Method and apparatus for measuring water depth in sand dunes using remote sensing images

Abstract

This invention provides a method and apparatus for measuring sand wave depth using remote sensing images, relating to the field of optical remote sensing technology. This invention extracts sand wave morphology parameters through spectral analysis and inverts them with water depth, enabling large-scale and rapid water depth measurement using multispectral imagery without relying on traditional acoustic detection. Simultaneously, by optimizing the measurement path based on a location information value function, the path planning during the measurement process is optimized, reducing redundant measurement areas and improving measurement efficiency. Furthermore, an error correction algorithm using Kriging spatial interpolation is employed. Based on the residual values ​​between the measured high-precision water depth data and the inverted data, an error estimation surface is generated, and error correction is performed through pixel-by-pixel algebraic operations. Spatial registration ensures the comparison and matching of measured and inverted data, solving the application problems of traditional remote sensing methods in complex water areas and under unstable lighting conditions.

Description

Technical Field

[0001] This invention relates to the field of optical remote sensing technology, specifically to a method and apparatus for measuring the water depth of sand waves using remote sensing images. Background Technology

[0002] In cross-sea wind power projects, electricity needs to be transmitted from the offshore wind farm to the onshore power grid control center via submarine cables. The route selection, safe laying, and long-term operation and maintenance of submarine cables are the lifeline of the entire project, and all of this depends on a precise understanding of the seabed topography, landforms, and seabed conditions. Sand waves are sedimentary landforms shaped by water currents on the seabed, like sand dunes in a desert. They move slowly or change shape with ocean currents and storms. For cables lying on the seabed, when sand waves migrate, the cables at the troughs may be suspended in the water because the bottom support is hollowed out. They are prone to fatigue damage due to water current eddy vibration and eventually break. The movement of sand wave crests may bury the cables, which will bring great difficulties to subsequent inspection, maintenance, and fault location.

[0003] However, traditional techniques rely solely on shipborne acoustic measurements or remote sensing water depth inversion measurements. Even with densely packed survey lines, shipborne acoustic measurements lack actual data for the areas between them, relying entirely on mathematical interpolation algorithms to infer topography. For complex and rapidly changing micro-landforms like sand waves, the interpolation results are highly uncertain, potentially missing or distorting crucial sand wave features. Similarly, remote sensing water depth inversion measurements suffer from limited spatial resolution of satellite imagery, resulting in insufficient morphological characterization of small-scale sand waves and steep sand wave flanks. Furthermore, traditional optical remote sensing measurements are easily affected by factors such as water transparency, lighting conditions, and climate change, limiting inversion accuracy. Existing water depth inversion models are poorly suited to complex water areas and cannot effectively handle errors during the inversion process, leading to low measurement accuracy and an inability to precisely extract key parameters such as wave height and slope.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for measuring the water depth of sand waves using remote sensing images, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The method for measuring the water depth of sand waves using remote sensing images includes the following steps:

[0008] Step 1: Acquire multispectral images of the water area to be measured, and extract sand wave morphology parameters through spectral analysis. Based on water optics theory, establish a water depth inversion model between sand wave morphology parameters and water depth. Apply the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured.

[0009] Step 2: Perform topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. Establish a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value, and with the total survey line length and maximum survey line spacing as constraints, use a metaheuristic algorithm to solve the location information value function to obtain the optimal survey line.

[0010] Step 3: Use acoustic detection method to measure according to the optimal survey line to generate high-precision measured water depth data in the study area. Spatially register the high-precision measured water depth data and the water depth inversion data in a unified coordinate system. Through position matching, calculate the residual between the two point by point to obtain the error value between the measured high-precision water depth value and the water depth inversion value.

[0011] Step 4: Based on the obtained error value, the Kriging spatial interpolation algorithm is used to obtain the error estimate. The error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data in a unified geographic coordinate system to obtain the corrected water depth data.

[0012] Furthermore, the morphological parameters of the sand wave include bottom sediment reflectivity, water attenuation coefficient, and deep-water remote sensing reflectivity.

[0013] Furthermore, the specific steps for extracting sand wave morphology parameters are as follows:

[0014] Spectral coefficients are set, and Fourier transform is performed on the spectral curve of each pixel in the multispectral image. Low-pass filtering is used to extract the baseline signal, and band-pass filtering is used to extract the characteristic signals of each band. Inverse Fourier transform is performed on the baseline and the characteristic signals of each band to obtain the baseline and the characteristic spectra of each band. The characteristic spectra of each band are multiplied by the spectral coefficients to obtain the characteristics of each band. The baseline spectrum is added to the characteristics of each band to obtain the background reflectance curve of each spectrum. The center wavelengths of the blue band, green band, red band and near-infrared band are determined, and the background reflectance at the center wavelength of each band of each pixel is extracted.

[0015] Set the spectral index and the scaling factor for each band, calculate the spectral index power of the bottom reflectance in the blue, green, red, and near-infrared bands to obtain the spectral value for each band, and calculate the product of the scaling factor and the spectral value for each band to obtain the water body attenuation coefficient.

[0016] A reflection threshold is set. For each pixel in the multispectral image, the reflectance of the near-infrared band is compared with the reflection threshold. If the reflectance of the near-infrared band is less than or equal to the reflection threshold, it is marked as a deep-water pixel. The reflectance of the blue, green, red and near-infrared bands in the deep-water pixel is extracted to obtain the deep-water remote sensing reflectance of each band.

[0017] Furthermore, the specific steps for constructing the water depth inversion model are as follows:

[0018] Texture modulation depth is extracted from the multispectral image of the water area to be measured. The difference between the bottom reflectance and the deep water remote sensing reflectance is calculated to obtain the first difference value. A calibration constant is set, and the product of the calibration constant and the first difference value is calculated to obtain the first value value. Logarithmic operation is performed based on the ratio of the first value value and the texture modulation depth to obtain the water depth prediction variable. The water depth is obtained by calculating the water depth prediction variable and the two-way band water body attenuation coefficient.

[0019] Furthermore, the specific steps for obtaining the water depth slope, water depth curvature, and local water depth standard deviation are as follows:

[0020] A two-dimensional coordinate system is constructed based on the multispectral image of the water area to be measured. For each pixel in the multispectral image, the water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid with the pixel as the center. The first water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth difference is also obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The second water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first water depth value and the second water depth value.

[0021] The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The first water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The second water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first water depth value and the second water depth value.

[0022] The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The third water depth value is obtained by the difference between the water depth difference and twice the water depth at point x. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The fourth water depth value is obtained by the difference between the water depth difference and twice the water depth at point x. The water depth curvature is obtained by calculating the average water depth between the third and fourth water depth values.

[0023] Furthermore, the specific steps for constructing the information value function are as follows:

[0024] The parameters of water depth slope, water depth curvature, and local water depth standard deviation are normalized, and the location information value function is obtained by weighted fusion of the normalized parameters.

[0025] Furthermore, the specific steps for solving the location information value function to obtain the optimal survey line are as follows:

[0026] Within the study area, K parallel survey lines are generated using a heuristic initialization method, and these lines are used as the initial survey line layout scheme. The total measurement length does not exceed the maximum survey line length, and the distance between adjacent survey lines does not exceed the maximum allowable distance.

[0027] The total coverage information value function is obtained by summing the information values ​​of all pixels within the study area by double summation and calculating the sum of the information values ​​of pixels covered by at least one survey line.

[0028] All total coverage information value functions are arranged in descending order, and the survey line layout scheme is selected from the current population through a tournament selection process to enter the next generation;

[0029] The selected outstanding individuals are paired up, some parameters are exchanged to generate new survey line layout schemes, and the survey line layout schemes are changed by randomly fine-tuning the line spacing. The survey line layout scheme with the highest fitness in each generation is directly retained to the next generation. Through iterative screening, the optimal survey line is obtained.

[0030] Furthermore, the specific steps to obtain the corrected water depth data are as follows:

[0031] Multiply the water depth inversion error values ​​of all measured points by the Kriging weights to obtain the optimal weight for all measured points, and sum the optimal weights of all measured points to obtain the error estimate of the grid cells.

[0032] The error estimate is then summed pixel-by-pixel in a unified geographic coordinate system with the water depth inversion data to obtain the corrected water depth data.

[0033] The present invention also provides an apparatus for measuring the depth of sand waves using remote sensing images, the measuring apparatus being used to perform the above-described measurement method, comprising:

[0034] The model building module acquires multispectral images of the water area to be measured, extracts sand wave morphology parameters through spectral analysis, establishes a water depth inversion model between sand wave morphology parameters and water depth based on water optics theory, and applies the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured.

[0035] The survey line calculation module performs topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. It also establishes a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value and with the total survey line length and maximum survey line spacing as constraints, a metaheuristic algorithm is used to solve the location information value function to obtain the optimal survey line.

[0036] The error acquisition module uses acoustic detection to measure along the optimal survey line, generating high-precision measured water depth data within the study area. The high-precision measured water depth data and the water depth inversion data are spatially registered in a unified coordinate system. Through position matching, the residual between the two is calculated point by point to obtain the error value between the high-precision measured water depth value and the water depth inversion value.

[0037] The water depth data module uses the Kriging spatial interpolation algorithm to obtain an error estimate based on the obtained error value. The error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data in a unified geographic coordinate system to obtain the corrected water depth data.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] This invention extracts sand wave morphology parameters through spectral analysis and inverts them with water depth, enabling large-scale and rapid water depth measurement using multispectral imagery without relying on traditional acoustic detection. Simultaneously, by performing topographic analysis on the water depth inversion data, features such as water depth slope and curvature are extracted, and the measurement path is optimized based on the location information value function, thus optimizing path planning during the measurement process, reducing redundant measurement areas, and improving measurement efficiency.

[0040] This invention also employs the Kriging spatial interpolation algorithm for error correction. Based on the residual values ​​of the measured high-precision water depth data and the inverted data, it can generate an error estimation surface and perform error correction through pixel-by-pixel algebraic operations. Through spatial registration, it ensures the comparison and matching of the measured data and the inverted data, allowing the error correction to improve the accuracy of each measurement point in detail. This solves the application problems of traditional remote sensing methods in complex waters and unstable lighting conditions. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0042] Figure 2 This is a function curve of bottom sediment reflectance versus water depth inversion value;

[0043] Figure 3 A comparison table of measured high-precision water depth values ​​and water depth inversion values;

[0044] Figure 4This is a schematic diagram of the overall device of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0046] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0047] Example:

[0048] Please see Figure 1-3 The present invention provides a technical solution:

[0049] The method for measuring the water depth of sand waves using remote sensing images includes the following steps:

[0050] Step 1: Acquire multispectral images of the water area to be measured, and extract sand wave morphology parameters through spectral analysis. Based on water optics theory, establish a water depth inversion model between sand wave morphology parameters and water depth. Apply the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured.

[0051] In this embodiment, the morphological parameters of the sand wave include bottom reflectivity, water attenuation coefficient, and deep-water remote sensing reflectivity.

[0052] In this embodiment, the specific steps for extracting sand wave morphology parameters are as follows:

[0053] Spectral coefficients are set, and Fourier transform is performed on the spectral curve of each pixel in the multispectral image. Low-pass filtering is used to extract the baseline signal, and band-pass filtering is used to extract the characteristic signals of each band. Inverse Fourier transform is performed on the baseline and the characteristic signals of each band to obtain the baseline and the characteristic spectra of each band. The characteristic spectra of each band are multiplied by the spectral coefficients to obtain the characteristics of each band. The baseline spectrum is added to the characteristics of each band to obtain the background reflectance curve of each spectrum. The center wavelengths of the blue band, green band, red band and near-infrared band are determined, and the background reflectance at the center wavelength of each band of each pixel is extracted.

[0054] Set the spectral index and the scaling factor for each band, calculate the spectral index power of the bottom reflectance in the blue, green, red, and near-infrared bands to obtain the spectral value for each band, and calculate the product of the scaling factor and the spectral value for each band to obtain the water body attenuation coefficient.

[0055] The mathematical expression for calculating the water body attenuation coefficient is:

[0056] ;

[0057] In the formula, The water body attenuation coefficient represents the total attenuation ability of water body to absorb and scatter radiation of a specific frequency (corresponding band). The larger the value, the weaker the ability of radiation to penetrate the water body. Indicates the first The band scaling factor has a range of values. The value is determined by the inherent optical properties of the water body (such as pure water, suspended solids, and CDOM content), and its value is determined by expert experience. This represents the spectral index, and its value range is... This reflects the sensitivity of the water body attenuation coefficient to spectral frequencies. At that time, the higher the frequency / shorter the wavelength, the greater the water attenuation coefficient; its value was determined by expert experience. Indicates the first Substrate reflectance in each band, where i corresponds to the four bands B / G / R / NIR ( ), The time indicates the blue band. The time indicates the green band. The time indicates the red band. Time indicates the near-infrared band;

[0058] A reflection threshold is set. For each pixel in the multispectral image, the reflectance of the near-infrared band is compared with the reflection threshold. If the reflectance of the near-infrared band is less than or equal to the reflection threshold, it is marked as a deep-water pixel. The reflectance of the blue, green, red and near-infrared bands in the deep-water pixel is extracted to obtain the deep-water remote sensing reflectance of each band.

[0059] In this embodiment, Fourier transform converts the spectral curve from the wavelength domain to the frequency domain, low-pass filtering accurately extracts the low-frequency baseline, and band-pass filtering separates the high-frequency interference features of each band, achieving effective decoupling of the two types of signals. Inverse Fourier transform converts the baseline signal and feature signal in the frequency domain back to the wavelength domain, resulting in an interpretable spectral curve. The role of spectral coefficients is to quantify the weight of water body interference: after calibration with measured data, the differences in interference intensity in different bands can be eliminated. The superposition of the baseline spectrum and the weighted feature spectrum essentially restores the true spectrum of bottom sediment reflection, and the final output bottom sediment reflectance curve can be directly used to extract the reflectance value of the target band.

[0060] In this embodiment, the specific steps for constructing the water depth inversion model are as follows:

[0061] Texture modulation depth is extracted from the multispectral image of the water area to be measured. The difference between the bottom reflectance and the deep-water remote sensing reflectance is calculated to obtain the first difference value. A calibration constant is set, and the product of the calibration constant and the first difference value is calculated to obtain the first value. Logarithmic operation is performed based on the ratio of the first value to the texture modulation depth to obtain the water depth prediction variable. The water depth is obtained by calculating the water depth prediction variable and the two-way band water attenuation coefficient. The mathematical expression for calculating the water depth is:

[0062] ;

[0063] In the formula, This represents the water depth inversion value; This represents the calibration constant, the value of which is determined through expert experience, and its range is [range missing]. ; This represents the texture modulation depth, and its value range is... ;express Indicates the first Band deep-water remote sensing reflectance.

[0064] In this embodiment, 28 sets of water depth inversion model data were collected, where the calibration constant and texture modulation depth were global variables. The calibration constant was 0.015 and the texture modulation depth was 0.006. The data are shown in Table 1.

[0065] Table 1: Relationship between seabed reflectance, water attenuation coefficient, deep-water remote sensing reflectance, and water depth inversion value

[0066]

[0067] According to Table 1 and Figure 2It can be seen that as the water depth increases from 0.8m to 3.5m, the reflectivity of the bottom sediment in the green light band increases synchronously from 0.350 to 0.550, an increase of 57.1%. This trend is consistent with the physical mechanism of shallow water remote sensing: the greater the water depth, the weaker the attenuation effect of the water body on the bottom sediment reflective signal (combined with the change in the attenuation coefficient), and the higher the bottom sediment reflectivity captured by the sensor; the water attenuation coefficient ranges from 0.080. The value of 0.250 is completely consistent with the trend of bottom sediment reflectance. This is because an increase in bottom sediment reflectance usually corresponds to an increase in the content of suspended matter on the bottom of the water. Suspended matter enhances the absorption and scattering of green light by the water, leading to an increase in the attenuation coefficient. The deep-water remote sensing reflectance in the green light band is around 0.0030. In the 0.0080 range, the reflectance increases slowly with increasing water depth, with an increase of 166.7%. This characteristic reflects the stability of the optical properties of water bodies in deep water areas—the impact of increasing water depth on deep-water remote sensing reflectance is far less than the impact on bottom sediment reflectance; the first 21 data sets (H=0.8) In the 2.8m range, the bottom reflectance, water attenuation coefficient, and deep-water remote sensing reflectance all increased with a fixed step size, and the data were evenly distributed; the last 7 sets of data (H=2.9m) As the step size increases (3.5m), the parameter increase accelerates, reflecting that the response sensitivity of the bottom sediment and water optical properties increases when the water depth is greater than 2.8m.

[0068] In this embodiment, texture modulation depth is a quantitative indicator of the contrast strength of sand waves in remote sensing images. The amplitude of the sand wave signal can be obtained from the difference between the reflectance at the peak and the trough of the sand wave. The texture modulation depth can be obtained from the amplitude of the sand wave signal and the average intensity of the background signal.

[0069] Step 2: Perform topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. Establish a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value, and with the total survey line length and maximum survey line spacing as constraints, use a metaheuristic algorithm to solve the location information value function to obtain the optimal survey line.

[0070] In this embodiment, the specific steps for obtaining the water depth slope, water depth curvature, and local water depth standard deviation are as follows:

[0071] A two-dimensional coordinate system is constructed based on the multispectral image of the water area to be measured. For each pixel in the multispectral image, with that pixel as the center, the water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction. The first water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth difference is also obtained by calculating the water depth values ​​of two pixels apart in the y-direction. The second water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first and second water depth values. The mathematical expression for calculating the water depth slope is:

[0072] ;

[0073] in,

[0074] ;

[0075] ;

[0076] In the formula, Indicates position The slope at a point is a scalar quantity representing the steepness of the terrain at that point. Represents the row index of a cell. The column index representing the cell; Indicates in pixel The water was deep there. Rate of change along the x-direction; Represents a pixel The water depth at that location; This indicates the water depth value of the adjacent cell on the right (east side); This indicates the water depth value of the adjacent pixel on the left (west side); Represents the cell size in the x-direction (spatial resolution); represents the pixel size in the x-direction. The water was deep there. along Rate of change of direction; This indicates the water depth value of the adjacent pixel above (north side); Indicates the water depth value of the adjacent cell below (south side); indicates the cell size in the y direction (spatial resolution), usually related to... Equal (square pixels);

[0077] The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The first water depth value is obtained by comparing the water depth difference with the actual horizontal distance between the two pixels. The water depth difference is also obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The second water depth value is obtained by comparing the water depth difference with the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first and second water depth values. Therefore, the mathematical expression for calculating the water depth curvature is:

[0078] ;

[0079] in,

[0080] ;

[0081] ;

[0082] In the formula, Indicates position The (average) curvature at a point represents the overall degree of curvature of the terrain surface at that point; Indicates in pixel The water was deep there. The second-order central difference along the x-direction is numerically approximated. ; Indicates in pixel The water was deep there. along Second-order central difference of direction, numerical approximation ;;

[0083] The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The third water depth value is obtained by subtracting this difference from the water depth at twice the x-point. Similarly, the water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The fourth water depth value is obtained by subtracting this difference from the water depth at twice the x-point. The water depth curvature is obtained by calculating the average water depth between the third and fourth water depth values. Therefore, the mathematical expression for calculating the local water depth standard deviation is:

[0084] ;

[0085] in, ;

[0086] ;

[0087] In the formula, Represents a pixel The local water depth standard deviation measures the dispersion of water depth values ​​in the neighborhood centered on that point (i.e., local topographic relief). Indicates the location at coordinates The pixel water depth value at that location; Indicates The arithmetic mean of the water depths of all pixels within the central window; The window size must be an odd number (e.g., 3, 5, 7, etc.), and the neighborhood side length (number of pixels) used for statistics. The window radius (in pixels) represents the distance from the center pixel to the window boundary.

[0088] In this embodiment, the specific steps for establishing the location information value function are as follows:

[0089] After normalizing the parameters of water depth slope, water depth curvature, and local water depth standard deviation, and then weighting and fusing the normalized parameters, a location information value function is obtained. The mathematical expression for this location information value function is then established as follows:

[0090] ;

[0091] In the formula, Represents a pixel The higher the value of the information at a location, the more important that location is in the survey line layout (the more complex the terrain and the richer the information). The weighting coefficient representing the water depth gradient has a range of values. ; This indicates the normalized water depth gradient. The original gradient has been normalized to eliminate the influence of dimensions and orders of magnitude. The weighting coefficient representing the mean curvature has a range of values. ; This represents the normalized water depth curvature. The original water depth curvature can be positive (concave) or negative (convex), but both types of curvature increase the complexity of the terrain. Therefore, the absolute value is taken so that it makes a positive contribution to the value. The weighting coefficient representing the local standard deviation of water depth has a range of values. ,and ; This represents the normalized standard deviation of local water depth. The original measurement measures the degree of local water depth variation, and the normalized version is also scaled to the mean. Interval.

[0092] In this embodiment, the larger the value of the local water depth standard deviation, the more drastic the water depth change within the window; the smaller the value, the flatter the terrain within the window.

[0093] In this embodiment, the specific steps for normalizing the parameters of water depth slope, water depth curvature, and local water depth standard deviation are as follows:

[0094] To calculate the global statistics of water depth slope, water depth curvature, and local water depth standard deviation parameters, the mathematical expressions for calculating the maximum and minimum values ​​of these parameters are as follows:

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] In the formula, This represents the minimum global slope. This represents the maximum global slope. This represents the minimum global curvature. Indicates the global maximum curvature; This represents the minimum global local standard deviation. This represents the maximum value of the global local standard deviation;

[0102] By normalizing the parameters of water depth slope, water depth curvature, and local water depth standard deviation using Min-Max normalization, the mathematical expression for normalizing these parameters using Min-Max normalization is as follows:

[0103] ;

[0104] ;

[0105] .

[0106] In this embodiment, the weighting coefficients are calibrated using historical data. Due to the periodic undulations of sand waves, curvature (convex crests and concave troughs) is the most significant feature; the slope varies moderately, so the slope is generally moderate, but larger at the crest / trough transitions; the local undulations are regular, so the local standard deviation reflects the variation in sand wave amplitude (wave height). Therefore, in sand wave regions, curvature should be given the highest weight, as it directly reflects the spatial frequency and morphology of the sand waves.

[0107] In this embodiment, the specific steps for solving the location information value function to obtain the optimal survey line are as follows:

[0108] Within the study area, K parallel survey lines are generated using a heuristic initialization method, and these lines are used as the initial survey line layout scheme. The total measurement length does not exceed the maximum survey line length, and the distance between adjacent survey lines does not exceed the maximum allowable distance.

[0109] By doubly summing all pixels within the study area, the total coverage information value function is obtained by summing the information values ​​of pixels covered by at least one survey line. The mathematical expression of the total coverage information value function is as follows:

[0110] ;

[0111] In the formula, Represents the set of survey lines The total coverage information value function depends on the survey line layout, where Represents the set of survey lines; Indicates the coverage indicator variable, For a binary variable, when When, it represents a pixel. Covered by at least one survey line, when When, it represents a pixel. Not covered by the survey line Layout of survey lines Decision: When the survey line passes through a pixel or its vicinity (considering the width of the survey line), the pixel is marked as 1;

[0112] The objective function is then:

[0113] ;

[0114] The mathematical expression for the total survey line length constraint is:

[0115] ;

[0116] in,

[0117] ;

[0118] In the formula, This indicates the total number of survey lines, i.e., the number of survey lines laid out. Indicates the first The length of the survey line; Indicates the maximum permissible total length of survey lines; Indicates the first The total number of path points for each survey line; and Indicates survey line Upper The x and y coordinates of each point;

[0119] The mathematical expression for the maximum survey line spacing constraint is:

[0120] ;

[0121] In the formula, Indicates the vertical distance between adjacent survey lines; Indicates the maximum permissible spacing;

[0122] All total coverage information value functions are arranged in descending order, and the survey line layout scheme is selected from the current population through a tournament selection process to enter the next generation;

[0123] The selected outstanding individuals are paired up, some parameters are exchanged to generate new survey line layout schemes, and the survey line layout schemes are changed by randomly fine-tuning the line spacing. The survey line layout scheme with the highest fitness in each generation is directly retained to the next generation. Through iterative screening, the optimal survey line is obtained.

[0124] In this embodiment, the number of initial survey line layout schemes is 50-100. The parameters in each survey line layout scheme are randomly selected within the allowable range, and the initial population is evenly distributed in the search space to fully explore possible solutions.

[0125] In this embodiment, the starting point of the first survey line is determined based on the information value of each pixel, and the basic azimuth angle of the survey line is determined based on regional topographic features (such as the main water flow direction). Using the baseline spacing, K parallel survey lines are generated perpendicular to the foundation orientation. Each survey line layout scheme (individual) uses parametric coding: Let the foundation orientation angle be θ, and the starting point of the first survey line be... , length is , No. The vertical offset of the survey line relative to the first line is The length scaling factor is .

[0126] In this embodiment, the steps for calculating its fitness value are as follows:

[0127] The specific location of each survey line is calculated based on chromosome parameters. Based on the coverage width of the survey lines, it is determined which seabed pixels are scanned by these lines. The information value of all covered pixels is accumulated to obtain the original total value score of the layout. If the total survey line length and the spacing between adjacent survey lines exceed the upper limit, corresponding penalty points are deducted. Finally, based on... The overall fitness of each survey line layout scheme is determined, where a higher fitness indicates that the layout has high value and satisfies the constraints. The mathematical expression for the length penalty is:

[0128] ;

[0129] In the formula, This indicates the length penalty, which is the penalty value when the total survey line length exceeds the upper limit. This represents the length penalty coefficient, a positive number that controls the strictness of the length constraint (the larger the value, the heavier the penalty). This represents the total length of all survey lines;

[0130] The mathematical expression for the spacing penalty is:

[0131] ;

[0132] In the formula, This indicates the spacing penalty, which is the penalty value when the survey line spacing exceeds the upper limit. This represents the spacing penalty coefficient, a positive number that controls the strictness of the spacing constraint. This indicates the actual maximum spacing between survey lines (the maximum vertical distance between adjacent survey lines).

[0133] The mathematical expression for overall fitness is:

[0134] .

[0135] In this embodiment, to prevent premature convergence, a niche technique is employed, which involves calculating the similarity between individuals and penalizing similar individuals; each generation uses probability... Introduce entirely new random individuals; increase the mutation rate when the population diversity index is below a threshold.

[0136] Step 3: Use acoustic detection method to measure according to the optimal survey line to generate high-precision measured water depth data in the study area. Spatially register the high-precision measured water depth data with the water depth inversion data in a unified coordinate system. Through position matching, calculate the residual between the two points one by one to obtain the error value between the high-precision measured water depth value and the water depth inversion value.

[0137] In this embodiment, based on the obtained measured high-precision water depth data and water depth inversion data, the error value is obtained by calculating the residual between the two point by point. The mathematical expression for calculating the error value is as follows:

[0138] ;

[0139] In the formula, This represents the error between the measured high-precision water depth value at point p and the water depth inversion value; This represents the measured high-precision water depth value at point p; This represents the water depth inversion value at point p.

[0140] In this embodiment, 28 sets of error data between measured high-precision water depth values ​​and water depth inversion values ​​were statistically analyzed, and the data are shown in Table 2:

[0141] Table 2: Comparison Table of Measured High-Precision Water Depth Values ​​and Water Depth Inversion Values

[0142]

[0143] According to Table 2 and Figure 3It can be seen that positive bias (measured > inverted) appears in serial numbers 1, 7, 15, 22 and 23 (a total of 5 times), negative bias (measured < inverted) is the majority, there is no single systematic shift, which is consistent with the characteristics of random small fluctuations in actual remote sensing inversion; the bias is bidirectionally distributed (no single systematic shift), which is consistent with the comparison logic between acoustic measurement (centimeter-level accuracy) and remote sensing inversion (millimeter-level residual), and there are no abnormal error points.

[0144] Step 4: Based on the obtained error value, the Kriging spatial interpolation algorithm is used to obtain the error estimate. The error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data in a unified geographic coordinate system to obtain the corrected water depth data.

[0145] In this embodiment, the specific steps for obtaining the corrected water depth data are as follows:

[0146] Multiply the water depth inversion error values ​​of all measured points by the Kriging weights to obtain the optimal weight for all measured points, and sum the optimal weights of all measured points to obtain the error estimate of the pixel;

[0147] The error estimate is then combined with the water depth inversion data in a unified geographic coordinate system using a pixel-by-pixel algebraic summation to obtain the corrected water depth data.

[0148] The mathematical expression for the error estimate is:

[0149] ;

[0150] In the formula, Represents a pixel The estimation error; Point Kriging weights;

[0151] The mathematical expression for performing pixel-by-pixel algebraic summation correction is:

[0152] ;

[0153] In the formula, This indicates the corrected water depth value.

[0154] In this embodiment, the mathematical expression for calculating the Kriging weights is:

[0155] ;

[0156] In the formula, Represents a known point With known points The model variation function value between the two points quantifies the spatial difference between the attribute values; the greater the distance, the larger this value usually is. Represents the Lagrange multipliers; Indicates the total number of measured points; Represents a known point Interpolation point The model variation function values ​​between;

[0157] In this equation, the spatial difference between the point to be interpolated and any known point (right side) should be equal to the pairwise spatial differences between all known points (left side), then weighted according to their contribution to the prediction. The Kriging weights are obtained by performing a weighted average.

[0158] In this embodiment, calculating the Kriging weights requires determining how the error varies with distance using a theoretical variogram model. Skipping this step would be problematic. Without proper calculation, weights with clear statistical significance and spatial optimality cannot be obtained, and subsequent error estimation and correction lose their scientific basis. Therefore, the mathematical expression for the theoretical variogram model is:

[0159] ;

[0160] In the formula, Represents the theoretical variogram model; Indicates lag distance The experimental variability function; Indicates the lag distance; Indicates approximately the distance The point logarithm;

[0161] In this formula, if The value is also very small, indicating that the error value is small for two points that are very close to each other. and They are very close (the square of the difference is small), which conforms to the first law of geography, that is, things that are close are more related than things that are far apart. The value usually increases and eventually plateaus, meaning that when two points are far enough apart, their errors are no longer correlated, the squared mean of the differences tends to a stable value, and the Kriging equations... That is based on The fitted theoretical variation function model.

[0162] In this embodiment, the reliability of the estimate needs to be quantified by estimating the variance. A small variance value indicates that the estimate is reliable, while a large variance value indicates that the estimate has high uncertainty. Therefore, the mathematical expression for calculating the variance of the Kriging estimate is:

[0163] ;

[0164] In the formula, Indicates in grid cells Kriging estimate of variance at the location; This represents the theoretical variogram value at a distance d.

[0165] Please see Figure 4 The present invention also provides an apparatus for measuring the depth of sand waves using remote sensing images, the measuring apparatus being used to perform the above-described measurement method, comprising:

[0166] The model building module acquires multispectral images of the water area to be measured, extracts sand wave morphology parameters through spectral analysis, establishes a water depth inversion model between sand wave morphology parameters and water depth based on water optics theory, and applies the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured.

[0167] The survey line calculation module performs topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. It also establishes a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value and with the total survey line length and maximum survey line spacing as constraints, a metaheuristic algorithm is used to solve the location information value function to obtain the optimal survey line.

[0168] The error acquisition module uses acoustic detection to measure along the optimal survey line, generating high-precision measured water depth data within the study area. The high-precision measured water depth data and the water depth inversion data are spatially registered in a unified coordinate system. Through position matching, the residual between the two is calculated point by point to obtain the error value between the high-precision measured water depth value and the water depth inversion value.

[0169] The water depth data module uses the Kriging spatial interpolation algorithm to obtain an error estimate based on the obtained error value. This error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data within a unified geographic coordinate system to obtain the corrected water depth data.

[0170] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0171] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0172] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0173] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for measuring the water depth of sand waves using remote sensing images, characterized in that, The specific steps include: Step 1: Acquire multispectral images of the water area to be measured, and extract sand wave morphology parameters through spectral analysis. Based on water optics theory, establish a water depth inversion model between sand wave morphology parameters and water depth. Apply the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured. Step 2: Perform topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. Establish a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value, and with the total survey line length and maximum survey line spacing as constraints, use a metaheuristic algorithm to solve the location information value function to obtain the optimal survey line. Step 3: Use acoustic detection method to measure according to the optimal survey line to generate high-precision measured water depth data in the study area. Spatially register the high-precision measured water depth data and the water depth inversion data in a unified coordinate system. Through position matching, calculate the residual between the two point by point to obtain the error value between the measured high-precision water depth value and the water depth inversion value. Step 4: Based on the obtained error value, the Kriging spatial interpolation algorithm is used to obtain the error estimate. The error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data in a unified geographic coordinate system to obtain the corrected water depth data.

2. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The morphological parameters of sand waves include bottom sediment reflectivity, water attenuation coefficient, and deep-water remote sensing reflectivity.

3. The method for measuring the water depth of sand waves using remote sensing images according to claim 2, characterized in that: The specific steps for extracting sand wave morphology parameters are as follows: Spectral coefficients are set, and Fourier transform is performed on the spectral curve of each pixel in the multispectral image. Low-pass filtering is used to extract the baseline signal, and band-pass filtering is used to extract the characteristic signals of each band. Inverse Fourier transform is performed on the baseline and the characteristic signals of each band to obtain the baseline and the characteristic spectra of each band. The characteristic spectra of each band are multiplied by the spectral coefficients to obtain the characteristics of each band. The baseline spectrum is added to the characteristics of each band to obtain the background reflectance curve of each spectrum. The center wavelengths of the blue band, green band, red band and near-infrared band are determined, and the background reflectance at the center wavelength of each band of each pixel is extracted. Set the spectral index and the scaling factor for each band, calculate the spectral index power of the bottom reflectance in the blue, green, red, and near-infrared bands to obtain the spectral value for each band, and calculate the product of the scaling factor and the spectral value for each band to obtain the water body attenuation coefficient. A reflection threshold is set. For each pixel in the multispectral image, the reflectance of the near-infrared band is compared with the reflection threshold. If the reflectance of the near-infrared band is less than or equal to the reflection threshold, it is marked as a deep-water pixel. The reflectance of the blue, green, red and near-infrared bands in the deep-water pixel is extracted to obtain the deep-water remote sensing reflectance of each band.

4. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The specific steps for constructing a water depth inversion model are as follows: Texture modulation depth is extracted from the multispectral image of the water area to be measured. The difference between the bottom reflectance and the deep water remote sensing reflectance is calculated to obtain the first difference value. A calibration constant is set, and the product of the calibration constant and the first difference value is calculated to obtain the first value value. Logarithmic operation is performed based on the ratio of the first value value and the texture modulation depth to obtain the water depth prediction variable. The water depth is obtained by calculating the water depth prediction variable and the two-way band water body attenuation coefficient.

5. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The specific steps for obtaining water depth slope, water depth curvature, and local water depth standard deviation are as follows: A two-dimensional coordinate system is constructed based on the multispectral image of the water area to be measured. For each pixel in the multispectral image, the water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid with the pixel as the center. The first water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth difference is also obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The second water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first water depth value and the second water depth value. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The first water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The second water depth value is obtained by the ratio of the water depth difference to the actual horizontal distance between the two pixels. The water depth slope is obtained by taking the Euclidean norm of the first water depth value and the second water depth value. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the x-direction of the grid. The third water depth value is obtained by the difference between the water depth difference and twice the water depth at point x. The water depth difference is obtained by calculating the water depth values ​​of two pixels apart in the y-direction of the grid. The fourth water depth value is obtained by the difference between the water depth difference and twice the water depth at point x. The water depth curvature is obtained by calculating the average water depth between the third and fourth water depth values.

6. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The specific steps for constructing the information value function are as follows: The parameters of water depth slope, water depth curvature, and local water depth standard deviation are normalized, and the location information value function is obtained by weighted fusion of the normalized parameters.

7. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The specific steps for solving the location information value function to obtain the optimal survey line are as follows: Within the study area, K parallel survey lines are generated using a heuristic initialization method, and these lines are used as the initial survey line layout scheme. The total measurement length does not exceed the maximum survey line length, and the distance between adjacent survey lines does not exceed the maximum allowable distance. The total coverage information value function is obtained by summing the information values ​​of all pixels within the study area by double summation and calculating the sum of the information values ​​of pixels covered by at least one survey line. All total coverage information value functions are arranged in descending order, and the survey line layout scheme is selected from the current population through a tournament selection process to enter the next generation; The selected outstanding individuals are paired up, some parameters are exchanged to generate new survey line layout schemes, and the survey line layout schemes are changed by randomly fine-tuning the line spacing. The survey line layout scheme with the highest fitness in each generation is directly retained to the next generation. Through iterative screening, the optimal survey line is obtained.

8. The method for measuring the water depth of sand waves using remote sensing images according to claim 1, characterized in that: The specific steps to obtain the corrected water depth data are as follows: Multiply the water depth inversion error values ​​of all measured points by the Kriging weights to obtain the optimal weight for all measured points, and sum the optimal weights of all measured points to obtain the error estimate of the grid cells. The error estimate is then summed pixel-by-pixel in a unified geographic coordinate system with the water depth inversion data to obtain the corrected water depth data.

9. A device for measuring the water depth of sand dunes using remote sensing images, characterized in that: The apparatus is used to perform the method for measuring sand wave depth using remote sensing images as described in any one of claims 1-8, comprising: The model building module acquires multispectral images of the water area to be measured, extracts sand wave morphology parameters through spectral analysis, establishes a water depth inversion model between sand wave morphology parameters and water depth based on water optics theory, and applies the established water depth inversion model to the multispectral images to generate water depth inversion data covering the area to be measured. The survey line calculation module performs topographic analysis on the water depth inversion data to obtain characteristic parameters such as water depth slope, water depth curvature, and local water depth standard deviation. It also establishes a location information value function between the location information value and the water depth slope, water depth curvature, and local water depth standard deviation. With the goal of maximizing the location information value and with the total survey line length and maximum survey line spacing as constraints, a metaheuristic algorithm is used to solve the location information value function to obtain the optimal survey line. The error acquisition module uses acoustic detection to measure along the optimal survey line, generating high-precision measured water depth data within the study area. The high-precision measured water depth data and the water depth inversion data are spatially registered in a unified coordinate system. Through position matching, the residual between the two is calculated point by point to obtain the error value between the high-precision measured water depth value and the water depth inversion value. The water depth data module uses the Kriging spatial interpolation algorithm to obtain an error estimate based on the obtained error value. The error estimate is then used to perform a pixel-by-pixel algebraic summation on the water depth inversion data in a unified geographic coordinate system to obtain the corrected water depth data.

Images