CN103632160B - Combined kernel function RVM hyperspectral classification method fusing multi-scale morphological characteristics - Google Patents

Abstract

The invention provides a combined kernel function RVM hyperspectral classification method fusing multi-scale morphological characteristics. The method comprises the following steps: (1) performing dimensionality reduction on the hyperspectral image by using principal component transformation; (2) performing spatial feature extraction on the hyperspectral image after principal component transformation by adopting mathematical morphological transformation; (3) according to the theory of kernel functions, combined kernel functions based on addition, multiplication and weighted addition are respectively constructed; fusing spectral and spatial features of the image using the combined kernel function method; (4) the combined kernel function RVM classifier is used for classifying the hyperspectral images, and an AVIRIS hyperspectral image is used for a classification experiment. Compared with the traditional RVM classifier based on the spectral features, the classification precision of the combined kernel function RVM is remarkably improved on the premise that the training time is not obviously increased. The method disclosed by the invention is strong in stability and insensitive to the number of samples.

Description

Combined kernel function RVM hyperspectral classification method fusing multi-scale morphological characteristics

Technical Field

The invention relates to the technical field of hyperspectral image processing methods and application, in particular to a combined kernel function RVM hyperspectral classification method fusing multi-scale morphological characteristics.

Background

The hyperspectral image has the advantage of high spectral resolution and is widely concerned at home and abroad. The spectrum coverage range of the hyperspectral image is from visible light to near infrared, and almost continuous wave band information of ground objects can be acquired. On one hand, the extremely high spectral resolution of the hyperspectral image can identify finer ground object types, and challenges are brought to the traditional remote sensing image classification method.

The traditional hyperspectral supervised classification method comprises the following steps: maximum likelihood methods, artificial neural networks, and the like. The neural network method has difficult parameter initialization, easy occurrence of local optimization and over-learning phenomena and slow training process. Often, a sufficient number of training samples cannot be obtained, and estimation of prior knowledge of each category is influenced; one difficulty in hyperspectral image classification is that with the increase of the number of bands, the classification accuracy by directly using all band information may be reduced, i.e., the so-called dimensionality disaster (Hughes phenomenon) occurs.

Support Vector Machines (SVMs) are increasingly gaining attention in hyperspectral classification. The method achieves higher precision in hyperspectral classification than the traditional method. But SVM methods also have disadvantages. For example: a penalty coefficient C must be given, the parameter must be determined through a large number of cross validation or additional optimization algorithms, the calculation complexity is high, and the result is greatly influenced; the kernel function must satisfy the Mercer condition; although the number of support vectors has a certain sparsity compared with the number of training samples, the number of support vectors still linearly increases with the increase of the number of training samples, and the model prediction time increases.

In 2000, research on the application of relevant vector Machine classifiers (RVM) was presented in the field of pattern recognition. Compared with the SVM, the RVM method has the following advantages: the model has no penalty coefficient C, so that the sensitivity to the hyper-parameter is reduced; the kernel function does not need to satisfy the Mercer condition; the sparsity of the solution is high. This makes the RVM-based hyperspectral classification method have application potential in image classification problems with high real-time requirements. However, the existing research of the hyperspectral classification method based on RVM is based on the spectral characteristics of the image, and the spatial characteristics of the image are not fully utilized.

The classification precision can be improved by introducing the spatial features of the images into the classifier, and the method relates to a spatial feature fusion method. There are two common spatial feature fusion methods: the simplest spatial feature fusion strategy is to perform spatial information filtering on the classification result graph after the classification is finished, however, the method is greatly influenced by the size of the template. The other method is that the spatial features and the spectral features of the image are combined to form a feature vector, and the number of the wave bands of the hyperspectral image is large, so that the data volume is increased rapidly by the wave band synthesis method, and the wave band redundancy is caused. Although the dimensionality of the data can be reduced by using the feature extraction method, the feature extraction takes a long time and needs prior knowledge in some cases.

Recently, research and application of combined kernel function methods have emerged in the field of pattern recognition. The combined kernel function method has been applied to the fields of text classification, pattern recognition and the like by combining with an SVM classifier. In these studies, however, the construction of the combined kernel function was based on a single feature space. Since research and application of the RVM classifier are still in the research stage, research on the combined kernel function RVM is not uncommon, although feature extraction and power load prediction using the combined kernel function RVM are also studied. In these studies, however, the construction of the combined kernel function was still based on a single feature space. The RVM classifier based on the combined kernel functions constructed by different feature spaces is not reported. In the field of remote sensing image processing, research and application of a combined kernel function RVM classifier combining spatial features and spectral features are not reported.

Disclosure of Invention

The invention aims to provide a combined kernel function RVM hyperspectral classification method fusing multi-scale morphological characteristics aiming at the defects of the existing method. The method aims to fully combine the spatial characteristics and the spectral characteristics of the hyperspectral images so as to improve the classification precision.

The steps of the invention are shown in the attached figure 1, and the combined kernel function RVM hyperspectral classification method fused with the multi-scale morphological characteristics is characterized by comprising the following steps:

the method comprises the following steps: and performing principal component transformation on the hyperspectral image. The spectral features and the spatial features are fused in the classification process, so that the classification precision can be effectively improved, but the data volume is increased rapidly, and meanwhile, the classification precision is reduced when the data dimension is increased to a certain degree. The image is therefore first reduced in dimension herein using the PCA transformation (principal components Analysis). Obtaining the feature vector of the training sample setx_n∈R^d，t_n∈ R. where N is the number of samples in the training sample set x_kRepresenting the kth sample. y is_kIs the label corresponding to sample k.

Step two: and performing spatial feature extraction on the hyperspectral image after principal component transformation by adopting mathematical morphological transformation. Obtaining the space characteristic vector of the imageMathematical morphology morphological features of an image can be obtained by Opening and closing operations. The invention adopts the opening and closing operation based on reconstruction to extract the spatial characteristics of the image. In order to fully utilize the multi-scale characteristics of the image space characteristics, the size of the morphological operation template is gradually increased in the calculation process, and the image is subjected to iterative opening and closing operation to obtain the multi-scale morphological characteristic vector of the image, which is used as the space characteristics of the image.

Step three: respectively constructing a combined kernel function based on addition, multiplication and weighted addition according to the theory of the kernel function; the spectral and spatial features of the image are fused using the combined kernel function approach. Wherein, the spectral feature is a spectral feature vector composed of all original wave bands of the imageThe space features are feature vectors extracted by a multi-scale morphological method

Step four: obtaining training samples and testing samples through feature extractionFeature vector x of a sample_n={x^s,x^wFrom the spectral feature vector of the sampleAnd spatial feature vectorComposition of. And using the combined kernel function as a kernel function of the RVM classifier to train the classifier and classify the hyperspectral image.

Preferably, in the second step, the spatial feature extraction is performed on the image with the transformed principal components based on the multi-scale morphological method, and the specific implementation manner is as follows:

(1) and performing open reconstruction operation on the image. Is provided withIs an open reconstruction operator, the expression of which is:

${\mathrm{\γ}}_{\mathrm{\λ}}^{*}={\mathrm{\δ}}^{\left(\mathrm{rec}\right)}(\mathrm{f\ΘB},f)$

wherein f Θ B represents the erosion operation on the image.

Let Δ γ (x) denote the morphological feature of the image obtained by the open reconstruction operation, and the morphological feature Δ γ (x) obtained by the open reconstruction operation is obtained by continuously performing the closed reconstruction operation on the image using a series of square structural elements whose sizes are gradually increased:

$\mathrm{\Δ\γ}\left(x\right)=\{{\mathrm{\Δ\γ}}_{\mathrm{\λ}}:{\mathrm{\Δ\γ}}_{\mathrm{\λ}}=|{\mathrm{\Π\γ}}_{\mathrm{\λ}}-{\mathrm{\Π\γ}}_{\mathrm{\λ}-1}|,\∀\mathrm{\λ}\∈[1,n\left]\right\}$

wherein n is the number of ON operations. According to the morphological definition, when λ =0, Π γ₀(x)=I(x)。

(2) Is provided withThe closed reconstruction operator is an expression for performing closed reconstruction operation on each principal component image, and the expression is as follows:

wherein,indicating that the image is dilated.

Using a series of square structural elements with gradually increasing sizes to continuously perform closed reconstruction operation on the image, thereby obtaining the morphological characteristics of the imageThe mathematical expression of (a) is:

wherein n is the number of times of the closing operation. According to the definition of morphology, when λ =0,

(3) morphological features based on open reconstruction operationsAnd obtaining the multi-scale morphological characteristics delta (x) of a single principal component waveband by the morphological characteristics delta gamma (x) obtained by closed reconstruction operation, wherein the mathematical expression of the multi-scale morphological characteristics delta (x) is as follows:

where n is the number of opening and closing operations, and c =1, 2.

(4) And respectively carrying out open reconstruction operation and closed reconstruction operation on each wave band of the principal component image, calculating the multi-scale morphological characteristic delta (x) of a single principal component wave band, and finally obtaining the spatial characteristic of the image.

Preferably, the RVM hyperspectral classification method of the combined kernel function fused with the multi-scale morphological characteristics includes the third step, the spectral kernel matrix K in the calculation of the combined kernel functions in the three forms_sUsing radial basis kernel function calculation, spectral kernel matrix K_sThe calculation formula of (a) is as follows:

$K_s=\exp {(-\mathrm{\γ}||x_i^s-x_j^s|\left|\right)}^2$

wherein x is^sThe spectral feature vector is composed of the original wave band of the image, and gamma is a radial basis kernel function parameter, and is calculated by a cross validation method.

Preferably, the RVM hyperspectral classification method is a spatial kernel matrix K_wAdopting a radial basis kernel function, the calculation formula is as follows:

$K_w=\exp {(-\mathrm{\γ}||x_i^w-x_j^w|\left|\right)}^2$

wherein x is^wThe space feature vector is extracted based on a multi-scale morphology method, and gamma is a radial basis kernel function parameter and is calculated by a cross validation method.

Preferably, the RVM hyperspectral classification method of the combined kernel function fused with the multi-scale morphological characteristics sets the spectral characteristics of the image asThe spatial characteristics of the image areThe spectral and spatial features were normalized to (0, 1):

$x^s=\frac{x^s-x_{\min }^s}{x_{\max }^s-x_{\min }^s}$

$x^w=\frac{x^w-x_{\min }^w}{x_{\max }^w-x_{\min }^w}$

preferably, in the method for classifying hyperspectral of combined kernel function RVM fused with multi-scale morphological features, in step three, a specific construction method of the combined kernel function is as follows:

setting the spectral characteristics of the image asThe spatial characteristics of the image areUsing two non-linear transformations phi₁(.) and phi₂(.) respectively transforming the spectral features of the image and the spatial features of the image into Hilbert space H₁And H₂In (1). Are constructed separately. Three forms of combined kernel function to fuse spectral features and space of imagesAnd (5) characterizing. Respectively based on a combined kernel function K of an addition operation_sumCombining kernel function K based on weighted addition_weightAnd a combined kernel function K based on multiplication_product. The three forms of combined kernel function are calculated as follows:

(a) the addition-based combined kernel function K_sumThe mathematical expression of (a) is:

$K_{\mathrm{sum}}(x_i,x_j)=\{{\mathrm{\φ}}_1\left(x_i^s\right),{\mathrm{\φ}}_2\left(x_i^w\right)\}$

$=<\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\},\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}>$

$=K_s(x_i^s,x_j^s)+K_w(x_i^w,x_j^w)$

wherein, K_sAnd K_wAnd respectively obtaining a nuclear matrix by calculating the spectral characteristic and the spatial characteristic through nonlinear transformation.

(b) At the weighted addition based combined kernel function K_weightBased on the above, a combined kernel function based on weighted addition is constructed, and the mathematical expression is as follows:

wherein mu is more than or equal to 0 and less than or equal to 1, and mu controls the weight of the two kernel functions. K_sAnd K_wAnd respectively forming a kernel matrix by the spectral characteristics and the spatial characteristics.

(c) The combination kernel function K based on multiplication operation_productThe mathematical expression of (a) is as follows:

$K_{\mathrm{product}}(x_i,x_j)=\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}$

$=K_s(x_i^s,x_j^s)*K_w(x_i^w,x_j^w),$

wherein, K_sAnd K_wRespectively the spectral characteristicsAnd a kernel matrix formed with the spatial features.

Preferably, in the method for classifying hyperspectral by using combined kernel function RVM fused with multi-scale morphological features, the training process of the combined kernel function RVM classifier in the fourth step is as follows:

(1) the RVM model is originally used for solving two-class classification problems, and the hyperspectral image classification belongs to a multi-class classification problem. Firstly, aiming at two types of classified RVM classifiers, a training sample is constructedWherein x is_n∈R^d，t_n∈ R. target value t_nCalculated using the formula:

t_n=y(x_n;w)+_n

wherein, errors_nAre independent and obey a zero mean Gauss distribution with variance σ²I.e. p (t)_n|x)=N(t_n|y(x_n),σ²)。

(2) Decision function y (x) of RVM_n) Calculated using the formula:

$y(x_i;w)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[w_{i}K(x,x_i)+w_0]$

wherein, w = (w)₀,w₁,...,w_n)^TAs a weight coefficient, K (x, x)_i) Is the kernel function of the RVM classifier. Different from the prior method, the kernel function of the RVM classifier adopts the combined kernel functions in the three steps, namely the addition kernel K_sumMultiplication core K_weightAnd a kernel function K based on weighted addition_product。

(3) For the target value t_nAnd constructing a conditional probability density function by adopting Bernoulli distribution to calculate. The likelihood function p (t | w) of the training sample set is calculated by adopting Bernoulli distribution, and the calculation formula of the likelihood function of the training sample set is as follows:

$p\left(t\right|w)=\underset{n=1}{\overset{N}{\mathrm{\&Pi;}}}\mathrm{\&sigma;}{\left\{y(x_n;w)\right\}}^{t_n}{[1-\mathrm{\&sigma;}\{y(x_n;w)\left\}\right]}^{1-t_n}$

wherein, w_iIs a weight vector of RVM, the obedient mean is 0, the variance isThe gaussian conditional probability distribution of (a), namely:

$p\left(w\right|\mathrm{\&alpha;})=\underset{i=0}{\overset{N}{\mathrm{\&Pi;}}}N\left(w_i\right|0,{\mathrm{\&alpha;}}_i^{-1})$

wherein, α = [ α ]₀,α₁,α₂,...，α_N]^Tα is the super parameter vector for determining the prior probability of the weight vector, and is solved by the fast sequence sparse Bayes method.

(4) After y (x) is calculated, y (x) is mapped to [0,1] by a Sigmoid function to perform category determination. Sigmoid function expression:

σ(y)=1/(1+e^-y)

(5) and solving the multi-classification combined kernel function RVM problem. And (3) converting the multi-class classification problem into a series of two-class classification problems by adopting a One-to-One method (One Against One, OAO), and then solving by adopting the steps (1) to (5). The method comprises the following specific steps: finding out all samples of different classes in a training sample set T (i, j), pairwise matching the samples to form a multi-class classifier, and totallyThere are P = k (k-1)/2. Composing a training sample set of two classes of problems with training samples belonging to the two classesSeparately obtaining P discriminant functions f_(i，j)(x) In that respect When classifying, training samples are obtainedRespectively calculating P discriminant functions f_(i，j)(x) In that respect If f_(i，j)(x) And =1, judging that X is the i type, and adding a ticket to the i type, otherwise, judging that X is the j type, and adding a ticket to the j type. And finally, summing the number of votes obtained by the k categories in the P discrimination function results, wherein the category with the largest number of votes is the final judgment category.

The invention has the characteristics and effects that:

(1) the method is applied to hyperspectral image classification, and can effectively fuse the spatial characteristics and the spectral characteristics of the images. Compared with the traditional RVM method based on the spectral characteristics, the method disclosed by the invention can obviously improve the classification precision on the premise of not increasing the training time. The invention constructs three forms of combined kernel function RVM classifiers, wherein the overall accuracy OA and Kappa coefficients of the combined kernel function RVM classifier based on multiplication are respectively improved by 4.2 percent and 5.05 percent. The overall accuracy OA and Kappa coefficients of the weighted addition based combined kernel function RVM classification method are respectively improved by 4.24% and 4.98%. The overall classification precision is improved most obviously by the addition-based combined kernel function RVM classification method, and the overall precision OA and Kappa coefficients are respectively improved by 4.21 percent and 4.95 percent.

(2) The method disclosed by the invention is strong in stability and insensitive to the number of samples. With the increase of training samples, the classification precision of the RVM method of the three forms of combined kernel functions is improved. However, when the proportion of the training samples to the total samples exceeds a certain proportion, the classification precision of the RVM method tends to be stable. The RVM method of the combined kernel function has strong stability and is insensitive to the size of a training sample set. The method has certain advantages and application potential in the hyperspectral image classification problem under the condition of rare samples.

Drawings

In order that the invention may be readily understood, specific embodiments thereof will now be described with reference to the accompanying drawings.

Fig. 1 shows a schematic flow diagram according to the invention.

FIG. 2 shows a hyperspectral image of an Indian Pine experimental area of a preferred embodiment of the present invention.

FIG. 3 shows a typical physical distribution plot of an Indian Pine experimental zone in accordance with a preferred embodiment of the present invention.

FIG. 4 shows a spatial feature map extracted from an Indian Pine experimental region image using a multi-scale morphology method according to a preferred embodiment of the present invention.

Fig. 5 is a diagram showing classification results of a preferred embodiment of the present invention respectively using the existing method and the RVM classification method based on three types of combination kernel functions according to the present invention. Wherein, fig. 5(a) shows the classification result of the conventional RVM based on the spectral characteristics on the hyperspectral image; FIG. 5(b) shows the addition-based kernel (K) in the present invention_sum) The classification result of the hyperspectral image by the combined kernel function RVM; FIG. 5(c) shows the result of classifying the hyperspectral images based on the combined kernel function RVM of the multiplication kernel (KProduct) in the invention; fig. 5(d) shows the result of classifying the hyperspectral image based on the combined kernel function (kwight) RVM classification result of weighted addition in the present invention.

Detailed Description

The invention provides a novel combined kernel function RVM hyperspectral classification method fused with multi-scale morphological characteristics. The method is used for carrying out real hyperspectral data classification experiments, and compared and researched in the aspects of precision, sparsity and the like by a combined kernel function RVM classification method and a traditional RVM classification method purely based on spectral characteristics.

The invention is described in further detail below with reference to the drawings and preferred embodiments. The computer hardware environment adopted by the experiment is Intel Core2 dual-Core CPU and 1.58GHz/3.25GB memory. The software environment is Microsoft Windows XP, Matlab R2008 a. The algorithm of the invention is implemented by MATLAB R2008 a.

The correspondence between the constituent elements in the claims and the specific examples in the embodiments can be exemplified as follows. The description herein is intended to confirm that a specific example for supporting the subject matter recited in the claims is described in the embodiment, and since an example is described in the embodiment, it does not mean that the specific example does not represent an element. On the contrary, even if a specific example is included herein as an element feature corresponding to one constituent element, it does not mean that the specific example does not represent any other constituent element.

Furthermore, the description herein does not imply that all subject matter corresponding to the specific examples set forth in the embodiments is cited in the claims. In other words, the description herein does not deny the entity that the corresponding embodiment contains the specific examples but does not contain in any of its claims, that is, the entity that can be filed or added with a possible invention after a later amendment.

It should be noted that "system" herein means a process made up of two or more devices.

Obviously, the user terminal may be constituted by a personal computer. Further, the user terminal may also be constituted by, for example, a cellular phone, any other PDA (personal digital assistant) tool, an AV (audio video) device, a CE (consumer electronics) such as a home electric appliance (home electric power) device, or the like.

"network" means an organization to which at least two devices are connected, and in which a piece of information can be transmitted from one device to the other. The devices establishing communication via the network may be separate from each other or may be internal modules constituting one machine.

"communication" may mean both wireless communication and wired communication. However, it may also be communication that mixes wireless and wired communication, more specifically, communication that takes wireless communication in a certain section and wired communication in another section. Likewise, it may also be a communication: communication from one device to another is wired and communication in the opposite direction is wireless.

FIG. 2 shows a hyperspectral image of a preferred embodiment of the invention. The image is a hyperspectral image of an Indian Pine experimental area taken by the AVIRIS sensor in 1992. The image size was 145X 145, there were 220 bands in total, and the wavelength range covered was 0.4 μm to 2.5 μm. The spectra of various ground objects in the region are relatively similar and the classification difficulty is high, and the method is standard data for the performance test of a hyperspectral classification algorithm. The water absorption band and low signal-to-noise band of the data were removed beforehand before the experiment, leaving 169 bands.

Fig. 3 shows the ground verification data of the hyperspectral image, which contains 16 ground object classes, and the experiment of the present invention uses 9 typical ground objects, which contains 9345 sample points.

Table 1 shows a sample case of the hyperspectral image:

TABLE 1 number of samples of example experimental zone of Indian Pine

The following detailed description is made with reference to the accompanying drawings and embodiments:

1. the method mainly comprises the following implementation steps:

1.1 image feature extraction and dimension reduction. The specific implementation mode is as follows: and reducing the dimension of the input hyperspectral image by adopting a principal component transformation (PCA) method.

Table 2 shows the feature values and cumulative contribution rates of the experimental area images subjected to the PCA transformation. As can be seen from Table 2, the first three principal components of the hyperspectral image already contain more than 99% of information content of the image, so the first 3 principal component wave bands of PCA conversion are selected in an experiment, and the spatial features of the image are extracted on the basis.

TABLE 2 principal Components transformation results of image in Indian Pine experimental area

FIG. 4 shows a multi-scale morphological feature map of an Indian Pine experimental area image in accordance with a preferred embodiment of the present invention. In the experiment of the invention, a square structural element is used as a template for morphological operation. The number of iterations n is 5.

1.2 extracting the spatial features of the image on the principal component image obtained in the step one by using the multi-scale morphology method. In order to effectively utilize the multi-scale characteristic of image space information, the invention uses a series of structure elements SE with gradually increasing radius to repeatedly carry out morphological open reconstruction and closed reconstruction operation on the image. The method comprises the following concrete steps:

(1) and performing open reconstruction operation on the principal component image. Is provided withIs an open reconstruction operator, the expression of which is:

${\mathrm{\&gamma;}}_{\mathrm{\&lambda;}}^{*}={\mathrm{\&delta;}}^{\left(\mathrm{rec}\right)}(\mathrm{f\&Theta;B},f)$

wherein f Θ B represents the erosion operation on the image.

Let Δ γ (x) denote the morphological feature of the image obtained by the open reconstruction operation, and the morphological feature Δ γ (x) obtained by the open reconstruction operation is obtained by continuously performing the closed reconstruction operation on the image using a series of square structural elements whose sizes are gradually increased:

$\mathrm{\&Delta;\&gamma;}\left(x\right)=\{{\mathrm{\&Delta;\&gamma;}}_{\mathrm{\&lambda;}}:{\mathrm{\&Delta;\&gamma;}}_{\mathrm{\&lambda;}}=|{\mathrm{\&Pi;\&gamma;}}_{\mathrm{\&lambda;}}-{\mathrm{\&Pi;\&gamma;}}_{\mathrm{\&lambda;}-1}|,\&ForAll;\mathrm{\&lambda;}\&Element;[1,n\left]\right\}$

wherein n is the number of ON operations. According to the morphological definition, when λ =0, Π γ₀(x)=I(x)。

(2) Is provided withIs a closed reconstruction operator, and the expression for performing closed reconstruction operation on each wave band of the principal component image is as follows:

wherein,indicating that the image is dilated.

Using a series of square structural elements with gradually increasing sizes to continuously perform closed reconstruction operation on the image, thereby obtaining the morphological characteristics of the imageThe mathematical expression of (a) is:

wherein n is the number of times of the closing operation. According to the definition of morphology, when λ =0,

(3) morphological features based on open reconstruction operationsAnd obtaining the multi-scale morphological feature delta (x) of the image by the morphological feature delta gamma (x) obtained by the closed reconstruction operation, wherein the mathematical expression is as follows:

where n is the number of opening and closing operations, and c =1, 2.

(4) And (3) respectively performing the calculation of the steps (1) to (3) on each wave band of the main component image to obtain a spatial feature vector of the image.

1.3 fusing the spatial and spectral features of the image using a combined kernel function, the implementation steps are as follows:

according to Mercer's theorem and its deduction: suppose k₁And k₂Is a nucleus, X, X', X ∈ R, a ∈ R, as defined on X × X⁺F (-) is a real-valued function defined on X φ: X → R^NThen the following function remains the kernel function: (1) k (x, x') = k₁(x,x')+k₂(x,x')；(2)k(x,x')=ak₁(x,x')；(3)k(x,x')=k₁(x,x')·k₂(x,x')。

According to the Mercer theorem and the properties thereof, the non-negative linear combination of different kernel functions still meets the Mercer condition and can still be used as the kernel function. The invention constructs a combined kernel function based on the Mercer theorem and properties thereof. Defining the spectral characteristics of the sample asSpatial characteristicsWherein the spectral characteristicsIs a spectral feature vector constructed using all the original bands of the image. Spatial characteristicsThe spatial feature vector is extracted by the image by adopting a multi-scale morphological method. K_sAnd K_wRespectively, a spectral kernel matrix and a spatial kernel matrix obtained by calculation according to corresponding kernel functions.

(1) Calculating a spectral kernel matrix K from spectral features of an image_sAnd the space kernel K_wBy the basis functions ofA radial basis kernel function. The specific calculation method of the spectrum kernel matrix is as follows:

$K_s=\exp {(-\mathrm{\&gamma;}||x_i^s-x_j^s|\left|\right)}^2$

wherein x is^sIs a spectral feature vector, and gamma is a radial basis kernel function parameter, controlling the width of the kernel function. The parameter γ is determined by a cross-validation method.

(2) Computing a spatial kernel matrix K using radial basis kernel functions_wThe calculation formula of the space kernel matrix is as follows:

$K_w=\exp {(-\mathrm{\&gamma;}||x_i^w-x_j^w|\left|\right)}^2$

wherein x is^wThe method is a space feature vector extracted based on a multi-scale morphology method, gamma is a radial basis kernel function parameter, and the width of a kernel function is controlled. The parameter γ is determined by a cross-validation method.

(3) Calculating a combined kernel function K based on addition from spectral feature vectors and spatial feature vectors of the image according to the following formula_sum：

$K_{\mathrm{sum}}(x_i,x_j)=\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}$

$=<\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\},\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}>$

$=K_s(x_i^s,x_j^s)+K_w(x_i^w,x_j^w)$

Wherein the spectral characteristicsIs a spectral feature vector constructed using all the original bands of the image. Spatial characteristicsThe spatial feature vector is extracted by the image by adopting a multi-scale morphological method. K_sAnd K_wRespectively, a spectral kernel matrix and a spatial kernel matrix obtained by calculation according to corresponding kernel functions.

(4) From the spectral and spatial feature vectors of the image, a combined kernel function based on weighted addition is calculated, which is mathematically expressed as follows:

where 0. ltoreq. mu. ltoreq.1, which controls the weight of the two kernel functions.

(5) Calculating a combined kernel function based on multiplication operation by the spectral feature vector and the spatial feature vector of the image, wherein the mathematical expression is as follows:

$K_{\mathrm{product}}(x_i,x_j)=\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}$

$=K_s(x_i^s,x_j^s)*K_w(x_i^w,x_j^w),$

wherein the spectral characteristicsIs a spectral feature vector constructed using all the original bands of the image. Spatial characteristicsThe spatial feature vector is extracted by the image by adopting a multi-scale morphological method. K_sAnd K_wRespectively, a spectral kernel matrix and a spatial kernel matrix obtained by calculation according to corresponding kernel functions.

1.4 training of a combined kernel function RVM classifier, which comprises the following specific steps:

(1) first, two classes of classification combination kernel function RVM classifiers are trained. The method comprises the following specific steps:

obtaining training samples and testing samples through feature extractionx_n∈R^d，t_n∈ R. where N is the number of samples in the training sample set x_kDenotes the kth sample, y_kIs the label corresponding to sample k.

For a given training samplex_n∈R^d，t_n∈ R. wherein the target value t_nCan be expressed as:

t_n=y(x_n;w)+_n

wherein,_nerror is expressed, is independent and follows a zero mean Gauss distribution with variance σ²I.e. p (t)_n|x)=N(t_n|y(x_n),σ²)

Decision function y (x)_n) For a linear combination of basis functions, the calculation formula is:

$y(x_i;w)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[w_{i}K(x,x_i)+w_0]$

wherein, w = (w)₀,w₁,...,w_n)^TAre weight coefficients. K (x, x)_i) Is kernel function, unlike the prior art, the kernel functions of the RVM classifier of the present invention are respectively the addition-based combined kernel function K of the present invention_sumCombining kernel function K based on weighted addition_weightAnd a multiplication-based combined kernel function K_product. The specific calculation method adopts the calculation flow of the combined kernel function as claimed in claim 1 to calculate.

(2) Calculating a conditional probability density function by adopting Bernoulli distribution, and firstly calculating a likelihood function of a training sample set according to the following formula:

$p\left(t\right|w)=\underset{n=1}{\overset{N}{\mathrm{\&Pi;}}}\mathrm{\&sigma;}{\left\{y(x_n;w)\right\}}^{t_n}{[1-\mathrm{\&sigma;}\{y(x_n;w)\left\}\right]}^{1-t_n}$

wherein, w_iIs a weight vector of RVM, subject to a mean of 0 and a variance ofGaussian conditional probability distribution of (c):

$p\left(w\right|\mathrm{\&alpha;})=\underset{i=0}{\overset{N}{\mathrm{\&Pi;}}}N\left(w_i\right|0,{\mathrm{\&alpha;}}_i^{-1})$

wherein, α = [ α ]₀,α₁,α₂,...,α_N]^TAnd α is an N +1 dimensional hyperparametric vector.

σ (y) is a Sigmoid function, and the calculation formula is as follows:

σ(y)=1/(1+e^-y)

(3) and training a multi-class classification combined kernel function RVM classifier. The method of the invention adopts a One-to-One method (OAO) to decompose a multi-class classification problem into a series of two classes of classification problems and solve the ground object class to which the pixel belongs. The method comprises the following specific steps: and finding out all different classes in the training sample set T, pairwise matching to form a multi-class classifier, wherein the total number of the classifiers is P = k (k-1)/2. Forming a training sample set T (i, j) of two types of problems by using training samples belonging to the two types, then solving the two types of problems, and respectively solving P discriminant functions f_(i，j)(x) In that respect In the classification, the input samples X are respectively sent to P discriminant functions f_(i，j)(x) If f is_(i，j)(x) And if not, judging that the X is the i type, and obtaining a ticket by the i type, otherwise, judging that the X is the j type, and obtaining a statistical ticket by the j type. The number of votes obtained by the k categories in the P discrimination function results is the final judgment category with the largest number of votes.

2. Example results

2.1 experiment one

The first experiment compares the performance of the conventional single feature-based RVM classification method with the three combined kernel function RVM classification methods of the present invention in terms of accuracy, solution sparsity and computational efficiency 3. The experiment adopts 4 indexes of Overall Accuracy (OA), Kappa Coefficient (KC), training time and number of basis functions as evaluation criteria of the performance of the classifier. In the first experiment, various samples are divided into two parts according to the number at random and are used as training samples and testing samples. Training samples are randomly extracted from the samples shown in fig. 2, and samples occupying 50% of the class are extracted from each class as training samples. The radial basis kernel function parameters are obtained by a cross validation method.

FIG. 5 shows a preferred embodiment of the present inventionThe classification result of the conventional RVM classification method is illustrated in fig. 5(a), wherein the classification result of the hyperspectral image by the conventional RVM method based on spectral features is illustrated in fig. 5 (a); FIG. 5(b) shows the combination kernel function (K) based on addition in the present invention_sum) The classification result of the hyperspectral image by the combined kernel function RVM method; FIG. 5(c) shows a multiplication core based on (K) in the present invention_product) The classification result of the hyperspectral image by the combined kernel function RVM method; FIG. 5(d) shows a combined kernel function (K) based on weighted addition in the present invention_weight) And (5) classifying the hyperspectral images by an RVM method.

As can be seen from fig. 5, the spectrum-based RVM classification method has higher accuracy at the C3, C4, C5 and C9 classes with higher classification separability, and has more false classifications for five crops, i.e., C1, C2, C6, C7 and C8, with lower separability.

Table 3 shows a comparison of performance of experimental zone images based on the three forms of the combined kernel function RVM method described herein and RVM methods based on the simplex spectral features. Wherein, K_sumRepresenting an addition-based combined kernel function; k_productRepresenting a combined kernel function based on multiplication; k_weightRepresenting a kernel function based on weighted addition. K_sAnd K_wRespectively representing functions based on a spectral feature kernel and functions based on a spatial feature kernel; the weighting coefficients of the weighted addition kernel function are tested at intervals of 0.1 from 0 to 1. The results of the weighted addition kernel with a weight of 0.8 are shown in table 3.

TABLE 3 Performance testing of experimental zone images based on different method classifications

Table 4 shows the classification accuracy of each class of experimental zone images based on the combined kernel function RVM and the simplex spectral feature based RVM classifier. Wherein, K_sumRepresenting combined kernel functions based on weighted addition；K_productRepresenting a combined kernel function based on multiplication; k_weightRepresenting a combined kernel function based on weighted addition. The combined kernel function weight value of the weighted addition in the table is 0.8. K_sAnd K_wRespectively representing a spectral feature-based kernel function and a spatial feature-based kernel function;

TABLE 4 Classification precision of images in the Experimental region for classes based on different methods (kernel function parameters 1)

From the above table 3, the following conclusions can be drawn:

(1) in the aspect of training time: the training time of the combined kernel function RVM classifier is not significantly increased compared to a single feature based RVM classifier. Wherein, the RVM training time based on the multiplication kernel function is equivalent to the RVM of a single kernel function. The training time of the RVM classifier based on the multiplicative kernel is slightly higher than the spectral kernel RVM.

(2) Sparsity of the model: the number of Relevance Vectors (RVs) of the combined kernel function RVM is not significantly increased over RVMs based on a single feature. Wherein, the number of related vectors of the RVM classifier of the addition core is lower than that of the classifier with single feature.

(3) And (3) classification precision: compared with the RVM classifier which solely uses the spectral characteristics and the spatial characteristics, the classification precision of the RVM with the combined kernel function is obviously improved. The invention constructs three forms of combined kernel function RVM classifiers, wherein the overall accuracy OA and Kappa coefficients of the combined kernel function RVM classifier based on multiplication are respectively improved by 4.2 percent and 5.05 percent. The overall accuracy OA and Kappa coefficients of the weighted addition based combined kernel function RVM classification method are respectively improved by 4.24% and 4.98%. The overall classification precision is improved most obviously by the addition-based combined kernel function RVM classification method, and the overall precision OA and Kappa coefficients are respectively improved by 4.21 percent and 4.95 percent.

As can be seen from table 4, after the multi-scale morphological features are integrated, the classification accuracy of almost all the classes is improved. Especially for five types which are difficult to classify, namely C1, C2, C6, C7 and C8, the introduction of the spatial features has a remarkable effect of improving the classification accuracy of the types. As can be seen from table 4 above, the spectral signature comparison is good at identifying the several categories C3, C4, C6, C9, while the spatial information comparison is good at identifying C5, C8. The spectral feature and the spatial feature of the image have certain complementarity, and the fusion method of the combined kernel function integrates the complementary characteristics of the spectral feature and the spatial feature, so that the highest overall classification precision is obtained.

In conclusion, the performance of the three combined kernel function RVM classifiers is superior to that of the traditional RVM classifier based on spectral characteristics.

2.2 experiment two

In order to examine the stability of the method, namely the influence of the training samples on the algorithm of the invention, the second experiment further randomly selects samples which account for 50%, 60% and 80% of the original training samples from the training sample set of the first experiment as the training samples, and the test data set keeps the original samples unchanged. The radial basis kernel function parameters are obtained by a cross validation method.

Table 5 shows the overall accuracy of each class of classification of the experimental zone images based on the three forms of the combined kernel function RVM method. In table, K_sumRepresenting a combined kernel function based on weighted addition; k_productRepresenting a combined kernel function based on multiplication; k_weightRepresenting a kernel function based on weighted addition. K_sAnd K_wRespectively representing functions based on a spectral feature kernel and functions based on a spatial feature kernel; the weighting coefficients of the weighted addition kernel function are tested at intervals of 0.1 from 0 to 1. The results of the weighted addition kernel with a weight of 0.8 are shown in table 5.

TABLE 5 Total accuracy of classes classified based on different methods when selecting different numbers of training samples

As can be seen from table 5 above: with the increase of training samples, the classification precision of the RVM method of the three forms of combined kernel functions is improved. However, when the proportion of the training samples to the total samples exceeds a certain proportion, the classification precision of the RVM method tends to be stable. The RVM method of the combined kernel function has strong stability and is insensitive to the size of a training sample set.

In conclusion, compared with the RVM classifier which independently uses the spectral features and the spatial features, the training time and the number of related vectors of the RVM classifier with the three combined kernel functions are not obviously increased, the OA and Kappa coefficients of the overall classification precision are obviously improved, and the RVM classifier is insensitive to the size of a training sample set and has strong stability. Experiments show that the method has certain advantages and application potentials in the hyperspectral image classification problem under the condition of rare samples.

It should be noted that, the experiment of the present invention uses kernel functions satisfying the Mercer condition to train the classifier, and as the RVM does not require kernel functions satisfying the Mercer condition, there are more kernel functions that can be used to train the RVM classifier. How to select the kernel function of the RVM and the corresponding parameters is yet to be further studied. In addition, the invention adopts a morphological method to extract the spatial characteristics of the image, and can also further extract the shape characteristics and other characteristics of the image to participate in classification together with the spectral characteristics. Meanwhile, the method for combining kernel functions is not limited to the case of two kernel functions, and other features of the image can be fused to jointly form the kernel functions and be used for training the RVM classifier.

The foregoing detailed description has set forth various embodiments of the systems and/or processes via examples and/or diagrams. To the extent that such diagrams and/or illustrations contain one or more functions and/or operations, those skilled in the art will appreciate that each function and/or operation of the diagrams or embodiments can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof.

It should be understood that the methods described herein may be implemented in connection with hardware or software or, where appropriate, with a combination of both. Thus, the methods of the present invention may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program code is executed on a programmable computer, the computing device typically includes a processor, a storage medium readable by the processor (including volatile memory and/or storage elements), at least one input device, and at least one output device. One or more programs that may implement or utilize the processes described in connection with the present invention, e.g., through the use of an API, reusable controls, or the like. Such programs are preferably implemented in a high level procedural or object oriented programming language to communicate with a computer system. However, the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language, and combined with hardware implementations.

It should be noted that the scope of the approach of the hyperspectral image classification method based on RVM and multi-scale morphology of the present invention includes, but is not limited to, any combination of the above parts.

While the invention has been particularly shown and described with reference to a preferred embodiment thereof, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the scope of the invention as set forth in the following claims. The foregoing detailed description has been presented in conjunction with specific embodiments of this invention, but is not intended to limit the invention thereto. Any simple modifications of the above embodiments according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims (3)

1. A combined kernel function RVM hyperspectral classification method fused with multi-scale morphological features is characterized by comprising the following steps:

the method comprises the following steps: performing dimensionality reduction on the hyperspectral image by adopting principal component transformation to obtain a feature vector of a training sample set

Wherein N represents the number of samples of the training sample set, x_kA k-th sample, y, representing the training sample set_kRepresenting a label corresponding to the kth sample;

step two: performing spatial feature extraction on the hyperspectral image after principal component transformation by adopting mathematical morphological transformation;

step three: respectively constructing a combination kernel function based on addition, multiplication and weighted addition by adopting a kernel function theory, fusing the spectral characteristics and the spatial characteristics of the image by using the combination kernel function,

wherein the spectral feature is a spectral feature vector composed of all original bands of the imageThe space features are feature vectors extracted by adopting a multi-scale morphological method

Step four: obtaining training samples and testing samples through feature extractionFeature vector x of a sample_n＝{x^s,x^wFrom the spectral feature vector of the sampleAnd the spatial feature vectorThe combined kernel function is used as a kernel function of an RVM classifier, training of the classifier is carried out, and the hyperspectral image is classified;

in the second step, the spatial feature extraction comprises the following steps:

(1) using a square structural element, the mathematical expression is:

${\mathrm{\&gamma;}}_{\mathrm{\&lambda;}}^{*}={\mathrm{\&delta;}}^{\left(rec\right)}(f\mathrm{\&Theta;}B,f)$

wherein,expressing an opening reconstruction operator, f theta B expressing the corrosion operation on the image, pi gamma (x) expressing the morphological characteristics of the image obtained by the opening reconstruction operation,

and respectively operating each principal component image to obtain a multiscale morphological characteristic Π gamma (x) based on open reconstruction, wherein the mathematical expression is as follows:

$\&Pi;\mathrm{\&gamma;}\left(x\right)=\{\&Pi;{\mathrm{\&gamma;}}_{\mathrm{\&lambda;}}:\&Pi;{\mathrm{\&gamma;}}_{\mathrm{\&lambda;}}={\mathrm{\&gamma;}}_{\mathrm{\&lambda;}}^{*}\left(x\right),\&ForAll;\mathrm{\&lambda;}\&Element;\&lsqb;0,n\&rsqb;\}$

wherein n is the number of ON operations, and when λ is 0,

(2) and performing closed reconstruction operation on the principal component image, wherein the mathematical expression is as follows:

wherein,it is indicated that the dilation operation is performed on the image,is a closed reconstruction operator, and uses the square structural elements to respectively operate each principal component image to obtain the multi-scale morphological characteristics based on closed reconstructionThe mathematical expression is as follows:

wherein n is the number of times of the closing operation, and when λ is 0,

(3) after the opening reconstruction operation and the closing reconstruction operation, performing difference operation by using two adjacent morphological characteristic images to obtain the multi-scale morphological characteristics of the image, wherein the mathematical expression of the multi-scale morphological characteristics is as follows:

where n is the number of opening and closing operations, and c is 1, 2.

2. The RVM hyperspectral classification method based on the combined kernel function fused with the multi-scale morphological features as claimed in claim 1, wherein in the third step, the construction method of the combined kernel function comprises the following steps:

(1) the spectral characteristics of the image areThe spatial characteristics of the image areThe kernel matrixes of the corresponding spectral characteristics and spatial characteristics are respectively K_sAnd K_wNormalizing the spectral feature and the spatial feature to (0, 1):

$\begin{array}{c}{x}^s=\frac{x^s-x_{min}^s}{x_{\max }^s-x_{min}^s}\\ x^w=\frac{x^w-x_{min}^w}{x_{\max }^w-x_{min}^w}\end{array};$

(2) calculating a spectral kernel matrix K from spectral features of the image_sAnd the space kernel K_wThe basis function of the spectrum nuclear matrix adopts a radial basis kernel function, and the mathematical expression of the calculation method of the spectrum nuclear matrix is as follows:

$K_s=\exp {(-\mathrm{\&gamma;}||x_i^s-x_j^s|\left|\right)}^2$

wherein x is^sIs a spectral feature vector, gamma is a radial basis kernel function parameter, and is confirmed by a cross validation methodDetermining a parameter gamma;

(3) computing a spatial kernel matrix K using radial basis kernel functions_wThe mathematical expression of the calculation formula of the space kernel matrix is as follows:

$K_w=\exp {(-\mathrm{\&gamma;}||x_i^w-x_j^w|\left|\right)}^2$

wherein x is^wThe method comprises the steps of extracting a space feature vector based on a multi-scale morphology method, determining a parameter gamma through a cross validation method, wherein the gamma is a radial basis kernel function parameter;

(4) the mathematical expression of the computing method of the combined kernel function based on the addition operation is as follows:

$\begin{array}{c}{K}_{sum}(x_i,x_j)=\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}\\ =<\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\},\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}>\\ =K_s(x_i^s,x_j^s)+K_w(x_i^w,x_j^w);\end{array}$

(5) the mathematical expression of the calculation method for constructing the combined kernel function based on the weighted addition on the basis of the combined kernel function based on the addition operation is as follows:

wherein mu is more than or equal to 0 and less than or equal to 1, and mu controls the weight of the two kernel functions;

(6) the mathematical expression of the computing method of the combined kernel function based on the multiplication operation is as follows:

$\begin{array}{c}{K}_{product}(x_i,x_j)=\{{\mathrm{\&phi;}}_1\left(x_i^s\right),{\mathrm{\&phi;}}_2\left(x_i^w\right)\}\\ =K_s(x_i^s,x_j^s)*K_w(x_i^w,x_j^w)\end{array}$

wherein x is^sThe spectral feature vector is composed of original wave bands of the image, gamma is a radial basis kernel function parameter, and the width of the kernel function is controlled.

3. The RVM hyperspectral classification method based on the combined kernel function fused with the multi-scale morphological features as claimed in claim 1, wherein the training process of the RVM classifier in the fourth step comprises the following steps:

(1) construction training sampleWherein x is_n∈R^d，t_n∈ R, target value t_nThe following mathematical expression is used for calculation:

t_n＝y(x_n；w)+_n

wherein, errors_nAre independent and obey a zero mean Gauss distribution with variance σ²I.e. p (t)_n|x)＝N(t_n|y(x_n),σ²)；

(2) Decision function y (x) of RVM_n) The following mathematical expression is used for calculation:

$y(x_i;w)=\underset{i=1}{\overset{N}{\&Sigma;}}\&lsqb;w_{i}K(x,x_i)+w_0\&rsqb;$

wherein w ═ w₀,w₁,...,w_n)^TDenotes the weight coefficient, K (x, x)_i) Representing the kernel function of the RVM classifier, wherein the kernel function of the RVM classifier adopts the combined kernel function in the step three, namely an addition kernel K_sumMultiplication core K_weightAnd a kernel function K based on weighted addition_product；

(3) For the target value t_nThe likelihood function p (t | w) of the training sample set is calculated as follows:

$p\left(t\right|w)=\underset{n=1}{\overset{N}{\&Pi;}}\mathrm{\&sigma;}{\left\{y(x_n;w)\right\}}^{t_n}{\&lsqb;1-\mathrm{\&sigma;}\left\{y(x_n;w)\right\}\&rsqb;}^{1-t_n}$

wherein, w_iIs a weight vector of RVM, the obedient mean is 0, the variance isThe gaussian conditional probability distribution of (a), namely:

$p\left(w\right|\mathrm{\&alpha;})=\underset{i=0}{\overset{N}{\&Pi;}}N\left(w_i\right|0,{\mathrm{\&alpha;}}_i^{-1})$

wherein α ═ α₀,α₁,α₂,...,α_N]^Tα, representing the hyperparametric vector for determining the prior probability of the weight vector, and solving by a fast sequence sparse Bayes method;

(4) after y (x) is calculated, mapping y (x) into [0,1] through a Sigmoid function to carry out category judgment, wherein the mathematical expression of the Sigmoid function is as follows:

σ(y)＝1/(1+e^-y)；

(5) finding out all samples of different classes in a training sample set T (i, j), pairwise matching the samples to form a multi-class classifier, wherein the total P is k (k-1)/2, and using the training samples belonging to the two classes to form a training sample set of two classes of problemsSeparately obtaining P discriminant functions f_(i,j)(x) When classified, the training samples areRespectively calculating P discriminant functions f_(i,j)(x) If f is_(i,j)(x) And finally, integrating the number of votes obtained by the k categories in the P discrimination function results, wherein the category with the largest number of votes is the final judgment category.