A spatial feature extraction method for enhanced two-dimensional singular spectrum analysis

Abstract

The present invention discloses a spatial feature extraction method for enhancing two-dimensional singular spectrum analysis, which utilizes the local similarity of pixels to enhance the spatial feature extraction effect. Based on the traditional 2DSSA, the present invention proposes an improved adaptive window to replace the fixed window, and combines the neighborhood similarity of the target pixel to realize the embedding process, and obtains a trajectory matrix with low rank; singular value decomposition is performed on the low rank trajectory matrix, and the maximum singular value obtained is larger than the maximum singular value obtained by the fixed window, and has a higher proportion in all singular values, corresponding to more spatial information; the spatial sub-component corresponding to the maximum singular value is reconstructed as a feature to obtain the final feature component, which removes the influencing components such as noise while enhancing the spatial structure information. The present invention can solve the problems of diverse spatial scales and noise in hyperspectral images, overcome the shortcomings of the traditional 2DSSA method, enhance the feature extraction effect of images, and improve the accuracy of image classification.

Description

Technical Field

[0001] The invention belongs to the technical field of remote sensing image processing, and in particular relates to a spatial feature extraction method for enhanced two-dimensional singular spectrum analysis. Background Art

[0002] With the advancement of sensor and satellite technology, hyperspectral remote sensing has become one of the important earth observation technologies that has developed rapidly in the past 30 years. It has played an important role in the fields of land object classification, target identification, environmental management and mineral surveying and mapping, and has become an important means to promote national economic development and construction. Although hyperspectral images contain rich spectral information, there is a phenomenon of "same object, different spectrum, same spectrum, different objects", which will cause serious "salt and pepper noise" misclassification in classified images. In addition, the band of hyperspectral images is narrow, and each channel receives less light energy, which makes the signal-to-noise ratio low and some bands have serious noise, which brings challenges to the interpretation of images. Therefore, it is necessary to effectively extract features from hyperspectral data.

[0003] Spatial feature extraction methods can solve problems such as spectral variability and band noise. It uses artificially designed operators or filter windows to calculate with the pixels of grayscale images, thereby extracting multiple features such as context, texture, shape, etc. in the image, thereby eliminating the influence of noise. In hyperspectral images, a widely used type of spatial feature extraction method is mathematical morphology, which mainly extracts the shape characteristics of the image. Through basic morphological operations, including corrosion, expansion, opening and closing operations, image components that are meaningful for expressing and depicting the shape of the target area, such as boundaries and connected areas, can be extracted from the image. However, this method also has some disadvantages: for example, a series of operations will bring high computational complexity, and the shape connectivity of different objects is easy to cause confusion. In addition, some texture feature extraction methods, such as gray level co-occurrence matrix (GLCM), Gabor filtering and local binary pattern (LBP), can fully reflect the gradient changes of the image in different directions and obtain spatial correlation, but their accuracy is usually limited.

[0004] Two-dimensional Singular Spectral Analysis (2DSSA) is a matrix decomposition algorithm proposed by N. Golyandina et al. in 2010, and its applicability in images was explained. J. Zabalza et al. first applied 2DSSA to hyperspectral images in 2015, and extracted spatial features band by band, achieving results superior to general spatial techniques. Based on singular value decomposition (SVD), 2DSSA can decompose the original grayscale image into several sub-images. Different sub-images contain information such as spatial trends, textures, edges, and noise. By selecting appropriate sub-images for reconstruction, the main spatial structure content of the original image can be obtained, and the influencing components such as noise can be removed. In addition, it constructs the trajectory matrix corresponding to the entire image through different embedding windows, which can simultaneously contain the local and global spatial features of the image, and well considers the global correlation.

[0005] However, similar to other widely used spatial technologies, 2DSSA also has some disadvantages. First, the above algorithms usually use regular shapes or fixed-size windows for processing, ignoring the complexity of the shape and scale of the image objects, that is, the area used for spatial feature extraction does not match the spatial structure of the image. In addition, 2DSSA usually selects the spatial trend component corresponding to the maximum singular value as the reconstructed feature image, but other singular values ​​also correspond to some useful information, which causes the loss of some spatial information, mainly manifested in the reduction of edge differences of objects and few texture features. The image will be too smooth, resulting in a decrease in classification accuracy, especially for smaller objects. In order to effectively extract spatial features from hyperspectral images, the algorithm needs to be improved and enhanced. Summary of the invention

[0006] In view of the above-mentioned problems, the present invention aims to provide a spatial feature extraction method for enhanced two-dimensional singular spectrum analysis. This method can improve the problems of edge blur, detail loss and small amount of spatial information caused by the traditional 2DSSA fixed window by adaptively embedding a window combined with the neighborhood information of the target pixel, enhance the feature extraction effect of the image, and improve the accuracy of the image classification.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows: a spatial feature extraction method for enhancing two-dimensional singular spectrum analysis, characterized in that it comprises the following steps:

[0008] Step 1: Eigendecomposition based on adaptive window

[0009] 1) Adaptive embedding: Select remote sensing hyperspectral images and determine the size of the embedding window based on the number of each target spectral pixel and its similar spectral pixels;

[0010] 2) Constructing the trajectory matrix: for any band, stretch each target pixel and similar pixel into a column vector, and record the corresponding spatial position. By arranging the column vectors corresponding to the pixels of the whole image, the trajectory matrix is ​​obtained;

[0011] 3) Singular value decomposition: Performing singular value decomposition on the trajectory matrix can obtain a certain number of singular values ​​and corresponding singular vectors;

[0012] Step 2: Feature reconstruction based on enhanced maximum singular value

[0013] 4) Trajectory matrix reconstruction: Select the maximum singular value and its corresponding singular vector to reconstruct the trajectory matrix;

[0014] 5) Pixel reprojection: For each column vector in the reconstructed trajectory matrix, combined with the spatial position information recorded in 2), each pixel value is reprojected to the original spatial position;

[0015] 6) Pixel correction: Some pixels are selected multiple times in step 1) and included in multiple column vectors to obtain multiple reconstructed values, and the multiple reconstructed values ​​are averaged to obtain the final pixel value.

[0016] Furthermore, in step 1), the adaptive embedding method is as follows: define the hyperspectral image X to be processed, determine its size as N = R × C, the number of bands as B, satisfy R = 145, C = 145 and B = 200, and represent the image X as a set of all spectral pixels, as The embedding window size is determined as L. For any spectral pixel p i , then (L-1) similar pixels are selected in the entire image, and the similarity measure is the normalized Euclidean distance, and the calculation formula is:

[0017]

[0018] Among them, s ij Represents pixel p i and pixel p j Similarity, select each pixel p i The (L-1) similar pixels form the adaptive embedding window corresponding to the pixel.

[0019] Furthermore, it is characterized in that, in step 2), the trajectory matrix is ​​constructed band by band, specifically: the original image X is represented as a set of all band images, which is For a certain band image X i , and its corresponding pixel value is Each pixel value x kAll pixels in the corresponding embedded window are stretched into a column vector And record the spatial position of the pixel in the embedded window, and arrange the column vectors obtained from all pixels in the whole image to obtain the trajectory matrix G, as shown in the following formula:

[0020]

[0021] Furthermore, in step 3), the trajectory matrix G is subjected to singular value decomposition to obtain the singular value (λ 1 ≥λ 2 ≥...≥λ L ) and the corresponding singular vectors: left singular vector (U 1 ,U 2 ,...,U L ) and the right singular vectors (V 1 ,V 2 ,...,V L ), the trajectory matrix can be written as the sum of multiple sub-matrices:

[0022] G=G 1 +G 2 +...+G L

[0023]

[0024] Among them, G i Represents the submatrix corresponding to the i-th singular value, which is constructed from the singular values ​​and the corresponding singular vectors.

[0025] Further, in step 4), the submatrix G corresponding to the maximum singular value is selected 1 As the reconstruction of the trajectory matrix G:

[0026]

[0027] in Represents the reconstructed trajectory matrix G 1 Each column vector of .

[0028] The beneficial effects of the present invention are: compared with the original 2DSSA, the present invention obtains a trajectory matrix through adaptive window embedding, which fully considers the complexity and diversity of the shape of the ground objects compared with the fixed window; the trajectory matrix has a low rank property, which can increase the proportion of the maximum singular value, thereby enhancing the spatial characteristics of the reconstructed image, and retaining the main spatial identification information while removing the influencing components such as noise.

[0029] 2DSSA usually selects the component corresponding to the maximum singular value as the extracted spatial feature, and the proportion of the maximum singular value in all singular values ​​is related to the information content of the spatial feature. The present invention adopts an adaptive embedding window, and can obtain an enhanced maximum singular value through trajectory matrix construction and SVD, thereby improving the element similarity of the trajectory matrix column vector, so that it has low rank, increases the proportion of the maximum singular value, and enhances the spatial feature. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is an overall flow chart of the spatial feature extraction method based on enhanced 2DSSA of the present invention.

[0031] Figure 2 Schematic diagram of the adaptive embedding window of the present invention (taking L=9 as an example, a. fixed window of 2DSSA; b. adaptive window of enhanced 2DSSA).

[0032] Figure 3 This is a comparison diagram of the maximum singular values ​​of the enhanced 2DSSA of the present invention and the traditional 2DSSA (a. comparison of the maximum singular values ​​of 2DSSA and enhanced 2DSSA; b. comparison of the maximum singular value proportions of 2DSSA and enhanced 2DSSA).

[0033] Figure 4 These are the feature extraction effect diagram and classification result diagram of the enhanced 2DSSA of the present invention (a. original band diagram - taking the 20th band as an example; b. feature extraction diagram of 2DSSA; c. feature extraction diagram of enhanced 2DSSA; d. original image classification diagram; e. classification diagram of 2DSSA; f. classification diagram of enhanced 2DSSA). DETAILED DESCRIPTION

[0034] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0035] The spatial feature extraction method of enhanced 2DSSA provided by the present invention is suitable for processing the Indian Pine hyperspectral remote sensing image acquired by the AVIRIS (Airborne Visible Infrared Imaging Spectrometer) sensor. The spatial resolution of the original data acquired by AVIRIS is 10 meters, the spectral resolution is 10 nanometers, the spectral range is 400-2400 nanometers, and it includes a total of 224 spectral bands, of which 4 bands are removed because they are all zero values. In addition, the Indian Pine image data contains 20 bands that are easily affected by water absorption, namely bands 104-108, 150-163 and 220, so these bands are also removed. The Indian Pine image used in this case includes a total of 200 bands, with an image size of 145×145 pixels, and a total of 16 types of land objects including various crops such as corn and wheat.

[0036] like Figure 1 As shown, a spatial feature extraction method for enhancing two-dimensional singular spectrum analysis includes the following steps:

[0037] Step 1: Eigendecomposition based on adaptive window

[0038] 1) Adaptive embedding: Select remote sensing hyperspectral images and determine the size of the embedding window based on the number of each target spectral pixel and its similar spectral pixels. It is mainly based on the original hyperspectral image and selects similar pixels corresponding to the target pixel based on the similarity of the spectral pixel vector.

[0039] The specific embedding method is as follows: define the hyperspectral image X to be processed, determine its size as N = R × C, the number of bands as B, satisfy R = 145, C = 145 and B = 200, and represent the image X as the set of all spectral pixels, as The embedding window size is determined as L. For any spectral pixel p i , then (L-1) similar pixels are selected in the entire image, and the similarity measure is the normalized Euclidean distance, and the calculation formula is:

[0040]

[0041] Among them, s ij Represents pixel p i and pixel p j Similarity, select each pixel p i The (L-1) similar pixels of the pixel form the adaptive embedding window corresponding to the pixel. The embedding window of the traditional 2DSSA and the constructed adaptive window are Figure 2It can be seen from the comparison that the embedding window of the latter mainly contains pixels of the same type, and the influence from pixels of other categories is small, which effectively improves the consistency of pixels in the embedding window. It is mainly based on the original hyperspectral image, selects similar pixels corresponding to the target pixel according to the similarity of the spectral pixel vector, and records the spatial position of each similar pixel to guide the subsequent operation of each band image.

[0042] 2) Construct the trajectory matrix: For any band, stretch each target pixel and similar pixels into a column vector. The number of similar pixels selected for each target pixel is consistent to ensure that the number of rows in the constructed trajectory matrix is ​​consistent, and record the corresponding spatial position to guide the subsequent operation of each band image. The trajectory matrix is ​​obtained by arranging the column vectors corresponding to the pixels of the entire image;

[0043] The trajectory matrix is ​​constructed band by band. The specific method is as follows: the original image X is represented as a set of all band images, which is For a certain band image X i , and its corresponding pixel value is Each pixel value x k All pixels in the corresponding embedded window are stretched into a column vector And record the spatial position of the pixel in the embedded window, and arrange the column vectors obtained from all pixels in the whole image to obtain the trajectory matrix G, as shown in the following formula:

[0044]

[0045] The trajectory matrix G has some pixels with the same value on the anti-diagonal line and has low rank. The number of similar pixels selected for each target pixel in step 2) is consistent to ensure that the number of rows in the constructed trajectory matrix is ​​consistent. The trajectory matrix constructed using similar pixels has two characteristics:

[0046] ① It does not have the structure of Hankel-block-Hankel matrix, and only some pixel values ​​on the anti-diagonal line are the same;

[0047] ② It has low rank, and each column vector is composed of similar pixel values ​​with small differences.

[0048] 3) Singular value decomposition: By performing singular value decomposition on the trajectory matrix, a certain number of singular values ​​and corresponding singular vectors can be obtained. The specific method is as follows:

[0049] Perform singular value decomposition on the trajectory matrix G and obtain the singular value (λ 1 ≥λ 2 ≥...≥λ L ) and the corresponding singular vectors: left singular vector (U 1 ,U 2,...,U L ) and the right singular vectors (V 1 ,V 2 ,...,V L ), the trajectory matrix can be written as the sum of multiple sub-matrices:

[0050] G=G 1 +G 2 +...+G L

[0051]

[0052] Among them, Gi represents the submatrix corresponding to the i-th singular value, which is constructed by the singular values ​​and the corresponding singular vectors. The amount of spatial information it contains is measured by the size of the singular values. The number of singular values ​​is equal to the number of rows of the trajectory matrix. The distribution of the obtained singular values ​​is different from the distribution of singular values ​​in the original 2DSSA process, that is, it is more concentrated. Steps 2) and 3) are to perform eigendecomposition on the trajectory matrix constructed from each band image.

[0053] Step 2: Feature reconstruction based on enhanced maximum singular value

[0054] 4) Trajectory matrix reconstruction: Select the maximum singular value and its corresponding singular vector to reconstruct the trajectory matrix. The specific reconstruction method is as follows:

[0055] The original trajectory matrix has a low rank property and can be approximated as a rank-1 matrix. Therefore, all its spatial information is mainly concentrated on the submatrix corresponding to the maximum singular value, and the maximum singular value is much larger than the remaining singular values, such as Figure 3 As shown. In addition, smaller singular values ​​usually correspond to influencing components such as noise in the image, which need to be removed. Therefore, the submatrix G1 corresponding to the largest singular value is selected as the reconstruction of the trajectory matrix G:

[0056]

[0057] in Represents the reconstructed trajectory matrix G 1 Each column vector of . G1 can remove the influence of noise while retaining the main information as much as possible. Compared with the singular values ​​after traditional 2DSSA decomposition, it has two characteristics:

[0058] ①The largest singular value accounts for a higher proportion of all singular values;

[0059] ②The value of the maximum singular value is larger.

[0060] 5) Pixel reprojection: For each column vector in G1, combined with the corresponding spatial position recorded in step 2), each pixel in the column vector is projected back to the original spatial position. Compared with the pixels at the original position, the pixels in G1 are feature extracted, the similarity of the pixels inside the ground objects is improved, and the differences between land types are also preserved and enhanced to a certain extent.

[0061] 6) Pixel correction: The adaptive window of enhanced 2DSSA is for each pixel of the image. Its selection of similar pixels will cause the pixel at a certain position to be selected and calculated multiple times, that is, the same pixel is contained in different column vectors of the trajectory matrix. After reprojecting the pixels in the G1 column vector, multiple pixel values ​​will be assigned to the spatial position that is selected multiple times. At this time, it is necessary to average the multiple pixel values ​​and use the average value as the final pixel value.

[0062] Steps 5) and 6) are the process of reprojecting the trajectory matrix reconstructed by the maximum singular vector into an image size matrix. Step 6) averages the pixel values ​​that have been selected and transformed multiple times to eliminate the influence of transformation errors; in addition, this averaging is mostly concentrated in the uniform parts of the image and less at the edges, which can reduce the probability of blurred edges. Steps 4), 5), and 6) are the singular vectors corresponding to the maximum singular value, which reconstruct the original band image, and the reconstructed image is the feature extraction result.

[0063] The enhanced 2DSSA is applied to all bands of the image to obtain the feature image after spatial feature extraction. Taking band 20 as an example, the feature extraction effects of the original band, 2DSSA and enhanced 2DSSA are compared. The results are as follows: Figure 4 As shown in (a)-(c), it can be seen that compared with the original band, 2DSSA and enhanced 2DSSA can extract the main spatial context information and remove the influence of noise; compared with 2DSSA, enhanced 2DSSA retains more detailed information of the image, such as the edge and some texture features of the ground objects, and enhances the spatial identification features of the ground objects.

[0064] According to the obtained feature images, the support vector machine (SVM) classifier is used to classify them to further verify the validity of the features.

[0065] In the classification experiment, 2% of the samples were randomly selected from the images for training, and the remaining samples were used for testing. The sampling method was stratified sampling, and the samples in the training set and the test set did not overlap. The accuracy evaluation indicators include three: overall accuracy (OA), average accuracy (AA) and kappa coefficient. In addition, in order to avoid systematic errors and reduce random deviations, the experiment counted the average classification accuracy and standard deviation under 10 independent training and testing.

[0066] Table 1 shows the overall classification accuracy and standard deviation of the original Indian Pines image, the traditional 2DSSA and the method of the present invention after SVM classification, with the embedding window L = 49. It can be seen that the enhanced 2DSSA of the present invention can achieve significantly better classification accuracy than the traditional 2DSSA, and the average accuracy is more stable. The classification results correspond to the classification diagram shown in Figure 1. Figure 4 As shown in (d)-(f), it can be seen that the classification result of enhanced 2DSSA has effectively eliminated the classification "salt and pepper noise" phenomenon existing in the original image, and reduced the strip misclassification in 2DSSA, with less misclassification at the edge of the object.

[0067] Table 1 Comparison of feature classification accuracy

[0068]

[0069] The principle of the present invention is: this method uses the local similarity of pixels to enhance the spatial feature extraction effect. Based on the traditional 2DSSA, the present invention proposes an improved adaptive window to replace the fixed window, combines the neighborhood similarity of the target pixel to realize the embedding process, and obtains a trajectory matrix with low rank; the low rank trajectory matrix is ​​subjected to singular value decomposition, and the maximum singular value obtained is larger than the maximum singular value obtained by the fixed window, and has a higher proportion in all singular values, corresponding to more spatial information; the spatial sub-component corresponding to the maximum singular value is reconstructed as a feature to obtain the final feature component, which removes the influencing components such as noise while enhancing the spatial structure information. The present invention can solve the problems of diverse spatial scales and noise in hyperspectral images, overcome the shortcomings of the traditional 2DSSA method, enhance the feature extraction effect of images, and improve the accuracy of image classification.

[0070] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A spatial feature extraction method for enhancing two-dimensional singular spectrum analysis, characterized in that: The following steps are involved: Step 1: Eigendecomposition based on adaptive window 1) Adaptive embedding: Select remote sensing hyperspectral images and determine the size of the embedding window based on the number of each target spectral pixel and its similar spectral pixels; 2) Constructing the trajectory matrix: for any band, stretch each target pixel and similar pixel into a column vector, and record the corresponding spatial position. By arranging the column vectors corresponding to the pixels of the whole image, the trajectory matrix is ​​obtained; 3) Singular value decomposition: Performing singular value decomposition on the trajectory matrix can obtain a certain number of singular values ​​and corresponding singular vectors; Step 2: Feature reconstruction based on enhanced maximum singular value 4) Trajectory matrix reconstruction: Select the maximum singular value and its corresponding singular vector to reconstruct the trajectory matrix; 5) Pixel reprojection: For each column vector in the reconstructed trajectory matrix, combined with the spatial position information recorded in 2), each pixel value is reprojected to the original spatial position; 6) Pixel correction: Some pixels are selected multiple times in step 1) and included in multiple column vectors to obtain multiple reconstructed values, and the multiple reconstructed values ​​are averaged to obtain the final pixel value.

2. The spatial feature extraction method of enhanced two-dimensional singular spectrum analysis according to claim 1, characterized in that: In step 1), the adaptive embedding method is as follows: define the hyperspectral image X to be processed, determine its size as N = R × C, the number of bands as B, satisfy R = 145, C = 145 and B = 200, and represent the image X as a set of all spectral pixels, as The embedding window size is determined as L. For any spectral pixel p i , then (L-1) similar pixels are selected in the entire image, and the similarity measure is the normalized Euclidean distance, and the calculation formula is: Among them, s ij Represents pixel p i and pixel p j Similarity, select each pixel p i The (L-1) similar pixels form the adaptive embedding window corresponding to the pixel.

3. The spatial feature extraction method of enhanced two-dimensional singular spectrum analysis according to claim 2, characterized in that: In step 2), the trajectory matrix is ​​constructed band by band. The specific method is as follows: the original image X is represented as a set of all band images, which is For a certain band image X i , and its corresponding pixel value is Each pixel value x k All pixels in the corresponding embedded window are stretched into a column vector And record the spatial position of the pixel in the embedded window, and arrange the column vectors obtained from all pixels in the whole image to obtain the trajectory matrix G, as shown in the following formula:

4. The spatial feature extraction method of enhanced two-dimensional singular spectrum analysis according to claim 3 is characterized in that: In step 3), the trajectory matrix G is subjected to singular value decomposition to obtain singular values ​​(λ1≥λ2≥...≥λ L ) and the corresponding singular vectors: left singular vectors (U1,U2,...,U L ) and the right singular vectors (V1,V2,...,V L ), the trajectory matrix can be written as the sum of multiple sub-matrices: G=G1+G2+...+G L Among them, G i Represents the submatrix corresponding to the i-th singular value, which is constructed from the singular values ​​and the corresponding singular vectors.

5. The spatial feature extraction method of enhanced two-dimensional singular spectrum analysis according to claim 4, characterized in that: In step 4), the submatrix G1 corresponding to the maximum singular value is selected as the reconstruction of the trajectory matrix G: in Represents each column vector of the reconstructed trajectory matrix G1.

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