CN104636758B

CN104636758B - A kind of SAR image suitability Forecasting Methodology based on support vector regression

Info

Publication number: CN104636758B
Application number: CN201510075677.6A
Authority: CN
Inventors: 杨卫东; 王梓鉴; 曹治国; 邹腊梅; 桑农; 刘婧婷; 张洁; 刘晓
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2015-02-12
Filing date: 2015-02-12
Publication date: 2018-02-16
Anticipated expiration: 2035-02-12
Also published as: CN104636758A

Abstract

The invention discloses a kind of radar image suitability Forecasting Methodology based on support vector regression.Methods described includes：Study stage, extraction SAR image multidimensional characteristic form study collection；After study collection sample characteristics pretreatment, study collection L is classified as₁、L₂, then with study collection L₁Training Support Vector Machines, and L is collected to study with obtained SVM models₂Classified, the fitting percentage of each sample is calculated according to the distance between classification accuracy rate, sample characteristics and class heart；Afterwards suitability anticipation function model is obtained using study collection feature and its corresponding fitting percentage, fitting recurrence；Forecast period, to SAR image to be assessed, extraction character pair is as test sample data, input adaptation anticipation function model after data prediction, calculates the fitting percentage of the image.The present invention is according to the intensity and texture and structural characteristic of SAR image, it is established that the functional relation between SAR image fitting percentage and characteristic information, the matching performance of this method energy accurate evaluation SAR image by experimental verification.

Description

SAR image adaptability prediction method based on support vector regression

Technical Field

The invention belongs to the technical field of machine learning, pattern recognition and template matching, and particularly relates to a Synthetic Aperture Radar (SAR) image suitability prediction method based on support vector regression.

Background

The selection of the SAR scene matching sub-area is a core technology of scene matching, and mainly analyzes, evaluates and predicts the matching positioning performance (namely adaptability) of the SAR scene matching area so as to determine whether the selected matching sub-area is suitable for matching. So far, no mature scheme exists for selecting the matching region, most tasks are manually completed, scientific analysis is difficult to perform generally, and the requirement of practical application is difficult to meet by manually estimating the adaptation performance of the selected matching sub-region. And so far, there is no method for making quantitative and probabilistic predictions of matching region selection.

In the selection of the matching sub-area, scholars at home and abroad carry out a great deal of research, and the main method provided is to select the scene matching sub-area by using the image description characteristic parameters such as similarity, correlation length, gray variance, cross-correlation peak characteristic, information entropy, texture energy ratio, multi-resolution self-similarity measure and the like of the scene matching sub-area. However, the methods only consider the influence of a single factor on the matching performance, and fix other indexes in the experiment, and the relevance of the factors is not considered, so that the scene matching subregion selection criterion has low adaptability and poor anti-interference performance.

In the prior published literature, methods for prediction of the suitability of SAR images have not yet formed a mature solution and are applied in engineering practice, nor have quantitative, probabilistic prediction solutions be made for the suitability of SAR images.

Disclosure of Invention

The invention provides a SAR image adaptation performance prediction method based on a support vector regression aiming at the problem of SAR image adaptation performance evaluation in an SAR scene matching system, which specifically comprises the following steps:

(1) extracting light and shade target density and structure significant intensity characteristics of SAR training images, forming sample information corresponding to each SAR image by a characteristic set and given positive and negative category attributes, and forming a learning set by the sample information corresponding to all the SAR training images;

(2) preprocessing the characteristic data of the learning samples, namely removing the coupling relation of every two-dimensional characteristic of the sample set data in the learning set, and normalizing the characteristic after the coupling relation is removed according to the dimension;

(3) dividing the learning set after data preprocessing into a learning set L₁And a learning set L₂Using learning set L₁The sample training support vector machine in the method obtains SVM classifier models of positive/negative attribute samples and Gaussian distribution characteristics of positive/negative sample characteristics; using learning sets L₂The sample tests the performance of the classifier, the category attribute of each sample after being classified by the SVM classifier model is counted, and the learning set L is calculated according to the given positive and negative category attribute information₁Probability P that class center feature of middle positive/negative sample belongs to positive/negative sample₊、P_-；

(4) Using learning sets L₁Positive/negative sample class-heart feature and its corresponding probability of belonging to positive/negative sample, and L in learning set₁The Gaussian distribution characteristics of each dimension characteristic of the positive/negative samples are obtained, the mapping relation of the probability that each dimension characteristic of each sample of the learning set belongs to the positive/negative sample is obtained, and therefore L of each learning set is calculated₂Probability p of each dimension feature of sample belonging to positive/negative category_j ⁺、p_j ^-Then calculates the learning set L₂Adaptation rate p of each dimension characteristic of sample_{j_match}；

(5) Classification learning set L by controlling variable method and corresponding SVM model₂Is classified with accuracy P_(j,k)Calculating a learning set L₂Sensitivity of each dimensional feature to suitability;

(6) the learning set L obtained according to the step (4)₂Adaptation rate of each dimension characteristic and learning set L obtained in step (5)₂The sensitivity of each dimension characteristic of the sample is calculated to obtain a learning set L₂Sample adaptation rate; learning set L₂The sample adaptation rate and the characteristic information of each dimension form a learning set L₂New sample ofInformation;

(7) learning set L obtained in step (5)₂Fitting regression on new sample information to obtain an image suitability prediction function model;

(8) and (3) for the SAR image to be evaluated, extracting all dimension characteristic information of the SAR image according to the methods in the steps (1) and (2), preprocessing data, and predicting the adaptation rate of the SAR image to be evaluated through the sample adaptation prediction model in the step (7) by the processed data.

Compared with the prior art, the invention has the technical effects that:

in the prior art, a method for evaluating the matching performance of the SAR image does not form a mature solution, most tasks are manually completed and are generally difficult to scientifically analyze, and the matching performance of a selected matching sub-area is manually estimated, so that the requirement of practical application is difficult to meet. The method obtains a support vector regression model by training, establishes a functional relation between the adaptation rate and the characteristic information of the SAR image, predicts the adaptation performance of the SAR sub-area, and expands the field to probability prediction, so that the result is more accurate. The defect of artificially and subjectively evaluating the screening subarea is overcome, the stability is improved, and the quality of the screened SAR matching subarea is improved.

The invention provides a SAR image matching performance evaluation method based on a support vector regression machine, which comprises the steps of extracting features of an SAR image, training a support vector machine model, classifying and learning samples by using the support vector machine, obtaining the adaptation rate of each sample according to a classification result and the Gaussian distribution characteristics of the samples, training the support vector regression machine by using sample data with the adaptation rate, and fitting a regression prediction function model; and finally, evaluating the SAR image to be evaluated by using the function model to obtain the adaptation rate. According to the SAR image adaptive prediction method, multiple machine learning and mode recognition methods are comprehensively used according to SAR imaging characteristics and sub-area structural strength textural features, adaptive prediction of SAR images is achieved, a set of systematic SAR image adaptive prediction method is formed, the field of matching area selection is expanded to probability prediction, the method based on manual screening is effectively improved, accuracy of SAR matching sub-area screening is improved, and the method has great significance for research and development of SAR matching sub-area selection.

Drawings

FIG. 1 is a general flow chart of the SVM-based SAR image adaptation method of the present invention;

FIG. 2 is a partial SAR image in an embodiment of the invention;

FIG. 3 is a partial SAR image to be evaluated in the embodiment of the present invention;

FIG. 4 is a diagram of a predicted SAR image adaptation probability prediction result in an embodiment of the present invention;

fig. 5 is a graph of the predicted adaptation rate and the corresponding SAR image verification result in the embodiment of the present invention, wherein:

FIG. 5(a) shows the SAR image with poor matching performance and the predicted adaptation rate (p is more than or equal to 0 and less than 0.4);

FIG. 5(b) shows SAR images with moderate matching performance and the predicted adaptation rate (p is more than or equal to 0.4 and less than 0.7);

FIG. 5(c) shows the SAR image with strong matching performance and the predicted adaptation rate (p is more than or equal to 0.7 and less than or equal to 1).

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

The invention provides a SAR image suitability prediction method based on a support vector regression, the general flow of which is shown in figure 1, and the specific process of the method is as follows:

1 learning phase

1.1 data preparation phase

Extracting intensity such as uniformity, divergence, light and dark target density and structure significant intensity of the SAR image and multi-dimensional characteristics of a texture structure, calibrating a matching result of the SAR image and a real-time image to be used as category attributes, using the multi-dimensional characteristics and the category attributes as sample information corresponding to each SAR image, and forming a sample set by samples corresponding to all the SAR images. The invention selects two-dimensional characteristics of light and shade target density and structure obvious intensity and category attributes as sample information.

1.1.1 feature extraction

As shown in fig. 1, a partial SAR training sample image in an embodiment of the present invention is shown. Extracting multi-dimensional characteristic information such as divergence, uniformity, light and dark target density, structural significant strength and the like of each SAR image;

uniformity r:

where μ is the mean of the gray scale and σ is the standard deviation of the gray scale.

Divergence div:

wherein σ₁Respectively representing the standard deviation of the pixel set with the gray value smaller than the SAR image gray mean value mu. Accordingly, σ₂And the standard deviation of a pixel set with the gray value larger than the SAR image gray mean value mu is represented.

Bright and dark target density: and the dark target pixel points represent points with gray values larger than 2/3 of the SAR image full-image gray value, and the dark target pixel points represent points with gray values smaller than 1/3 of the SAR image full-image gray value.

The structure has obvious strength: and (3) performing binary edge extraction on the radar image, and removing noise of the connected domain mark with less number of pixels by using a connected domain marking method to mark the ratio of the total number of pixels to the image width, height and width mean value.

The invention finally selects the two-dimensional characteristics of light and dark target density and structure obvious strength through experiments.

1.1.2 Positive and negative Category attributes

Marking the category attribute of each sample according to the matching result of the SAR image and the real-time image, if the matching is suitable, marking the attribute as +1, and taking the sample as a sample in a matching area; if not, the sample is marked as-1, and is a sample of the non-adaptive area.

Two-dimensional characteristic information of light and shade target density and structure significant strength of the SAR image and positive and negative category attributes are extracted to serve as sample information corresponding to each image, and samples corresponding to all the SAR images form a sample set.

1.2 data preprocessing

Performing data preprocessing on the sample set characteristic data, namely removing the coupling relation of each two-dimensional characteristic of the sample set characteristic data, and normalizing according to the dimension characteristic;

1.2.1 decoupling relationships

By analyzing the distribution of the relationship between each two-dimensional feature in the sample space, it can be seen that the linear relationship between each two-dimensional feature is not obvious and can be considered as non-linearly related. We removed the coupling relationship between features using Schmidt orthogonalization. Here, the feature matrix Z ═ { Z ═ is used₁,Z₂,...,Z_mDenotes the m-dimensional features of the sample set.

If vector Z₁,Z₂,...,Z_mLinearly independent, reference vector b₀＝(1,0,...,0)^TLet us order

Then b is₁，b₂，…，b_mOrthogonal pairwise to form an orthogonal vector set, and unitizing the orthogonal vector set to obtain a matrix X, wherein X is { X ═ X₁，X₂，…，X_m}；

The process from matrix Z to matrix X is called Schmidt orthogonalization. After the original data is processed based on Schmidt orthogonalization, the coupling relation among all dimensional features of the sample can be removed, and the original data has the same reference vector, so that the influence of the change of a certain one-dimensional feature on the matching accuracy can be considered conveniently later.

1.2.2 normalization of features in each dimension

Assuming decoupling, the m-dimensional feature set of n samples is represented as:

in the above formula, x_ijRepresenting the jth dimension characteristic vector value of the ith sample, normalizing the samples according to dimensions, and setting the jth dimension characteristic x of the ith sample_ijNormalized to y_ijThen the mapping of x → y is as follows:

[y_min,y_max]to be provided withConstant normalized interval, x_max＝max(x_1j,x_2j,…x_nj)^T，x_min＝min(x_1j,x_2j,…x_nj)^T。

The normalized sample set feature matrix is

In the above formula, y_nmRepresenting the m-dimension characteristic vector value of the n-th sample after normalization, all data are in [0,1 ] after normalization by the invention]Within the range.

1.3 probability of each dimension feature belonging to a positive/negative sample

1.3.1 training support vector machine

Dividing the processed sample set data into a learning set L due to the difference between samples₁And a learning set L₂Using learning set L₁A sample training Support Vector Machine (SVM) performs parameter optimization on a Gaussian kernel function c and a penalty coefficient g in the SVM, selects the optimal parameters c and g, and trains an SVM model. Using learning sets L₂The sample tests the performance of the classifier, counts the class attributes after the classification of the SVM classifier model obtained by the classification, and obtains the classification accuracy of positive/negative classes by referring to the given positive and negative class attribute information, namely the learning set L₁The class center feature of the positive/negative sample belongs to the probability P of the positive/negative sample₊、P_-。

Set learning set L₂The number of samples with positive attribute is n₁The number of samples with negative attribute is n₂Learning set L₁After the trained SVM classifier is classified, k is₁A positive attribute sample is divided into negative samples with k₂Dividing the negative attribute sample into positive samples, defining a learning set L₁The feature vector of the positive sample centroid isLearning set L₁The class center of the negative sample is characterized in thatWherein x is_i ⁺、x_i ^-Are respectively a learning set L₁Features of the positive and negative samples, then the learning set L₁The class center feature of the positive/negative sample belongs to the probability P of the positive and negative samples₊、P_-Comprises the following steps:

1.3.2 L₂probability p that each dimension feature of a sample belongs to a positive sample_j ⁺

Set learning set L₁The mean value of the class centers of the positive attribute samples is characterized asCorresponding to a probability of belonging to a positive sample of P₊Wherein x is_i ⁺＝(x_i1,x_i2,…x_ij) For positive samples, the sample characteristics obey a Gaussian distribution x₊～N(μ⁺,σ⁺²). Assuming that the sample characteristics of the learning set and the probability of the learning set belonging to the positive sample are in a mapping relation, and obtaining L according to the Gaussian distribution of the positive sample₂Sample j-th dimension feature belongs to positive sample probability p_j ⁺Comprises the following steps:

wherein,is the mean of the j-th dimension features of the positive samples,variance of j-th dimension feature of positive sample, C₁、C₂Is a linear coefficient;

when x is mu_jWhen, the probability P that the positive class center belongs to the positive sample corresponds to₊；

When x is + ∞, the probability of belonging to a positive sample is highest at this time, and is considered to be 1 at this time;

when x is ═ infinity, the probability of belonging to a positive sample is the lowest at this time, and it is considered to be 0 at this time.

The function is expressed as x ═ mu_jIs segmented into

1.3.3 L₂Probability of each dimension feature of sample belonging to negative sample

The same theory is as 1.3.2, and a learning set L is set₁The negative attribute sample class center is characterized byCorresponding to a probability of belonging to a negative example of P_-Wherein x is_i ^-＝(x_i1,x_i2,…x_ij) For negative samples, the sample characteristics obey a Gaussian distribution x_-～N(μ^-,σ^-2). Assuming that the sample characteristics of the learning set and the probability of the learning set belonging to the negative sample are in a mapping relation, and obtaining the learning set L according to the Gaussian distribution of the negative sample₂Probability that j-th dimension feature of sample belongs to negative sampleIs composed of

Wherein,is the class center of the j-th dimension feature of the negative sample,variance of j-th dimension characteristic of negative sample, C₁'、C₂' is a linear coefficient;

when x is mu_-When, the probability P that the negative class center belongs to the negative sample corresponds to_-；

When x is ═ infinity, the probability of belonging to a negative sample is highest at this time, and it is considered to be 1 at this time;

when x ∞ is + ∞, the probability of belonging to a negative sample is lowest at this time, which is considered to be 0 at this time.

By applying the function toSegmented into the above formula

1.3.4 L₂Adaptation rate p of each dimension characteristic of sample_j：

L is obtained by this step₂Probability P that j-th dimension feature of sample belongs to positive/negative sample_j ⁺、P_j ^-And L is₂Adaptation rate p of each dimension characteristic of sample_{j_match}。

1.4 sensitivity of features in each dimension

Classification learning set L by controlling variable method and corresponding SVM model₂Is classified with accuracy P_(j,k)Calculating a learning set L₂Sensitivity of each dimension characteristic of the sample to adaptability;

considering that different sample characteristics have different effects on matching performance, we introduce the concept of "sensitivity", as follows:

changing the learning set L₂J-th dimension eigenvector x of sample matrix_jSimultaneously controlling the rest m-1 dimensional feature vectors to be unchanged when x is_j＝(k,k,k,…k)^TThe sample matrix is

k is changed from 0,0.1 and 0.2 … 1.0.0 in sequence, after the sample matrix is preprocessed, the previous SVM training model is used for classifying X', and the number of correctly classified samples is n_(j,k)If the total number of samples is n, the classification accuracy at this time is determinedRecording the maximum value P of the classification accuracy_jmaxAnd a minimum value P_jmin：

P_jmax＝max{P_(j,k)|k＝0,0.1,...,1.0}

P_jmin＝min{P_(j,k)|k＝0,0.1,...,1.0}

The value after the m dimensions are normalized is used as the sensitivity of the adaptation rate of the corresponding dimension characteristic, namely the contribution correct rate or weight of the final adaptation rate.

Wherein, W_jAnd the weight value corresponding to the j-th dimension characteristic vector.

1.5 calculating the Adaptation Rate of sample i

Learning set L obtained according to step 1.3₂Probability that each dimension feature vector of the sample belongs to positive/negative samples and learning set L obtained in step 1.4₂The sensitivity of each dimension characteristic vector of the sample is calculated to obtain a learning set L₂Adaptation rate per sample, and learning set L₂The adaptation rate of the sample and the characteristic information of each dimension form a new learning set L₂Sample information;

the resulting learning set L₂The matching accuracy of the middle sample is

a+b＝1

Where m denotes the dimension of the sample feature vector, W_jSensitivity, P, of sample matching performance to j-dimension feature vector_j ⁺Representing the probability, P, that a sample j-dimensional feature vector belongs to a positive sample_j ^-Representing the probability that the j-th dimension of the sample feature vector belongs to a negative sample when P_j ⁺→ 1 time, P_j ^-→ 0; when P is present_j ⁺Time → 0, P_j ^-→ 1; if a is 0.5 and b is 0.5, then

1.6 regression function model

New learning set L from step 1.5₂And fitting regression on the sample set information to obtain an image suitability prediction function model.

For the learning set samples, we utilize the learning set L₂Characteristic x of each sample_iAnd step 1.5 calculating the obtained adaptation rate P_iForm a new learning set L₂Sample, sample point attribute information may be represented as (x)_i，P_i). And (3) performing parameter optimization on the SVM parameters c and g by using the method in the step 1.3.1, and selecting the parameters c and g when the classification performance of the SVM classifier is optimal. The libsvm library function of professor Taiwan Chinen is used for assisting in establishing a sample adaptation rate prediction model, and a new learning set L obtained in the previous step is utilized₂Training SVM classifier model by sample to obtain learning set L₂The fitness prediction model of the sample f (x).

We use the Mean Squared Error (MSE) and the squared correlation coefficient (r)²) To verify the performance of the predictive model.

Wherein, y_iRepresents the input adaptation rate, f (x), of the training sample i_i) Denotes the adaptation rate of the prediction of the training sample i and l denotes the number of training samples.

2 prediction phase

And predicting the adaptation rate of the SAR subimage to be evaluated by using a regression function model.

As shown in fig. 3, for a part of the SAR image to be evaluated in the embodiment of the present invention, for the SAR image to be evaluated, according to the method in step 1.1 of the learning phase, the light and dark target density and the structural significant intensity feature of the SAR training image are extracted and extracted, then the data preprocessing is performed according to the method in step 1.2, and the processed data predicts the adaptation rate of the SAR image to be evaluated through the sample adaptation rate regression prediction model in step 1.6, that is:

P_{MatchProbability}＝F(x₁,x₂,…,x_m)

wherein, P_{MatchProbability}Denotes the adaptation rate, x, of the sample_mRepresenting the m-dimension features of the sample.

As shown in fig. 4, the result of predicting the adaptation rate of the SAR image to be evaluated in the embodiment of the present invention is shown, where samples 1 to 12 are SAR images with poor matching performance (p is greater than or equal to 0 and less than 0.4); the samples 13-20 are SAR images with moderate matching (p is more than or equal to 0.4 and less than 0.7); the samples 21-31 are SAR images with strong matching performance (p is more than or equal to 0.7 and less than or equal to 1). FIG. 5 shows the predicted adaptation rate and the corresponding SAR image verification result in the embodiment of the present invention, where FIG. 5(a) shows the SAR image with poor matching performance and the predicted adaptation rate (p is greater than or equal to 0 and less than 0.4), i.e., the adaptation rates of samples 1-12 and the corresponding SAR image verification result, FIG. 5(b) shows the SAR image with moderate matching performance and the predicted adaptation rate (p is greater than or equal to 0.4 and less than 0.7), i.e., the adaptation rates of samples 13-20 and the corresponding SAR image verification result, and FIG. 5(c) shows the SAR image with strong matching performance and the predicted adaptation rate (p is greater than or equal to 0.7 and less than or equal to 1), i.e., the adaptation rates of samples 21-31 and the corresponding SAR image verification result.

Claims

1. A SAR image adaptability prediction method based on support vector regression is characterized by comprising the following steps:

(2) preprocessing the characteristic data in the learning set, namely removing the coupling relation of each two-dimensional characteristic of the characteristic data in the learning set, and normalizing the characteristic with the coupling relation removed according to the dimension characteristic;

(4) Using learning sets L₁Class-heart feature of positive/negative sample and corresponding probability of belonging to positive/negative sample, and learning set L₁The Gaussian distribution characteristics of each dimension characteristic of the medium positive/negative samples are obtained, the mapping relation of the probability that each dimension characteristic of each sample of the learning set belongs to the positive/negative sample is obtained, and therefore L of each learning set is calculated₂Probability p of each dimension feature of sample belonging to positive/negative category_j ⁺、p_j ^-Then calculates the learning set L₂Adaptation rate p of each dimension characteristic in sample_{j_match}J represents the dimension serial number of the characteristic vector, the value of j is 1 to m, and m represents the dimension of the sample characteristic vector;

(5) classification learning set L by controlling variable method and corresponding SVM model₂Is classified with accuracy P_(j,k)Calculating a learning set L₂Sensitivity of each dimension feature to adaptability, wherein k represents the value of each element in a j-dimension feature vector, and k sequentially changes from 0,0.1,0.2 … 1.0.0;

(6) the learning set L obtained according to the step (4)₂Adaptation rate of each dimension characteristic and learning set L obtained in step (5)₂The sensitivity of each dimension characteristic of the sample is calculated to obtain a learning set L₂The adaptation rate of the sample; learning set L₂The sample adaptation rate and the characteristic information of each dimension form a learning set L₂New sample information;

(7) new learning set L obtained from step (6)₂The information on the samples is used to determine,fitting regression to obtain an image suitability prediction function model;

(8) and (3) for the SAR image to be evaluated, extracting the corresponding characteristics of the SAR image to be evaluated according to the methods in the steps (1) and (2), preprocessing data, and predicting the adaptation rate of the SAR image to be evaluated through the adaptability prediction model in the step (7) by the processed data.

2. The method of claim 1, wherein the step (2) of removing the coupling relation for each two-dimensional feature of the feature data in the learning set is specifically:

let the characteristic matrix Z ═ Z₁,Z₂,...,Z_mDenotes the m-dimensional features of the learning set, with the reference vector b₀＝(1,0,...,0)^TLet us order

...

Then b is₁，b₂，…，b_mForming orthogonal vector groups by pairwise orthogonality, and unitizing the orthogonal vector groups to obtain a matrix X, wherein X is { X1, X2, … and Xm }, and n is the total number of samples;

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mn>1</mn> </msub> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mn>2</mn> </msub> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <msub> <mi>X</mi> <mi>m</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mi>m</mi> </msub> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>b</mi> <mi>m</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>。

3. the method according to claim 1 or 2, wherein the normalization of the features after the coupling relationship is removed in the step (2) according to the dimensional features specifically comprises:

let the i j dimension of the sample be the feature x_ijNormalized to y_ijThen the mapping of x → y is as follows:

[y_min,y_max]for a set normalization interval, x_max＝max(x_1j,x_2j,…x_nj)^T，x_min＝min(x_1j,x_2j,…x_nj)^T；

The normalized sample set feature matrix is

Wherein, y_nmAnd representing the m-dimension characteristic vector value of the n-th sample after normalization.

4. The method according to claim 1 or 2, wherein the learning set L is calculated in the step (3)₁Probability P that class-center feature of positive/negative sample belongs to positive and negative sample₊、P_-The method specifically comprises the following steps:

set learning set L₂The number of samples with positive attribute is n₁The number of samples with negative attribute is n₂Learning set L₁After the trained SVM classifier is classified, k is₁A positive attribute sample is divided into negative samples with k₂Dividing the negative attribute sample into positive samples, defining a learning set L₁The class center of the positive sample is characterized in thatn represents the total number of samples, learning set L₁The class center of the negative sample is characterized in thatWherein x is_i ⁺、x_i ^-Are respectively a learning set L₁Features of the positive and negative samples, then the learning set L₁The class center feature of the positive/negative sample belongs to the probability P of the positive and negative samples₊、P_-Comprises the following steps:

5. the method according to claim 1 or 2, wherein the learning set L is obtained in the step (4) as follows₂Adaptation rate of each dimension characteristic of the sample:

(4.1)L₂probability p that each dimension feature of a sample belongs to a positive sample_j ⁺；

Is provided with L₁The mean value of the class centers of the positive attribute samples is characterized asCorresponding to a probability of belonging to a positive sample of P₊Wherein x is_i ⁺＝(x_i1,x_i2,…x_ij) For positive samples, the sample characteristics obey a Gaussian distribution x₊～N(μ⁺,σ⁺2) (ii) a Assuming that the sample characteristics of the learning set and the probability of the learning set belonging to the positive sample are in a mapping relation, and obtaining L according to the Gaussian distribution of the positive sample₂Sample j-th dimension feature belongs to positive sample probability p_j ⁺Comprises the following steps:

<mrow> <msup> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>+</mo> </msup> <mo>=</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> <mo>*</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>+</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mrow> <mo>+</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>+</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> </mrow>

when x is ═ infinity, the probability of belonging to a positive sample is lowest at this time, and it is considered to be 0 at this time;

the function is expressed as x ═ mu_jIs segmented into

<mrow> <msup> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>+</mo> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>2</mn> <msub> <mi>P</mi> <mo>+</mo> </msub> <mo>*</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>+</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>+</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mrow> <mo>+</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&le;</mo> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mo>*</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mo>+</mo> </msub> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>+</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>+</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mrow> <mo>+</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <msub> <mi>P</mi> <mo>+</mo> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&GreaterEqual;</mo> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

(4.2)L₂Probability of each dimension feature of sample belonging to negative sample

Is provided with L₁The negative attribute sample class center is characterized byCorresponding to a probability of belonging to a negative example of P_-Wherein x is_i ^-＝(x_i1,x_i2,…x_ij) For negative samples, the sample characteristics obey a Gaussian distribution x_-～N(μ^-,σ^_-2) (ii) a Assuming that the sample characteristics of the learning set and the probability of the learning set belonging to the negative sample are in a mapping relation, and obtaining L according to the Gaussian distribution of the negative sample₂Probability that j-th dimension feature of sample belongs to negative sampleComprises the following steps:

<mrow> <msubsup> <mi>p</mi> <mi>j</mi> <mo>-</mo> </msubsup> <mo>=</mo> <msup> <msub> <mi>C</mi> <mn>1</mn> </msub> <mo>&prime;</mo> </msup> <mo>*</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>-</mo> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>-</mo> </msubsup> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> <mi>d</mi> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>&prime;</mo> </msup> </mrow>

wherein,is the mean of the j-th dimension features of the negative samples,variance of j-th dimension characteristic of negative sample, C₁'、C₂' is a linear coefficient;

when x is + ∞, the probability of belonging to the negative sample is the lowest, and the probability is considered to be 0;

by applying the function toSegmented into the above formula

<mrow> <msup> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>-</mo> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>2</mn> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mo>-</mo> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>P</mi> <mo>-</mo> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&le;</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <msub> <mi>P</mi> <mo>-</mo> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mo>-</mo> <mi>&infin;</mi> </mrow> <mi>x</mi> </msubsup> <mi>exp</mi> <mrow> <mo>(</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>-</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msubsup> <mi>&sigma;</mi> <mi>j</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&GreaterEqual;</mo> <msubsup> <mi>&mu;</mi> <mi>j</mi> <mo>-</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>

(4.3)L₂Adaptation rate p of each dimension characteristic of sample_j：

L is obtained by this step₂Probability P that j-th dimension feature of sample belongs to positive/negative sample_j ⁺、P_j ^-And L₂Adaptation rate P of each dimension characteristic of sample_{j_match}。

6. The method according to claim 1 or 2, wherein the step (5) is performed by calculating the learning set L as follows₂Sensitivity of each dimensional feature of the sample to suitability:

changing the learning set L₂J-th dimension eigenvector x of sample matrix_jSimultaneously controlling the rest m-1 dimensional feature vectors to be unchanged when x is_j＝(k,k,k,…k)^TK varies sequentially from 0,0.1,0.2 … 1.0.0 with a sample matrix of

<mrow> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>11</mn> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mn>12</mn> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mi>k</mi> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mi>m</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>21</mn> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mn>22</mn> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mi>k</mi> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mi>k</mi> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

After preprocessing the sample matrix, classifying X' by using the previous SVM training model to obtain n samples with correct classification number_(j,k)If the total number of samples is n, the classification accuracy at this time is determinedRecording the maximum value P of the classification accuracy_jmaxAnd a minimum value P_jmin：

P_jmax＝max{P_(j,k)|k＝0,0.1,...,1.0}

P_jmin＝min{P_(j,k)|k＝0,0.1,...,1.0}

The values after the m dimensionalities are normalized are used as the sensitivity of the adaptation rate of the corresponding dimensionality characteristics;

<mrow> <msub> <mi>W</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>P</mi> <mrow> <mi>j</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>

<mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>W</mi> <mi>j</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow>

wherein, W_jAnd adapting the sensitivity of the rate for the j-th dimension of the feature vector.

7. A method according to claim 1 or 2, characterised in thatThe step (6) obtains the learning set L as follows₂Adaptation rate P of the ith sample_i：

<mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>a</mi> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>W</mi> <msup> <mi>j</mi> <mo>*</mo> </msup> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>+</mo> </msup> <mo>-</mo> <msup> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>-</mo> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> </mrow>

a+b＝1

Where m denotes the dimension of the sample feature, W_jSensitivity, P, representing adaptation rate of j-th dimension feature vector_j ⁺Represents L₂Probability that the j-th feature of a sample belongs to a positive sample, P_j ^-Represents L₂The probability that the j-th dimension feature of a sample belongs to a negative sample,

when P is present_j ⁺→ 1 time, P_j ^-→0，P_i→1；

When P is present_j ⁺Time → 0, P_j ^-→1，P_i→0；

If a is 0.5 and b is 0.5, then

<mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0.5</mn> <mo>*</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>m</mi> </munderover> <msub> <mi>W</mi> <msup> <mi>j</mi> <mo>*</mo> </msup> </msub> <mrow> <mo>(</mo> <msup> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>+</mo> </msup> <mo>-</mo> <msup> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>-</mo> </msup> <mo>)</mo> </mrow> <mo>+</mo> <mn>0.5.</mn> </mrow>

8. The method of claim 1 or 2, wherein the features extracted in step (1) are:

bright and dark target density: the proportion of light and dark target pixel points is that the light target pixel points represent points with gray values larger than 2/3 of the SAR image full-image gray value, and the dark target pixel points represent points with gray values smaller than 1/3 of the SAR image full-image gray value;