A fuzzy C-means unmixing method based on the closeness distance of mixing kernel space

Abstract

The present invention discloses a fuzzy C-means unmixing method based on hybrid kernel spatial compactness distance, comprising: S1, obtaining remote sensing original images through Landsat datasets; S2, preprocessing the obtained remote sensing images, further calculating the pixel purity index of the images, extracting endmember information, and constructing training samples; S3, improving the classic fuzzy C-means unmixing model through hybrid kernel functions and support vector data description theory (SVDD) to obtain a fuzzy C-means unmixing model (AD-HKFCM); S4, unmixing the remote sensing image dataset through the fuzzy C-means unmixing model (AD-HKFCM), thereby obtaining an abundance map of endmembers corresponding to the regional region, i.e., an unmixing result. According to the present invention, costs are saved and rapid, large-scale, real-time monitoring of regional image ground objects is achieved, the accuracy and robustness of the unmixing results are improved, and better unmixing results are obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of remote sensing image processing, and in particular to a fuzzy C-means unmixing method based on hybrid kernel space compactness distance. Background Art

[0002] In recent years, automatic classification methods have been widely used in remote sensing image processing. Existing classification methods can be categorized as hard classification and soft classification. Hard classification assumes that a single pixel corresponds to a specific feature and should be assigned to a specific category. Classification methods such as maximum likelihood, support vector machines, and random forests are all examples of hard classification. However, in real-world scenarios, low- and medium-resolution remote sensing data often contain mixed pixels, and a single pixel may correspond to multiple features. Using hard classification methods can lead to misclassification or omission. In contrast, soft classification techniques decompose mixed pixels through spectral analysis, improving image classification accuracy to the sub-pixel level. Mixed pixel decomposition models can be categorized as linear or nonlinear, depending on the spectral mixing patterns of the pixels. In real-world scenarios, different features are often evenly mixed in small patches. This results in multiple reflections and scattering of electromagnetic waves between the features, requiring nonlinear models to describe these processes. While various nonlinear mixing models have been proposed, these are often subject to residual errors and are computationally complex.

[0003] In recent years, researchers have proposed a new approach to transforming the image mixed pixel decomposition problem into a constrained nonlinear regression problem when endmember spectra are known. However, existing mixed pixel decomposition models have limitations in accuracy and versatility. The fuzzy C-means model is a commonly used mixed pixel decomposition method, but the classic fuzzy C-means unmixing algorithm has limited ability to handle nonlinear problems, is sensitive to outliers, and ignores the compactness of the distribution of the points to be classified in the feature space.

[0004] Glossary: Support vector data description (SVDD) Hybrid kernel fuzzy C-means unmixing model based on affinity distance (AD-HKFCM)

[0005] Weighted SVDD (weighted SVDD, WSVDD)

[0006] Affinity distance (AD)

[0007] Kernel fuzzy C-means clustering model (KFCM)

[0008] Gaussian Kernel Fuzzy C-means (G-KFCM

[0009] Hybrid Kernel Fuzzy C-Means (H-KFCM)

[0010] Gaussian kernel fuzzy support vector data description (G-FSVDD)

[0011] Hybrid Kernel Fuzzy Support Vector Data Description (H-FSVDD)

[0012] Root mean square error (RMSE)

[0013] Signal-to-noise ratio (SNR) Summary of the Invention

[0014] In order to address the shortcomings of the prior art, the present invention aims to provide a fuzzy C-means unmixing method based on the spatial compactness distance of a hybrid kernel, which saves costs and enables rapid, large-scale, real-time monitoring of regional imagery and ground objects, improves the accuracy and robustness of the unmixing results, and obtains better unmixing results. In order to achieve the above-mentioned purpose and other advantages of the present invention, a fuzzy C-means unmixing method based on the spatial compactness distance of a hybrid kernel is provided, comprising:

[0015] S1. Obtain original remote sensing images through Landsat dataset;

[0016] S2. Preprocess the acquired remote sensing images, further calculate the pixel purity index of the images, extract endmember information, and construct training samples;

[0017] S3, the classic fuzzy C-means unmixing model is improved by using the hybrid kernel function and support vector data description theory to obtain the fuzzy C-means unmixing model;

[0018] S4. The remote sensing image dataset is unmixed by using the fuzzy C-means unmixing model to obtain the abundance map of the end members corresponding to the regional area, i.e., the unmixing result.

[0019] Preferably, in step S2, radiation correction is performed on the acquired remote sensing image data, including radiation calibration and atmospheric correction; and a method of correcting images by images is adopted to perform geometric correction on the image data to obtain pre-processed image data.

[0020] Preferably, in step S3, the remote sensing image pixel purity index is calculated, and by combining the hybrid kernel function and the kernel fuzzy C-means clustering model, the sample set is nonlinearly mapped to a high-dimensional space, and C-means clustering is performed in the space to obtain training samples of the support vector data description model.

[0021] Preferably, considering global and local performance, the polynomial kernel function and the radial basis kernel function are combined to obtain a hybrid kernel function with strong extrapolation and internalization capabilities. The calculation formula is:

[0022] K mix =λK poly +(1-λ)K rbf (1)

[0023] Where K mix is the mixed kernel function, K poly is the polynomial kernel function, K rbf is the radial basis kernel function, λ∈(0,1), which represents the mixing scale factor of the two kernel functions. The larger λ is, the better the performance of the mixed kernel function.

[0024] In order to more accurately represent the influence of different sample points, the weighted SVDD model based on membership is selected for training. The objective function expression of WSVDD is:

[0025] F=R 2 +C∑ i w i δ i st||x i -a|| 2 ≤R 2 +δ i (2)

[0026] Where R represents the radius of the hypersphere, C is the penalty factor. Adjusting C can control the relationship between the size of the hypersphere and the number of error samples. a is the center of the hypersphere, and w is the penalty factor. i Represents the weight of the sample point, which is determined by the membership obtained by the mixed kernel fuzzy C-means model.

[0027] Preferably, step S4 specifically includes the following steps:

[0028] S41, determining the initial values of the number of ground feature categories M, the fuzziness parameter t, the algorithm iteration stop parameter ε, the mixing parameter λ of the mixing kernel function, the width parameter δ of the radial basis kernel function, and the order q of the polynomial kernel function;

[0029] S42. Use the kernel fuzzy C-means model to classify the sample points and obtain the membership value of each sample point to each type of ground feature; wherein, the membership expression of each sample point in the constructed demixing model AD-HKFCM is:

[0030]

[0031] Among them, d(x0,a i ) represents the distance from the sample point x0 to the center of the i-th category a i The absolute distance;

[0032] S43, constructing a WSVDD model based on membership degree, and optimizing the relevant parameters in step S41 using a grid search method;

[0033] S44, obtain the center of each category hypersphere, use it as the category center, calculate the AD value of each sample point to the category center, and update the membership value and classification results; R i is the radius of the hypersphere of type i, then the distance from point x0 to the center of type i a i The formula for the closeness distance AD is:

[0034]

[0035] S45, repeat steps S43 and S44 until the iteration termination condition is met Obtain the final membership value of each sample point to each category;

[0036] S46. Design simulation experiments for the constructed AD-HKFCM unmixing model to evaluate the effectiveness of the algorithm and the unmixing effect.

[0037] Compared with the prior art, the present invention has the following beneficial effects: the technical solution saves costs and realizes rapid, large-scale, real-time monitoring of regional image features. By integrating support vector data description theory and kernel function theory, a fuzzy C-means unmixing model based on the spatial closeness distance of the mixed kernel is constructed. This model improves the traditional fuzzy C-means unmixing model and improves the accuracy and robustness of the unmixing results to a certain extent by effectively reducing errors caused by problems such as outliers and end-member differences. It effectively solves the problem of low accuracy of image classification results caused by the presence of a large number of mixed pixels in medium and low spatial resolution images. The generated model can obtain good unmixing results for both pure pixels and mixed pixels. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Flowchart of the fuzzy C-means unmixing method based on the hybrid kernel space compactness distance according to the present invention;

[0039] Figure 2 A flow chart of constructing an unmixing model for the fuzzy C-means unmixing method based on the mixing kernel space compactness distance according to the present invention;

[0040] Figure 3An algorithm advantage flow chart for designing an experimental verification algorithm for generating an unmixing model based on the fuzzy C-means unmixing method based on the mixing kernel space closeness distance according to the present invention;

[0041] Figure 4 It is a long-term unmixed abundance map of the study area according to the fuzzy C-means unmixing method based on the mixing kernel spatial compactness distance of the present invention. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0043] Reference Figure 1-4 A fuzzy C-means unmixing method based on the spatial closeness distance of the mixing kernel comprises the following steps:

[0044] S1. Obtaining original remote sensing images through the Landsat dataset. Obtaining optical remote sensing images from the Landsat dataset as data for pixel unmixing. In this embodiment of the present invention, remote sensing images of the study area are obtained. When obtaining data, it is necessary to consider the multispectral remote sensing data required for subsequent model verification.

[0045] S2. Preprocess the acquired remote sensing image, further calculate the pixel purity index of the image, extract endmember information, and construct a training sample. Step S2 includes the following sub-steps:

[0046] S21: Perform radiometric correction on the acquired remote sensing image data, including radiometric calibration and atmospheric correction;

[0047] The radiation calibration is performed using the radiance data in the data header file to obtain the atmospheric apparent reflectance of the corresponding data; the image is then atmospherically corrected using the FLAASH atmospheric correction method of the MODTRAN4+ radiation transfer model to obtain the image dataset after radiation correction.

[0048] S22: Using an image-based image correction method, geometric correction is performed on the image data to obtain pre-processed image data.

[0049] During geometric correction, a remote sensing image is used as a reference image, and the same-name points are selected on the reference image and the image to be corrected. All images are corrected to obtain the preprocessed image set.

[0050] In this embodiment of the present invention, in step S3, the purity index of the remote sensing image pixel is calculated, the hybrid kernel function is combined with the kernel fuzzy C-means clustering model (KFCM), the sample set is nonlinearly mapped to a high-dimensional space, and C-means clustering is performed in the space to obtain training samples for the support vector data description model (SVDD);

[0051] Among them, considering the global and local performance, the polynomial kernel function and the radial basis kernel function are combined to obtain a hybrid kernel function with strong extrapolation and internalization capabilities. The calculation formula is:

[0052] K mix =λK poly +(1-λ)K rbf (1)

[0053] Where K mix is the mixed kernel function, K poly is the polynomial kernel function, K rbf is the radial basis kernel function, λ∈(0,1), which represents the mixing scale factor of the two kernel functions. The larger λ is, the better the performance of the mixed kernel function.

[0054] The polynomial kernel function has good global performance and strong extrapolation ability, and its extrapolation ability increases as the degree of the polynomial decreases. However, the polynomial kernel function has many parameters and high computational complexity; the formula of the polynomial kernel function is:

[0055] K poly (x i ,x j )=((x i ·x j )+1) q (2)

[0056] The Gram matrix is composed of the inner product operations of any k (k≤n) vectors in n-dimensional Euclidean space. The necessary and sufficient condition for judging a kernel function is the corresponding Gram matrix (elements are composed of K(x n ,x m ) determine) in all sets {x n} are all positive semidefinite under the choice of .

[0057] The Gaussian radial basis kernel function is a kernel function with strong localization. This function has good performance for data of various sizes and requires fewer parameters than the polynomial kernel function. It is currently the most widely used kernel function. Its formula is:

[0058]

[0059] In order to more accurately represent the influence of different sample points, the weighted SVDD (WSVDD) model based on membership is selected for training; the objective function expression of WSVDD is:

[0060] F=R 2 +C∑ i w i δ i st||x i -a|| 2 ≤R 2 +δ i (4)

[0061] Where R represents the radius of the hypersphere, C is the penalty factor. Adjusting C can control the relationship between the size of the hypersphere and the number of error samples. a is the center of the hypersphere, and w is the penalty factor. i Represents the weight of the sample point, which is determined by the membership obtained by the mixed kernel fuzzy C-means model.

[0062] S3, the classic fuzzy C-means unmixing model is improved by using the hybrid kernel function and support vector data description theory to obtain the fuzzy C-means unmixing model;

[0063] S4, unmixing the remote sensing image dataset using the fuzzy C-means unmixing model, thereby obtaining an abundance map of the end members corresponding to the region, i.e., the unmixing result. Step S4 includes the following sub-steps:

[0064] S41: Determine the initial values of the number of ground feature categories M, the fuzziness parameter t, the algorithm iteration stop parameter ε, the mixing parameter λ of the mixing kernel function, the width parameter δ of the radial basis kernel function, and the order q of the polynomial kernel function;

[0065] S42: Use the kernel fuzzy C-means model to classify the sample points and obtain the membership value of each sample point to each type of ground feature; wherein, the membership expression of each sample point in the constructed demixing model AD-HKFCM is:

[0066]

[0067] Among them, d(x0,a i ) represents the distance from the sample point x0 to the center of the i-th category a i The absolute distance;

[0068] S43: Construct a WSVDD model based on membership degree and use the grid search method to optimize the relevant parameters in S41;

[0069] S44: Obtain the center of each category hypersphere, use it as the category center, calculate the AD value of each sample point to the category center, and update the membership value and classification results; R i is the radius of the hypersphere of type i, then the distance from point x0 to the center of type i a i The formula for the closeness distance AD is:

[0070]

[0071] S45: Repeat steps S43 and S44 until the iteration termination condition is met Obtain the final membership value of each sample point to each category;

[0072] S46: Design simulation experiments for the constructed AD-HKFCM unmixing model to evaluate the effectiveness of the algorithm and the unmixing effect.

[0073] like Figure 2 As shown in the figure, it is a flowchart for constructing a fuzzy C-means unmixing model based on the hybrid kernel space compactness distance. In order to improve the accuracy of the classification results, it is necessary not only to calculate the distance from the sample point to the category center, but also to consider the relationship and distribution compactness of the sample points in the feature space.

[0074] After constructing the unmixing model, the embodiment of the present invention evaluated the unmixing effect and robustness of the newly generated model compared with the traditional model through design experiments. Figure 3 As shown in Figure 2, experimental verification was carried out using hyperspectral simulated data and multispectral real data.

[0075] In the experiment, the root mean square error (RMSE) was selected as the indicator to evaluate the unmixing accuracy of the mixed pixel decomposition model with an image as a whole. The calculation formula is as follows:

[0076]

[0077] Among them, N represents the number of pixels in the data set, B represents the size of the image, and r i represents the abundance obtained from the experiment, Represents the reference abundance. The smaller the RMSE value, the higher the accuracy of the mixed pixel decomposition result; conversely, the lower the accuracy.

[0078] The hyperspectral simulation data experiment uses a digital spectral library to randomly select spectra as endmembers and employs a bilinear Fan model to generate hyperspectral simulation data. A certain signal-to-noise ratio (SNR) is added to the simulated data to verify the advantages of the constructed unmixing model over traditional models.

[0079] The calculation formula of the signal-to-noise ratio SNR is as follows:

[0080]

[0081] Where x represents the original signal, n represents the corresponding noise, and E[*] represents the expected value.

[0082] The multispectral real data experiment selected real multispectral remote sensing data from different regions as the images to be demixed. The accuracy of the constructed model was further compared with other models, and the model's applicability was evaluated. Other models include: Gaussian Kernel Fuzzy C-Means (G-KFCM), Hybrid Kernel Fuzzy C-Means (H-KFCM), Gaussian Kernel Fuzzy Support Vector Data Description (G-FSVDD), and Hybrid Kernel Fuzzy Support Vector Data Description (H-FSVDD). The images to be demixed were two multispectral remote sensing data sets (30-meter resolution Landsat-OIL images) from Chongming Island, Shanghai, taken on August 13, 2013 (Region 1) and February 27, 2022 (Region 2).

[0083] Table 1 Unmixing accuracy (RMSE) of hyperspectral simulation data under different models

[0084]

[0085] As shown in Table 1, to verify the robustness of the algorithm, the embodiment of the present invention gradually increased the noise intensity by adding 20dB, 40dB, 60dB, and 80dB of Gaussian white noise to the simulated data. The mixed pixel decomposition accuracy and effectiveness of different algorithms under the influence of different noise levels were tested. It was found that among the five models, G-KFCM had the highest RMSE in the simulated data unmixing results at four noise levels, all exceeding 0.33. The newly constructed AD-HKFCM model achieved the highest unmixing accuracy, with all RMSEs less than 0.26.

[0086] Table 2 Unmixing accuracy (RMSE) of multispectral real data under different models

[0087]

[0088] Table 2 shows that, similar to the unmixing results for the hyperspectral simulation data, the models with the highest to lowest unmixing accuracy are AD-HKFCM, H-FSVDD, G-FSVDD, H-KFCM, and G-KFCM, for both Regions 1 and 2. In other words, AD-HKFCM outperforms the other four models in unmixing performance, whether in areas covered by a single large feature or in areas where different features are evenly distributed over a small area.

[0089] In the embodiment of the present invention, in step S5, the constructed fuzzy C-means unmixing model AD-HKFCM based on the mixing kernel spatial compactness distance is used to process the Landsat image for unmixing to obtain an unmixed abundance map corresponding to each end member in the region.

[0090] The study area of the embodiment of the present invention includes four types of land features: vegetation, water bodies, bare land and artificial surfaces. The fuzzy C-means unmixing model based on the hybrid kernel spatial compactness distance constructed in step S4 is used to unmix the processed regional remote sensing image to obtain the abundance map of the four end members of the region. Figure 4 The figure shows a long-term unmixing abundance map of the study area according to an embodiment of the present invention, wherein the brighter the color, the higher the proportion of the end member in a single pixel.

[0091] The number of devices and processing scales described herein are intended to simplify the description of the present invention, and applications, modifications, and variations of the present invention will be apparent to those skilled in the art.

[0092] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A fuzzy C-means unmixing method based on the spatial closeness distance of the mixing kernel, characterized in that: The following steps are involved: S1. Obtain original remote sensing images through Landsat dataset; S2. Preprocess the acquired remote sensing images, further calculate the pixel purity index of the images, extract endmember information, and construct training samples; S3. The classical fuzzy C-means unmixing model is improved by using a hybrid kernel function and support vector data description theory to obtain a hybrid kernel fuzzy C-means unmixing model. Here, by combining the hybrid function with the kernel fuzzy C-means clustering model, the sample set is nonlinearly mapped to a high-dimensional space, and C-means clustering is performed in the space to obtain training samples for the support vector data description model. Considering global and local performance, the polynomial kernel function and the radial basis kernel function are combined to obtain a hybrid kernel function with strong extrapolation and interpolation capabilities. The calculation formula is: (1) Where, is the mixed kernel function, is a polynomial kernel function, is the radial basis kernel function, , represents the mixing scale factor of the two kernel functions, The larger it is, the better the performance of the hybrid kernel function; In order to more accurately represent the influence of different sample points, the weighted SVDD model based on membership is selected for training. The objective function expression of the weighted SVDD model is: ， (2) Where, represents the radius of the hypersphere, is the penalty factor, regulating The relationship between the size of the hypersphere and the number of error samples can be controlled. is the center of the hypersphere, represents the weight of the sample point, Determined by the membership obtained by the mixed kernel fuzzy C-means model; S4. Unmixing the remote sensing image dataset using the fuzzy C-means unmixing model, thereby obtaining the abundance map of the corresponding end members in the region, i.e., the unmixing result.

2. The fuzzy C-means unmixing method based on the mixing kernel space closeness distance according to claim 1, characterized in that: In step S2, the acquired remote sensing image is preprocessed, including radiation calibration and atmospheric correction. Specifically, radiation correction is performed on the acquired remote sensing image data respectively; the image data is geometrically corrected by using an image-by-image correction method to obtain preprocessed image data.

3. The fuzzy C-means unmixing method based on the mixing kernel space closeness distance according to claim 1, characterized in that: Step S4 specifically includes the following steps: S41. Determine the number of ground object categories M, the fuzziness parameter t, and the algorithm iteration stop parameter ; S42. Use the kernel fuzzy C-means model to classify the sample points and obtain the membership value of each sample point to each type of ground feature; wherein, the membership expression of each sample point in the constructed demixing model AD-HKFCM is: (3) in, Represents sample points To the jth category center The absolute distance; S43, constructing a weighted SVDD model based on the degree of membership, and optimizing the relevant parameters in step S41 using a grid search method; S44. Obtain the center of each category hypersphere, use it as the category center, calculate the closeness distance value from each sample point to the category center, and update the membership value and classification results; For the The radius of the hypersphere, then the point To Category Center The formula for the closeness distance is: (4) S45, repeat steps S43 and S44 until the iteration termination condition is met , obtain the final membership value of each sample point to each category; S46. Design simulation experiments for the constructed AD-HKFCM unmixing model to evaluate the effectiveness of the algorithm and the unmixing effect.

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