Surface water level extraction method based on SWOT satellite pixel cloud product

Abstract

The invention discloses a surface water level extraction method based on an SWOT satellite pixel cloud product. The surface water level extraction method comprises the following steps: S1, extracting a water body range in a research area according to a multi-source remote sensing image; s2, according to SWOT satellite pixel cloud product data, extracting a water surface elevation in the research area; and S3, removing abnormal values of different scales according to the water surface elevations of different types of inland water bodies, and extracting corresponding surface water levels. According to the method provided by the invention, the scientific representativeness of an inland water level extraction result can be ensured, meanwhile, two different treatment flows for rivers and lakes are also provided, the time resolution and the overall precision of water level inversion are improved, and a technical support is provided for application and popularization of an SWOT satellite pixel cloud product in inland water level extraction.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite altimetry applications, and particularly relates to a method for extracting surface water levels based on SWOT satellite pixel cloud products. Background Art

[0002] Surface water level is an important indicator for studying the dynamic changes of surface water. Strengthening the monitoring ability of surface water levels and accurately and comprehensively monitoring the water level changes of rivers and lakes are of great significance for flood control and disaster reduction in the basin, water resource management and allocation, and the ecological environment protection of rivers and lakes. Traditional surface water level measurement methods usually rely on ground stations, cross-section water level gauges or manual surveys. These methods have significant spatial limitations and high labor costs. At the same time, due to the uneven distribution of ground monitoring stations, there are still many challenges in applying them in complex terrains and remote areas. Relying solely on conventional hydrological observation methods cannot provide effective and continuous water level observation values, making it difficult to meet the needs of dynamic monitoring.

[0003] With the continuous development of remote sensing technology, satellite altimetry technology provides a new technical path for water level monitoring. Satellite altimetry is a new type of remote sensing technology that emits electromagnetic waves to the ground and measures the round-trip propagation time of the echo, thereby accurately retrieving the heights of the ocean and land surfaces. It can conduct large-scale, high-precision, and periodic surface exploration, with unparalleled advantages over other observation technologies. It can overcome the limitations of traditional surface water level monitoring, provide a wider spatial coverage, make up for the lack of water level monitoring in data-deficient areas, and has become an important technical means for monitoring the heights of global oceans and inland waters.

[0004] The SWOT satellite, as an epoch-making space hydrology mission, is designed specifically for global water resource dynamic monitoring. The Ka-band radar interferometer it carries can perform interferometric measurements of the water surface heights of more than 90% of the Earth's surface in a 120-km-wide strip through dual-antenna interferometric radar technology. It can conduct high-resolution monitoring of global surface water and for the first time achieve continuous two-dimensional observation of global surface water bodies. One of the core products of the SWOT satellite is the high-resolution pixel cloud product (L2_HR_PIXC), which includes information such as the geolocation and elevation of water bodies. However, the pixel cloud product data of the SWOT satellite contains a large number of outliers affected by noise, such as the mislabeling of "dark water" features caused by satellite attitude changes, phase unwrapping errors, and the influence of terrain or other geographical features. How to effectively remove outliers is crucial for the accuracy of water level extraction. Therefore, it is urgent to develop a method for extracting surface water levels with high precision, large scale, and systematicness by using the high-resolution pixel cloud data of the SWOT satellite, combined with multi-source remote sensing information and efficient data processing technology. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, the surface water level extraction method based on SWOT satellite pixel cloud products provided by the present invention uses multi-source remote sensing data and high-resolution data of SWOT satellite pixel clouds, and combines algorithms such as the distribution, classification attributes, and statistical filtering of SWOT satellite pixel cloud products to propose a surface water level extraction method based on SWOT satellite pixel cloud products, realizing high-precision dynamic monitoring of surface water levels and providing important technical support for hydrological research and water resource management.

[0006] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: a surface water level extraction method based on SWOT satellite pixel cloud products, including the following steps:

[0007] S1. Extract the water body range in the study area according to multi-source remote sensing images;

[0008] S2. Extract the water surface elevation in the study area according to the SWOT satellite pixel cloud product data;

[0009] S3. Perform outlier rejection processing on the water surface elevations of different types of inland water bodies at different scales, and extract the corresponding surface water levels.

[0010] Further, the step S1 includes the following sub-steps:

[0011] S11. Obtain Sentinel-1 and Sentinel-2 remote sensing images within the study period of the study area respectively;

[0012] S12. Obtain the boundary range of inland water bodies in the study area, determine the boundary buffer zone, and clip the Sentinel-1 and Sentinel-2 remote sensing images in the study area according to it; the inland water bodies include rivers and lakes;

[0013] S13. Calculate the water body index and perform threshold segmentation on the clipped Sentinel-1 or Sentinel-2 remote sensing image to obtain the corresponding water body range;

[0014] S14. Perform binarization processing on the extracted water body range, and export the processed raster data as a surface vector file for clipping the pixel cloud data.

[0015] Further, in the step S13, for the Sentinel-1 remote sensing image, remove the speckle noise through Refined Lee filtering, and automatically select an appropriate threshold according to the dual-polarization water body index SDWI to extract the water body range in the study area by using the Otsu method;

[0016] For Sentinel-2 remote sensing images, select the remote sensing images with cloud cover less than 20% during the study period, and according to the Automatic Water Extraction Index (AWEIsh), use Otsu's method to automatically select an appropriate threshold to extract the water body range in the study area;

[0017] In step S14, when binarizing the extracted water body range, preferably select the Sentinel-2 remote sensing image synchronized with the SWOT satellite overpass time to extract the water body range. When the Sentinel-2 remote sensing image is interfered by cloud cover and the water body range cannot be effectively extracted, the water body range extraction result of the Sentinel-1 remote sensing image is used.

[0018] Furthermore, in step S13, the Dual Polarization Water Index (SDWI) is:

[0019] SDWI = ln(10 × VV × VH) - 8

[0020] In the formula, VV / VH represents two different polarization modes;

[0021] In step S14, the Automatic Water Extraction Index (AWEIsh) is:

[0022] AWEIsh = Blue + 2.5 × Green - 1.5 × (NIR + SWIR1) - 0.25 × SWIR2

[0023] In the formula, Blue represents the blue band; Green represents the green band; NIR represents the near-infrared band; SWIR1 / 2 represents the short-wave infrared band.

[0024] Furthermore, step S2 includes the following steps:

[0025] S21. Obtain the SWOT satellite pixel cloud product data within the study period of the study area;

[0026] S22. Save the specific fields in the SWOT satellite pixel cloud product data as a CSV file;

[0027] S23. Clip the CSV file according to the area vector file of the water body range in the study area to extract the CSV file within the water body range of the study area;

[0028] S24. Calculate the water surface elevation of the study area according to the specific fields of the CSV file within the water body range of the study area.

[0029] Furthermore, in step S24, the water surface elevation (WSE) of the study area is:

[0030] WSE = height - geoid - solid_earth_tide - load_tide - pole_tide

[0031] In the formula, height represents the water surface height, that is, the height of the water surface in the study area relative to the reference ellipsoid; geoid represents the height difference between the geoid and the reference ellipsoid; solid_earth_tide represents the height of the solid earth tide; load_tide represents the height of the load tide; pole_tide represents the height of the pole tide.

[0032] Furthermore, the step S3 includes the following sub - steps:

[0033] S31. Initially remove outliers from the water surface elevation in the study area;

[0034] S32. On the basis of initially removing outliers;

[0035] For the pixel cloud data of inland water bodies that are rivers, adopt the multiple statistical filtering method. Through calculating the distances between sampling points and the neighborhood point sets for statistical analysis, identify and remove the outliers, and extract the corresponding surface water levels;

[0036] For the pixel cloud data of inland water bodies that are lakes, conduct pixel cloud data quality screening, open - water pixel cloud data screening, and multiple statistical filtering in sequence. Through calculating the distances between sampling points and the neighborhood point sets for statistical analysis, identify and remove the outliers, and extract the corresponding surface water levels.

[0037] Furthermore, in the step S31, the outliers in the water surface elevation are initially removed by the inter - quartile range method, and its formula is:

[0038] IQR = Q 3 - Q 1

[0039] WSE 异 < Q 1 - 1.5×IQR & WSE 异 > Q 3 + 1.5×IQR

[0040] In the formula, IQR represents the inter - quartile range, reflecting the dispersion degree of the middle 50% of the data in the water surface elevation, Q 3 represents the third quartile, Q 1 represents the first quartile, and WSE 异 represents the outliers in the water surface elevation.

[0041] Furthermore, in the step S32, the formula for statistical filtering is:

[0042]

[0043]

[0044]

[0045] T = μ + α×σ

[0046] In the formula, d i represents the average neighborhood distance; k represents the nearest neighbor point; p i represents each point in the point cloud; ||p i - p ij || represents the Euclidean distance between point p i and its j-th nearest neighbor; μ represents the global mean; σ represents the global standard deviation; T represents the threshold; α represents the proportionality coefficient; n represents the total number of points in the point cloud.

[0047] The beneficial effects of the present invention are as follows:

[0048] (1) The method for extracting the surface water level based on the SWOT satellite pixel cloud product proposed by the present invention can effectively eliminate the outliers and noise data of the pixel cloud product, greatly improve the extraction accuracy of the surface water level, and provide an efficient and accurate solution for extracting the surface water level.

[0049] (2) The present invention designs corresponding processing strategies for different inland water bodies such as rivers and lakes, significantly improving the applicability of the method in different inland water bodies, helping to accurately master the dynamic change law of inland water bodies, and providing an important basis for scientifically formulating water resource management strategies, optimizing dispatching schemes, and flood control and disaster reduction. Brief Description of the Drawings

[0050] Figure 1 The figure shows a flowchart of the method for extracting the surface water level based on the SWOT satellite pixel cloud product provided by an embodiment of the present invention.

[0051] Figure 2 The figure shows a comparison diagram of the distribution of river pixel clouds in the longitude direction and the filtering effect from the Yichang Hydrological Station to the Zhicheng Hydrological Station in the middle reaches of the Yangtze River provided by an embodiment of the present invention.

[0052] Figure 3 The figure shows a comparison diagram of the distribution of Taihu pixel clouds in the longitude direction and the filtering effect provided by an embodiment of the present invention.

[0053] Figure 4 The figure shows a comparison diagram of the elevation distribution of pixel clouds before and after statistical filtering of the river from the Yichang Hydrological Station to the Zhicheng Hydrological Station in the middle reaches of the Yangtze River provided by an embodiment of the present invention.

[0054] Figure 5 The figure shows a comparison diagram of the elevation distribution of pixel clouds before and after statistical filtering of Taihu provided by an embodiment of the present invention. Specific Embodiments

[0055] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0056] An embodiment of the present invention provides a method for extracting surface water levels based on SWOT satellite pixel cloud products, as Figure 1 shown, including the following steps:

[0057] S1. Extract the water body range within the study area based on multi-source remote sensing images;

[0058] S2. Extract the water surface elevation within the study area according to the SWOT satellite pixel cloud product data;

[0059] S3. Perform outlier removal processing on the water surface elevations of different types of inland water bodies at different scales to extract the corresponding surface water levels.

[0060] Step S1 of the embodiment of the present invention includes the following sub-steps:

[0061] S11. Obtain Sentinel-1 and Sentinel-2 remote sensing images within the study period of the study area respectively;

[0062] S12. Obtain the boundary range of the inland water bodies within the study area, determine the boundary buffer zone, and clip the Sentinel-1 and Sentinel-2 remote sensing images within the study area according to it; the inland water bodies include rivers and lakes;

[0063] S13. Calculate the water body index and perform threshold segmentation on the clipped Sentinel-1 or Sentinel-2 remote sensing image to obtain the corresponding water body range;

[0064] S14. Perform binarization processing on the extracted water body range, and export the processed raster data as a surface vector file for clipping the pixel cloud data.

[0065] In step S13 of this embodiment, for the Sentinel-1 remote sensing image, speckle noise is removed by Refined Lee filtering, and according to the dual-polarization water body index SDWI, the Otsu method is used to automatically select an appropriate threshold to extract the water body range within the study area;

[0066] For Sentinel-2 remote sensing images, select remote sensing images with cloud cover less than 20% during the study period, and use the Otsu method to automatically select an appropriate threshold to extract the water body range in the study area according to the Automatic Water Extraction Index (AWEIsh).

[0067] Among them, the Dual Polarization Water Index (SDWI) is as follows:

[0068] SDWI = ln(10 × VV × VH) - 8

[0069] In the formula, VV / VH represents two different polarization modes;

[0070] The Automatic Water Extraction Index (AWEIsh) is as follows:

[0071] AWEIsh = Blue + 2.5 × Green - 1.5 × (NIR + SWIR1) - 0.25 × SWIR2

[0072] In the formula, Blue represents the blue band; Green represents the green band; NIR represents the near-infrared band; SWIR1 / 2 represents the short-wave infrared band.

[0073] In step S14 of this embodiment, when binarizing the extracted water body range, preferentially select Sentinel-2 remote sensing images synchronized with the overpass time of the SWOT satellite to extract the water body range. When the Sentinel-2 remote sensing images are interfered by cloud cover and the water body range cannot be effectively extracted, the water body range extraction result of Sentinel-1 remote sensing images is used.

[0074] Specifically, when determining the water body range, make up for the limitations of a single data source according to the high precision of optical data and the all-weather ability of radar data, ensure the time continuity of the extracted water body range, and improve the spatio-temporal consistency matching the overpass time of the SWOT satellite.

[0075] Step S2 of the embodiment of the present invention includes the following steps:

[0076] S21. Obtain the SWOT satellite pixel cloud product data in the study area during the study period;

[0077] S22. Save the specific fields in the SWOT satellite pixel cloud product data as a CSV file;

[0078] S23. Clip the CSV file according to the surface vector file of the water body range in the study area, and extract the CSV file within the water body range of the study area;

[0079] S24. Calculate the water surface elevation of the study area according to the specific fields for the CSV file within the water body range of the study area;

[0080] Among them, the water surface elevation WSE of the study area is:

[0081] WSE = height - geoid - solid_earth_tide - load_tide - pole_tide

[0082] In the formula, height represents the water surface height, that is, the height of the water surface in the study area relative to the reference ellipsoid; geoid represents the height difference between the geoid and the reference ellipsoid; solid_earth_tide represents the height of the solid earth tide; load_tide represents the height of the load tide; pole_tide represents the height of the pole tide.

[0083] In this embodiment, the SWOT satellite pixel cloud product is the SWOT satellite L2_HR_PIXC pixel cloud product.

[0084] Step S3 of the embodiment of the present invention includes the following sub - steps:

[0085] S31. Initially remove outliers from the water surface elevation in the study area;

[0086] Among them, outliers in the water surface elevation are initially removed by the inter - quartile range method, and its formula is:

[0087] IQR = Q 3 - Q 1

[0088] WSE 异 < Q 1 - 1.5×IQR & WSE 异 > Q 3 + 1.5×IQR

[0089] In the formula, IQR represents the inter - quartile range, which reflects the dispersion degree of the middle 50% of the data in the water surface elevation, Q 3 represents the third quartile, Q 1 represents the first quartile, and WSE 异 represents the outlier of the water surface elevation.

[0090] S32. On the basis of initially removing outliers;

[0091] For the pixel cloud data where the inland water body is a river, adopt the multiple statistical filtering method, conduct statistical analysis by calculating the distance between the sampling point and the neighborhood point set, identify and remove the outlier points, and extract the corresponding surface water level;

[0092] For the pixel cloud data of inland water bodies that are lakes, the pixel cloud data quality screening, open water pixel cloud data screening, and multiple statistical filtering are performed in sequence. Statistical analysis is carried out by calculating the distance between the sampling point and the neighborhood point set to identify and remove outliers, and the corresponding surface water level is extracted.

[0093] In this embodiment, the formula for statistical filtering is:

[0094]

[0095]

[0096]

[0097] T = μ + α × σ

[0098] In the formula, d i represents the average neighborhood distance; k represents the nearest neighbor points; p i represents each point in the point cloud; ||p i - p ij || represents the Euclidean distance between point p i and its j-th nearest neighbor; μ represents the global mean; σ represents the global standard deviation; T represents the threshold; α represents the proportionality coefficient; n represents the total number of point clouds.

[0099] Among them, when extracting the surface water level of the pixel cloud data of inland water bodies that are rivers, through a large number of experiments, it is found that for the pixel cloud located on the river, if only the data with a quality flag of zero is selected, the pixel cloud may be empty; and even if the quality flag value is relatively high, the water surface elevation of some pixel points is still similar to that when the quality flag is zero. Therefore, in order to retain as many effective pixel cloud data as possible, after initially removing outliers, a method of further using multiple statistical filtering methods to identify and remove outliers is adopted. Figure 2 The figure shows the comparison diagram of the distribution of river pixel clouds in the longitude direction and the filtering effect from Yichang Hydrological Station to Zhicheng Hydrological Station in the middle reaches of the Yangtze River provided by the embodiment of the present invention; Figure 4 The figure shows the comparison diagram of the elevation distribution of pixel clouds before and after river statistical filtering from Yichang Hydrological Station to Zhicheng Hydrological Station in the middle reaches of the Yangtze River provided by the embodiment of the present invention.

[0100] When extracting the surface water level of the pixel cloud data of inland water bodies that are lakes, first, the pixel cloud data with reliable quality is screened, and the pixel cloud data with the quality flag attribute (geolocation_qual) of zero in the pixel cloud is screened out; next, the pixel cloud data with its self-classification as open water (class = 4) is further screened; finally, a method of multiple statistical filtering is further adopted, and statistical analysis is carried out by calculating the distance between the sampling point and the neighborhood point set to identify and remove outliers.

[0101] Specifically, the geolocation quality flag attribute (geolocation_qual) of the SWOT satellite pixel cloud product is used to evaluate the quality of geolocation data (including altitude, longitude, and latitude). A value of zero indicates reliable data quality, and the larger the value, the lower the reliability. There are 7 categories of pixel cloud products, namely land (class = 1), land near water (class = 2), water near land (class = 3), open water (class = 4), dark water (class = 5), low coherence water near land (class = 6), and open low coherence water (class = 7). Different classifications represent different pixel cloud classifications. In summary, only the pixel cloud data with a quality flag of zero and its own classification as open water are selected. Figure 3 The figure shows a comparison chart of the distribution and filtering effect of the Taihu pixel cloud in the longitude direction provided by an embodiment of the present invention. Figure 5 The figure shows a comparison chart of the elevation distribution of the pixel cloud before and after statistical filtering of the Taihu Lake provided by an embodiment of the present invention.

[0102] In the present invention, specific embodiments are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. At the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0103] Those of ordinary skill in the art will realize that the embodiments described here are for helping readers understand the principle of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various specific deformations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A surface water level extraction method based on SWOT satellite pixel cloud products, characterized in that: The following steps are involved: S1. Extract the scope of water bodies in the study area based on multi-source remote sensing images; S2. Extract the water surface elevation in the study area based on the SWOT satellite pixel cloud product data; S3. For the water surface elevations of different types of inland water bodies, outliers of different scales are eliminated to extract the corresponding surface water levels.

2. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 1 is characterized in that: The step S1 comprises the following sub-steps: S11. Obtain the Sentinel-1 and Sentinel-2 remote sensing images of the study area and the study period respectively; S12. Obtain the boundary range of inland water bodies in the study area, determine the boundary buffer zone, and clip the Sentinel-1 and Sentinel-2 remote sensing images in the study area based on the boundary buffer zone; the inland water bodies include rivers and lakes; S13, calculating the water body index and performing threshold segmentation on the cropped Sentinel-1 or Sentinel-2 remote sensing image to obtain the corresponding water body range; S14. Binarize the extracted water body range, and export the processed raster data as a surface vector file for clipping pixel cloud data.

3. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 2 is characterized in that: In step S13, for the Sentinel-1 remote sensing image, the speckle noise is removed by using the Refined Lee filter, and the Otsu method is used to automatically select a suitable threshold to extract the water range in the study area according to the dual-polarization water index SDWI; For Sentinel-2 remote sensing images, we screened out those with cloud cover less than 20% during the study period, and used the Otsu method to automatically select a suitable threshold to extract the water range in the study area based on the automatic water index AWEIsh. In step S14, when the extracted water body range is binarized, the Sentinel-2 remote sensing image synchronized with the SWOT satellite transit time is preferentially selected to extract the water body range. When the Sentinel-2 remote sensing image is interfered by cloud cover and the water body range cannot be effectively extracted, the water body range extraction result of the Sentinel-1 remote sensing image is used.

4. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 2 is characterized in that: In step S13, the dual polarization water index SDWI is: SDWI=ln(10×VV×VH)-8 In the formula, VV / VH represents two different polarization modes; In step S14, the automatic water index AWEIsh is: AWEIsh=Blue+2.5×Green-1.5×(NIR+SWIR1)-0.25×SWIR2 In the formula, Blue represents the blue band; Green represents the green band; NIR represents the near infrared band; SWIR1 / 2 represents the short-wave infrared band.

5. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 1 is characterized in that: The step S2 comprises the following steps: S21. Obtain SWOT satellite pixel cloud product data within the study area and study period; S22. Save the specific fields in the SWOT satellite pixel cloud product data as a CSV file; S23, cutting the CSV file according to the surface vector file of the water body range in the study area, and extracting the CSV file within the water body range in the study area; S24. For the CSV file within the water body range of the study area, calculate the water surface elevation of the study area according to specific fields.

6. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 5 is characterized in that: In step S24, the water surface elevation WSE of the study area is: WSE=height-geoid-solid_earth_tide-load_tide-pole_tide In the formula, height represents the water surface height, that is, the height of the water surface in the study area relative to the reference ellipsoid; geoid represents the height difference of the geoid relative to the reference ellipsoid; solid_earth_tide represents the solid earth tidal height; load_tide represents the load tidal height; pole_tide represents the pole tide height.

7. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 1 is characterized in that: The step S3 comprises the following sub-steps: S31. Preliminarily remove outliers from the water surface elevation within the study area; S32, on the basis of preliminary elimination of outliers; For pixel cloud data of inland water bodies such as rivers, multiple statistical filtering methods are used to perform statistical analysis by calculating the distance between sampling points and neighborhood point sets, identify and remove outliers, and extract the corresponding surface water levels; For the pixel cloud data of inland water bodies such as lakes, pixel cloud data quality screening, open water pixel cloud data screening and multiple statistical filtering are carried out in sequence. Statistical analysis is performed by calculating the distance between the sampling points and the neighborhood point set, outliers are identified and removed, and the corresponding surface water levels are extracted.

8. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 7 is characterized in that: In step S31, outliers in the water surface elevation are initially eliminated by using the interquartile range method, and the formula is: IQR=Q3-Q1 WSE 异 <Q1-1.5×IQR&WSE 异 >Q3+1.5×IQR In the formula, IQR stands for interquartile range, which reflects the degree of dispersion of the middle 50% of the data in the water surface elevation, Q3 stands for the third quartile, Q1 stands for the first quartile, and WSE stands for 异 Indicates outliers in water surface elevation.

9. The surface water level extraction method based on SWOT satellite pixel cloud products according to claim 7 is characterized in that: In step S32, the formula for statistical filtering is: T=μ+α×σ Where, d i represents the average neighborhood distance; k represents the nearest neighbor point; p i Represents each point in the point cloud; ||p i -p ij || represents point p i The Euclidean distance between the jth nearest neighbor; μ represents the global mean; σ represents the global standard deviation; T represents the threshold; α represents the scale factor; n represents the total number of point clouds.

Images