of the DBSCAN algorithm significantly depends on two key parameters: the neighborhood radius and the minimum number of points. Improper parameter selection may lead to significant differences in the denoising results. To solve this problem, the present invention uses DBSCAN with appropriate neighborhood radii and minimum point clouds in four study areas to denoise the data. In the ICESat-2 ATL03 algorithm theory basis document, it is considered that when the point cloud confidence is 3 and 4, the point cloud can be considered as a signal point. Therefore, based on the classification results of confidence, the signal points are those with confidence 3 and 4, and the point clouds with confidence 0, 1, and 2 are noise points.

[0079] The denoising effects of the improved DENCLUE denoising algorithm and the DBSCAN denoising algorithm are significantly better than the classification results based on confidence. Especially the improved DENCLUE denoising algorithm shows better discrimination ability when dealing with the noise between sea surface points and seabed points, effectively avoiding the situation of misjudging noise as signal points. In addition, this algorithm can retain more signal point clouds in the case of less data volume or greater data depth, which is crucial for subsequent data analysis and processing. Under the condition that the noise points are densely distributed during the day, the DBSCAN algorithm tends to misclassify the noise-dense area as signal points, which limits its application effect in a high-noise environment. The above situation mainly occurs because the DENCLUE algorithm can effectively filter noise during the clustering process, especially in the case of uneven data distribution. Through partition processing, DENCLUE can perform clustering in a local area, thereby reducing the impact of noise on the overall clustering result. While in a high-noise environment, DBSCAN may misjudge noise as signal points, resulting in a decline in the clustering effect.

[0080] 6.2 Precision Evaluation

[0081] Since the data of the Great Barrier Reef 2 is located in the coral reef and the DEM changes rapidly, the data of this area is not used for evaluation during verification. To further verify the accuracy of this method, the denoised data of three study areas were refracted corrected and their accuracy was evaluated against the actually measured water depth data. When the laser pulse emitted by ICESat-2 penetrates the water body, refraction occurs according to Snell's law. Therefore, before evaluating the water depth accuracy, the ICESat-2 data must be refracted corrected. Currently, the most widely used refraction correction method for ICESat-2 data is the refraction correction technique based on the assumption of mean sea level proposed by Parrish et al. This study adopted this method for refraction correction. The actually measured water depth data of the three areas are all in the WGS-84 coordinate system, and the seabed point data of ICESat-2 in this coordinate system can be directly used for comparison.

[0082] When analyzing the data of the three study areas (as Figure 11 shown), most of the data closely fit the 1:1 line, showing high consistency of the data. Despite being affected by seawater characteristics, refraction correction, and topographic changes, the water depth data shows slight deviations. Especially in the Great Barrier Reef area, a small number of noise points remaining during the denoising process led to abnormal points in the accuracy evaluation. Nevertheless, the correlation coefficients between the refraction-corrected ICESat-2 data and the in-situ water depth data all exceed 0.9, indicating an obvious correlation. This result confirms the effectiveness of the improved DENCLUE denoising algorithm in retaining seabed signal points, and it can maintain high data accuracy and reliability even in complex marine environments.

[0083] 7. Conclusion

[0084] The present invention proposes an improved DENCLUE algorithm aimed at optimizing the data processing flow to improve the denoising performance. This method first performs frequency statistics on the data to identify and eliminate the data in the area far from the signal points; subsequently, the remaining data is subjected to partition processing, laying the foundation for the application of the simulated annealing algorithm, which replaces the traditional hill-climbing method for denoising the partitioned data. The improved DENCLUE algorithm is significantly superior to the DBSCAN algorithm and the confidence-based classification method in terms of denoising effect. It can not only effectively remove the noise between the sea surface points and the seabed points, but also better retain the sparsely distributed signal points, which is crucial for maintaining data integrity.

[0085] Through the evaluation of the bathymetric accuracy of the Great Barrier Reef, Ganquan Island and Oahu, it is found that for the denoising method proposed in the present invention, the average relative error between the seabed data and the in-situ measured data is less than 1%, the coefficient of determination exceeds 0.9, the mean absolute error is less than 1.0 m, and the root mean square error is less than 1.5 m. These accuracy evaluation indicators are significantly better than traditional denoising methods such as DBSCAN, which proves the effectiveness and reliability of the improved DENCLUE algorithm in the processing of high-precision ICESat-2 data.

Claims

1. Photon counting lidar denoising method based on improved DENCLUE, characterized by The following steps are involved: 1) Select the research area and obtain the global positioning point cloud dataset of the research area; 2) Eliminate noise points far from the sea surface: The sea surface is directly identified by the method of high frequency statistics, and the point cloud data within the range of 5 meters above the sea surface and 50 meters below the sea surface are directly classified as noise point clouds; 3) Data segmentation: For the denoised data set, first determine the upper, lower, left, and right boundaries of the data in terms of along-track distance and height, calculate the center point, divide the data set into four quadrants, and calculate the number of point cloud data in each quadrant; If the number of point clouds in a quadrant is less than the preset noise point threshold noise_number, all point clouds in the quadrant are marked as noise points; If the number of point clouds in a quadrant is between noise_number and min_number, the point clouds in the quadrant can be clustered using improved DENCLUE. If the number of point clouds in a quadrant is greater than the preset minimum cluster size min_number, the quadrant is divided again to form four smaller quadrants, and the number of point clouds in each quadrant is repeatedly counted until the previous two conditions are met; 4) Use improved DENCLUE for denoising: The improved DENCLUE uses a simulated annealing algorithm to determine the density core.

2. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 1, characterized in that In step 3), min_number is calculated by dividing the total number of data points in the point cloud by the maximum distance of the point cloud along the track, and the result is rounded to the nearest multiple of 5, and this value does not exceed 50; noise_number is half of min_number, and is also rounded to the nearest multiple of 5, and its maximum value is also limited to 50.

3. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 1, characterized in that In step 4), for each data point p [ i ]=( x i , y i ), use kernel density estimation to calculate its local density. The kernel density estimation uses the Gaussian kernel function, and the formula is as follows: （1）， in, p [ j ]=( x j , y j ) are other points in the data set, h is the bandwidth parameter; n is the total number of point clouds in the dataset; After calculating the kernel density of each point, the simulated annealing algorithm is used to find the density attractor and calculate the new density estimate ρ accordingly. The simulated annealing algorithm accepts or rejects the new solution according to the Metropolis criterion of formula 2 to find the global optimal solution or a solution close to the global optimal solution. Among them, Δρ is the energy difference, which is the change in density in this case, and T is the temperature parameter of the simulated annealing. According to the Metropolis criterion, the calculated result of the probability P(accept) is between [0,1], indicating the probability of accepting the new solution. If P(accept) > 0.5, that is, close to 1, the new solution is accepted. If P(accept) ≤ 0.5, that is, close to 0, the new solution is rejected. （2） For every pair of density attractors p [ i ]and p [ j ], by calculating the Euclidean distance between them and comparing it with the sum of their respective radii to determine whether they are adjacent; when the distance between two attractors does not exceed the sum of their radii, an edge is drawn between the corresponding nodes of the graph, symbolically connecting the two adjacent attractors; this process ultimately constructs a graph in which the nodes represent density attractors and the edges map the proximity between them; as the graph is constructed, clusters are identified and defined.

4. The photon counting laser radar denoising method based on improved DENCLUE as claimed in claim 3, characterized in that In step 4), for ICESat-2 ATL03 data, the bandwidth h is automatically calculated based on the standard deviation of the selected point cloud multiplied by 0.2.

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