A hyperspectral image classification method based on dimension reduction of functional representation

Abstract

The application provides a hyperspectral image classification method based on function expression dimension reduction; first, the pixel spectral measure of the hyperspectral image is sequentially accumulated to construct an accumulated spectral curve with a monotone increasing characteristic; the accumulated spectral curve is fitted by a polynomial to obtain an optimal function expression; finally, the polynomial coefficients are taken as features, and SVM is used to realize hyperspectral image classification; in order to verify the effectiveness of the application, three hyperspectral image data are respectively experimented, and the application is compared with three related comparative algorithms for comparative analysis, and the results show that the overall accuracy of the application on the three hyperspectral images is 97.83%, 96.22% and 98.15% respectively, the overall accuracy is high, it is proved that the polynomial function expression coefficients are taken as features, the purpose of hyperspectral image feature dimension reduction can be achieved, the class separability is high, and high classification accuracy can be achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of hyperspectral remote sensing image classification, and particularly relates to a hyperspectral image classification method based on function expression dimension reduction. BACKGROUND

[0002] At present, hyperspectral image processing technology develops rapidly and has become a hot spot in the field of remote sensing. Hyperspectral remote sensing is a technology for acquiring more very narrow spectral continuous image data in the visible light, near-infrared, mid-infrared and thermal infrared band range of the electromagnetic spectrum, and each pixel has a nearly continuous spectral curve. The hyperspectral image has high dimension and contains rich spectral information, but at the same time, there are problems such as data redundancy due to large amount of data and high correlation between adjacent bands. In the process of hyperspectral image classification, the Hughes phenomenon is prone to occur due to high dimension and few labeled samples. Therefore, data dimension reduction is usually performed first before classification.

[0003] At present, the dimension reduction method for hyperspectral image can be divided into two categories: the first category is dimension reduction by band selection, which generally searches for band combination according to certain evaluation criteria to achieve the purpose of dimension reduction. The band selection method selects a subset of features from the original features, and the original features and the selected features are a kind of inclusion relationship without changing the original features. Therefore, this kind of dimension reduction method has the characteristics of simplicity, preservation of original image features, etc., but this kind of method assumes that the bands are independent of each other when selecting bands, without considering the correlation between the bands. In fact, due to the high spectral resolution of hyperspectral image, there is strong correlation between adjacent bands, so band selection often loses useful correlation information.

[0004] The second category is feature extraction dimension reduction based on data transformation, which can be divided into two subcategories. One is to map high-dimensional data to a low-dimensional space through linear or nonlinear transformation, so as to obtain a compact low-dimensional representation of the original data set. This kind of dimension reduction method cannot determine which part of the original feature space is used, and generally does not consider the arrangement order of the bands, often resulting in loss of part of the original data information, and further affecting the classification accuracy. SUMMARY

[0005] Based on the deficiencies of the prior art, the present application proposes a hyperspectral image classification method based on function expression dimension reduction, which introduces function expression, effectively utilizes the internal characteristics of the spectral measure of hyperspectral image changing with wavelength, and especially can more completely express the correlation between spectra.

[0006] A hyperspectral image classification method based on function expression dimension reduction, specifically comprising the following steps:

[0007] Step 1: download hyperspectral image data and its label data;

[0008] Step 2: accumulate the band vector of each pixel of the hyperspectral image in turn according to the arrangement order of the bands to construct a monotonically increasing accumulated spectral curve, and perform polynomial fitting on the obtained accumulated spectral curve, so that the characteristics of the accumulated spectral curve of each pixel are accurately expressed by a function expression, and the coefficients of the fitted polynomial are obtained;

[0009] First, given the hyperspectral image, z = {z i ,i=1,...,n}, where i is the pixel index, n is the total number of pixels, z i = {z ij ,j=1,...,m} is the spectral measure vector of pixel i, and z i is regarded as a high-density sampling of the spectral curve of pixel i, where j is the band index, m is the total number of bands, and z ij is the spectral measure of pixel i band j.

[0010] Then, the spectral measures of each band of the hyperspectral image are accumulated in turn according to the band sequence to obtain the accumulated spectral curve, so that the spectral curve with large fluctuations is changed into a monotonically increasing curve. The accumulated spectral curve is fitted by a polynomial, and y i = {y ij ,j=1,...,m} is the band sampling vector of the accumulated spectral curve, where:

[0011] (1)

[0012] Since z i and y i correspond to each band one by one, the above data structure conversion does not change the band-spectral feature relationship of the hyperspectral image, so that the transformed data structure can still maintain the similarity between the same ground object types and the difference between different ground object types;

[0013] Step 3: normalize the coefficients of the fitted polynomial;

[0014] Step 3.1: expression of the polynomial function;

[0015] Let the new hyperspectral image data obtained after the accumulated transformation of formula (1) be y, where y = {y i ,i=1,...,n}, y i = {y ij ,j=1,...,m} is regarded as a sampling of the accumulated spectral curve of pixel i at m band frequencies t j (j=1,...,m), which satisfies t1<t2<… <t m; let the polynomial function fitting the accumulated spectral curve of pixel i be f i (t), where t is frequency, then:

[0016] (2)

[0017] where, l is polynomial order index, k is the highest order of polynomial fitting, a il is the l-th order coefficient, a i = (a il , l = 0,..., k) is the coefficient set;

[0018] The error square sum of fitting polynomial (2) and the accumulated spectral curve at sampling points t j (j = 1,..., m) is:

[0019] (3)

[0020] where:

[0021]

[0022] where, k is the order of fitting, T is the sampling point set, A i is the polynomial coefficient matrix, Y i is the band sampling matrix, t j l is the value of the j-th band l-th order fitting sampling point, a il is the i-th pixel l-th order coefficient, y ij is the new hyperspectral image data;

[0023] Since the smaller the fitting error is, the more accurate the fitting is, the minimum error square sum is selected as the criterion; under the condition of minimizing equation (3), the polynomial coefficient matrix A i is:

[0024] (4)

[0025] where, T' is the transpose of matrix T;

[0026] Thus, when the fitting order is k (where k < n), the coefficient matrix A i obtained is a k+1 order characteristic matrix, which reduces the dimension;

[0027] Step 3.2: Normalization processing is performed on the reduced dimension characteristic data;

[0028] Since the polynomial function is composed of its highest order and each order coefficient, under the condition of given highest order, each order coefficient is used to uniquely express the polynomial; therefore, the polynomial coefficient vector a = {ai , i = 1,...,n}, where a i = (a il , l = 0,..., k ), as the feature vector of hyperspectral image classification;

[0029] For any pixel i, the orders of magnitude of a il (l = 0, 1,..., k ) are quite different, therefore, the same order coefficients of all pixels, a il (i = 0, 1,..., n ), are normalized to the same order of magnitude; let the normalized coefficient data be b = {b i , i = 0, 1,..., n}, where b i = (b il , l = 0, 1,..., k ),

[0030] (5)

[0031] where a lmax = max{a il , i = 1,..., n}, a lmin = min{a il , i = 1,..., n} ;

[0032] Step 4: input the normalized data of step 3 into the SVM classifier to realize classification;

[0033] Input the normalized data into the "one-to-one" multi-class SVM classifier, and construct a binary classifier between each two classes according to the class of its label data;

[0034] First, sample selection is performed on the normalized data according to the label data, and the same number of samples is selected for all categories; all categories have S samples to form a sample set B = {(x s , h s ),..., (x S , h S )}, where s is used to index the sample number, k + 1-dimensional feature x s ∈ b, h s ∈ {1, 2,..., H}, H is the number of classification categories corresponding to the hyperspectral image; the following classification surface equation is obtained:

[0035] (6)

[0036] Wherein, omega is a normal vector, which determines the direction of the hyperplane; e is a displacement term, which determines the distance between the hyperplane and the origin;

[0037] The constructed hyperplane with the maximum classification interval is finally converted into solving the following minimization problem through Lagrange change:

[0038] (7)

[0039] Wherein, alpha is a Lagrange multiplier vector.

[0040] That is, it is converted into solving the minimum value of the following formula:

[0041] (8)

[0042] Wherein, C is the coefficient of the relaxation variable, and xi is the relaxation variable.

[0043] The present application has the beneficial technical effects:

[0044] The present application changes the data structure of hyperspectral images, but does not change the data characteristics, improves the fitting effect of the spectral curve, simply and accurately expresses the spectral curve form, directly achieves the effect of reducing the dimension, realizes the classification of hyperspectral images without introducing additional dimension reduction algorithm, obtains good classification accuracy, and improves the efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The hyperspectral image standard classification diagram of the embodiment of the present application;

[0046] Figure 2 The Salinas image spectral curve and the polynomial fitting curve of the embodiment of the present application;

[0047] Figure 3 The Salinas image classification result of the embodiment of the present application;

[0048] Figure 4 The Salinas image quantitative classification analysis of the embodiment of the present application;

[0049] Figure 5 The Pavia University image spectral curve and the polynomial fitting curve of the embodiment of the present application;

[0050] Figure 6 The Pavia University image classification result of the embodiment of the present application;

[0051] Figure 7 The Pavia University image quantitative classification analysis of the embodiment of the present application;

[0052] Figure 8 Pavia Center image spectral curve and polynomial fitting curve of the embodiment of the application;

[0053] Figure 9 Pavia Center image classification result of the embodiment of the application;

[0054] Figure 10 Pavia Center image quantitative classification analysis of the embodiment of the application;

[0055] Figure 11 Different hyperspectral image running time of the embodiment of the application. DETAILED DESCRIPTION

[0056] The application will be further described below in combination with the drawings and embodiments;

[0057] Since the spectral curve in the hyperspectral image usually has large fluctuation, it is difficult to accurately express the details of some wavebands when fitting the spectral curve. In comparison, the characteristic data which changes monotonously is easier to select a function with relatively simple form for fitting, and the fitting accuracy is higher. Meanwhile, the spectral reflectance of the same ground object is similar, and the spectral reflectance of different ground objects is different, and accordingly, the change rule of the cumulative spectral curve of the same ground object is similar, and the change rule of the cumulative spectral curve of different ground objects is different. The polynomial expression of the cumulative spectral curve of each pixel can reflect the change trend, curve form and the numerical value after fitting of the function image of the pixel. In order to better express and analyze the image pixel characteristics, a hyperspectral image classification method based on function expression dimension reduction is proposed.

[0058] A hyperspectral image classification method based on function expression dimension reduction, specifically comprising the following steps:

[0059] Step 1: download the hyperspectral image data and its label data on the website;

[0060] Step 2: add and sum the waveband vectors of each pixel of the hyperspectral image in turn according to the arrangement order of the wavebands, construct a monotonically increasing cumulative spectral curve, and perform polynomial fitting on the obtained cumulative spectral curve, so that the cumulative spectral curve characteristics of each pixel are accurately expressed by a function expression, and the coefficients of the fitting polynomial are obtained;

[0061] First, a hyperspectral image is given, z = {z i ,i=1,...,n}, wherein i is a pixel index, n is the total number of pixels, z i =(z ij ,j=1,...,m) is a spectral measure vector of pixel i, and zi High-density sampling of the spectral curve of pixel i, where j is the band index, m is the total number of bands, and z ij is the spectral measure of pixel i in band j;

[0062] Then, the spectral measures of each band of the hyperspectral image are sequentially accumulated in the order of the bands to obtain an accumulated spectral curve, thereby converting the spectral curve with large fluctuations into a monotonically increasing curve. The accumulated spectral curve is polynomial fitted, and let y i = (y ij , j = 1,..., m) be the band sampling vector of the accumulated spectral curve, where:

[0063] (1)

[0064] Since each band in z i corresponds to each band in y i , the above data structure conversion does not change the band-spectral feature relationship of the hyperspectral image, so that the transformed data structure can still maintain the similarity between the same ground object types and the difference between different ground object types;

[0065] Step 3: Normalizing the coefficients of the fitted polynomial;

[0066] Step 3.1: Expression of the polynomial function;

[0067] Let the new hyperspectral image data obtained after the accumulation transformation, i.e., equation (1), be y, where y = {y i , i = 1,..., n}, y i = (y ij , j = 1,..., m) is regarded as the sampling of the accumulated spectral curve of pixel i at m band frequencies t j (j = 1,..., m), which satisfies t1 < t2 < … < t m ; let the polynomial function fitting the accumulated spectral curve of pixel i be f i (t), where t is the frequency, then:

[0068] (2)

[0069] where l is the polynomial order index, k is the highest order of the polynomial fitting, a il is the l-th order coefficient, and a i = (a il , l = 0,..., k) is the coefficient set;

[0070] The error sum of squares of the fitted polynomial (2) and the accumulated spectral curve at the sampling points t j (j = 1,..., m) is:

[0071] (3)

[0072] wherein:

[0073]

[0074] wherein, k is the order of fitting, T is the set of sampling points, A i is the polynomial coefficient matrix, Y i is the band sampling matrix, t j l is the value of the jth band lth order fitting sampling point, a il is the i pixel lth order coefficient, y ij is the new hyperspectral image data i pixel j band spectral value;

[0075] Since the smaller the fitting error is, the more accurate the fitting is, the minimum error sum of squares is selected as the criterion; under the condition of minimizing equation (3), the polynomial coefficient matrix A i is solved:

[0076] (4)

[0077] wherein, T' is the transpose of matrix T;

[0078] Thus, when the fitting order is k (wherein k < n), the coefficient matrix A i obtained is a k+1 order characteristic matrix, which reduces the dimension;

[0079] Step 3.2: Normalization processing is performed on the reduced dimension characteristic data;

[0080] Since the polynomial function is composed of its highest order and each order coefficient, under the condition of given highest order, each order coefficient is used to uniquely express the polynomial; therefore, the polynomial coefficient vector a = {a i , i = 1,...,n} is selected, wherein a i = (a il , l = 0,..., k), as the characteristic vector of hyperspectral image classification;

[0081] For any pixel i, the order of magnitude of a il (l = 0, 1,..., k ) is very different, and when used as a feature for classification, the coefficient with very small value does not play any role in the calculation result; therefore, the same order coefficient of all pixel points, a il (i = 0, 1,..., n ), is normalized to the same order of magnitude; let the normalized coefficient data be b = {b i, i =0, 1,...,n}, where b i = (b il ,l=0, 1,...,k ),

[0082] (5)

[0083] where a lmax = max{a il , i = 1,..., n}, a lmin = min{a il , i = 1,..., n} ;

[0084] Step 4: input the normalized data of step 3 into the SVM classifier to realize classification;

[0085] Input the normalized data into the "one-to-one" multi-classification SVM classifier, and according to the class of the label data, construct a binary classifier between each two classes;

[0086] First, sample selection is performed on the normalized data according to the label data, and without loss of generality, the same number of samples is selected for all categories. Since the present application is to prove that the data can be used for classification, the number of training samples has little effect, therefore, the training samples of the present application are uniformly set to 10% of the total number of samples. The total number of samples is the normalized data and its label data. All categories have S samples to form a sample set B={(x1, h1),…, (x s , h s ),...,(x S , h S}, where s is used to index the sample number, k+1 dimensional feature x s ∈b,h s ∈{1, 2,..., H}, H is the number of classification categories corresponding to the hyperspectral image; the following classification surface equation is obtained:

[0087] (6)

[0088] where ω is the normal vector, which determines the direction of the hyperplane; e is the displacement term, which determines the distance between the hyperplane and the origin;

[0089] The hyperplane with the largest classification interval is constructed by Lagrange change, which is finally converted into solving the following minimization problem:

[0090] (7)

[0091] Wherein, alpha is a Lagrange multiplier vector.

[0092] Solve the minimum value of the following formula:

[0093] (8)

[0094] Wherein, C is the coefficient of the relaxation variable, and xi is the relaxation variable.

[0095] In order to verify the feasibility and effectiveness of the proposed application to hyperspectral image classification, Salinas, Pavia University and Pavia Center hyperspectral images are selected as experimental data. Among them, the spatial resolution of Salinas image is 3.7m, the image size is 512*217 pixels, 108-112, 154-167 and 224 bands are excluded in the experiment, and the remaining 204 bands; the spatial resolution of Pavia University and Pavia Center images is 1.3m, the image size is 610*340 pixels and 1096*715 pixels respectively, and the number of image bands is 103 and 102 respectively. The application selects three kinds of comparison algorithms and the algorithm proposed in the application for comparison experiment. Among them, the first comparison algorithm is to obtain the mean value of the original spectrum curve expressed by the Poisson distribution model (PDM) as the characteristic value of each hyperspectral image; the second comparison algorithm is to obtain two principal components containing most information of each hyperspectral image as characteristic values by PCA, and the information obtained from three hyperspectral images accounts for 99.5%, 98.1% and 97.8% respectively; the third comparison algorithm is to fit the spectrum curve by cubic B-spline, and the new principal component obtained by FPCA is used as the characteristic value. The three kinds of comparison algorithms all use SVM as the classifier. The above three kinds of comparison algorithms are referred to as PDM+SVM, PCA+SVM and FPCA+SVM algorithms in the following.

[0096] In order to prevent the occurrence of underfitting or overfitting, while retaining the advantage of dimensionality reduction of hyperspectral image, it can be found through a large number of experiments that when the fitting order is determined as four, the fitting and classification effect of hyperspectral image is better.

[0097] As Figure 1 The standard classification diagram of the hyperspectral image used in the application is shown in the figure, because the composition materials and main components of some categories in the target ground object are the same or similar, the spectral reflectivity is also similar, and then the spectral reflectivity curve similarity is high, the known ground object is reinducted according to the composition materials and main components. Among them, as Figure 1 (a) shows the standard classification of Salinas hyperspectral image ground object, which is marked as C1-C15 categories; as Figure 1(b) shows the Pavia University hyperspectral image feature standard, which is classified into categories C1-C6; Figure 1 (c) shows the standard classification of objects in the Pavia Center hyperspectral image, which are denoted as C1-C9.

[0098] like Figure 2 (a)-(o) show the fourth-order polynomial fitting results of the accumulated spectral curves of 15 types of objects in the Salinas image, where the dotted line is the accumulated spectral curve and the solid line is the fitted accumulated spectral curve. Figure 2 It can be seen that the function fitting curves of different ground objects are generally different. The polynomial fitting curve is closer to the cumulative spectrum curve, so the polynomial can better express the changing trend of the cumulative curve. Figure 3 (a)-(d) show the classification results of PDM+SVM, PCA+SVM, FPCA+SVM and the algorithm of the present invention, respectively.

[0099] Figure 3 (a)-(d) From the visual observation, it can be observed that for the classification results of categories C1, C3, C10 and C15, the classification effect of the PCA+SVM algorithm is the worst, the classification effects of the PDM+SVM algorithm and the FPCA+SVM algorithm are comparable, and the classification effect of the algorithm of the present invention is significantly better than the above three comparison algorithms; for the classification results of category C2, the accuracy of the PCA+SVM, PDM+SVM and FPCA+SVM algorithms is comparable, and the classification effect of the algorithm of the present invention is significantly better than the above three comparison algorithms; for the classification results of categories C11, C12, C13 and C14, the classification effect of the PDM+SVM algorithm is the worst, the classification effect of the PCA+SVM algorithm for categories C11 and C12 is not good, the classification effect of the FPCA+SVM algorithm for category C14 is not good, and the classification effect of the algorithm of the present invention is significantly better than the three comparison algorithms.

[0100] In order to quantitatively describe the classification results of Salinas hyperspectral imagery, Figure 3 The classification results of (a)-(d) are evaluated for accuracy, and the confusion matrix of each is calculated. The corresponding user accuracy, product accuracy, overall accuracy and kappa coefficient are calculated based on the confusion matrix. Figure 4 .Depend on Figure 4 It can be observed that the user accuracy and product accuracy of the algorithm of the present invention for all land feature classifications are both above 90%, which is significantly better than the accuracy of the three comparison algorithms; the overall accuracy of the algorithm of the present invention reaches 97.83%, which is 6.47%, 3.60% and 1.77% higher than the PDM+SVM algorithm, PCA+SVM algorithm and FPCA+SVM algorithm respectively. The kappa coefficient of the algorithm of the present invention is higher than that of the three comparison algorithms.

[0101] likeFigure 5 (a)-(f) show the fourth-order polynomial fitting curves of the accumulated spectral curves of six types of ground objects in the Pavia University image, where the dotted line is the accumulated spectral curve and the solid line is the fitted accumulated spectral curve; Figure 5 (a)-(f) show that the function fitting curves of different objects are generally different. The polynomial fitting curve fits the cumulative spectrum curve better, so the fitting polynomial can better express the changing trend of the cumulative curve. Figure 6 Shown are the classification results of the Pavia University image, where Figure 6 (a)-(d) are the classification results of PDM+SVM, PCA+SVM, FPCA+SVM and the algorithm of the present invention, respectively. Figure 6 From the visual observation, it can be observed that the classification effect of PCA+SVM algorithm is the worst, the classification effect of PDM+SVM algorithm and FPCA+SVM algorithm is comparable, and the overall classification effect of the algorithm of the present invention is significantly better than the above three comparison algorithms. Figure 6 The quantitative accuracy evaluation results of (a)-(d) are shown in Figure 7 .

[0102] from Figure 7 It can be observed that, under the classification of the algorithm of the present invention, the accuracy of the hyperspectral image of Pavia University is above 90% except for the accuracy of the C4 category products, which is significantly better than the accuracy of the three comparison algorithms; the overall accuracy of the algorithm of the present invention reaches 96.22%, which is 4.61%, 3.97% and 2.55% higher than that of the PDM+SVM, PCA+SVM and FPCA+SVM algorithms respectively. The kappa coefficient of the algorithm of the present invention is higher than that of the three comparison algorithms.

[0103] like Figure 8 (a)-(i) show the fourth-order polynomial fitting curves of the cumulative spectrum curves of 9 types of ground objects in the Pavia Center image, where the dotted line is the cumulative spectrum curve and the solid line is the fitted cumulative spectrum curve; Figure 8 From (a) to (i), we can see that the function fitting curves of different ground objects are generally different. The polynomial fitting curve fits the cumulative spectrum curve better, so the fitting polynomial can better express the changing trend of the cumulative curve.

[0104] like Figure 9 Shown are the classification results of the Pavia Center image, where Figure 9 (a)-(d) are the classification results of the PDM+SVM algorithm, PCA+SVM algorithm, FPCA+SVM algorithm and the algorithm of the present invention, respectively. Figure 9It can be observed visually that the PDM+SVM algorithm and the PCA+SVM algorithm have the worst classification effect, the FPCA+SVM algorithm has a general classification effect, and the overall classification effect of the algorithm is obviously better than that of the three comparative algorithms. Figure 9 The quantitative accuracy evaluation results of the classification results are shown in Figure 10 .

[0105] It can be observed from Figure 10 that, in the classification of the Pavia Center hyperspectral image by the algorithm, except for the product accuracy and user accuracy of the C3 and C4 classes, the other accuracies are all above 90%, which is obviously better than the accuracies of the three comparative algorithms; the overall accuracy of the algorithm reaches 98.15%, which is 4.60%, 3.96% and 1.34% higher than that of the PDM+SVM algorithm, the PCA+SVM algorithm and the FPCA+SVM algorithm respectively, and the kappa coefficient of the algorithm is higher than those of the three comparative algorithms.

[0106] In order to quantitatively analyze the efficiency of the algorithm for the classification of the hyperspectral image, the running time of the feature extraction and classification process of the algorithm and the three comparative algorithms is recorded for the three hyperspectral images, as shown in Figure 11 It can be observed from Figure 11 that the running time of the dimension reduction of the algorithm is obviously reduced compared with the PDM+SVM algorithm, and the working efficiency is slightly shortened compared with the FPCA algorithm; in the classification stage, the running time of the algorithm is obviously less than that of the other three comparative algorithms. It can be concluded that, compared with the direct fitting of the original spectral curve and the subsequent dimension reduction and classification, the polynomial function expression accumulated spectral curve dimension reduction and classification proposed in the algorithm has obvious advantages in both classification accuracy and running efficiency.

Claims

1. A hyperspectral image classification method based on functional expression dimensionality reduction, characterized in that: The specific steps include: Step 1: Download hyperspectral image data and its label data; Step 2: The band vectors of each pixel of the hyperspectral image are accumulated and summed in the order of the band arrangement to construct a monotonically increasing cumulative spectrum curve. The obtained cumulative spectrum curve is then fitted with a polynomial so that the cumulative spectrum curve characteristics of each pixel can be accurately represented by a function expression and the coefficients of the fitting polynomial are obtained. Step 3: Normalize the coefficients of the fitting polynomial; Step 3.1: Expression of polynomial function; The new hyperspectral image data obtained after the cumulative transformation (Equation (1)) is set to y, where y = {y i ,i=1,..., n},y i =(y ij ,j=1,...,m) is considered as the cumulative spectrum curve of pixel i in the m-band frequency t j The sampling at (j=1,...,m) satisfies t1 <t2<… <t m ; Let the polynomial function fitting the accumulated spectrum curve of pixel i be f i (t), where t is the frequency, then: (2) Among them, l is the polynomial order index, k is the highest order of polynomial fitting, a il is the l-order coefficient, a i =(a il ,l =0, ..., k) is the coefficient set; Fitting polynomial (2) and the accumulated spectrum curve at sampling point t j The sum of squared errors for (j=1,...,m) is: (3) in: ； Among them, k is the order of fitting, T is the set of sampling points, A i is the polynomial coefficient matrix, Y i is the band sampling matrix, t j l is the value of the fitting sampling point of the lth order term in the jth band, a il is the l-th order coefficient of the i-th pixel, y ij It is new hyperspectral image data; Since the smaller the fitting error, the more accurate the fitting, the minimum sum of squared errors is selected as the criterion; under the condition of minimizing formula (3), solve the polynomial coefficient matrix A i for: (4) Where T' is the transpose of matrix T; It can be obtained that when the fitting order is the k-th order and k < n, the obtained coefficient matrix A i is a characteristic matrix of the (k + 1)-th order, reducing the dimension; Step 3.2: Normalize the feature data after dimensionality reduction; Since a polynomial function consists of its highest order and coefficients of each order, under the condition of a given highest order, the polynomial is uniquely expressed using coefficients of each order; therefore, the polynomial coefficient vector a = {a i , i = 1, ..., n}, where a i = (a il , l = 0, ..., k), as the feature vector for hyperspectral image classification; For any pixel i, a il The order of magnitude of (l = 0, 1, ..., k) varies greatly, so the same order coefficients of all pixels, a il (i = 0, 1, ..., n), normalized to the same order of magnitude; let the normalized coefficient data be b = {b i , i =0, 1, ...,n}, where b i = (b il ,l=0, 1, ...,k ), (5) Among them, a lmax = max{a il , i = 1, ..., n}, a lmin = min{a il , i = 1, ..., n}; Step 4: Input the normalized data in step 3 into the SVM classifier to achieve classification.

2. The hyperspectral image classification method based on functional expression dimensionality reduction according to claim 1, characterized in that: The coefficients of the fitting polynomial obtained in step 2 are specifically: First, given a hyperspectral image, z= {z i ,i=1,...,n}, where i is the pixel index, n is the total number of pixels, z i = (z ij ,j=1,...,m) is the spectral measurement vector of pixel i, z i It is regarded as a high-density sampling of the spectral curve of pixel i, where j is the band index, m is the total number of bands, and z ij is the spectral measure of pixel i in band j; Then the spectral measurements of each band of the hyperspectral image are accumulated in sequence according to the band sequence to obtain the accumulated spectral curve, thereby changing the spectral curve with large fluctuations into a monotonically increasing curve; a polynomial fitting is performed on the accumulated spectral curve, and y is set i =(y ij ,j=1,...,m) is the band sampling vector of the accumulated spectrum curve, where: (1) Because z i with y i The bands in the data structure correspond one to one, so the above data structure conversion does not change the band-spectral characteristic relationship of the hyperspectral image, so that the transformed data structure can still maintain the similarity between the same type of land features and the difference between different types of land features.

3. The hyperspectral image classification method based on functional expression dimensionality reduction according to claim 1, characterized in that: The implementation classification described in step 4 is specifically as follows: The normalized data is input into a "one-to-one" multi-classification SVM classifier, and a binary classifier is constructed between each two classes according to the category of its label data; First, sample selection is performed on the normalized data according to the label data, and the same number of samples is selected for all categories; a total of S samples of all categories constitute the sample set B={(x1, h1),…, (x s , h s ),... ,(x S , h S )}, where s is used to index the sample number, and k+1 dimensional feature x s ∈b,h s ∈{1, 2, ..., H}, where H is the number of classification categories corresponding to the hyperspectral image; the following classification surface equation is obtained: (6) Among them, ω is the normal vector, which determines the direction of the hyperplane; e is the displacement term, which determines the distance between the hyperplane and the origin; The constructed hyperplane with the largest classification interval is transformed into solving the following minimization problem through Lagrangian transformation: (7) Where α is the Lagrange multiplier vector; That is, it is converted to solving the minimum value of the following formula: (8) Where C is the coefficient of the slack variable and ξ is the slack variable.

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