A fast calculation method for sandy coastal erosion based on multi-period remote sensing images

Abstract

The present invention relates to the technical field of sandy coast erosion detection, and specifically to a method for quickly calculating the amount of sandy coast erosion based on multi-period remote sensing images, comprising the following steps: S1: first selecting a target sandy coastline area and collecting multi-period remote sensing images of the area; S2: processing the remote sensing images in S1 to distinguish the coastline and its adjacent areas; S3: tracking the position changes of the coastline in the multi-period images to obtain coastline dynamic data; S4: combining the coastline dynamic data obtained in S3 with ground elevation data to construct a three-dimensional model of the coastline; S5: combining the dynamic data of the marine environment to calculate and predict the amount of erosion in different time periods; S6: verifying and calibrating the accuracy of the erosion calculation. The present invention, by integrating advanced remote sensing technology and dynamic data analysis, realizes real-time monitoring and accurate prediction of coastal erosion, providing a strong scientific basis for effective management and protection of the coastline.

Description

Technical Field

[0001] The invention relates to the technical field of sandy coast erosion detection, and in particular to a method for quickly calculating the amount of sandy coast erosion based on multi-period remote sensing images. Background Art

[0002] In the field of environmental monitoring and coastline management, coastal erosion is a major natural phenomenon with far-reaching impacts on ecosystems, human settlements and economic activities. Coastlines are constantly changing due to natural and human factors, especially on sandy coasts. Traditional coastal erosion monitoring methods rely on ground measurements and historical data analysis, which often fail to provide real-time or accurate erosion data, especially in widespread or difficult-to-reach areas. In addition, existing monitoring technologies often ignore the combined effects of complex environmental dynamics such as tides, waves and wind, which are key factors affecting coastline changes.

[0003] The main problem with existing technologies is the lack of a system that can comprehensively consider multiple environmental factors and conduct real-time monitoring and prediction. In addition, existing methods often require a lot of manpower and material resources for ground surveys, which is economically and time-unsustainable.

[0004] Therefore, it is necessary to develop a new technical solution that can utilize advanced remote sensing technology and data analysis methods to integrate ocean dynamics and physical models of sandy coastal erosion to provide more accurate, economical and systematic shoreline erosion monitoring and prediction. Summary of the invention

[0005] Based on the above purpose, the present invention provides a method for quickly calculating the amount of sandy coastal erosion based on multi-period remote sensing images.

[0006] The rapid calculation method of sandy coastal erosion based on multi-period remote sensing images includes the following steps:

[0007] S1: First, select the target sandy coastline area and collect multiple remote sensing images of the area. Then, use data assimilation technology to integrate remote sensing data from different time points and different sensors to form a unified data framework.

[0008] S2: Use a preset multi-scale image segmentation algorithm to process the remote sensing image integrated in S1 to distinguish the coastline, the boundary line of high tide and low tide and its adjacent areas;

[0009] S3: Based on S2, dynamic boundary detection technology is used to automatically track the position changes of the coastline and low-tide edge in multiple images to obtain dynamic data of the upper and lower boundaries of the beach;

[0010] S4: Combine the dynamic data of the coastline and low tide boundary obtained in S3 with the ground elevation data to construct a three-dimensional model of the beach to show the vertical and horizontal changes of the sandy coastline;

[0011] S5: Based on the three-dimensional model of S4, the ocean dynamics and sandy coastal erosion physical models are introduced, combined with the dynamic data of the marine environment, to calculate and predict the erosion amount in different time periods;

[0012] S6: Verify and calibrate the accuracy of erosion calculation by comparing and analyzing the calculation results in S5 with ground measured data and historical erosion records.

[0013] Furthermore, the S1 specifically includes:

[0014] S11: First, the target coastline area is determined and selected through the Geographic Information System (GIS) technology, and the area is defined using GIS to select the predetermined sandy coastline;

[0015] S12: Based on the area selected in S11, multiple remote sensing platforms are used to collect multi-period remote sensing images of the area. The multiple remote sensing platforms include optical satellites, synthetic aperture radar satellites and infrared sensors. The images collected during the collection process should include images of different seasons and weather conditions to obtain a comprehensive data set. The timestamps and environmental conditions of the images should be recorded synchronously for each period of image collection to provide auxiliary information for subsequent data assimilation.

[0016] S13: Use data assimilation technology to integrate the remote sensing data collected in S12, and use the ensemble Kalman filter to uniformly process the remote sensing data to eliminate data errors and inconsistencies caused by differences in different remote sensing platforms and time differences, and finally form a unified data framework to provide a data basis for coastline erosion analysis.

[0017] Furthermore, the S2 specifically includes:

[0018] S21: Before applying the multi-scale image segmentation algorithm, the data frame integrated in S1 is first preprocessed, including grayscale processing, denoising and contrast enhancement of the remote sensing image to improve the visual distinction of the coastline and its adjacent areas in the image;

[0019] S22: Use the preset multi-scale image segmentation algorithm to identify and distinguish image features at different scales. Specifically, first identify the geomorphic features at the macro scale, including the general direction of the coastline, and then finely distinguish the specific boundaries and morphology of the coastline, the high tide and low tide boundary and its adjacent areas at the micro scale;

[0020] S23: Based on S22, the boundary optimization technology is used to refine the boundaries of the coastline, high tide and low tide boundaries and their adjacent areas. By analyzing multiple factors such as terrain gradient, texture differences and color changes, the boundary lines of each area are accurately adjusted and optimized;

[0021] S24: Finally, the processed image in S23 is compared and verified with the field measurement data and historical maps. Through comparative analysis, it is checked whether the recognition results of the coastline and its adjacent areas are accurate.

[0022] Furthermore, the S22 specifically includes:

[0023] S221: On a macro scale, a regional growing algorithm based on image texture and color homogeneity is used to perform preliminary identification of landform features. A seed point is set, and then the surrounding pixels with similar texture or color characteristics to the seed point are merged into one region. The specific formula is expressed as:

[0024] Among them, R represents the final area, P is the pixel set, S is the seed point set, n is the number of seed points, similarity() is the similarity test function, and T is the threshold;

[0025] S222: At the microscopic scale, an edge detection-based algorithm is used to further refine the specific boundaries and morphology of the coastline, high tide and low tide boundary and its adjacent areas. Specifically, the Canny edge detection algorithm is used to identify the boundaries by calculating the gradient strength and direction of the image. The formula is: and Among them, G is the magnitude of the gradient, G x and G y is the gradient of the image in the horizontal and vertical directions, Θ is the direction of the gradient, and the Canny algorithm also includes non-maximum suppression and double threshold processing steps to ensure that the edge details are accurately captured.

[0026] Furthermore, the S3 specifically includes:

[0027] S31: First, use the latest coastline identified and optimized in S2 as the initialization boundary;

[0028] S32: Before starting tracking, ensure accurate alignment between multiple remote sensing images. Specifically, use image registration technology to correct any image offset caused by changes in sensor position or environmental factors by calculating the optimal transformation between the two images. Use mutual information as the registration criterion. The calculation formula is: Among them, X and Y represent two remote sensing images that need to be registered; p X,Y(x, y) represents the joint probability density function of the simultaneous occurrence of pixel values ​​x and y in image X and image Y; p X (x) and p Y (y) is the marginal probability density function of pixel values ​​x and y in image X and image Y, that is, the probability of x and y appearing in their respective images; log is the natural logarithm, which is used to calculate the logarithm of the ratio of two probabilities, reflecting the statistical dependence of X and Y;

[0029] S33: Use dynamic boundary detection technology based on optical flow to automatically track the position changes of the coastline and the high tide and low tide boundary in multiple images. The optical flow method predicts the dynamic changes of the coastline by analyzing the movement of each pixel over time. The specific formula is: x u+f y v+f t =0, where f x and f y is the spatial derivative of the image, which indicates the rate of change of the brightness of the image in the horizontal direction x and the vertical direction y; f t is the time derivative of the image, indicating the brightness change of the image in the time dimension; u and v represent the horizontal and vertical velocity components of each pixel in the image respectively;

[0030] S34: Collect all the coastline change data tracked in S33 and conduct integrated analysis, including calculating the movement distance and direction of the coastline at each time point, and statistical analysis of the change trend, to provide dynamic input data for the final erosion calculation.

[0031] Furthermore, the S4 specifically includes:

[0032] S41: Before building the 3D coastline model, first integrate and preprocess the coastline dynamic data and ground elevation data from S3. The preprocessing includes data cleaning, formatting, and coordinate system unification to ensure that all data are consistent in spatial reference, providing a basis for building the 3D model.

[0033] S42: Using the integrated data, the digital elevation model technology is applied to generate the three-dimensional terrain of the coastline and its adjacent areas. Specifically, the interpolation method is used to generate the terrain surface. The formula is:

[0034]

[0035] Where z is the elevation value of the interpolation point; x, y are the geographic coordinates of the interpolation point; z i is the elevation value of the known point; d i is the distance from the known point to the interpolation point; i is the weight factor; p is a positive constant used to adjust the influence of the distance weight, and its value is 2;

[0036] S43: On the generated three-dimensional terrain model, according to the dynamic data of the coastline tracked in S3, the three-dimensional path of the coastline is calculated and depicted. Specifically, the two-dimensional position data of the coastline is converted into three-dimensional space coordinates using linear interpolation method. The formula is: Among them, z t is the elevation on the coastline at time point t; x t is the horizontal position of the coastline at time t; z t1 and z t2 is the elevation value at known time points t1 and t2; x t1 and x t2 is the corresponding horizontal position;

[0037] S44: Refine and optimize the initially constructed 3D model, including smoothing the 3D path of the coastline and adjusting the texture and color of the model to enhance the realism and readability of the model;

[0038] S45: Finally, the constructed three-dimensional coastline model is compared and verified with the actual topographic survey data to ensure the accuracy of the model, and the model is adjusted according to the verification results, including correcting the elevation data of the terrain or the path data of the coastline.

[0039] Furthermore, the S44 specifically includes:

[0040] S441: In the refinement stage of the 3D model, the 3D path of the coastline is first smoothed to eliminate jagged or irregular edges caused by interpolation and measurement errors. Specifically, the B-spline curve method is used to smooth the path points. The specific formula is: Among them, S(t) is the smoothed three-dimensional path point; P i is the original path point; B i,k (t) is a B-spline basis function of degree k, t is a parameter, which varies in the interval [0, 1];

[0041] S442: Then, the texture and color of the 3D model are adjusted to enhance the realism and readability of the model. The texture mapping and color adjustment include the following steps:

[0042] S4421: Perform texture mapping, apply pixel-by-pixel texture mapping technology, map the real-world terrain texture to the surface of the 3D model, and use the following formula to calculate the texture coordinates:

[0043] Among them, (u, v) is the texture coordinate; (x, y) is the coordinate of the model surface point; x min ,x max ,ymin ,y max are the minimum and maximum values ​​of the coordinates of the model surface points;

[0044] S4422: Adjust the color to improve the distinction according to the different terrain features and environmental conditions of the coastline. Use linear interpolation to adjust the color to match the elevation or erosion degree of the terrain. The specific color adjustment formula is: Where c is the adjusted color value; c min and c max are the minimum and maximum values ​​of the color range; z is the elevation value; min and z max are the minimum and maximum values ​​of the elevation.

[0045] Furthermore, the S5 specifically includes:

[0046] S51: Integrate the ocean dynamics model into the three-dimensional coastline model to simulate the impact of tidal, wave and wind environmental factors on coastline erosion. The ocean dynamics model includes tidal model, wave model and wind model. The tidal model is used to calculate the water level changes caused by tides; the wave model is used to evaluate the impact of wave height, period and direction on the coastline; the wind model is used to analyze wind speed and direction, and its impact on water flow and sand material movement;

[0047] S52: The physical model of sandy coastal erosion is introduced, combined with ocean dynamics data, to calculate the erosion amount. The formula includes comprehensive consideration of tidal height, wave impact and wind force. The specific calculation formula is:

[0048] Where E is the erosion amount, H w is the wave height, H t is the tidal height, τ w is the wave impact force, F w is the wind force, ρ s is the density of sandy material, K is the erosion coefficient;

[0049] S53: Combine the physical model output of S52 and the shoreline change data in S34 to calculate the current erosion amount and predict the future erosion trend. Then integrate and update the calculation results directly into the 3D model to reflect the new position and shape of the shoreline.

[0050] Furthermore, the S53 specifically includes:

[0051] S531: Combine the shoreline dynamic data in S34 with the physical model output. The formula is: Among them, E total is the comprehensive erosion amount, E i is the single erosion amount at each time point;

[0052] S532: Use dynamic simulation technology to predict future erosion based on marine environmental data and historical coastline change patterns. During the simulation, the amount of erosion in the future time period is calculated using the following formula: E future =E current +ΔE, where E future is the future erosion, E current is the current amount of erosion, and ΔE is the expected change;

[0053] S533: directly updating the calculated erosion results into the three-dimensional model to reflect the new position and shape of the coastline. The updating process includes adjusting the vertex coordinates of the two-dimensional model to reflect the position change after erosion.

[0054] Furthermore, the S6 specifically includes:

[0055] S61: Collect ground-based measured data and historical erosion records, and ensure that the data covers the same time period and spatial range as the results calculated in S5. The data include the actual measured coastline location, erosion depth and environmental conditions;

[0056] S62: Preprocess and align the collected ground-based data with the historical erosion records to ensure that they are consistent with the erosion data calculated in S5 in time and space. Specifically, a spatial registration algorithm is used to align different data sources. The registration formula is: T = A·X+b, where T is the registered data; A is the transformation matrix used to adjust the scale and rotation; X is the original data point; and b is the translation vector.

[0057] S63: Calculate error indicators by comparing the calculation results in S5 with the ground measured data. Specific error analysis methods include root mean square error and mean absolute error.

[0058] S64: According to the error analysis results, the parameters of the erosion calculation model are adjusted. The calibration process is specifically performed through a gradient descent optimization algorithm. The optimization goal is to minimize the error function. The formula is: Where J(θ) is the error function; m is the number of samples; h θ (x i ) is the model prediction value; y i is the actual value; θ is the model parameter;

[0059] S65: After the model is calibrated, it is verified again using ground measured data to ensure that the calibrated model can accurately predict the amount of erosion. Through repeated iterative optimization and verification, an accurate erosion calculation model is finally obtained.

[0060] Beneficial effects of the present invention:

[0061] The present invention, by combining advanced remote sensing technology and multi-dimensional data analysis methods, provides a new coastal erosion monitoring and prediction system. The system can collect multi-period remote sensing images of the coastline in real time, and integrate data from different time points and different sensors through data assimilation technology. This not only allows real-time monitoring of coastline changes, but also can accurately predict future erosion trends through integrated ocean dynamics and sandy coastal erosion physical models. This combination of real-time and predictive capabilities significantly improves the timeliness and effectiveness of management and response measures to coastline changes.

[0062] The present invention reduces the reliance on ground surveys by utilizing automated remote sensing data collection and processing, significantly reducing monitoring costs. In addition, by optimizing the data collection and analysis process, the method improves the efficiency of resource utilization, making coastal erosion monitoring not only economical and efficient, but also more environmentally friendly.

[0063] The data and analysis results generated by the present invention can be directly used to support the formulation of coastline management and protection strategies. The output includes reports on erosion trends and predictions of future erosion risks. This information is a valuable decision support tool for environmental protection organizations and related stakeholders. By providing scientific and accurate data support, the system helps to formulate more effective coastal protection measures and enhance the ability to deal with coastline erosion and related environmental issues. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only for the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0065] Figure 1 A schematic diagram of a method for quickly calculating the amount of sandy coastal erosion according to an embodiment of the present invention;

[0066] Figure 2 Schematic diagram of a method for constructing a three-dimensional model of a coastline according to an embodiment of the present invention. DETAILED DESCRIPTION

[0067] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0068] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. The words "include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0069] like Figure 1-Figure 2 As shown in the figure, the rapid calculation method of sandy coastal erosion based on multi-period remote sensing images includes the following steps:

[0070] S1: First, select the target sandy coastline area and collect multiple remote sensing images of the area. Then, use data assimilation technology to integrate remote sensing data from different time points and different sensors to form a unified data framework.

[0071] S2: Use the preset multi-scale image segmentation algorithm to process the remote sensing images integrated in S1 to distinguish the coastline, the boundary line of high tide and low tide and its adjacent areas. This step provides the necessary geospatial information for accurate calculation of erosion by identifying geographical features at different scales;

[0072] S3: Based on S2, dynamic boundary detection technology is used to automatically track the position changes of the coastline and low-tide edge in multiple images to obtain dynamic data of the upper and lower boundaries of the beach;

[0073] S4: Combine the dynamic data of the coastline and low tide boundary obtained in S3 with the ground elevation data to construct a three-dimensional model of the beach to show the vertical and horizontal changes of the sandy coastline, providing a multi-dimensional analysis basis for the calculation of erosion;

[0074] S5: Based on the three-dimensional model of S4, the ocean dynamics and sandy coastal erosion physical models are introduced, combined with the dynamic data of the marine environment (such as tides, waves, wind, etc.), to calculate and predict the erosion amount in different time periods;

[0075] S6: By comparing and analyzing the calculation results in S5 with the ground measured data and historical erosion records, the accuracy of the erosion calculation is verified and calibrated. This step ensures the practicality and scientificity of the method and provides a guarantee for the accuracy of the final result.

[0076] S1 specifically includes:

[0077] S11: First, the target coastline area is determined and selected through the Geographic Information System (GIS) technology, and the GIS is used to define the area and select the predetermined sandy coastline. This step relies on high-precision map data and historical records of coastline changes to determine the specific scope of the monitoring area;

[0078] S12: Based on the area selected in S11, multiple remote sensing platforms are used to collect multi-period remote sensing images of the area. The multiple remote sensing platforms include optical satellites, synthetic aperture radar (SAR) satellites, and infrared sensors. The images collected during the collection process should include images of different seasons and weather conditions to obtain a comprehensive data set. The timestamps and environmental conditions of the images should be recorded synchronously for each period of image collection to provide auxiliary information for subsequent data assimilation.

[0079] S13: Using data assimilation technology, the remote sensing data collected in S12 are integrated, and the ensemble Kalman filter is used to uniformly process the remote sensing data to eliminate data errors and inconsistencies caused by differences in different remote sensing platforms and time differences, and finally form a unified data framework that is continuous in time and consistent in space, providing a high-quality and high-precision data foundation for coastline erosion analysis; through precise positioning of GIS technology and comprehensive utilization of multi-source remote sensing data, the present invention effectively improves the coverage and accuracy of data, making the calculation of coastal erosion more accurate and efficient. The application of data assimilation technology further ensures the consistency and comprehensiveness of the data, making the calculation of erosion more reliable in time series.

[0080] S2 specifically includes:

[0081] S21: Before applying the multi-scale image segmentation algorithm, the data frame integrated in S1 is first preprocessed, including grayscale processing, denoising and contrast enhancement of the remote sensing image to improve the visual distinction of the coastline and its adjacent areas in the image;

[0082] S22: Use the preset multi-scale image segmentation algorithm to identify and distinguish image features at different scales. Specifically, first identify the geomorphic features at the macro scale, including the general direction of the coastline, and then finely distinguish the specific boundaries and morphology of the coastline, the high tide and low tide boundary and its adjacent areas at the micro scale;

[0083] S23: Based on S22, the boundary optimization technology is used to refine the boundaries of the coastline, high tide and low tide boundary and its adjacent areas. By analyzing multiple factors such as terrain gradient, texture difference and color change, the boundary line of each area is accurately adjusted and optimized to ensure the accuracy and continuity of the coastline;

[0084] S24: Finally, the processed image in S23 is compared and verified with the field measurement data and historical maps. Through comparative analysis, the accuracy of the identification results of the coastline and its adjacent areas is checked. If necessary, the segmentation algorithm is adjusted to ensure the accuracy and quality of the final output data. Through the above steps, S2 can not only effectively use the multi-scale image segmentation algorithm to distinguish the coastline and its adjacent areas, but also improve the accuracy and detail expression of coastline identification through boundary optimization technology. This method enhances the availability and reliability of the data, provides a solid foundation for subsequent erosion calculations, and also optimizes the overall analysis efficiency and result accuracy.

[0085] S22 specifically includes:

[0086] S221: On a macro scale, a regional growing algorithm based on image texture and color homogeneity is used to perform preliminary identification of landform features. A seed point is set, and then the surrounding pixels with similar texture or color characteristics to the seed point are merged into one region. The specific formula is expressed as:

[0087] Among them, R represents the final area, P is the pixel set, S is the seed point set, n is the number of seed points, similarity() is the similarity test function, and T is the threshold. The purpose of this step is to quickly and roughly identify the general direction and main geomorphic structure of the coastline, and provide guidance for micro-scale processing;

[0088] S222: At the microscopic scale, an edge detection-based algorithm is used to further refine the specific boundaries and morphology of the coastline, high tide and low tide boundary and its adjacent areas. Specifically, the Canny edge detection algorithm is used to identify the boundaries by calculating the gradient strength and direction of the image. The formula is: and Among them, G is the magnitude of the gradient, G x and G y is the gradient of the image in the horizontal and vertical directions, Θ is the direction of the gradient, and the Canny algorithm also includes non-maximum suppression and double threshold processing steps to ensure that the details of the edge are accurately captured. In this way, the boundaries of the coastline and its adjacent areas are accurately calibrated and the morphology is described in detail; through the rapid identification of macro-scale geomorphic features and detailed boundary demarcation at the micro scale, this step can effectively distinguish and identify the coastline and its adjacent areas. The region growing algorithm at the macro scale provides an efficient landform recognition method, while the Canny edge detection at the micro scale ensures high precision of the boundary and clarity of the morphology. This multi-scale processing method not only improves the accuracy and efficiency of image segmentation, but also provides important geospatial information for the calculation of coastal erosion.

[0089] S3 specifically includes:

[0090] S31: First, the latest coastline identified and optimized in S2 is used as the initialization boundary. This initialization process ensures that the dynamic boundary detection technology starts from an accurate and verified baseline, providing a stable starting point for subsequent dynamic tracking;

[0091] S32: Before starting tracking, ensure accurate alignment between multiple remote sensing images. Specifically, image registration technology is used to correct any image offset caused by changes in sensor position or environmental factors by calculating the optimal transformation between the two images. Mutual Information (MI) is used as the registration criterion. The calculation formula is: Among them, X and Y represent two remote sensing images that need to be registered; p X,Y (x, y) represents the joint probability density function of the simultaneous occurrence of pixel values ​​x and y in image X and image Y; p X (x) and p Y (y) is the marginal probability density function of pixel values ​​x and y in image X and image Y, that is, the probability of x and y appearing in their respective images; log is the natural logarithm, which is used to calculate the logarithm of the ratio of two probabilities, reflecting the statistical dependence of X and Y;

[0092] S33: Use dynamic boundary detection technology based on optical flow to automatically track the position changes of the coastline and the high tide and low tide boundary in multiple images. The optical flow method predicts the dynamic changes of the coastline by analyzing the movement of each pixel over time. The specific formula is: x u+f y v+f t =0, where f x and f y is the spatial derivative of the image, which indicates the rate of change of the brightness of the image in the horizontal direction x and the vertical direction y; f t is the time derivative of the image, indicating the brightness change of the image in the time dimension; u and v represent the horizontal and vertical velocity components of each pixel in the image, indicating the movement speed of the pixel on the image plane;

[0093] S34: Collect all the coastline change data obtained by tracking in S33 and conduct integrated analysis, including calculating the movement distance and direction of the coastline at each time point, and statistical analysis of the change trend, to provide dynamic input data for the final erosion calculation; the specific steps include:

[0094] S341: Calculate the moving distance and direction of the coastline. The moving distance and direction are determined by comparing the position changes of the coastline in the continuous images at each time point. Specifically, assuming that the positions of the coastline at time t1 and t2 are p1(x1'y1) and p2(x2, y2) respectively, the moving distance D and direction θ can be calculated by the following formula:

[0095]

[0096] Where D represents the straight-line distance between the coastline points at two time points; x1, y1, x2, y2 represent the coordinate positions of the coastline at the two time points; θ represents the direction of movement, which is the angle from the first time point to the second time point;

[0097] S342: Statistical analysis of changing trends, specifically using linear regression analysis to evaluate the trend of coastline movement, can be expressed by the following formula to express the trend equation of the coastline position changing over time: y = β0 + β1t + ∈, where y is the dependent variable, representing the position of the coastline at a specific time; t is the independent variable, representing time; β0 and β1 are regression coefficients, where β0 is the intercept and β1 is the slope, representing the rate of change of position over time; ∈ is the error term, representing the deviation between the observed value and the model predicted value; through the above series of steps, S3 not only effectively utilizes advanced image processing and analysis technology to automatically track the dynamic changes of the coastline, but also ensures the accurate alignment of data and the continuity of analysis. This dynamic boundary detection method provides an efficient and automated way to monitor the time series changes of the coastline, enhances the scientificity and accuracy of coastal erosion monitoring and prediction, and provides important technical support for coastal management and environmental protection.

[0098] S4 specifically includes:

[0099] S41: Before building the 3D coastline model, first integrate and preprocess the coastline dynamic data and ground elevation data from S3. The preprocessing includes data cleaning, formatting, and coordinate system unification to ensure that all data are consistent in spatial reference, providing a basis for building the 3D model.

[0100] S42: Using the integrated data, the digital elevation model (DEM) technology is applied to generate the three-dimensional terrain of the coastline and its adjacent areas. Specifically, the interpolation method is used to generate the terrain surface. The formula is:

[0101]

[0102] Where z is the elevation value of the interpolation point; x, y are the geographic coordinates of the interpolation point; z i is the elevation value of the known point; d iis the distance from the known point to the interpolation point; i is a weight factor, which is inversely correlated with the distance; p is a positive constant used to adjust the influence of the distance weight, and its value is 2;

[0103] S43: On the generated three-dimensional terrain model, according to the dynamic data of the coastline tracked in S3, the three-dimensional path of the coastline is calculated and depicted. Specifically, the two-dimensional position data of the coastline is converted into three-dimensional space coordinates using linear interpolation method. The formula is: Among them, z t is the elevation on the coastline at time point t; x t is the horizontal position of the coastline at time t; z t1 and z t2 is the elevation value at known time points t1 and t2; x t1 and x t2 is the corresponding horizontal position;

[0104] S44: Refine and optimize the initially constructed 3D model to improve the accuracy and visual effect of the model, including smoothing the 3D path of the coastline and adjusting the texture and color of the model to enhance the realism and readability of the model;

[0105] S45: Finally, the constructed three-dimensional coastline model is compared and verified with the actual topographic survey data to ensure the accuracy of the model, and the model is adjusted according to the verification results, including correcting the elevation data of the terrain or the path data of the coastline to ensure the scientificity and practicality of the model.

[0106] S44 specifically includes:

[0107] S441: In the refinement stage of the 3D model, the 3D path of the coastline is first smoothed to eliminate jagged or irregular edges caused by interpolation and measurement errors. Specifically, the B-spline curve method is used to smooth the path points. The specific formula is: Among them, S(t) is the smoothed three-dimensional path point; P i is the original path point; B i,k (t) is a B-spline basis function with degree k, t is a parameter, and varies in the interval [0, 1]. B-spline curve provides a flexible way to control the shape of the curve, and can adjust the smoothness of the curve as needed, effectively improving the visual display quality of the coastline.

[0108] S442: Then, the texture and color of the 3D model are adjusted to enhance the realism and readability of the model. The texture mapping and color adjustment include the following steps:

[0109] S4421: Perform texture mapping, apply pixel-by-pixel texture mapping technology, map the real-world terrain texture to the surface of the 3D model, and use the following formula to calculate the texture coordinates:

[0110] Among them, (u, v) is the texture coordinate; (x, y) is the coordinate of the model surface point; x min ,x max ,y min ,y max are the minimum and maximum values ​​of the coordinates of the model surface points;

[0111] S4422: Adjust the color to improve the distinction according to the different terrain features and environmental conditions of the coastline. Use linear interpolation to adjust the color to match the elevation or erosion degree of the terrain. The specific color adjustment formula is: Where c is the adjusted color value; c min and c max are the minimum and maximum values ​​of the color range; z is the elevation value; min and z max are the minimum and maximum values ​​of the elevation; the application of the above steps not only optimizes the visual effect of the 3D coastline model, making it more realistic and detailed, but also improves the resolution and usability of the model. Through smoothing and fine adjustment of texture and color, the scientific and educational value of the model is enhanced, providing researchers and decision makers with a high-quality visual analysis tool.

[0112] S5 specifically includes:

[0113] S51: Integrate the ocean dynamics model into the three-dimensional coastline model to simulate the impact of tidal, wave and wind environmental factors on coastline erosion. The ocean dynamics model includes tidal model, wave model and wind model. The tidal model is used to calculate the water level changes caused by tides; the wave model is used to evaluate the impact of wave height, period and direction on the coastline; the wind model is used to analyze wind speed and direction, and its impact on water flow and sand material movement;

[0114] S52: The physical model of sandy coastal erosion is introduced, combined with ocean dynamics data, to calculate the erosion amount. The formula includes comprehensive consideration of tidal height, wave impact and wind force. The specific calculation formula is:

[0115] Where E is the erosion amount, H w is the wave height, H t is the tidal height, τ w is the wave impact force, F w is the wind force, ρ sis the density of the sandy material, K is the erosion coefficient, which is used to convert the calculated physical action into erosion;

[0116] S53: Combine the physical model output of S52 and the coastline change data in S34 to calculate the current erosion and predict future erosion trends. Then, the calculation results are directly integrated and updated into the three-dimensional model to reflect the new position and shape of the coastline. The above method not only improves the accuracy of erosion prediction, but also enhances the adaptability of the model to environmental changes, so that the model can be used not only for current erosion assessment, but also for long-term coastline management and planning. In addition, by updating the model in real time and performing real-time analysis, the changes in the coastline can be reflected in real time, providing support for decision-making and helping to formulate more effective coastal protection and restoration strategies.

[0117] S53 specifically includes:

[0118] S531: Combine the shoreline dynamic data (such as movement distance and direction) in S34 with the physical model output, and the formula is: Among them, E total is the comprehensive erosion amount, E i is the single erosion amount at each time point;

[0119] S532: Use dynamic simulation technology to predict future erosion based on marine environmental data (waves, tides and wind) and historical coastline change patterns. During the simulation, the amount of erosion in the future time period is calculated using the following formula: E future =E current +ΔE, where E future is the future erosion, E current is the current amount of erosion, and ΔE is the expected change;

[0120] S533: The calculated erosion results are directly updated to the 3D model to reflect the new position and shape of the coastline. The updating process includes adjusting the vertex coordinates of the 2D model to reflect the position change after erosion. By combining the dynamic coastline data of S34 and the comprehensive physical model prediction, this method not only improves the accuracy of erosion prediction, but also enhances the model's adaptability to environmental changes, making the model not only suitable for current erosion assessment, but also for long-term coastline management and planning.

[0121] S6 specifically includes:

[0122] S61: Collect ground-based measured data and historical erosion records, and ensure that the data covers the same time period and spatial range as the results calculated in S5. The data include the actual measured coastline location, erosion depth and environmental conditions;

[0123] S62: Preprocess and align the collected ground-based data with the historical erosion records to ensure that they are consistent with the erosion data calculated in S5 in time and space. Specifically, a spatial registration algorithm is used to align different data sources. The registration formula is: T = A·X+b, where T is the registered data; A is the transformation matrix used to adjust the scale and rotation; X is the original data point; and b is the translation vector.

[0124] S63: By comparing the calculation results in S5 with the ground measured data, the error index is calculated. The specific error analysis methods include root mean square error (RMSE) and mean absolute error (MAE). The calculation formula is as follows:

[0125] Mean Square Error (RMSE):

[0126] Mean Absolute Error (MAE): in, is the erosion amount calculated in S5; is the actual observed erosion; n is the number of samples;

[0127] S64: According to the error analysis results, the parameters of the erosion calculation model are adjusted to improve the accuracy of the model. The calibration process is specifically performed through a gradient descent optimization algorithm. The optimization goal is to minimize the error function. The formula is: Where J(θ) is the error function; m is the number of samples; h θ (x i ) is the model prediction value; y i is the actual value; θ is the model parameter;

[0128] S65: After the model is calibrated, the ground measured data is used again for verification to ensure that the calibrated model can accurately predict the amount of erosion. Through repeated iterative optimization and verification, an accurate erosion calculation model is finally obtained. Through the above steps, S6 not only verifies the accuracy of the erosion calculation, but also significantly improves the reliability and accuracy of the model through systematic error analysis and calibration process. The calibrated model can more accurately reflect the actual coastal erosion situation and provide a solid scientific basis for coastline management and protection.

[0129] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A rapid calculation method for sandy coastal erosion based on multi-period remote sensing images, characterized in that: The following steps are involved: S1: First, select the target sandy coastline area and collect multiple remote sensing images of the area. Then, use data assimilation technology to integrate remote sensing data from different time points and different sensors to form a unified data framework. S2: Use a preset multi-scale image segmentation algorithm to process the remote sensing image integrated in S1 to distinguish the coastline, the boundary line of high tide and low tide and its adjacent areas; S3: Based on S2, dynamic boundary detection technology is used to automatically track the position changes of the coastline and low-tide edge in multiple images to obtain dynamic data of the upper and lower boundaries of the beach; S4: Combine the dynamic data of the coastline and low tide boundary obtained in S3 with the ground elevation data to construct a three-dimensional model of the beach to show the vertical and horizontal changes of the sandy coastline; S5: Based on the three-dimensional model of S4, the ocean dynamics and sandy coastal erosion physical models are introduced, combined with the dynamic data of the marine environment, to calculate and predict the erosion amount in different time periods; S6: Verify and calibrate the accuracy of erosion calculation by comparing and analyzing the calculation results in S5 with ground measured data and historical erosion records.

2. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 1 is characterized in that: The S1 specifically includes: S11: First, the target coastline area is determined and selected through the Geographic Information System (GIS) technology, and the area is defined using GIS to select the predetermined sandy coastline; S12: Based on the area selected in S11, multiple remote sensing platforms are used to collect multi-period remote sensing images of the area. The multiple remote sensing platforms include optical satellites, synthetic aperture radar satellites and infrared sensors. The images collected during the collection process should include images of different seasons and weather conditions to obtain a comprehensive data set. The timestamps and environmental conditions of the images should be recorded synchronously for each period of image collection to provide auxiliary information for subsequent data assimilation. S13: Use data assimilation technology to integrate the remote sensing data collected in S12, and use the ensemble Kalman filter to uniformly process the remote sensing data to eliminate data errors and inconsistencies caused by differences in different remote sensing platforms and time differences, and finally form a unified data framework to provide a data basis for coastline erosion analysis.

3. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 1 is characterized in that: The S2 specifically includes: S21: Before applying the multi-scale image segmentation algorithm, the data frame integrated in S1 is first preprocessed, including grayscale processing, denoising and contrast enhancement of the remote sensing image to improve the visual distinction of the coastline and its adjacent areas in the image; S22: Use the preset multi-scale image segmentation algorithm to identify and distinguish image features at different scales. Specifically, first identify the geomorphic features at the macro scale, including the general direction of the coastline, and then finely distinguish the specific boundaries and morphology of the coastline, the high tide and low tide boundary and its adjacent areas at the micro scale; S23: Based on S22, the boundary optimization technology is used to refine the boundaries of the coastline, high tide and low tide boundaries and their adjacent areas. By analyzing multiple factors such as terrain gradient, texture differences and color changes, the boundary lines of each area are accurately adjusted and optimized; S24: Finally, the processed image in S23 is compared and verified with the field measurement data and historical maps. Through comparative analysis, it is checked whether the recognition results of the coastline and its adjacent areas are accurate.

4. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 3 is characterized in that: The S22 specifically includes: S221: On a macro scale, a regional growing algorithm based on image texture and color homogeneity is used to perform preliminary identification of landform features. A seed point is set, and then the surrounding pixels with similar texture or color characteristics to the seed point are merged into one region. The specific formula is expressed as: Among them, R represents the final area, P is the pixel set, S is the seed point set, n is the number of seed points, similarity() is the similarity test function, and T is the threshold; S222: At the microscopic scale, an edge detection-based algorithm is used to further refine the specific boundaries and morphology of the coastline, high tide and low tide boundary and its adjacent areas. Specifically, the Canny edge detection algorithm is used to identify the boundaries by calculating the gradient strength and direction of the image. The formula is: and Among them, G is the magnitude of the gradient, G x and G y is the gradient of the image in the horizontal and vertical directions, Θ is the direction of the gradient, and the Canny algorithm also includes non-maximum suppression and double threshold processing steps to ensure that the edge details are accurately captured.

5. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 4 is characterized in that: The S3 specifically includes: S31: First, use the latest coastline identified and optimized in S2 as the initialization boundary; S32: Before starting tracking, ensure accurate alignment between multiple remote sensing images. Specifically, use image registration technology to correct any image offset caused by changes in sensor position or environmental factors by calculating the optimal transformation between the two images. Use mutual information as the registration criterion. The calculation formula is: Among them, X and Y represent two remote sensing images that need to be registered; p X，Y (x, y) represents the joint probability density function of the simultaneous occurrence of pixel values ​​x and y in image X and image Y; p X (x) and p Y (y) is the marginal probability density function of pixel values ​​x and y in image X and image Y, respectively, that is, the probability of x and y appearing in their respective images; log is the natural logarithm, which is used to calculate the logarithm of the ratio of two probabilities, reflecting the statistical dependence of X and Y; S33: Use dynamic boundary detection technology based on optical flow to automatically track the position changes of the coastline and the high tide and low tide boundary in multiple images. The optical flow method predicts the dynamic changes of the coastline by analyzing the movement of each pixel over time. The specific formula is: x u+f y v+f t =0, where f x and f y is the spatial derivative of the image, which indicates the rate of change of the brightness of the image in the horizontal direction x and the vertical direction y; f t is the time derivative of the image, indicating the brightness change of the image in the time dimension; u and v represent the horizontal and vertical velocity components of each pixel in the image respectively; S34: Collect all the coastline change data tracked in S33 and conduct integrated analysis, including calculating the movement distance and direction of the coastline at each time point, and statistical analysis of the change trend, to provide dynamic input data for the final erosion calculation.

6. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 1, characterized in that: The S4 specifically includes: S41: Before building the 3D coastline model, first integrate and preprocess the coastline dynamic data and ground elevation data from S3. The preprocessing includes data cleaning, formatting, and coordinate system unification to ensure that all data are consistent in spatial reference, providing a basis for building the 3D model. S42: Using the integrated data, the digital elevation model technology is applied to generate the three-dimensional terrain of the coastline and its adjacent areas. Specifically, the interpolation method is used to generate the terrain surface. The formula is: Where z is the elevation value of the interpolation point; x, y are the geographic coordinates of the interpolation point; z i is the elevation value of the known point; d i is the distance from the known point to the interpolation point; i is the weight factor; p is a positive constant used to adjust the influence of the distance weight, and its value is 2; S43: On the generated three-dimensional terrain model, according to the dynamic data of the coastline tracked in S3, the three-dimensional path of the coastline is calculated and depicted. Specifically, the two-dimensional position data of the coastline is converted into three-dimensional space coordinates using linear interpolation method. The formula is: Among them, z t is the elevation on the coastline at time point t; x t is the horizontal position of the coastline at time t; z t1 and z t2 is the elevation value at known time points t1 and t2; x t1 and x t2 is the corresponding horizontal position; S44: Refine and optimize the initially constructed 3D model, including smoothing the 3D path of the coastline and adjusting the texture and color of the model to enhance the realism and readability of the model; S45: Finally, the constructed three-dimensional coastline model is compared and verified with the actual topographic survey data to ensure the accuracy of the model, and the model is adjusted according to the verification results, including correcting the elevation data of the terrain or the path data of the coastline.

7. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 6 is characterized in that: The S44 specifically includes: S441: In the refinement stage of the 3D model, the 3D path of the coastline is first smoothed to eliminate jagged or irregular edges caused by interpolation and measurement errors. Specifically, the B-spline curve method is used to smooth the path points. The specific formula is: Among them, S(t) is the smoothed three-dimensional path point; P i is the original path point; B i，k (t) is a B-spline basis function of degree k, t is a parameter, which varies in the interval [0, 1]; S442: Then, the texture and color of the 3D model are adjusted to enhance the realism and readability of the model. The texture mapping and color adjustment include the following steps: S4421: Perform texture mapping, apply pixel-by-pixel texture mapping technology, map the real-world terrain texture to the surface of the 3D model, and use the following formula to calculate the texture coordinates: Among them, (u, v) is the texture coordinate; (x, y) is the coordinate of the model surface point; x min , x max ,y min ,y max are the minimum and maximum values ​​of the coordinates of the model surface points; S4422: Adjust the color to improve the distinction according to the different terrain features and environmental conditions of the coastline. Use linear interpolation to adjust the color to match the elevation or erosion degree of the terrain. The specific color adjustment formula is: Where c is the adjusted color value; c min and c max are the minimum and maximum values ​​of the color range; z is the elevation value; min and z max are the minimum and maximum values ​​of the elevation.

8. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 1, characterized in that: The S5 specifically includes: S51: Integrate the ocean dynamics model into the three-dimensional coastline model to simulate the impact of tidal, wave and wind environmental factors on coastline erosion. The ocean dynamics model includes tidal model, wave model and wind model. The tidal model is used to calculate the water level changes caused by tides; the wave model is used to evaluate the impact of wave height, period and direction on the coastline; the wind model is used to analyze wind speed and direction, and its impact on water flow and sand material movement; S52: The physical model of sandy coastal erosion is introduced, combined with ocean dynamics data, to calculate the erosion amount. The formula includes comprehensive consideration of tidal height, wave impact and wind force. The specific calculation formula is: Where E is the erosion amount, H w is the wave height, H t is the tidal height, τ w is the wave impact force, F w is the wind force, ρ s is the density of sandy material, K is the erosion coefficient; S53: Combine the physical model output of S52 and the shoreline change data in S34 to calculate the current erosion amount and predict the future erosion trend. Then integrate and update the calculation results directly into the 3D model to reflect the new position and shape of the shoreline.

9. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 8, characterized in that: The S53 specifically includes: S531: Combine the shoreline dynamic data in S34 with the physical model output. The formula is: Among them, E total is the comprehensive erosion amount, E i is the single erosion amount at each time point; S532: Use dynamic simulation technology to predict future erosion based on marine environmental data and historical coastline change patterns. During the simulation, the amount of erosion in the future time period is calculated using the following formula: E future =E current +ΔE, where E future is the future erosion, E current is the current amount of erosion, and ΔE is the expected change; S533: directly updating the calculated erosion results into the three-dimensional model to reflect the new position and shape of the coastline. The updating process includes adjusting the vertex coordinates of the two-dimensional model to reflect the position change after erosion.

10. The method for rapidly calculating the amount of sandy coastal erosion based on multi-period remote sensing images according to claim 9, characterized in that: The S6 specifically includes: S61: Collect ground-based measured data and historical erosion records, and ensure that the data covers the same time period and spatial range as the results calculated in S5. The data include the actual measured coastline location, erosion depth and environmental conditions; S62: Preprocess and align the collected ground-based data with the historical erosion records to ensure that they are consistent with the erosion data calculated in S5 in time and space. Specifically, a spatial registration algorithm is used to align different data sources. The registration formula is: T = A·X+b, where T is the registered data; A is the transformation matrix used to adjust the scale and rotation; X is the original data point; and b is the translation vector. S63: Calculate error indicators by comparing the calculation results in S5 with the ground measured data. Specific error analysis methods include root mean square error and mean absolute error. S64: According to the error analysis results, the parameters of the erosion calculation model are adjusted. The calibration process is specifically performed through a gradient descent optimization algorithm. The optimization goal is to minimize the error function. The formula is: Where J(θ) is the error function; m is the number of samples; h θ (x i ) is the model prediction value; y i is the actual value; θ is the model parameter; S65: After the model is calibrated, it is verified again using ground measured data to ensure that the calibrated model can accurately predict the amount of erosion. Through repeated iterative optimization and verification, an accurate erosion calculation model is finally obtained.

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