CN1932850A - Remoto sensing image space shape characteristics extracting and sorting method - Google Patents

Abstract

A method for extracting and classifying spatial shape features of remote sensing images, which detects the spatial shape structure features of the pixel by extending a series of equally spaced direction lines around the central pixel, the number of direction lines is 5-48, and the direction line The length of is controlled by the homogeneity threshold and the maximum length threshold, which are not equal to each other, reflecting the anisotropy of the image; the direction line histogram of the pixel reflects its context structure characteristics, in order to extract spatial structure features more effectively, and reduce Dimensionality of the feature, using six statistical measures of length, width, pixel shape index, aspect ratio, weighted mean, and variance to extract the direction line histogram feature of each pixel; using spectral and spatial structure feature fusion classification method , while choosing one of various neural networks and machine learning algorithms to process high-dimensional feature spaces. The invention has simple calculation, high program operation efficiency and less manual intervention, is suitable for automatic classification of high-resolution remote sensing images, and can effectively improve the classification accuracy and efficiency of such images.

Description

A Method of Spatial Shape Feature Extraction and Classification of Remote Sensing Images

technical field

The invention belongs to the technical field of computer remote sensing image processing and pattern recognition, and is a new method of extracting image shape and structure features by using the context spectrum similarity distribution of remote sensing images, and classifying high-dimensional spectral and spatial features with neural networks and support vector machines Methods.

Background technique

High-spatial-resolution remote sensing images can provide a large number of surface features, and the rich detailed information of the internal components of the same object category can be represented, the spatial information is more abundant, and the size, shape, and relationship between adjacent objects are better reflected. . However, the spectral statistical characteristics of this new type of remote sensing images are not as stable as those of low-resolution images, and the spatial distribution of ground objects is complex, and similar objects show great spectral heterogeneity, which is manifested in the increase of intra-class variance and the decrease of inter-class variance. The spectra of different ground objects overlap with each other, which makes the traditional spectral classification methods unable to obtain satisfactory results. Therefore, in recent years, remote sensing applications have proposed many spatial feature operators to make up for the lack of spectral features. Various methods related to spatial structure feature extraction are current research hotspots. The following is a brief description of the typical methods that are currently being studied.

The gray level co-occurrence matrix (GLCM) method is a texture and spatial feature extraction operator widely used in the field of remote sensing image processing. sex. GLCM generally detects the relationship between pixel point pairs in the directions of 0°, 45°, 90° and 135°, and forms four gray-level co-occurrence matrices. Usually, the superposition of four directions is used to eliminate the influence of the direction. Spatial co-occurrence properties as a measure of texture. The gray space of the fine texture changes rapidly, but the change of the coarse texture is not obvious with the increase of the distance. Using different spatial measures to filter the space of the co-occurrence matrix can extract a series of statistical attributes describing the characteristics of the texture structure. Commonly used gray level co-occurrence matrix statistical measures include: mean, variance, entropy, energy, homogeneity, contrast, etc. Each statistical measure can be used as a texture feature image, also known as an auxiliary band, to be classified together with spectral features. The advantage of this method is that it can not only reflect the differences in the spatial characteristics of ground objects, but also be compatible with various classification systems. Selecting different statistical attributes as indicators according to the characteristics of different ground objects can achieve the purpose of effectively extracting ground object information. Related references are: Yun Zhang. Optimisation of building detection in satellite images by combining multispectral classification and texture filtering. ISPRSJournal of Photogrammetry and Remote Sensing, 1999, 54(8): 50～60; .Proceeding of IEEE, 1979, 67:786-804; and R.M.Haralik, K.Shanmugam, and D.Its'hak.Textural features for image classification,IEEE trans.Syst.Man Cybnet.,vol.SMC-3,pp. 610-621, 1973.

Mathematical morphological transformation can also effectively extract the spatial features of images. It obtains spatial structural features through various morphological operations and transformations, and obtains multi-scale results through different operational structural elements. Commonly used morphological operators include dilation, erosion, watershed transformation, opening and closing operations, and so on. Pesaresi used different scales of opening and closing operations to construct the morphological profile of the image, and used the neural network to classify the multi-scale morphological features. He believed that the opening and closing operations used in remote sensing images can detect the neighborhood area Darker or brighter structural units; Benediktsson proposed the concept of derivation of morphological profile on this basis, using the difference between the opening and closing operation results between adjacent scales as a new image structure feature, and using BP neural network The network classifies this feature and obtains a higher classification accuracy. References are: M.Pesaresi, and.J.A.Benediktsson, "A new approach for the morphological segmentation of high-resolution satellite imagery," IEEE Transactions on Geoscience and Remote Sensing, vol.39, no.2, pp.309-320, Feb, 2001; J.A.Benediktsson, M.Pesaresi, and K.Arnason, “Classification and feature extraction for remote sensing images from urban areas based on morphological transformations,” IEEE Transactions on Geoscience and RemoteSensing, vol.41, no.9, pp. 1940-1949, Sep, 2003; J.A.Benediktsson, J.A.Palmason, and J.R.Sveinsson, "Classification of hyperspectral data from urban areas based on extended morphological profiles," IEEE Transactions on Geoscience and RemoteSensing, vol.43, no.3 -491, Mar, 2005.

In addition, straight lines are also an important structural feature of images. Different image areas show different straight line features. Unsalan can distinguish urban (urban), suburban (suburban) and rural areas (rural area) by using the line features of images. He believes that within a certain range, the straight lines extracted from rural image areas are often relatively short and randomly distributed, which is caused by the lack of human activities in this area; while urban images show the opposite characteristics, the linear distribution It is more regular and the detected straight line is longer. Unsalan and Boyer used this feature to extract the straight line features of the image, and used the probability relaxation algorithm combined with the normalized difference vegetation index (NDVI) to classify the remote sensing image, and achieved good results. References such as: C.Unsalan, K.L.Boyer, "Classifying land development in high-resolution panchromatic satellite images using straight-line statistics," IEEE Transactions on Geoscience and Remote Sensing, vol.42, no.4, pp.907-919, April , 2004; C.Unsalan, K.L.Boyer, "Classifying land development in high-resolution panchromatic satellite imagery using hybrid structural-multispectral features," IEEE Transactions on Geoscience and Remote Sensing, vol.42, no.12, pp.2840-2850 , 2004.

Summarizing the above methods, it is found that although the principles of various spatial feature extraction algorithms are different, they still have a commonality to a certain extent, that is, they all use the gray distribution characteristics of images in a certain area to extract features. The invention proposes a series of spatial characteristic indices (SI) and a high spatial resolution remote sensing image classification method based on fusion of shape and spectral features. Shape and spectrum are the specific manifestations of remote sensing image texture, especially in high-resolution images where the details of ground objects are fully expressed, and the relationship between adjacent pixels and their jointly represented shape characteristics become important factors for classification. The invention uses the relationship between pixel and its neighborhood to describe its spatial structure, and at the same time, in order to make more comprehensive use of image features, it proposes a shape and spectrum fusion classification method based on support vector machines.

The design principles of the algorithm are: 1). Using the spectral similarity of adjacent pixels, the purpose is to consider the spatial context characteristics of the pixels; 2). Make the pixels in the same shape area have the same or similar eigenvalues. It is to enhance the homogeneity of the high-resolution image and smooth the noise to a certain extent; 3). Try to enlarge the feature value between the pixels in different shape areas, which is to make full use of the detail characteristics of the high-resolution image.

The starting point of the present invention is to use the neighborhood gray similarity to measure the structural information of the context, which is similar to the idea of the gray co-occurrence matrix. Both of them transform the spectral space, and GLCM transforms the spectral space into the co-occurrence matrix space, SI Then the spectral space is transformed into the direction line distance space. Their main differences are: 1). GLCM uses a fixed window operation, while SI cancels the window setting, and the length of each direction line is different. The algorithm is distributed according to different structures. Flexible processing can effectively use the anisotropy of the image; 2). GLCM first reduces the gray level of the image, and then calculates the number of pixels with the same gray value, while SI retains the gray feature of the original image, and then uses the same The qualitative threshold counts the number of pixels with similar gray values; 3). GLCM detects 4 directions, while SI detects more than 20 directions. The above characteristics enable SI to achieve better results than GLCM in remote sensing image feature extraction and classification.

Contents of the invention

The invention proposes a method for extracting and classifying spatial structure features of remote sensing images, which describes the spatial shape distribution of its context through the spectral similarity of the pixel and its neighborhood, and then inputs the normalized shape and spectral features into the classifier for classification , it can achieve better results than GLCM in remote sensing image feature extraction and classification.

The technical solution provided by the present invention is: a method for extracting and classifying spatial structure features of remote sensing images, which is characterized in that: detecting the spatial shape structure features of a central pixel by extending a series of equally spaced direction lines around the central pixel, The number of direction lines is 5-48, and the length of the direction lines is controlled by the homogeneity threshold and the maximum length threshold, which are not equal to each other, reflecting the anisotropy of the image; the histogram of the direction lines of the pixel reflects its context structure characteristics , in order to extract spatial structure features more effectively and reduce the dimensionality of features at the same time, the six statistical measures of length, width, pixel shape index, aspect ratio, weighted mean, and variance are used to extract the direction line histogram of each pixel Features: The method of fusion classification of spectral and spatial structure features is adopted, and at the same time, a method is selected among various neural networks and machine learning algorithms to process high-dimensional feature spaces.

The method for extracting and classifying spatial shape features of remote sensing images as described above includes the following steps:

1. First, the direction line is defined as a series of line segments passing through the central pixel. Their length and direction are different. The length is determined by the spectral homogeneity measure and threshold between adjacent pixels. The distance between adjacent direction lines is The angles of are set to equal radians;

2. The extension of the direction line starts from a central pixel and extends in two opposite directions at the same time. The extension condition of the direction line is: the homogeneity threshold of adjacent pixels and the length limit of the direction line are met, and each direction line follows the above Conditions are expanded and extended, and if one of the conditions is not true, the expansion of the direction line is terminated;

3. Track and obtain all direction lines of the central pixel, calculate the length of all direction lines, and select from two length calculation formulas according to different calculation requirements: city-block distance and Euclidean distance;

4. Obtain the lengths of all direction lines around the central pixel, arrange the series of length values in clockwise order to form the direction line histogram of the pixel, and extract the space of the pixel according to the distribution of the histogram Shape features, using the following six feature measures: length (length), width (width), pixel shape index (pixel shape index), length-width ratio (length-width ratio), weighted mean (weighted mean), variance (variance );

5. Traversing the entire image, calculating the direction line histogram and corresponding statistical measures of each pixel;

6. Combine the spectral information of the original image and the extracted spatial shape features to classify, and use different methods to normalize the spectral information and spatial information;

7. Input the mixed features into the classifier. The following classifiers are available for users to choose: minimum distance classifier (MDC), maximum likelihood classifier (MLC), multi-layer perceptron network (MLP), radial basis neural network (RBF), Probabilistic Neural Network (PNN) and Support Vector Machine (SVM), users can choose the most suitable classifier according to different requirements;

8. Set up and train the classifier, and then input spectral and spatial mixed features to classify carefully to get the final classification result.

The method for extracting and classifying spatial shape features of remote sensing images as described above is characterized in that: the number of direction lines D available for selection is: 12, 16, 20, 24, and the default setting is D=20.

Principle of the present invention is:

One, for the neighborhood spectral distribution characteristics of a certain central pixel, track and obtain all its direction lines, set the number of direction lines of a central pixel as D, and D is greater than 4; the present invention provides multiple optional D values , in general, the larger the value of D, the stronger the ability of the algorithm to describe the spatial neighborhood of the image, but when D increases to a certain extent, the improvement of accuracy is not obvious, and at the same time, more processing time is consumed. The D values that can be selected by the user are: 12, 16, 20, 24, and the default setting is D=20;

2. To calculate the length of the direction line, there are two calculation methods to choose from: Euclidean distance and block distance. The former can more effectively reflect the length difference of the direction line, and the latter can achieve the effect of smoothing and filtering and save calculation time. Users Can be flexibly set according to needs;

3. Calculating the lengths of all D direction lines of the central pixel, and storing them sequentially in a clockwise direction, as the direction line histogram of the pixel, to prepare for subsequent feature extraction steps;

4. Traverse the entire image, and obtain the direction line histogram of all pixels;

5. Use the proposed six feature measures: length, width, pixel shape index, aspect ratio, weighted mean, and variance to extract the histogram features of each pixel, while reducing the dimensionality of spatial features;

6. Users can choose whether to perform feature transformation according to the specific situation. The provided feature transformation methods include: decision edge feature extraction algorithm (DBFE), principal component analysis (PCA) and similarity index (Similarity Index). The purpose of feature transformation is to reduce the dimensionality of spatial features while increasing the category separability of feature space;

7. The extracted spatial structure features and spectral information are preprocessed and normalized respectively. The spectral information adopts the method of maximum-minimum linear stretching. The spatial features are preprocessed by histogram equalization method because the value span is too large. . The purpose of normalization is to effectively classify in the next step;

8. Select the appropriate classifier for mixed features, the options include: minimum distance classifier, maximum likelihood classifier, multi-layer perceptron network, radial basis neural network, probabilistic neural network, support vector machine. The minimum distance classifier is suitable for 1-dimensional feature input, and the maximum likelihood method is fast and stable, but it is not as good as machine learning algorithms in high-dimensional feature processing capabilities. Neural network methods are research hotspots for processing multi-dimensional remote sensing data in recent years. The present invention utilizes machine learning The latest achievement support vector machine to deal with spectral and shape mixed features, in order to maximize the use of these features for decision-making;

Nine, select the training sample, set the parameters of the classifier, the parameter setting of the support vector machine (SVM) is automated, and use the famous leave-one-out (LOO) method to determine the penalty coefficient and kernel parameters of the SVM;

10. Classify the mixed features of spectrum and space structure, and obtain the classification result.

Features of the present invention: the concept of direction lines is defined, and the spatial shape and structural features of the pixel are detected by extending a series of equally spaced direction lines around the central pixel, which is a new way of extracting spatial features. The direction line can detect a maximum of 48 directions, which is much higher than the 4 directions of the gray-level co-occurrence matrix, and has a stronger ability to describe the neighborhood. The length of the direction line is controlled by the homogeneity threshold and the maximum length threshold, which are not equal to each other. The anisotropy of the image is realized; the context structure characteristics are reflected by the direction line histogram of the pixel. In order to extract the spatial structure feature more effectively and reduce the dimension of the feature, the present invention proposes length, width, and pixel shape index , aspect ratio, weighted mean, and variance, these six statistical measures extract the histogram features of the direction line of each pixel; adopt the fusion classification method of spectral and spatial structure features, and provide a variety of neural networks and machine learning algorithms to deal with high-dimensional Feature space, in which the support vector machine can generate new features that the original data does not have through kernel space mapping, and also avoid the decisive influence of spectral or spatial information in decision-making. The invention has simple calculation, high program operation efficiency and less manual intervention, is suitable for automatic classification of high-resolution remote sensing images, and can effectively improve the classification accuracy and efficiency of such images.

Description of drawings

Fig. 1 is a schematic diagram of a direction line of an embodiment of the present invention;

Fig. 2 is the flow chart of the main program operation of the embodiment of the present invention;

Fig. 3 is a flow chart of the direction line extension and tracking algorithm of the embodiment of the present invention;

Fig. 4 is the flow chart of the direction line histogram feature extraction algorithm of the embodiment of the present invention;

Fig. 5 is a spectral-structural feature classifier based on neural network and machine learning according to an embodiment of the present invention.

Detailed ways

1. Theoretical basis

The basic theory that the present invention uses mainly comprises:

(1) Support Vector Machine: It is a new learning method based on statistical learning theory, which embodies the consistency of the learning process and the principle of structural risk minimization, and it minimizes the confidence range on the basis of keeping the empirical risk fixed , by comprehensively considering the empirical risk and the confidence range, and taking a compromise according to the principle of structural risk minimization, the decision function with the least risk is obtained. Its core idea is to map the samples in the input space to the high-dimensional kernel space through nonlinear transformation, and obtain the optimal linear decision surface with low VC dimension (complexity) in the high-dimensional kernel space.

The basic principle of SVM is: Suppose the training samples are {(x ₁ , y ₁ ), (x ₂ , y ₂ ), ..., (x _N , y _N )}, where x _i ∈ R ^d represents the input pattern, y _i ∈ {±1} denotes the target output. Suppose the optimal decision surface equation is: w ^T x _i + b = 0, then the weight vector w and bias b must satisfy the constraints:

y _i (w ^T x _i +b)≥1-ξ _i

Among them, _ξi is the slack variable under the condition of linear inseparability, which represents the deviation degree of the model from the ideal linear condition. The goal of SVM is to find a decision surface that minimizes the average misclassification error on the training data, and the following optimization problem can be derived:

$\mathrm{<span\; class="notranslate">\; \&Phi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; C</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

C is a positive parameter specified by the user, which indicates the degree of punishment of SVM for misclassified samples, and is a balance parameter between the proportion of misclassified samples and the complexity of the algorithm. Using the Lagrange multiplier method, the solution of the optimal decision surface can be transformed into the following constrained optimization problem:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>$

Where {α _i } _i=1 ^N is the Lagrange multiplier, and (5) satisfies the constraints:

$\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0,0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2,3</span>}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}$

K(x, x _i ) is a kernel function that satisfies the Mercer theorem. There are two commonly used kernels:

Polynomial kernel function: K=(x ^T x _i +1) ^p , the exponent p is determined by the user;

Radial basis kernel function: $K=\exp (-\frac{1}{2{\mathrm{\&sigma;}}^2}{\left|\right|x-x_i\left|\right|}^2),$ The width σ is the same for all cores and is specified by the user;

The support vector machine (SVM) is selected as the classifier of spatial features, considering its non-parametric characteristics without the assumption of normal distribution of feature space, and the mapping of high-dimensional kernel space is more suitable for multi-dimensional spatial feature input, because SVM provides The model complexity of the model has nothing to do with the input feature dimension, which makes the features of the input pattern diversified, and the kernel function maps the input features to the high-dimensional kernel space, which may generate new features that the original data do not have, making the original spectrum inseparable. The addition of spatial features becomes separable. In the classification system, the application of SVM should pay attention to:

(a). The setting of SVM is mainly the choice of kernel function, that is, to choose between polynomial kernel and RBF kernel. According to the characteristics of high-resolution images, due to the large variance between classes, the spectral characteristics of the samples of the same kind of ground objects are relatively scattered, rather than tightly surrounding some centers, that is, the spectral samples of high-resolution images have no obvious centers, and the samples There is no weight size, and for the RBF kernel, the output of the input sample far away from the center of the node is almost zero, and the sample has different weights and response values according to the distance from the center, but the polynomial kernel does not have locality , so it is more suitable as a kernel function for high-resolution image input features.

(b). C is a regularization parameter, or penalty coefficient. In the feature space, C controls the deviation degree of the model to be divided to the decision surface. When C increases, the degree of deviation increases, and when C decreases, it can be The degree of deviation is reduced. Its setting is related to the distribution of samples, support vectors, and patterns to be divided in the feature space. Considering the relationship between classification time and accuracy, the selection of C is meaningful, and the appropriate value can obtain the best in the least time. As a result, the efficiency of the classification system is improved.

(c). The selection of sample areas for SVM should also be based on the characteristics of high-resolution images, and the different spectral characteristics of the same surface features must be fully considered.

(2) Probabilistic neural network (PNN): The probabilistic neural network was proposed by Specht. Its essence is the combination of Bayes decision rules and multi-layer perceptron. The network is divided into 3 layers: input layer, pattern layer and output layer. The training of PNN is very simple. The samples of K classes are arranged in K pools in the mode layer in turn. For a certain pool_i, i=1, 2, 3, ... K, K is the total number of categories or the number of modes, and there are N _i modes. neuron, for each input vector y, the activation value of the jth neuron of pool_i is:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; d</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; [</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span>$

In the formula, w _i ^(j) represents the weight vector of the jth neuron of pool_i, which is determined by the training samples. The output layer has K neurons, representing K patterns, where the value of the i-th output is:

${\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>$

The decision takes a "winner takes all" approach:

If: O _k ＞O _i , i≠k, and i, k∈[1, K], then: y∈C _k

The training of PNN is a very simple one-time process. For each training sample x, assuming it is the i-th mode, that is, x∈C _i , then the training process is just adding a new neuron to the mode layer pool_i element, and assign its weight vector w _i ^(j) as x.

2. The structure of shape and structure features

The design principles of PSI are: 1). Using the spectral similarity of adjacent pixels, the purpose is to consider the spatial context characteristics of the pixels; 2). Make the pixels in the same shape area have the same or similar eigenvalues. It is to enhance the homogeneity of the high-resolution image and smooth the noise to a certain extent; 3). Try to enlarge the feature value between the pixels in different shape areas, which is to make full use of the detail characteristics of the high-resolution image.

First, the direction line is defined as a series of line segments passing through the central pixel. As shown in Figure 1, their lengths are different, and their length is determined by the spectral homogeneity measure and threshold between adjacent pixels. The tracking and calculation steps of the direction line are as follows:

1). Homogeneity measure:

${\mathrm{<span\; class="notranslate">\; pH</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; sur</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; cen</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}$

Among them, PH _i (x, y) represents the homogeneity measurement value of the current neighborhood pixel (x, y) on the i-th direction line, p _s ^cen represents the spectral value of the central pixel on the band s, p _s ^sur represents the spectral value of the current neighborhood pixel on the band s, and n represents the number of bands.

2). Expansion of direction lines: each direction line starts from the central pixel and expands to both sides according to specific rules. The conditions for the expansion of the i-th direction line are: (a). PH _i of the current pixel (x, y) less than the threshold T1; (b). The total length of the direction line is less than the threshold T2. The theoretical value of T1 should be the average value of the intra-class mean square error of various samples, which can be adjusted according to the specific situation in the experiment; T2 is the scale factor, which should be determined according to the size of the object of interest, or T2 can be used The variation of extracts multi-scale information.

3). Let D be the total number of direction lines of a pixel, traverse the entire image, follow 1) and 2) to track and obtain all D direction lines of each pixel.

4). Calculate the length of the i-th direction line:

${\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

or d _i =max{|m ^e1 -m ^e2 |, |n ^e1 -n ^e2 |}

Where (m ^e1 , n ^e1 ) represents the row and column number of the pixel coordinates at one end of the direction line, and (m ^e2 , n ^e2 ) represents the row and column number of the other end point. Therefore, the direction line length sequence of any pixel (i, j) is obtained: d(i, j)=[d ₁ , d ₂ , . . . , d _D ].

3. Implementation process

(1) Set the parameters T1, T2 and D of the feature extraction algorithm. By default, T1 takes the average value of the intra-class mean square error of various samples, T2 takes 0.35 times the length or width of the image, and D=20. All D direction lines of a certain central pixel are tracked and calculated according to the thresholds T1 and T2. In specific operations, the threshold value can be flexibly adjusted according to the running results.

(2) Choose the calculation formula for the length of the direction line, Euclidean distance or block distance. The former can effectively reflect the difference between the lengths of direction lines, and the latter can reduce the calculation time while smoothing the spatial characteristics. The length of the direction line for a central cell is then calculated according to the selected distance formula.

(3) Store all direction line lengths of the central pixel sequentially in a clockwise direction to form a D-dimensional direction line histogram. Traverse the entire image, track and obtain the direction lines of all pixels, and store the direction line histogram of each pixel for feature extraction.

(4), measure with six kinds of features proposed by the present invention: length, width, pixel shape index, aspect ratio, weighted mean, variance extract the statistical attribute of each pixel direction line histogram, like this, each pixel Just form the characteristic of 6-dimensional space structure.

The calculation methods of these 6 statistical features are as follows:

(a). Length (length):

$\mathrm{<span\; class="notranslate">\; length</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

where H(i, j) represents the direction line histogram of pixel (i, j).

(b). Width (width):

$\mathrm{<span\; class="notranslate">\; width</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

(c). Pixel shape index (mean):

$\mathrm{<span\; class="notranslate">\; mean</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}$

(d). Weighted mean (w-mean):

$\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; mean</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; st</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; D.</span>}$

where _ki represents the length of the i-th direction line, α is the scaling factor, and st _i is the variance of the gray value of the pixels that make up the i-th direction line, which is used to limit the weight of unrobust direction lines in feature statistics.

(e). Aspect ratio (ratio):

$\mathrm{<span\; class="notranslate">\; ratio</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; min</span>}}{\mathrm{<span\; class="notranslate">\; sort</span>}}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; max</span>}}{\mathrm{<span\; class="notranslate">\; sort</span>}}}^{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}$

in ${\underset{\max }{\mathrm{sort}}}^{\mathrm{no}}\left(h(i,j)\right)$ and ${\underset{\min }{\mathrm{sort}}}^{\mathrm{no}}\left(h(i,j)\right)$ Respectively represent the n maximum and minimum values in the histogram of the pixel (i, j) direction.

(d). Standard deviation (SD):

$\mathrm{<span\; class="notranslate">\; SD</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; SD</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\sqrt{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; mean</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

(5) If there are fewer spectral bands and more spatial structure feature dimensions, you can choose to perform feature selection operations. This classification system provides three dimensionality reduction and feature selection algorithms: Independent Component Analysis (ICA), Decision Edge Feature Extraction (DBFE) and Similarity Index algorithm (Similarity Index). Because the similarity index method is easy to calculate, requires the least CPU time, and can also ensure calculation accuracy, this method is used by default.

(a). Independent component analysis:

The basic principle of ICA is: Given a feature vector set x, the task of the algorithm is to determine an N×N invertible matrix W, and perform a linear transformation on the vector set:

y=Wx

Let the result vectors y(i), i=1, 2, . . . N be independent of each other. The key to the ICA algorithm lies in the independent discriminant method,

Here, the interaction information between the minimized variables is used to estimate the W matrix. The mutual information between y components is defined as:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

where H(y(i)) is the joint entropy of y(i). The statistical independence between y(i) is equivalent to I(y) being 0, because at this time the product of the joint probability density and the corresponding marginal probability density is equal, and the minimization of formula (3) is equivalent to the maximization of the following formula :

$\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; det</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Deriving W on both sides of the above formula, sorting out the iterative formula of the gradient descent method:

W(t)＝W(t-1)+μ(t)(IE[φ(y)y ^T ])W ^-T (t-1)

(b). Decision Edge Feature Extraction (DBFE):

The algorithm can make full use of the characteristics of the classifier and select the required features from the decision boundary. The theoretical basis of DBFE is to use the position of the decision edge of each category to eliminate redundant feature information.

(c). Similarity Index (Similarity Index);

The feature similarity between variables is used to filter the transformed spectral bands. Let p be the signal dimension before feature selection, and q be the signal dimension after feature selection. The task of the algorithm is to delete the (p-q) dimensional signal from the feature set. . The algorithm uses Maximal Information Compression Index (MICI) to exclude p-dimensional features:

$\mathrm{<span\; class="notranslate">\; MICI</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cov</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; var</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}$

When MICI(x, y) is 0, it means that the two features are linearly correlated, and the error of feature selection is 0; when MICI(x, y) increases, the correlation between the two features decreases, and the error of feature selection increase. MICI(x, y) is the eigenvalue of two feature pairs (x, y) projected in the direction of their principal components, representing the error of feature compression. The feature selection algorithm in this paper is as follows:

1). Normalize the p-dimensional features to [0, 1].

2). Calculate the compression index of each pair of features one by one, and find the maximum MICI, assuming it corresponds to the band a, b.

3). Calculation $S_a=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{MICI}(a,i)$ and $S_b=\underset{i=1}{\overset{q}{\mathrm{\&Sigma;}}}\mathrm{MICI}(b,i),$ Comparing the size of S _a and S _b , if S _a > S _b , the band a is deleted; otherwise, the band b is deleted.

4). Let p=p-1, if p=q, then the algorithm is terminated; if not, go to (2) to continue execution.

(6) Store the spatial structure features of each pixel, and participate in decision-making and classification together with the original spectral band as an auxiliary band.

(7) Preprocessing and normalizing the spectral features and structural shape features so as to be input to the classifier. Due to the differences in spectral information and spatial features, different methods are used to normalize the two:

(8) Select an appropriate classifier. The default classifier is support vector machine (SVM), which is due to its fast calculation speed and significant advantages in processing high-dimensional mixed features.

(9) Select training samples according to prior knowledge, train and learn from the selected classification, and then classify the images to obtain the final classification map.

Claims (3)

1. A method for extracting and classifying spatial shape features of remote sensing images, characterized in that: the spatial shape structural features of the pixel are detected by extending a series of equally spaced direction lines around the central pixel, and the number of direction lines is within 5 -48, the length of the direction line is controlled by the homogeneity threshold and the maximum length threshold, which are not equal to each other, reflecting the anisotropy of the image; the histogram of the direction line of the pixel reflects its context structure characteristics, in order to extract more effectively Spatial structure features, while reducing the dimensionality of features, using six statistical measures of length, width, pixel shape index, aspect ratio, weighted mean, and variance to extract the direction line histogram features of each pixel; using spectral and spatial Structural feature fusion classification method, while choosing a method among various neural networks and machine learning algorithms to deal with high-dimensional feature spaces. 2. The method for extracting and classifying spatial shape features of remote sensing images as claimed in claim 1, characterized in that it comprises the following steps: ①. First, the direction line is defined as a series of line segments passing through the central pixel. Their length and direction are different. The length is determined by the spectral homogeneity measure and threshold between adjacent pixels. The distance between adjacent direction lines is The angles of are set to equal radians; ②. The extension of the direction line starts from a central pixel and extends in two opposite directions at the same time. The extension condition of the direction line is: the homogeneity threshold of adjacent pixels and the length limit of the direction line are met, and each direction line follows the above Conditions are expanded and extended, and if one of the conditions is not true, the expansion of the direction line is terminated; ③. Track and obtain all direction lines of the central pixel, calculate the length of all direction lines, and select from two length calculation formulas according to different calculation requirements: city-block distance and Euclidean distance; ④. Obtain the lengths of all direction lines surrounding the central pixel, arrange the series of length values in clockwise order to form a histogram of direction lines of the pixel, and extract the space of the pixel according to the distribution of the histogram Shape features, using the following six feature measures: length (length), width (width), pixel shape index (pixel shape index), length-width ratio (length-width ratio), weighted mean (weighted mean), variance (variance ); ⑤ Traversing the entire image, calculating the direction line histogram and corresponding statistical measures of each pixel; ⑥. Combine the spectral information of the original image and the extracted spatial shape features for classification, and use different methods to normalize the spectral information and spatial information; ⑦. Input the mixed features into the classifier. The following classifiers are available for users to choose: minimum distance classifier (MDC), maximum likelihood classifier (MLC), multi-layer perceptron network (MLP), radial basis neural network (RBF), Probabilistic Neural Network (PNN) and Support Vector Machine (SVM), users can choose the most suitable classifier according to different requirements; ⑧. Set up and train the classifier, and then input spectral and spatial mixed features to classify carefully to get the final classification result. 3. The method for extracting and classifying spatial shape features of remote sensing images according to claim 1 or 2, characterized in that: the number of direction lines D available for selection is: 12, 16, 20, 24, and the default setting is D=20.

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