A three-dimensional water quality spatial interpolation method based on remote sensing images

Abstract

The present invention relates to the field of water quality monitoring technology, and specifically to a three-dimensional water quality spatial interpolation method based on remote sensing images, comprising: S1: obtaining a multispectral remote sensing image and multiple sampling values ​​of a region to be interpolated; S2: processing the multispectral remote sensing image and the sampling values ​​to obtain a predicted mean; S3: performing depth expansion on the sampling points where the sampling values ​​are located according to the predicted mean, and generating multiple prediction errors corresponding to the predicted positions of the sampling points; S4: predicting the predicted positions according to the prediction errors and the predicted mean, so as to complete the three-dimensional spatial interpolation of the region to be interpolated. The beneficial effect of the present invention is that by combining the predicted mean generated by regression analysis based on multispectral remote sensing images and the prediction error generated based on the empirical Bayesian Kriging regression method, a more accurate prediction process is achieved, thereby improving the accuracy of three-dimensional spatial interpolation.

Description

Technical Field

[0001] The invention relates to the technical field of water quality monitoring, and in particular to a three-dimensional water quality spatial interpolation method based on remote sensing images. Background Art

[0002] In order to solve the problems of water pollution and ecological environment deterioration caused by eutrophication, it is urgent to evaluate the water quality through water quality sampling point data. Water environment evaluation is inseparable from the full understanding and quantitative calculation of water quality spatial data. Among them, three-dimensional water quality attribute modeling can intuitively display the spatial distribution, change law and relationship between the internal attribute parameters of the water body by simulating the spatial position and dynamic changes of water body attribute parameters. It is an important means of quantitative analysis of water quality spatial data. Due to the uneven distribution of sampling points required for modeling, a reasonable interpolation method is needed to simulate water quality parameters.

[0003] Traditional interpolation methods are mainly divided into two categories: one is deterministic interpolation, which is to construct a fitting surface based on the smoothness of the entire spatial surface or the similarity between spatial information elements to predict data in unknown areas, such as the inverse distance weighted method (IDW), spline function method and trend surface method; the other is geostatistical interpolation, which analyzes the distribution law and related characteristics of sample points in the spatial range, fits and constructs the spatial structure model of sample points, and then predicts the change trend of the entire spatial area, such as the Kriging interpolation method.

[0004] Traditional spatial interpolation methods have different ideas on solving spatial weights. For example, the inverse distance weight method uses the inverse of the distance power as the spatial weight, and the Kriging method uses the semivariogram to solve the spatial weight between data. In general, spatial interpolation introduces the location of spatial elements, uses spatial statistics methods to solve spatial weights, and further predicts unknown regional data through the data of known observation elements. Due to objective factors such as the number of samples, different distribution patterns, and differences in the range of distribution areas, as well as simple mathematical formulas and the need for human intervention in modeling, traditional spatial interpolation methods are often difficult to accurately fit the spatial weight relationship in the study area, which to a certain extent restricts the prediction accuracy of spatial interpolation methods. Summary of the invention

[0005] In view of the above problems existing in the prior art, a three-dimensional water quality spatial interpolation method based on remote sensing images is now provided.

[0006] The specific technical solutions are as follows:

[0007] A three-dimensional water quality spatial interpolation method based on remote sensing images, comprising:

[0008] Step S1: obtaining a multispectral remote sensing image and a plurality of sampling values ​​of a region to be interpolated;

[0009] Step S2: Processing the multispectral remote sensing image and the sampling value to obtain a predicted mean value;

[0010] Step S3: performing deep expansion on the sampling point where the sampling value is located according to the predicted mean value, and generating a plurality of prediction errors corresponding to the predicted positions of the sampling points;

[0011] Step S4: predicting the predicted position according to the prediction error and the prediction mean value to complete the three-dimensional space interpolation of the area to be interpolated.

[0012] Preferably, step S2 comprises:

[0013] Step S21: performing independent principal component transformation on the multispectral remote sensing image to obtain a principal component transformed image;

[0014] Step S22: generating the predicted mean value according to the principal component transformation image and the sampling value.

[0015] Preferably, the step S21 includes:

[0016] Step S211: converting the multispectral remote sensing image into a data matrix, and calculating the covariance matrix of the data matrix;

[0017] Step S212: obtaining the eigenvectors and eigenvalues ​​of the covariance matrix, and generating a coefficient matrix according to the eigenvectors and the eigenvalues;

[0018] Step S213: generating a band component matrix according to the coefficient matrix, and transforming the band component matrix to obtain the principal component transformed image.

[0019] Preferably, in step S22, the method for generating the predicted mean value includes:

[0020] ;

[0021] in, is the predicted mean of the predicted position, is the coefficient, is the sampling point corresponding to the predicted position in the principal component transformation image. The principal component values.

[0022] Preferably, step S3 comprises:

[0023] Step S31: setting a depth expansion factor, and performing depth expansion on the sampling points based on the depth expansion factor to obtain a plurality of predicted positions corresponding to the sampling points;

[0024] Step S32: generating an anomaly value and a spatial weight for each predicted position;

[0025] Step S33: Generate a prediction error term corresponding to the predicted position according to the square interpolation and the spatial weight.

[0026] Preferably, in step S32, the method for generating the square mean includes:

[0027] ;

[0028] in, The distance from the sampling point is The semivariance of the predicted position, is the spatial distance between the predicted position and the sampling point, where the sampling point is , the predicted position is ， is the sampling value of the sampling point, is the anomaly value of the predicted location.

[0029] Preferably, in step S32, the method for generating the spatial weight includes:

[0030] ;

[0031] in, is the spatial weight, For the The semivariance of the predicted positions, For the The semivariance of the predicted positions.

[0032] Preferably, in step S33, the method for generating the prediction error term includes:

[0033] ;

[0034] in, is the prediction error term of the predicted position, For the The anomaly value for each predicted location.

[0035] Preferably, in step S4, the method for predicting the predicted position includes:

[0036] ;

[0037] in, is the predicted value of the predicted position, is the predicted mean of the predicted position, is the prediction error, is the coefficient, is the sampling point corresponding to the predicted position in the principal component transformation image. The principal component values, For the The anomaly value for the predicted location.

[0038] The above technical solution has the following advantages or beneficial effects: In view of the low accuracy of the three-dimensional water body spatial interpolation method in the prior art, the predicted mean of the area to be interpolated is generated based on the multispectral remote sensing image, and then the water quality sampling value on a certain plane is deeply expanded to generate the predicted error of the predicted position. By combining the predicted mean generated by the regression analysis based on the multispectral remote sensing image and the predicted error generated by the empirical Bayesian Kriging regression method, a more accurate prediction process is achieved, thereby improving the accuracy of the three-dimensional spatial interpolation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The embodiments of the present invention will be described more fully with reference to the attached drawings, which are provided for illustration and description only and are not intended to limit the scope of the present invention.

[0040] Figure 1 It is an overall schematic diagram of an embodiment of the present invention;

[0041] Figure 2 A schematic diagram of multispectral remote sensing images and sampling points in an embodiment of the present invention;

[0042] Figure 3 This is a schematic diagram of sub-steps of step S2 in an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of sub-steps of step S21 in an embodiment of the present invention;

[0044] Figure 5 This is a schematic diagram of sub-steps of step S3 in an embodiment of the present invention;

[0045] Figure 6 Schematic diagram of an interpolation model in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0048] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0049] The present invention comprises:

[0050] A three-dimensional water quality spatial interpolation method based on remote sensing images, such as Figure 1 As shown, including:

[0051] Step S1: obtaining a multispectral remote sensing image and a plurality of sampling values ​​of a region to be interpolated;

[0052] Step S2: Processing the multispectral remote sensing image and the sampling value to obtain the predicted mean;

[0053] Step S3: performing deep expansion on the sampling points where the sampling values ​​are located according to the predicted mean, and generating a plurality of prediction errors corresponding to the predicted positions of the sampling points;

[0054] Step S4: predicting the predicted position according to the prediction error and the prediction mean to complete the three-dimensional space interpolation of the interpolation area.

[0055] Specifically, in view of the low accuracy of water body interpolation calculation in a specific area in the three-dimensional water body spatial interpolation method in the prior art, in this embodiment, the principal component transformation of the multispectral remote sensing image is performed, and a linear regression analysis is performed in combination with the actual sampling value to generate a predicted mean value of the area to be interpolated, and then the water quality sampling value on a certain plane is deeply expanded based on the Kriging method to generate its prediction error. By combining the predicted mean value generated by the regression analysis based on the multispectral remote sensing image and the prediction error generated by the empirical Bayesian Kriging regression method, a more accurate prediction process is achieved, thereby improving the accuracy of the three-dimensional spatial interpolation.

[0056] In the implementation process, the above method is configured as a software embodiment in a specific computing device. Figure 2 As shown in the figure, the interpolation area refers to a water area that needs to be monitored for water quality. There are multiple sampling points for monitoring water quality in the water area. Each sampling point can be distributed at the same depth or different depths according to the actual situation. Multispectral remote sensing image refers to a multispectral remote sensing image corresponding to the interpolation area obtained by satellite remote sensing technology. The remote sensing image contains images of multiple bands. Sampling values ​​refer to multiple attribute data used to characterize water quality in the water area, such as chemical oxygen demand, dissolved oxygen, biochemical oxygen demand, active phosphate, lead, copper and other factors. Each sampling point corresponds to a set of sampling values ​​and the three-dimensional spatial coordinates of the sampling point.

[0057] In a preferred embodiment, Figure 3 As shown, step S2 includes:

[0058] Step S21: performing independent principal component transformation on the multispectral remote sensing image to obtain a principal component transformed image;

[0059] Step S22: Generate a predicted mean value based on the principal component transformation image and the sampling value.

[0060] Specifically, in order to achieve a faster processing speed, in this embodiment, the multispectral remote sensing image is first subjected to independent principal component transformation, and the repeated and redundant information between the bands in the multispectral remote sensing image is cleaned to generate a principal component transformation image. The principal components in the principal component transformation image are independent of each other, thereby achieving effective compression of the data volume and improving the processing speed.

[0061] In a preferred embodiment, Figure 4 As shown, step S21 includes:

[0062] Step S211: converting the multispectral remote sensing image into a data matrix, and calculating the covariance matrix of the data matrix;

[0063] Step S212: Obtain the eigenvectors and eigenvalues ​​of the covariance matrix, and generate a coefficient matrix according to the eigenvectors and eigenvalues;

[0064] Step S213: Generate a band component matrix according to the coefficient matrix, and transform the band component matrix to obtain a principal component transformation image.

[0065] Specifically, in order to achieve faster processing efficiency, in this embodiment, after preprocessing the remote sensing image, the preprocessed image is converted into a data matrix , and the data matrix Calculate the covariance matrix in turn , coefficient matrix , and the covariance matrix can be obtained by solving the characteristic equation The eigenvalues ​​of each band component matrix are constructed , by passing the band component matrix Restore it to a two-dimensional image to obtain the principal component analysis image The principal component analysis image Compared with the original remote sensing images, the repeated information between multiple bands is reduced, so the data volume is small, and the principal component analysis image The correlation coefficients between the multiple band components contained in the image are zero, which further reduces the amount of data. The first band component in the image reduces noise, which is beneficial for enhancing and analyzing detailed features.

[0066] During the implementation process, a data matrix can be constructed based on multispectral remote sensing images. Then, the data matrix Solve for its covariance matrix , based on the covariance matrix The covariance matrix can be easily calculated The eigenvalue of and the eigenvector , then based on the characteristic equation The band eigenvalue can be solved .

[0067] in, is the data matrix obtained based on the transformation of multispectral remote sensing images. For the The first pixels, is the eigenvalue of the covariance matrix, is the identity matrix, is the band characteristic value, .

[0068] Then, the band feature values Arrange from largest to smallest, according to the equation Generate unit eigenvectors corresponding to band eigenvalues , .

[0069] Then the unit eigenvector Find the transpose to generate the coefficient matrix , .

[0070] in, is the coefficient matrix, is the unit eigenvector, .

[0071] In a preferred embodiment, in step S24, the method for generating a band component matrix includes:

[0072] Specifically, when generating the coefficient matrix After that, the coefficient matrix With data matrix Multiply to get the band component matrix ,Right now: ;

[0073] in, is the band component matrix, is the coefficient matrix, is the data matrix.

[0074] The band component matrix The row vector of For the At this time, the band component matrix When each row of is restored to a two-dimensional image, we can get The band images are combined to form the principal component transformation image.

[0075] The principal component transformation image includes: ,in, Transform the image into principal components, For the Band images of component bands.

[0076] In a preferred embodiment, in step S22, the method for generating the predicted mean value includes:

[0077] ;

[0078] in, is the predicted mean of the predicted position, is the coefficient, is the sampling point corresponding to the predicted position in the principal component transformation image. The principal component values.

[0079] Specifically, in order to address the problem of low accuracy of water body interpolation operations in specific areas in the three-dimensional water body spatial interpolation methods in the prior art, in this embodiment, ordinary least squares (OLS) linear regression is performed on multiple principal component values ​​and measurement values ​​in the principal component transformation image, thereby achieving a better estimation of the predicted mean of the predicted position, thereby improving the accuracy of the interpolation operation.

[0080] In a preferred embodiment, Figure 5 As shown, step S3 includes:

[0081] Step S31: setting a depth expansion factor, and performing depth expansion on the sampling points based on the depth expansion factor to obtain a plurality of predicted positions corresponding to the sampling points;

[0082] Step S32: generating a square difference value and a spatial weight for each predicted position;

[0083] Step S33: Generate a prediction error term corresponding to the predicted position according to the square difference and the spatial weight.

[0084] Specifically, in order to achieve better prediction effects, in this embodiment, by setting the depth collision factor, the original single sampling point is vertically pulled up in the depth direction. By multiplying the depth expansion factor by the depth field value while keeping the horizontal coordinate unchanged, multiple prediction positions are formed for the single sampling point in the depth direction, thereby achieving better interpolation effects.

[0085] Furthermore, in order to achieve better prediction results, in this embodiment, in the spatial modeling of the sampling point structure, starting with the graph of the empirical semivariogram function, the square difference of the position pairs consisting of the sampling point and the predicted position is calculated, and the spatial weight is calculated based on the fitting model of the spatial relationship between the sampling point, the distance of the predicted position and the measured values ​​around the predicted position, so as to achieve a better prediction effect on the prediction error term of the predicted position.

[0086] As an optional implementation, in step S1, terrain data and water area data of the area to be interpolated are also collected, and the depth expansion factor is adjusted according to the terrain data and water area data.

[0087] In a preferred embodiment, in step S32, the method for generating the square difference value includes:

[0088] ;

[0089] in, The distance from the sampling point is The semivariance of the predicted position, is the spatial distance between the predicted position and the sampling point, where the sampling point is , the predicted position is ， is the sampling value of the sampling point, is the anomaly value at the predicted location.

[0090] In a preferred embodiment, in step S32, the method for generating the spatial weight includes:

[0091] ;

[0092] in, is the spatial weight, For the The semivariance of the predicted positions, For the The semivariance of the predicted positions.

[0093] In a preferred embodiment, in step S33, the method for generating the prediction error term includes:

[0094] ;

[0095] in, is the prediction error term of the predicted position, For the The anomaly value at the predicted location.

[0096] In a preferred embodiment, in step S4, the method for predicting the predicted position includes:

[0097] ;

[0098] in, is the predicted value of the predicted position, is the predicted mean of the predicted position, is the prediction error, is the coefficient, is the sampling point corresponding to the predicted position in the principal component transformation image. The principal component values, For the The anomaly value at the predicted location.

[0099] Specifically, in order to achieve better prediction accuracy, in this embodiment, after the prediction mean and prediction error term of each prediction position are obtained by the above method, the prediction can be calculated based on the new empirical semivariogram distribution, which is generated by merging the semivariograms in the semivariogram distribution within the point neighborhood. It has better accuracy than the three-dimensional space interpolation method in the prior art.

[0100] As an optional implementation, step S4 also includes: after obtaining the predicted value of each predicted position, coloring the predicted position according to the predicted value and superimposing it on the multispectral remote sensing image to form a Figure 6 The three-dimensional water quality model shown in the figure indicates the water quality of each point in the interpolation area through different colors, and switches the predicted position at different depths by changing the elevation parameters.

[0101] The present invention proposes an innovative modeling method for spatial interpolation to improve the prediction accuracy and prediction ability of spatial interpolation. The empirical Bayesian Kriging regression method is introduced, and the empirical Bayesian Kriging method is used in combination with the multispectral remote sensing image explanatory variable grid to affect the interpolation value. This method combines Kriging with regression analysis to make predictions that are more accurate than those made using regression analysis or Kriging alone.

[0102] Geostatistical interpolation through geostatistical analysis of two-dimensional spatial data is now very mature. Three-dimensional water quality sampling data usually changes faster in the vertical direction than in the horizontal direction. By introducing the depth expansion factor, it is possible to search for related features farther away in the search neighborhood and reduce the difference in the horizontal and vertical changes of the values.

[0103] Before building the model, the multispectral remote sensing images are transformed into principal components, and these principal components are used as explanatory variables in the model. The principal components are linear combinations (weighted sums) of the multispectral remote sensing images and are calculated so that each principal component is uncorrelated with any other principal component. Since the principal components are uncorrelated, they can be used to resolve multicollinearity (image bands are correlated with other bands) issues in the model.

[0104] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A three-dimensional water quality spatial interpolation method based on remote sensing images, characterized in that: include: Step S1: obtaining a multispectral remote sensing image and a plurality of sampling values ​​of a region to be interpolated; Step S2: Processing the multispectral remote sensing image and the sampling value to obtain a predicted mean value; Step S3: performing deep expansion on the sampling point where the sampling value is located according to the predicted mean value, and generating a plurality of prediction errors corresponding to the predicted positions of the sampling points; Step S4: predicting the predicted position according to the prediction error and the prediction mean to complete the three-dimensional space interpolation of the area to be interpolated; The step S2 comprises: Step S21: performing independent principal component transformation on the multispectral remote sensing image to obtain a principal component transformed image; Step S22: generating the predicted mean value according to the principal component transformation image and the sampling value; In step S22, the method for generating the predicted mean value includes: M(S0)=β0+β1X1+β2X2+…+β m X m ; Wherein, M(S0) is the predicted mean of the predicted position, β m is the coefficient, X m is the mth principal component value of the sampling point corresponding to the predicted position in the principal component transformation image; The step S3 comprises: Step S31: setting a depth expansion factor, and performing depth expansion on the sampling points based on the depth expansion factor to obtain a plurality of predicted positions corresponding to the sampling points; Step S32: generating a square difference value and a spatial weight for each predicted position respectively; Step S33: Generate a prediction error term corresponding to the predicted position according to the square difference value and the spatial weight.

2. The three-dimensional water quality spatial interpolation method according to claim 1, characterized in that: The step S21 comprises: Step S211: converting the multispectral remote sensing image into a data matrix, and calculating the covariance matrix of the data matrix; Step S212: obtaining the eigenvectors and eigenvalues ​​of the covariance matrix, and generating a coefficient matrix according to the eigenvectors and the eigenvalues; Step S213: generating a band component matrix according to the coefficient matrix, and transforming the band component matrix to obtain the principal component transformed image.

3. The three-dimensional water quality spatial interpolation method according to claim 1, characterized in that: In step S32, the method for generating the square difference value includes: Among them, γ (h) is the semivariance of the predicted position at a distance h from the sampling point, h is the spatial distance between the predicted position and the sampling point, wherein the sampling point is (x1, y1, z1), the predicted position is (x2, y2, z2), Z(S i ) is the sampling value of the sampling point, Z(S j ) is the square difference of the predicted position.

4. The three-dimensional water quality spatial interpolation method according to claim 1, characterized in that: In step S32, the method for generating the spatial weight includes: Among them, λ i is the spatial weight, γ (i) is the semivariance of the ith predicted position, γ (j) is the semivariance of the jth predicted position, and N is the total number of predicted positions.

5. The three-dimensional water quality spatial interpolation method according to claim 4, characterized in that: In step S33, the method for generating the prediction error term includes: Among them, ε(S0) is the prediction error term of the predicted position, Z(S i ) is the anomaly value of the i-th predicted position, N is the total number of predicted positions, λ i is the spatial weight.

6. The three-dimensional water quality spatial interpolation method according to claim 4, characterized in that: In step S4, the method for predicting the predicted position includes: in, is the predicted value of the predicted position, M(S0) is the predicted mean of the predicted position, ε(S0) is the prediction error, β m is the coefficient, X m is the mth principal component value of the sampling point corresponding to the predicted position in the principal component transformation image, Z(S i ) is the anomaly value of the i-th predicted position, N is the total number of predicted positions, λ i is the spatial weight.

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