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Abstract
The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) can obtain underwater elevation due to its strong penetration ability. However, the photons recorded by ICESat-2 include a large amount of noise that needs to be removed. Although density-based clustering methods can finish signal photon extraction, heterogeneous density and weak connectivity in photon data distribution impede their denoising performance, especially for sparse signals in deep water and drastic topographic change areas. In this paper, a novel fused denoising method based on the local outlier factor and inverse distance metric is proposed to overcome the above problems. The local outlier factor and inverse distance metric are calculated based on K-nearest neighbors (KNNs), taking into account not only the difference in density but also the directional uniformity of the data distribution. Using six trajectories under various seabed topographies, the proposed method is compared with state-of-the-art ICESat-2 photon denoising algorithms and official ATL03 results. The results indicate that the overall accuracy of the proposed method can surpass 96%, and the proposed method maintains higher recall but also has a lower false positive rate. Compared with the results of other methods, the proposed method can better adopt areas with abrupt topographic changes and deep water. The extracted signal strips are more unbroken and continuous. This study can contribute to pioneering a new perspective for ICESat-2 photon-counting data denoising research that is limited to using only density-based algorithms.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As a basic and essential geophysical parameter of the coastal environment, detailed and accurate shallow water depths are a main focus of navigation safety, ocean geomorphology, coral reef studies, and marine resource development [1–4]. With the development of remote sensing technology, satellite-derived bathymetry (SDB), based on in-situ bathymetry points as control points, is becoming a cost-effective way to rapidly and efficiently obtain large-scale and high-resolution bathymetry [5]. Most previous studies on SDB relied on high-precision in-situ water depth data that obtained from traditional measurement methods, including ship-based multibeam or single-beam sonar and airborne lidar [3,6–12]. However, these two techniques are generally time-consuming, labor-intensive, expensive, and difficult to use in dangerous and inaccessible areas that ships and aircraft cannot reach [2,13], which makes bathymetric control points extremely rare in many sea areas and hinders many coastal science, management, and engineering applications [14]. Fortunately, spaceborne lidar brought a novel opportunity for nearshore bathymetry, specifically, the successful launch of the Ice Cloud and Land Elevation Satellite-2 (ICESat-2) [14] was able to help overcome the existing challenges.
ICESat-2 which was launched on September 15, 2018, is the first spaceborne laser altimeter to be equipped with an advanced topographic laser altimeter system (ATLAS). ATLAS uses a green laser (532 nm) with a 10 kHz pulse repetition rate, obtaining continuous footprints of 17 m in diameter and an along-track sampling interval of 0.7 m [15,16]. In addition, ATLAS employs six beams arranged in three pairs, and the distance between the adjacent pair is approximately 3.3 km. Each pair contains strong and weak sub-beams with an energy ratio of 4: 1, and the distance between them is 90 m [15]. Although the primary goal of the ICESat-2 mission is measurements of sea ice freeboard and ice sheet elevation, previous studies have reported that shallow water bathymetry based on ICESat-2 ATL03 datasets is possible thanks to the water penetration capability of green lasers [14,17]. ICESat-2 ATL03 datasets can measure water depths up to 38 m in optically clear water [14,18]. However, due to the high detection sensitivity of photon-counting lidar, the received signals are greatly disturbed by water-column scattering and reflection, thus, it is necessary to identify noise photons and extract signals for subsequent bathymetric mapping.
The spatial characteristics and density distribution of photons differ significantly from those of other land surface types [19]. In photon-counting bathymetry, the density of the photons reflected by the water surface is higher than that in the water-column, and the density distribution of water-column photons becomes increasingly sparser with depth [20]. These distribution features have been attributed to heterogeneous density and weak connectivity which are challenging for signal identification. Heterogeneous density means that a cluster with uneven density is easily segmented into different parts and the sparse clusters are easily mistaken for noise, while weak connectivity makes it difficult to separate nearby clusters. As Chen et al. [20] and Leng et al. [21] noted, sparse signal photons in deep water tend to be identified as noise, and noise photons near the sea surface are difficult to extract because of weak connectivity. Therefore, resolving such problems is essential for ensuring and improving the accuracy of nearshore bathymetry. Unfortunately, few studies have considered the heterogeneous density and weak connectivity of ICESat-2 photon point cloud data in feature space. Currently, employing density-based clustering algorithms for ICESat-2 photon denoising is the main focus in most related works [4,21–26], but it is still insufficient to addressing the abovementioned challenges effectively using only the proximity of density. K-nearest neighbors (KNNs) are density-independent metrics that consider the directional uniformity of the data distribution [27,28]. However, there are few related works combining the outstanding characteristics of KNNs with the distribution pattern of ICESat-2 photon-counting data and applying it to photon point cloud denoising.
In this paper, a photon fusion denoising method based on the local outlier factor and inverse distance metric by calculating KNNs is proposed for the extraction of ICESat-2 signal photons. The advantage is to preserve the completeness of sparse signals since it utilizes KNNs that are irrelevant to the point density to search the neighboring points. To validate the effectiveness in different spatial and temporal conditions and water quality conditions, six trajectories of five study sites, including Dongdao Island, Shanhu Island, Huaguang Reef, Oahu Island, and Ailinginae Atoll, were selected for photon denoising. A multiple verification strategy based on in-situ bathymetry data and reference datasets obtained from ICESat-2 raw data, was utilized to quantitatively evaluate the photon extraction accuracy. Meanwhile, the denoising effect of the proposed method was compared with two density-based algorithms, including density-based spatial clustering of applications with noise (DBSCAN) and the clustering method of ordering points to identify the clustering structure (OPTICS). The ultimate purpose of this study is to explore whether the KNN-based algorithm can effectively extract signal photons, which is conducive to pioneering a new perspective for ICESat-2 photon-counting data denoising research limited to using the density-based algorithm.
2. Materials and methods
2.1 Study area
The Xisha Islands (also known as Paracel Islands), one of the four islands clusters in the South China Sea Islands, consists of the Yongle Islands and Xuande Islands. They are distributed in a sea area of more than 500000 $\textrm{k}{\textrm{m}^2}$, with a land area of approximately 10 $\textrm{k}{\textrm{m}^2}$. Our study area involves Shanhu Island, Huaguang Reef, and Dongdao Island. Shanhu Island (Fig. 1(c)) is located at 16°32′ N and 111°36′ E in the northwest of the Yongle Islands, which is 800 m long from east to west and more than 400 m wide from north to south. The island is slightly square and nearly elliptical, with an area of approximately 0.31 $\textrm{k}{\textrm{m}^2}$. Huaguang Reef (Fig. 1(b)), located within 16°09′ N - 16°17′ N and 111°34′ E - 111°49′ E, is one of the large atolls in the Xisha Islands. Dongdao Island (Fig. 1(d)), 16°40′ N and 112°44′ E, is east of the Xuande Islands. The island is a long strip with a length of approximately 2.4 km and a width of about 1 km. With a land area of approximately 1.7 $\textrm{k}{\textrm{m}^2}$, it is the second largest island in the Xisha Islands.
Fig. 1. The distribution of the study area selected (a. Location of five study sites; b. Huaguang Reef; c. Shanhu Island; d. Dongdao Island; e. Ailinginae Atoll; f. Oahu Island. The dotted lines in each study site and the green points in (c) represent the ICESat-2 trajectories used in this study and in-situ bathymetry data from Dongdao Island respectively)
Oahu Island (Fig. 1(f)), 21°26′ N and 158°00′ W, is positioned in the northwestern part of the Hawaiian Islands. The island is the third largest island in the Hawaiian Islands with an area of 1574 $\textrm{k}{\textrm{m}^2}$ and is the political, economic, cultural, and transportation center of the U.S. state of Hawaii.
Ailinginae Atoll (Fig. 1(e)) is one of 34 coral atolls in the Republic of the Marshall Islands, located at 11°10′ N and 166°20′ E in the north of the Ralik Chain Islands. The entire atoll is 27 km wide and 9 km wide, which is surrounded by coral reefs. The atoll is made up of 25 islets with a total area of 2.8 $\textrm{k}{\textrm{m}^2}$.
The five study sites have a variety of topography, and geomorphology, as well as different maximum water depths. Furthermore, the water quality in these regions was not only clear but also turbid. Thus, the study area selected is suitable for verifying the applicability and effectiveness of the algorithm.
2.2 Data
2.2.1 ICESat-2 ATL03 datasets
ATLAS is a highly sensitive photon-counting lidar system that transmits a green (532 nm) laser to penetrate water, making it possible to directly obtain weak signals reflected by underwater terrain through a satellite platform [29]. ATL03 data are ICESat-2 Level-2 global geolocated photon products and comprise six “gtx” groups (GT1L, GT1R, GT2L, GT2R, GT3L, GT3R). In ATL03, all photons recorded by ATLAS are expressed in latitude, longitude, arrival time, and ellipsoid height (based on the WGS84 ellipsoid benchmark) [30]. Due to carrying the sensitive detector, the photons of ATL03 raw data are extremely noisy; therefore, the “signal_conf_ph” dataset is given to each photon signal or noise label in the ATL03 file. With higher confidence (from 0 to 4), the photon is more likely a signal. Nevertheless, the result is rough and not suitable for SDB as control points [30,31].
Finally, considering the availability of in-situ bathymetry data and the quality of ICESat-2 data, six trajectories of ICESat-2 ATL03 data were selected to estimate the denoising performance of the proposed method. Table. 1 shows the details of the selected trajectories. Notably, only strong beam is employed for research due to its higher emission energy [30], resulting in a denser photon distribution compared to weak beam. Weak beam exhibits an extremely sparse photon distribution that makes it challenging to accurately reflect the true water depth even after noise removal. Consequently, prioritizing noise denoising for strong beam's photons is of greater value [21].
Table 1. Details of the ATLAS trajectories used in this study
2.2.2 Reference datasets of ICESat-2 by visual interpretation
To test the performance and accuracy of different methods, a multi-perspective verification strategy combining in-situ bathymetry data (see Section 2.2.3 for details) and visual interpretation reference data was applied.
Therefore, accurate reference data was produced to quantitatively evaluate the results acquired from the proposed method. By analyzing the distribution characteristics of the raw data, it was found that there are two dense lines (Fig. 2(a)). Many related works have confirmed that the photons on the straight line and the photons on the curve are sea surface photons and seafloor photons respectively, while the other photons are noise [14,17,20,21,26,32–35]. Hence, provided that the integrity and continuity of these two lines remain assured, the reference data extracted can be effectively utilized as a validation dataset [25,31]. In addition, to mitigate the potential impact of subjectivity on the extraction of reference data, the photons of official data (confidence level of 4) were incorporated as a fundamental criterion for reference data selection. According to the strategy above, signal photons of ICESat-2 are extracted by visual interpretation, and reference datasets of six trajectories are generated finally. An example of the classification results of the reference data is shown in Fig. 2(b).
Fig. 2. ATL03 raw data points distribution and reference data (a. the distribution of ATL03 raw data; b. example of the classification results of the reference data)
2.2.3 In-situ bathymetry data
Due to limitations in data access, only the in-situ data of Dongdao Island were used for accuracy assessment. In 2012, the First Institute of Oceanography, Ministry of Natural Resources, conducted a scientific survey in the South China Sea, and accumulated more than $3 \times {10^4}$ in-situ water depth points in the nearshore area of Dongdao Island with shipborne single-beam echosounder (Fig. 1(d)). The in-situ data have a centimeter-level error in this area and better spatial resolution (footprint diameter ≈ 10 m) than ICESat-2/ATLAS, making it suitable for accuracy verification. In addition, because the location of the in-situ bathymetry points does not correspond exactly to the signal photons extracted by ATL03, a raster map (10 m × 10 m) of in-situ bathymetry points is generated using kriging interpolation. Kriging interpolation is a widely used geospatial tool for estimating values at unknown locations, and has been confirmed that the method typically demonstrates high accuracy in geographic space [36]. Furthermore, cross validation was conducted by reserving a portion of the known data as a validation set to ensure accuracy of interpolation map. Finally, the pixel values of the raster map are extracted based on the coordinates of ICESat-2 signal photons for comparison [21,33].
2.3 Methods
ICESat-2 photon-counting data are characterized by heterogeneous density and weak connectivity. Heterogeneous density is epitomized by the different densities between the photons reflected by the water surface and the photons in the water-column. Weak connectivity is described by sparse photons as the water depth increases. These two characteristics make it difficult to remove noise photons near the water surface and extract deep water signals. Using the proximity of distance or density alone cannot solve the abovementioned problems effectively. Hence, an optimization denoising method based on density-distance fusion (Fig. 3) was proposed to overcome this issue. The proposed method mainly consists of three steps: (1) estimate k and the threshold; (2) calculate the local outlier factor of photons; and (3) calculate the inverse distance metric of photons.
2.3.1 Denoising based on the local outlier factor
ICESat-2 photon-counting data contain different kinds of outliers. Taking a global view of the dataset, many photons significantly deviate from the cluster, which can be regarded as global outliers. There are another kind of outliers due to scattering. These photons are outlying relative to their local neighborhoods, but they are relatively close to their neighboring signal photons, which are viewed as local outliers (Fig. 4).
The local outlier factor (LOF) computes the outlierness degree of each photon to identify the noise photon, and the outlierness degree refers to the relative density of the photons [37]. LOF starts by calculating the distance of k-nearest neighbor photons (Eq. (1)).
However, the sparse signal photons in deep-water areas still have a relatively small density, and the sparse signal photons are easily identified as noise. Hence, to accurately extract the signal photons, the local density relative to neighboring photons needs to be measured. The LOF is defined in terms of local relative density (Fig. 6(a)). The local relative density (local outlier factor) of the central photon is the average ratio of the local reachable density of the k-nearest neighbors of p to the local reachable density of the central photon (Eq. (4)).
Following the above formulae, the local outlier factors of all photons can be calculated. Then, the LOF threshold is estimated by computing the average LOF value of the k-nearest neighbors of each photon, and the average LOF values are sorted in ascending order. Next, an empirical confidence level (95%) is selected, and the average LOF of the top KNN percentile is determined as the LOF threshold. Any photon with an LOF value greater than the threshold is considered a noise, otherwise, it is a signal.
2.3.2 Denoising based on the inverse distance metric
After denoising based on the local outlier factor, there is still some edge noise in the seafloor. Therefore, a denoising method based on the inverse distance metric (IDM) is adopted to remove part of the edge noise (Fig. 6(b)). Similarly, the method based on the inverse distance metric also depends on KNN. The core idea of the method is to calculate the reciprocal of the sum of the distance between the central photon (p) and its KNNs (Eq. (5)).
Eventually, the IDMs of all photons are obtained. Similarly, the IDM threshold is estimated by computing the average IDM value of the k-nearest neighbors of each photon. If the photon is smaller than the threshold, the photon is labeled noise; otherwise, it is a signal.
2.3.3 Parameter k estimation
There is a controllable parameter k, which determines the photon number of nearest neighbors. For the value of k, excellent extraction performance needs to adopt an appropriate k value. A low k value means increased random errors, while an excessively high value of k makes distant and irrelevant photons affect the results. Although existing studies believed that k is an insensitive parameter in general [27], Zhang et al. [38] proposed that it is essential to select an appropriate k when the sample points are highly overlapped. In ICESat-2 photon-counting data, many photons are so close together that they almost overlap, especially in extremely shallow water areas where water and land coexist [39]. In this case, an optimized k is needed to separate land and sea. Therefore, this study employed the algorithm proposed by Zhang et al. [38], and the algorithm used the concept of validity rating to quantify the degree to which a data point resembles its KNNs. The specific process of the algorithm can be found in Zhang et al. [38].
2.3.4 Accuracy evaluation
To quantitatively evaluate the denoising accuracy, both visual interpretation reference data and in-situ bathymetry data are used. Based on reference data, overall accuracy (OA), precision (P), recall (R), F-measure (F), and false positive rate (FPR) are adopted. These metrics are calculated as follows:
where TP is the number of true signal photons that are correctly detected, TN is the number of true noise photons that are correctly detected, FP is the number of noise photons misclassified as signal photons, and FN is the number of signal photons misclassified as noise photons. In general, when OA, P, R, and F are higher and FPR is lower, the performance is better.Based on in-situ bathymetry data, the coefficient of determination (${R^2}$), root mean square error (RMSE), mean relative error (MRE), and mean absolute error (MAE) are computed according to Eq. (11)-Eq. (14).
3. Results
3.1 Visual comparison of denoising results
To examine the denoising effect of the proposed method intuitively, DBSCAN and OPTICS, which are density-based clustering algorithms, were employed for comparison with the proposed method. In addition, the ATL03 result (confidence level = 4) was also used to compare with the proposed method. Since the probability of photons being classified as signals is positively associated with its confidence level and photons of confidence level of four is more likely to be signals. Figures 7–12 show the results obtained by all methods in different terrain complexity. To be clear, seafloor photons can effectively reflect the topography of the seafloor, hence, this phenomenon was utilized to distinguish varying levels of topographic complexity based on the number of fluctuations observed in the seafloor photon line. Figures 7–9 represent the extraction results under complex terrain and Fig. 10–12 represent the extraction results under simple terrain. Considering that terrain complexity and water depth are the essential factors affecting ICESat-2 photon-counting data denoising, the extraction results of all methods are analyzed in detail from these two aspects.
3.1.1 Comparison of denoising results for varied terrain
Figures 7–9 and Figs. 10–12 show the denoising results of the four methods in different terrain complexity, with the former (Figs. 7–9) representing relatively complex terrain and the latter (Figs. 10–12) representing relatively simple terrain. Overall, the proposed method outperformed other methods on six datasets. Visually, DBSCAN and OPTICS cannot completely remove the noise photons, especially photons near the sea surface, while the proposed method removes most of the noise photons. Compared with the three algorithms, the ATL03 results were less satisfactory, which retained more abundant noise photons and hardly recognized signal photons in the case of dense noise (Fig. 7(a)) or deep-water areas (Fig. 12(a)).
Moreover, DBSAN and OPTICS accomplished the extraction of complex terrain signal strips in shallow water (<10 m) of Shanhu Island (Fig. 8), but for Dongdao Island and Huaguang Reef (in black ellipses of Fig. 7(b)-(c) and Fig. 9(b)-(c)), it was difficult for both algorithms to extract a complete continuous signal strip at the location of abrupt topographic changes. Instead, the proposed method achieved this (black ellipses of Fig. 7(d) and Fig. 9(d)). For areas with relatively simple terrain (Figs. 10–12), all three algorithms almost accomplished the extraction of complete signal strips in shallow water (<10 m), but DBSCAN and OPTICS made it easier to retain noise photons near the sea surface. What’s more, DBSCAN and OPTICS easily misidentified sparse signal photons of the sea surface as noise (orange ellipses of Fig. 10(b)-(c) and Fig. 11(b)-(c)).
3.1.2 Comparison of denoising results for different water depths
As the water depth increases, the number of photons received by the sensor gradually decreases, and the photon point cloud is correspondingly sparse due to the attenuation of light in the water [10]. Obviously, the proposed method eliminates most of the noise photons effectively. The extraction result of the proposed method takes into account the identification of dense signals near the water surface and sparse signals in deep water (green ellipses of Fig. 8(d) and Fig. 12(d)). However, in the green ellipses of Fig. 8(b)-(c) and Fig. 12(b)-(c), when the water depth exceeded 15 m, DBSCAN and OPTICS failed to extract deep-water signal photons completely, and almost all of these signals were removed as noise, losing extremely valuable bathymetric information about the deep-water area.
3.2 Multiple verification strategy of the extraction accuracy
3.2.1 Accuracy assessment based on reference datasets
Based on reference datasets via visual interpretation, the results of three algorithms and ATL03 were quantitatively evaluated first. The results for the evaluation indicators are shown in Tables. 2–7. All evaluation indicators of the proposed method are better than those of the other algorithms and better than the denoising results of ATL03. Therefore, the proposed method showed superior performance in the quantitative evaluation. Specifically, the OA and P of the proposed method are both higher than 96%. As mentioned in Section 2.3.4, R refers to the proportion of the recognized signal photons to the actual signal photons, and FPR refers to the proportion of the recognized noise photons to the actual noise photons. High R and low FPR show better denoising performance. However, it was found that DBSCAN and OPTICS had relatively high R in some sea areas (Huaguang Reef and Ailinginae Atoll), while they both had high FPR, which indicated that these two algorithms could not effectively remove part of the noise photons. In particular, the noise photons near the water surface were misidentified as signals, which also corresponded to Fig. 9(b)-(c) and Fig. 12(b)-(c). In contrast, the R values of the proposed method are higher than 96%, and the FPR values are significantly lower than the others. Having a high R while maintaining a low FPR in most cases further displayed the denoising advantage of the proposed method.
Table 2. Overall evaluation indicators for four methods of 20181116 in Dongdao Island
Table 3. Overall evaluation indicators for four methods of 20190222 in Shanhu Island
Table 4. Overall evaluation indicators for four methods of 20220109 in Oahu Island
Table 5. Overall evaluation indicators for four methods of 20220114 in Huaguang Reef
Table 6. Overall evaluation indicators for four methods of 20220715 in Huaguang Reef
Table 7. Overall evaluation indicators for four methods of 20220908 in Ailinginae Atoll
Notably, although the P, R, and FPR of the ATL03 results in some sea areas were perfect, this is because of excessive or insufficient denoising [40]. In Fig. 7(a), the ATL03 result recognized all the photons as noise photons except the sea surface photons, resulting in P = 100% and FPR = 0; furthermore, in Figs. 8(a), 9(a), 10(a), 11(a), and 12(a), the ATL03 result identified most of the noise photons near the sea surface as signal photons, resulting in R = 100%.
3.2.2 Accuracy assessment based on in-situ bathymetry data
To further validate the bathymetric accuracy of the proposed method, the in-situ data near Dongdao Island and ICESat-2 bathymetry data (namely, 20181116GT3R) calculated by following the method in Section 2.3 were utilized for correlation analysis. Figure 13 and Table. 8 show the bathymetric results obtained by the three algorithms. The ${R^2}$ of the proposed method was higher than those of DBSCAB and OPTICS, reaching above 0.90, and the corresponding slopes were 0.98, 0.87, and 0.74. This result indicated that the refraction corrected ICESat-2 bathymetry acquired by the proposed method had a stronger correlation with in-situ bathymetry. Furthermore, in Fig. 9 and Table. 8, it was found that the ICESat-2 bathymetry extracted by the proposed method had almost no outliers and higher accuracy, with 1.21 m RMSE and 0.84 m MAE. In conclusion, the bathymetry control points obtained by the proposed method could be used for SDB mapping.
Fig. 13. Scatterplots of ICESat-2 extracted depth and in-situ depth for different algorithms (a. DBSCAN; b. OPTICS; c. the proposed method)
Table 8. Accuracy and validation of photon-counting bathymetry
3.3 Photon extraction accuracy of different water depths
To compare the denoising capabilities of different algorithms at different water depths, the extraction accuracy of photons at different water depths was calculated, as shown in Fig. 14 below. The OA, P, and R of all the methods almost reached more than 97% in different sea areas when the water depth was less than 5 m; moreover, the FPR of the other two algorithms and the ATL03 denoising results were almost higher than that of the proposed method, which further and adequately demonstrated that the proposed method could effectively remove noise photons near the sea surface, while the other methods could not do the same.
Fig. 14. Quantitative evaluation of the performance of four methods at different water depths ((a)-(c) represent the result of <5 m, 5-10 m, and >10 m in Dongdao Island; (d)-(f) represent the result of <5 m, 5-10 m, and >10 m in Shanhu Island; (g)-(i) represent the result of <5 m, 5-10 m, and >10 m on 20220715 in Huaguang Reef ; (j)-(l) represent the result of <5 m, 5-10 m, and >10 m in Oahu Island; (m)-(o) represent the result of <5 m, 5-10 m, and >10 m on 20220114 in Huaguang Reef; (p)-(r) represent the result of <5 m, 5-10 m, and >10 m in Ailinginae Atoll)
Furthermore, the P, R, F, and OA of all results decreased gradually as depth increased. When the water depth was greater than 10 m, the FPRs of DBSCAN and OPTICS were lower than that of the proposed method, but the proposed method always had higher recall than the other algorithms. The reason was that when the depth was greater than 10 m, the signal photons were significantly sparse, and DBSCAN and OPTICS hardly recognized the signal photons of the deep seabed, resulting in identifying all of them as noise photons, such as Dongdao Island and Ailinginae Atoll. Therefore, FPR was relatively low and even tended to be 0. However, the proposed method could effectively identify the sparse photons in deep water areas, which caused a certain error rate.
4. Discussion
Based on the above results, it can be seen that the proposed method can always complete the extraction of sparse signal photons in deep water with satisfactory accuracy. This is because the proposed method takes into account the heterogeneous density and weak connectivity of ICESat-2 photon-counting data. As mentioned above, there are two important prior knowledge characteristics for the ICESat-2 photon distribution: one is that the density between signal photons and noise photons is different, and the other is that the seafloor signals gradually become sparser as the depth increases [4,14,17,20,21,26,32–34]. In previous studies, DBSCAN and OPTICS, which are both density-based algorithms were used extensively for photon denoising of ICESat-2 point data [22,26,32,41]. For density-based methods, the number of points within the neighborhood of each point is defined as its density and cluster circular neighborhoods of connected points whose densities are greater than the threshold [42,43]. Although these two algorithms excel in detecting signal photons and noise photons, they easily misidentify sparse clusters as noise (Figs. 15 and 16) and even split an entire cluster when the points are unevenly distributed [21,33].
Fig. 15. Comparison of extraction result using different methods in Shanhu Island ((a) result of DBSCAN; (b) result of OPTICS; (c) result of the proposed method)
Fig. 16. Comparison of extraction result using different methods in Ailinginae Atoll ((a) result of DBSCAN; (b) result of OPTICS; (c) result of the proposed method)
The proposed method takes into account not only the density differences in photon-counting data, but also the differences in its direction. First, the local outlier factor measures the anomaly of photon points not by its absolute local density but by its relative density to neighboring photon points. This has the advantage of allowing for unevenly distributed data with varying densities [44]. Then, the local outlier factor and inverse distance metric utilize KNNs to search the neighboring photons that are irrelevant to the photon density and can measure directional uniformity. Specifically, signal photons of the water surface and signal photons reflected by the seabed include neighboring photons within a certain direction range, while noise photons in the water column are likely to be surrounded by KNNs in all directions. Therefore, noise photons have large local outlier factors and a small inverse distance metric. Eventually, the proposed method could effectively extract sparse signal photons in deep-water areas and ensure the integrity of the signal strip in regions with abrupt topographic changes.
Nevertheless, this study is not without its shortcomings. Figures 8 and 10 present a challenge in distinguishing photons located between the seafloor and the sea surface. The close proximity of these photons to the signal photons makes it a formidable task for the algorithm to effectively discriminate between noise and signal. Additionally, in deep-water regions, particularly those exceeding 15 m in depth, the proposed algorithm occasionally misidentifies noise photons as signals (Fig. 12) or misidentifies signal photons as noise (Fig. 10).
5. Conclusions
This study proposed a density-distance fusion denoising method using the local outlier factor and inverse distance metric, which contemplated the heterogeneousness and complexity of the ICESat-2 photon distribution in the feature space. Six ATL03 datasets with different topographic characteristics and maximum depths were selected for experiments and validation. Comparing with the results generated by DBSCAN and OPTICS, the proposed method could precisely extract complete signal strips in regions with drastic topographic changes and identify signal photons with only a small amount of edge noise in deep-water areas. For the accuracy evaluation results based on reference data, the OA of the proposed method was significantly higher than that of other methods, and the proposed method could maintain a higher R but also have a lower FPR; for the regression analysis based on in-situ bathymetry, ${R^2}$ and RMSE are 0.90 m and 1.21 m, respectively, which showed that the signal photons extracted by the proposed method could be used as control points for SDB mapping. Finally, the results of the extraction accuracy at different water depths indicated that although the performance of all methods in extracting signal photons decreases with increasing water depth, the proposed method was always superior to the other methods. As an earlier denoising work based on KNNs, this study broke the limitation of only using density-based algorithms for photon-counting data, and this study contributes to a novel idea for future research on ICESat-2 denoising.
Funding
Shandong Natural Science Foundation (ZR2022QD104, ZR2023QD113); Qingdao Natural Science Foundation (23-2-1-73-zyyd-jch); Shandong Postdoctoral Innovation Project (SDCX-ZG-202202041); Open Research Fund Program of LIESMARS (22E01); National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology Open Fund.
Acknowledgments
We thank the National Aeronautics and Space Administration (NASA) for providing ICESat-2 data used in the article. More importantly, sincere thanks to the anonymous reviewers and members of the editorial team for the comments and contributions.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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