Spectral image ground object classification method combining spatial-spectral correlation and mixed-order similarity

Abstract

A spectral image surface feature classification method combining spatial-spectral correlation and mixed order similarity belongs to the field of remote sensing image processing and classification, and comprises the following steps: segmenting a first principal component extracted from a hyperspectral data set through entropy rate superpixel analysis, and stacking d-dimensional potential features extracted from each region to obtain a potential feature matrix; then, according to inter-band correlation coefficient matrix learning, hyperspectral inter-band similarity matrix learning and spatial-spectral joint correlation learning, a total objective function is obtained, and a coefficient matrix and an inter-band similarity matrix are solved until a total objective function value is converged; and finally, performing spectral clustering according to the solved similar matrix between the wavebands, selecting the wavebands with the maximum information entropy to form a waveband subset, classifying the obtained waveband subset by using a k-nearest neighbor algorithm to obtain a classification result, and calculating the classification accuracy. Compared with other methods, the classification accuracy is improved, and the performance is more stable.

Description

Technical Field

[0001] The invention belongs to the field of remote sensing image processing and classification, and in particular relates to a spectral image ground object classification method combining space-spectral correlation and mixed-order similarity. Background Art

[0002] In the field of remote sensing image processing and classification, hyperspectral image data is a widely available data. Dimensionality reduction and classification analysis of hyperspectral data can reduce the complexity of computational time, remove noise interference in the data set, and mine potential information such as the coverage ratio of land objects and landform characteristics. However, due to the large dimensionality of the original spectral image and the high degree of information duplication of bands with similar distances, the classification process is computationally intensive and susceptible to noise. Some existing classification methods directly use the original spectral image or only use simple dimensionality reduction methods, which do not fully utilize the spatial texture information of the original spectral image and the information between each band. The selected bands cannot achieve the ideal classification effect, which brings great challenges to the classification of hyperspectral image data. Therefore, effective and novel technical methods are needed to solve the classification problem of hyperspectral image data. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a spectral image object classification method combining spatial-spectral correlation and mixed-order similarity, the method comprising the steps of:

[0004] The first principal component is extracted from the hyperspectral image and divided into multiple regions. For each region, the potential features are extracted and the potential features of each region in each band are stacked to obtain a potential feature matrix.

[0005] The inter-band correlation coefficient matrix is ​​learned through the obtained latent feature matrix to obtain the coefficient matrix, and the latent feature matrix is ​​mapped to the Gaussian kernel space, polynomial kernel space and inverse polynomial kernel space respectively, and the different similarity matrices are superimposed to obtain a new similarity matrix.

[0006] The mixed-order similarity matrix is ​​calculated through the new similarity matrix, and the inter-band similarity matrix is ​​obtained by performing hyperspectral inter-band similarity matrix learning on the mixed-order similarity matrix. The spatial-spectral joint correlation learning is performed on the coefficient matrix and the inter-band similarity matrix to update the inter-band similarity matrix.

[0007] The total objective function is obtained by learning the inter-band correlation coefficient matrix, the inter-hyperspectral band similarity matrix and the spatial-spectral joint correlation, and the obtained total objective function is iteratively solved until the total objective function value converges.

[0008] The similarity matrix between bands is spectrally clustered to obtain the band clustering results, the information entropy of each band is calculated, and the band with the largest information entropy in each cluster is selected to form a band subset. The obtained band subset is classified by the k-nearest neighbor algorithm to obtain the classification result.

[0009] According to the obtained classification results, the classification accuracy of the spectral image dataset is calculated.

[0010] Furthermore, the expression formula for dividing the first principal component into N regions is:

[0011]

[0012] Where H represents the spectral image data, r i represents the i-th region after segmentation.

[0013] The potential feature expression formula of each region learning region is:

[0014]

[0015] Among them, Y (i) represents the potential feature matrix of the i-th region, I is the d-dimensional unit matrix, L (i) represents the symmetric normalized Laplacian matrix of the potential features of the i-th region, the L (i) The definition is as follows:

[0016]

[0017] Among them, W (i) is the similarity matrix constructed by the k nearest neighbor graph and Euclidean distance of the potential features of the i-th region, D (i) W (i) The original spectral data can be re-expressed as The d-dimensional potential features of each region in each band are stacked to obtain the potential feature matrix

[0018] Furthermore, the inter-band correlation coefficient matrix learning expression formula is:

[0019]

[0020] in,‖·‖ F is the F-norm, ‖·‖ * is the nuclear norm.

[0021] The three different similarity matrices R1, R2, and R3 obtained by mapping the potential feature matrix to the Gaussian kernel space, the polynomial kernel space, and the inverse polynomial kernel space are expressed as follows:

[0022]

[0023] R2=K2(f i ,f j )=(f i T f j +c) 2

[0024]

[0025] Among them, ||·||2 is the 2-norm, f i and f j Represent the i-th and j-th row elements of F respectively.

[0026] The three different similarity matrix superposition expression formulas are:

[0027]

[0028] Among them, R n is the nth similarity matrix, similarity matrix R s It is the result of superposition of R1, R2 and R3.

[0029] Furthermore, the mixed-order similarity matrix R is expressed as:

[0030]

[0031] in, and Respectively represent R s p-order and p-1-order matrices.

[0032] The similarity matrix learning expression formula between the hyperspectral bands is:

[0033]

[0034] in,‖·‖ F is the F norm, and S is the similarity matrix between bands.

[0035] The spatial-spectral joint correlation learning expression formula is:

[0036]

[0037] Among them, z i and z j denote the i-th and j-th columns of the coefficient matrix Z, respectively, S ij Represents the element in the i-th row and j-th column of S.

[0038] Furthermore, the overall objective function is expressed as:

[0039]

[0040] The augmented Lagrangian method is used to introduce the auxiliary variable L to express the formula:

[0041]

[0042] The coefficient matrix Z and auxiliary variable L are expressed as follows:

[0043]

[0044] Where Y1 is the Lagrange multiplier, μ>0 is the penalty parameter, I is the identity matrix, is the transpose of the Laplacian matrix of the matrix L.

[0045] The coefficient matrix is ​​expressed as follows after being solved by the Sylvester equation:

[0046]

[0047] Among them, the expression of Y1 is Y1=Y1+μ(ZL), and the expression of μ is μ=min(ρμ,μ max ), ρ>1 is the iteration step, μ max Indicates the maximum value of μ.

[0048] The S value in the total objective function is solved, and the expression formula is:

[0049]

[0050] Among them, R ij represents the i-th row and j-th column element of R. According to the above alternating solution method, the total objective function is iteratively solved until the total objective function value converges.

[0051] Furthermore, the similarity matrix S between bands is spectrally clustered based on the solution results to obtain the band clustering results, and the information entropy of each band is calculated. Then, according to the band clustering results and information entropy, the band with the largest information entropy in each cluster is selected to form a band subset, and then the band subset is classified using the k-nearest neighbor algorithm to obtain the classification result.

[0052] Furthermore, the classification accuracy rate on the spectral image dataset is calculated based on the obtained classification results.

[0053] The present invention provides a spectral image object classification method combining spatial-spectral correlation and mixed-order similarity, which has the following advantages:

[0054] (1) The method uses principal component analysis and entropy rate superpixel segmentation to divide the hyperspectral data into regions and extracts the potential features of each region. The obtained potential features can make more full use of the spatial information of the hyperspectral image and reduce noise interference.

[0055] (2) The method uses a method to map the similarity matrix between hyperspectral image bands into Gaussian kernel space, polynomial kernel space and inverse polynomial kernel space. The different similarity matrices obtained can better capture the local patterns and subtle features of the data, more flexibly express different feature combinations and interactions, thereby fully considering the global feature trends and more effectively reducing the impact of outliers and noise.

[0056] (3) The method adopts a mixed-order similarity calculation method, and the obtained mixed-order similarity matrix can more fully consider the inter-spectral information of the hyperspectral image and more effectively reduce noise interference.

[0057] (4) The method adopts spatial-spectral joint correlation learning, which can more effectively fuse the spatial and spectral information of hyperspectral image data, and the bands in the final band subset are more representative. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0059] Figure 1 It is a flow chart of the spectral image object classification method combining spatial-spectral correlation and mixed-order similarity provided by the present invention;

[0060] Figure 2 This is a diagram of the Indian Pines dataset with a size of 145*145 pixels and 200 valid bands. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0062] Exemplary Methods

[0063] like Figure 1The present invention provides a spectral image object classification method combining spatial-spectral correlation and mixed-order similarity, the method steps are as follows:

[0064] Step S110: obtaining the first principal component of the spectral image data by principal component analysis, and segmenting the obtained first principal component into N regions by entropy rate superpixel segmentation, the expression formula of which is as follows:

[0065]

[0066] Where H represents the spectral image data, r i represents the i-th region after segmentation.

[0067] Through spectral embedding learning, the potential features of each region are learned, and the expression formula is as follows:

[0068]

[0069] Among them, Y (i) represents the potential feature matrix of the i-th region, I is the d-dimensional unit matrix, L (i) Represents the symmetric normalized Laplacian matrix of the latent features of the i-th region.

[0070] The L (i) The expression formula is as follows:

[0071]

[0072] Among them, W (i) is the similarity matrix constructed by the k nearest neighbor graph and Euclidean distance of the potential features of the i-th region, D (i) W (i) The original spectral data can be re-expressed as The d-dimensional potential features of each region in each band are stacked to obtain the potential feature matrix

[0073] Step S120: Obtain the coefficient matrix Z by learning the potential feature matrix F obtained through the inter-band correlation coefficient matrix. The expression formula is as follows:

[0074]

[0075] in,‖·‖ F is the F-norm, ‖·‖ * is the nuclear norm, and Z is constrained by the nuclear norm so that Z has a low-rank structure.

[0076] By mapping the potential feature matrix F into the Gaussian kernel space, polynomial kernel space and inverse polynomial kernel space respectively, three different similarity matrices R1, R2 and R3 are obtained, and their expression formulas are as follows:

[0077]

[0078] R2=K2(f i ,f j )=(f i T f j +c) 2

[0079]

[0080] Among them, ||·||2 is the 2-norm, f i and f j Represent the i-th and j-th row elements of F respectively.

[0081] The similarity matrix R is obtained by superimposing the three similarity matrices s , and its expression formula is as follows:

[0082]

[0083] Among them, R n is the nth similarity matrix, similarity matrix R s It is the result of superposition of R1, R2 and R3.

[0084] Step S130: Using the similarity matrix R s Calculate its mixed-order similarity matrix R, which is expressed as follows:

[0085]

[0086] in, and Respectively represent R s p-order and p-1-order matrices.

[0087] According to the mixed-order similarity matrix R, the similarity matrix between hyperspectral bands is learned, and its expression formula is as follows:

[0088]

[0089] in,‖·‖ F is the F norm, and S is the similarity matrix between bands.

[0090] The coefficient matrix Z and the inter-band similarity matrix S are learned through space-spectrum joint correlation learning, and the expression formula is as follows:

[0091]

[0092] Among them, z i and z j denote the i-th and j-th columns of the coefficient matrix Z, respectively, S ij Represents the element in the i-th row and j-th column of S.

[0093] Step S140: The total objective function is obtained by learning the inter-band correlation coefficient matrix, the inter-band similarity matrix of the hyperspectral spectrum, and the spatial-spectral joint correlation. The expression formula is as follows:

[0094]

[0095] The coefficient matrix Z of the total objective function is iteratively solved by the alternating solution method and the gradient descent method. The augmented Lagrangian method is used to introduce the auxiliary variable L, which is expressed as follows:

[0096]

[0097] The formula obtained after using the Lagrangian method is solved by an alternating solution strategy to obtain the expressions for Z and L, which are expressed as follows:

[0098]

[0099] Where Y1 is the Lagrange multiplier, μ>0 is the penalty parameter, I is the identity matrix, is the transpose of the Laplacian matrix of the matrix L.

[0100] The expression of Z is obtained by solving the Sylvester equation, and its expression formula is as follows:

[0101]

[0102] The expression of Y1 is Y1=Y1+μ(ZL), and the expression of μ is μ=min(ρμ,μ max ), ρ>1 is the iteration step, μ max Indicates the maximum value of μ.

[0103] By using the alternating solution method and solving the S value in the total objective function, the expression formula is as follows:

[0104]

[0105] Among them, R ij Represents the element in the i-th row and j-th column of R.

[0106] The total objective function is iteratively solved by the above alternating solution method until the total objective function value converges.

[0107] Step S150: Obtain band clustering results through spectral clustering, calculate the information entropy of each band, select the band with the largest information entropy in each cluster to form a band subset based on the band clustering results and the information entropy, and classify the band subsets through the k-nearest neighbor algorithm to obtain classification results.

[0108] Step S160: Calculate the classification accuracy on the hyperspectral data set according to the obtained classification results.

[0109] Through this implementation, the hyperspectral data set is first divided into N regions, and then potential features are extracted to obtain a potential feature matrix. The total objective function is obtained by learning the inter-band correlation coefficient matrix, the inter-band similarity matrix of the hyperspectral bands, and the space-spectrum joint correlation. The coefficient matrix and the inter-band similarity matrix are solved according to the total objective function, and then spectral clustering is performed and band subsets are constructed according to the information entropy of each band. Finally, the band subsets are classified using the k-nearest neighbor algorithm to obtain the final classification result. After the classification result is obtained, the classification accuracy on the data set is calculated.

[0110] To further illustrate, assuming that a hyperspectral image data set is classified according to this embodiment, a classification result with higher accuracy than most methods will be obtained.

[0111] Detailed description of the invention Results

[0112] This implementation adopts the publicly available Indian Pines dataset, using 200 valid bands. The details of the dataset are as follows:

[0113] The Indian Pines dataset covers farmland and a small amount of forests, buildings, and other features in northwest Indiana. The dataset contains the following two files:

[0114] The hyperspectral image data file is a three-dimensional data matrix with a dimension of 145*145*220, where 145*145 represents the spatial size of the entire scene, i.e., it contains 21,025 pixels. The spectral vector corresponding to each pixel contains the reflectance values ​​of 220 bands, of which 200 valid bands are retained. Each pixel corresponds to a ground resolution of approximately 20 meters*20 meters.

[0115] The ground truth label file is a 145*145 two-dimensional matrix, where each label pixel corresponds one-to-one to the corresponding pixel position in the hyperspectral data; each element in the matrix is ​​an integer between 0 and 16, representing the ground feature category of an element.

[0116] In order to verify the superiority of this implementation (Ours), this implementation is compared with several existing spectral image object classification methods, including TOF, OPBS, ASPS_MN, ONR and other methods. The values ​​of OA, AA and Kappa indicators of these methods when using KNN, RF and SVM classifiers on the IndianPines public dataset are compared. The specific data comparison is shown in Table 1.

[0117] Table 1 Classification accuracy of Indian Pines dataset (%)

[0118]

[0119] By comparing the data in the above table, it can be clearly seen that Ours achieves the best performance and significantly improves the accuracy of spectral image classification. The quantitative results fully illustrate the superiority of Ours, because Ours can make better use of spatial information and inter-spectral information and better integrate the two, thereby obtaining a band subset containing more comprehensive information, thereby achieving an ideal classification effect. Ours obtains a more ideal band subset by performing dimensionality reduction processing on hyperspectral images, which can reduce the complexity of computational time while removing noise interference in the data set, thereby improving the classification accuracy of hyperspectral data images. A large number of experiments have shown that this method is superior to existing methods. Regarding the setting of parameters of this embodiment, in all experiments, the range of parameters α and β are uniformly tuned between 1e-8 and 1e4, the optimal order of mixed order similarity is adjusted between 3 and 8, the potential feature dimension is set to 5, and the number of neighbors is set to 15.

[0120] This embodiment proposes a spectral image object classification method that combines spatial-spectral correlation and mixed-order similarity, which is used to classify and analyze common hyperspectral images in life. The potential feature matrix of the hyperspectral image is obtained by stacking d-dimensional potential features, and then the total objective function is obtained by learning the inter-band correlation coefficient matrix, the hyperspectral inter-band similarity matrix and the spatial-spectral joint correlation. The coefficient matrix and the inter-band similarity matrix of the total objective function are iteratively solved, and then spectral clustering is performed and information entropy is calculated to obtain the band subset, and finally the final classification result is obtained by the k-nearest neighbor algorithm. The experimental results using three classifiers on the public dataset Indian Pines show that this embodiment has a higher classification accuracy and better superiority than other methods.

[0121] It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principles of the present invention, and do not constitute a limitation of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. In addition, the appended claims of the present invention are intended to cover all changes and modifications that fall within the scope and boundaries of the appended claims, or the equivalent forms of such scope and boundaries.

Claims

1. A spectral image object classification method combining spatial-spectral correlation and mixed-order similarity, characterized in that: The method comprises the steps of: A principal component analysis is performed on a hyperspectral data set to extract its first principal component, and the obtained first principal component is segmented by entropy rate superpixel to segment the spectral image into N regions; for each region, its d-dimensional potential features are extracted; The d-dimensional potential features of each region in each band are stacked to obtain the potential feature matrix F of the hyperspectral image data; According to the obtained potential feature matrix F, the inter-band correlation coefficient matrix is ​​learned to obtain the coefficient matrix Z; F is mapped to the Gaussian kernel space, polynomial kernel space and inverse polynomial kernel space respectively to obtain three different similarity matrices R1, R2, and R3, which are superimposed to obtain the similarity matrix R s ; According to the similarity matrix R s Calculate its mixed order similarity matrix R; perform hyperspectral inter-band similarity matrix learning based on the mixed order similarity matrix R to obtain the inter-band similarity matrix S; perform spatial-spectral joint correlation learning based on the coefficient matrix Z and the inter-band similarity matrix S to update the inter-band similarity matrix S; The total objective function is obtained according to the inter-band correlation coefficient matrix learning, the inter-band similarity matrix learning of the hyperspectral spectrum and the spatial-spectral joint correlation learning; the coefficient matrix Z and the inter-band similarity matrix S are iteratively solved for the obtained total objective function using the alternating solution method and the gradient descent method until the total objective function value converges; According to the solution results, the similarity matrix S between bands is spectrally clustered to obtain the band clustering results, the information entropy of each band is calculated, and the band with the largest information entropy in each cluster is selected to form a band subset; Classification is performed using the k nearest neighbor algorithm according to the band subset to obtain the classification result; According to the obtained classification results, the classification accuracy rate on the spectral image dataset is calculated.

2. The spectral image object classification method based on joint spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: The principal component analysis is performed on a spectral image data to obtain the first principal component of the spectral data; the entropy rate superpixel segmentation is performed on the obtained first principal component to divide the spectral image into N regions, as shown below: Where H represents the spectral image data, r i represents the i-th region after segmentation; for each region, its regional potential features are learned by spectral embedding, and the learned regional potential features are as follows: Among them, Y (i) represents the potential feature matrix of the i-th region, I is the d-dimensional unit matrix, L (i) represents the symmetric normalized Laplacian matrix of the potential features of the i-th region, L (i) The specific definitions are as follows: Among them, W (i) is the similarity matrix constructed by the k nearest neighbor graph and Euclidean distance of the potential features of the i-th region, D (i) W (i) The original spectral data can be re-expressed as H∈R b*N*d , stack the d-dimensional potential features of each region of each band to obtain the potential feature matrix F∈R b*Nd .

3. The spectral image object classification method based on joint spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: According to the obtained potential feature matrix F, the inter-band correlation coefficient matrix is ​​learned to obtain the coefficient matrix Z. The inter-band correlation coefficient matrix learning is defined as follows: in,‖·‖ F is the F-norm, ‖·‖ * is the nuclear norm, and Z is constrained by the nuclear norm so that Z has a low-rank structure; then, F is mapped to the Gaussian kernel space, the polynomial kernel space, and the inverse polynomial kernel space, respectively, to obtain three different similarity matrices R1, R2, and R3, which are defined as follows: R2=K2(f i ,f j )=(f i T f j +c) 2 Among them, ‖·‖2 is the 2-norm, f i and f j Respectively represent the i-th and j-th row elements of F; after obtaining R1, R2, and R3, the three similarity matrices are superimposed as shown below: Among them, R n is the nth similarity matrix, similarity matrix R s It is the result of superposition of R1, R2 and R3.

4. The spectral image object classification method based on joint spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: According to the similarity matrix R s Calculate its mixed-order similarity matrix R as follows: in, and Respectively represent R s The p-order and p-1-order matrices are used; according to the mixed-order similarity matrix R, the similarity matrix between hyperspectral bands is learned, which is defined as follows: in,‖·‖ F is the F norm, S is the inter-band similarity matrix; the spatial-spectral joint correlation learning is performed according to the coefficient matrix Z and the inter-band similarity matrix S, as shown below: Among them, z i and z j denote the i-th and j-th columns of the coefficient matrix Z, respectively, S ij Represents the element in the i-th row and j-th column of S.

5. The spectral image object classification method combining spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: The total objective function is obtained based on the inter-band correlation coefficient matrix learning, the hyperspectral inter-band similarity matrix learning, and the spatial-spectral joint correlation learning. The total objective function is defined as follows: The coefficient matrix Z of the total objective function is iteratively solved by the alternating solution method and the gradient descent method. The augmented Lagrangian method is used to introduce the auxiliary variable L, as shown below: Next, the alternating solution strategy is used to obtain the expressions for Z and L as follows: Where Y1 is the Lagrange multiplier, μ>0 is the penalty parameter, I is the identity matrix, is the transpose of the Laplace matrix of matrix L; then, by solving Z through the Sylvester equation, we can get the expression of Z as follows: The expression of Y1 is Y1=Y1+μ(ZL), and the expression of μ is μ=min(ρμ,μ max ), ρ>1 is the iteration step, μ max represents the maximum value of μ; The alternating solution method is used at the same time to solve the S value in the total objective function, as shown below: Among them, R ij Represents the i-th row and j-th column element of R; according to the above alternating solution method, the total objective function is iteratively solved until the total objective function value converges.

6. The spectral image object classification method combining spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: According to the solution results, the similarity matrix S between bands is spectrally clustered to obtain the band clustering results; the information entropy of each band is calculated; according to the band clustering results and the information entropy, the band with the largest information entropy in each cluster is selected to form a band subset; The k nearest neighbor algorithm is used to classify the band subsets to obtain the classification results.

7. The spectral image object classification method combining spatial-spectral correlation and mixed-order similarity according to claim 1 is characterized in that: According to the obtained classification results, the classification accuracy rate on the spectral image dataset is calculated.

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