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

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

Technical field

The invention belongs to machine learning, pattern-recognition, matching template technical field, and in particular to one kind is based on supporting vector Synthetic aperture radar (Synthetic Aperture Radar, SAR) image suitability Forecasting Methodology of recurrence, this method are being examined On the basis of considering SAR imaging characteristics and strength structure textural characteristics, the Adapter Property prediction to SAR image is realized, is passed through The Adapter Property prediction result accurate and effective that this method obtains.

Background technology

The selection of SAR scene matching aided navigation sub-districts is the core technology of scene matching aided navigation, mainly to SAR scene matching aided navigations region Analyzed, assessed, predicted with positioning performance (i.e. suitability), so that it is determined that selected matching sub-district is if appropriate for matching.At present Untill, the selection of Matching band there is no ripe scheme, and most of task is generally difficult to point of carry out science by being accomplished manually Analysis, the Adapter Property of the artificial selected matching sub-district of estimation, it is difficult to meet the needs of practical application.And so far, do not have also A kind of chosen to Matching band makes quantitative, probabilistic forecasting method.

In the selection of matching sub-district, domestic and foreign scholars have carried out substantial amounts of research, and the main method of proposition has with scape As the similitude of matching sub-district, correlation length, gray variance, cross-correlation peak value feature, comentropy, texture energy ratio and more points The characteristic parameter of the iamge descriptions such as resolution self-similar selects scene matching aided navigation sub-district.But these methods only consider it is single because Influence of the element to matching performance and other indexs are fixed in experiment, lack the correlation for considering these factors, result in scape Not strong as matching sub-district selection criterion adaptability, anti-interference is poor.

In existing disclosed document, the solution party of maturation is not yet formed on the foreseeable method of SAR image suitability Case, and applied in engineering practice, quantitative, probabilistic forecasting scheme is not also made to SAR image suitability.

The content of the invention

The present invention is directed in SAR scene matching aided navigation systems to SAR image Adapter Property evaluation problem, proposes that one kind is based on supporting The SAR image Adapter Property Forecasting Methodology of vector regression, is specifically included：

(1) the light and shade target density and the notable strength characteristic of structure of SAR training images are extracted, by characteristic set and given Positive and negative category attribute forms sample information corresponding to each SAR image, sample information structure science corresponding to all SAR training images Practise collection；

(2) learning sample characteristic is pre-processed, i.e., every two dimensional feature for concentrating sample set data to study is gone Except coupled relation, and pair and to remove coupled relation after feature by dimension normalization；

(3) the study collection after data prediction is divided into study collection L₁Collect L with study₂, collect L using study₁In sample instruction Practice SVMs, obtain the SVM classifier model of positive/negative two generic attributes sample and the Gauss of positive/negative two classes sample characteristics Distribution character；Collect L with study₂Test sample classifier performance, after counting each sample by SVM classifier category of model Category attribute, according to given positive and negative category attribute information, calculate study collection L₁In positive/negative sample class heart feature belong to positive/negative The probability P of sample₊、P_-；

(4) study collection L is utilized₁Positive/negative sample class heart feature and probability, the Yi Jixue for belonging to positive/negative sample corresponding to it Practise and concentrate L₁The Gaussian distribution feature of the positive/negative each dimensional characteristics of two classes sample, obtain study and collect each sample per dimensional feature category In the mapping relations of positive/negative sample probability, each study collection L is thus calculated₂The each dimensional characteristics of sample belong to positive/negative classification Probability p_j ⁺、p_j ^-, then calculate study collection L₂The fitting percentage p of each dimensional characteristics of sample_{j_match}；

(5) control variate method and corresponding SVM categories of model study collection L are passed through₂Classification accuracy rate P_(j,k), calculate study Collect L₂Sensitivity of each dimensional characteristics to suitability；

(6) the study collection L obtained according to step (4)₂The study collection L that each dimensional characteristics fitting percentage and step (5) obtain₂ The sensitivity of each dimensional characteristics of sample, study collection L is calculated₂Sample fitting percentage；Study collection L₂Sample fitting percentage is each with its Dimensional characteristics information structure study collection L₂New sample information；

(7) the study collection L obtained by step (5)₂New sample information, fitting recurrence obtain image suitability anticipation function Model；

(8) for SAR image to be assessed, according to the method for step (1) (2), each dimensional characteristics for extracting SAR image are believed Cease and carry out data prediction, the data after processing are predicted to be assessed by the sample suitability forecast model of step (7) The fitting percentage of SAR image.

Compared with prior art, technique effect of the invention is embodied in：

In the prior art, the method assessed on SAR image matching performance not yet forms the solution of maturation, big portion Point task is generally difficult to the analysis of carry out science by being accomplished manually, the matching performance of the artificial selected matching sub-district of estimation, It is difficult to meets the needs of practical application.The present invention is supported vector regression model using training, it is established that SAR image is fitted With the functional relation between rate and characteristic information, SAR sub-district Adapter Properties are predicted, and it is pre- that field is extended into probability Survey so that result is more accurate.The defects of human subjective assesses screening sub-district is overcome, stability is improved, improves screening SAR matching sub-district quality.

The invention provides a kind of SAR image matching performance appraisal procedure based on support vector regression, this method pair SAR image extracts feature, trains SVM model, then with SVM classification learning sample, according to classification results, sample This Gaussian distribution feature obtains the fitting percentage of each sample, is returned afterwards using the sample data training support vector with fitting percentage Machine, fit regression forecasting function model；Finally, SAR image to be assessed is assessed using function model, obtains fitting percentage.This hair It is bright that a variety of machine learning and mode identification method have been used according to SAR imaging characteristics and sub-district structural strength textural characteristics, synthesis, The suitability prediction to SAR image is realized, forms the SAR image suitability Forecasting Methodology of set of system, and Matching band is selected The field taken is extended to probabilistic forecasting, improve efficiently the method based on artificial screening, improves screening SAR matching sub-districts Accuracy, the research and development chosen to SAR matching sub-districts are significant.

Brief description of the drawings

Fig. 1 is the overview flow chart of the SAR image suitability method of the invention based on SVM；

Fig. 2 is part SAR image in the embodiment of the present invention；

Fig. 3 is part SAR image to be assessed in the embodiment of the present invention；

Fig. 4 is that the SAR image predicted in the embodiment of the present invention is adapted to probabilistic forecasting result figure；

The fitting percentage predicted in Fig. 5 embodiment of the present invention and corresponding SAR image the result figure, wherein：

Fig. 5 (a) is the SAR image of matching performance difference and the fitting percentage (0≤p ＜ 0.4) of prediction；

Fig. 5 (b) is the fitting percentage (0.4≤p ＜ 0.7) of the moderate SAR image of matching performance and prediction；

Fig. 5 (c) is the fitting percentage (0.7≤p≤1) of the strong SAR image of matching performance and prediction.

Embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below Conflict can is not formed each other to be mutually combined.

The invention provides a kind of SAR image suitability Forecasting Methodology based on support vector regression, its overall procedure As shown in figure 1, this method detailed process is：

1 study stage

1.1 data preparation stage

The notable intensity equal strength of the uniformity, divergence, light and shade target density, structure and the texture structure for extracting SAR image are more Dimensional feature, and demarcation SAR image are used as each with real-time figure matching result as category attribute, multidimensional characteristic and category attribute Sample information corresponding to SAR image, sample corresponding to all SAR images form sample set.The present invention chooses light and shade target density With this two dimensional feature of the notable intensity of structure and category attribute as sample information.

1.1.1 feature extraction

As shown in figure 1, it is part SAR training sample images in the embodiment of the present invention.The divergence of every width SAR image is extracted, The multidimensional characteristic information such as the uniformity, the notable intensity of light and shade target density, structure；

Uniformity r：

Wherein, wherein μ is gray average, and σ is gray standard deviation.

Divergence div：

Wherein, σ₁The standard deviation of pixel set of the gray value less than SAR image gray average μ is represented respectively.Correspondingly, σ₂ Represent the standard deviation of pixel set of the gray value more than SAR image gray average μ.

Light and shade target density：Ratio shared by light and shade target pixel points, bright target pixel points represent that gray value is schemed more than SAR As the point of full figure gray value 2/3, dark target pixel points represent that gray value is less than the point of SAR image full figure gray value 1/3.

The notable intensity of structure：Binary edge extraction is carried out to radar image, and utilizes connected component labeling method, removes few picture After the noise of number connected component labeling, mark sum of all pixels and the ratio of the wide wide average of height of image.

The present invention last chooses light and shade target density and the notable intensity of structure this two dimensional feature by testing.

1.1.2 positive and negative category attribute

According to SAR image and the category attribute of each sample of result queue of figure matching in real time, if being adapted to matching, mark For+1, to be adapted to area's sample；If being not suitable for matching, -1 is labeled as, for non-adaptation area's sample.

This bidimensional characteristic information of the notable intensity of light and shade target density, structure and positive and negative category attribute for extracting SAR image are made For sample information corresponding to each image, sample corresponding to all SAR images forms sample set.

1.2 data prediction

Data prediction is carried out to sample set characteristic, i.e., coupling is removed to every two dimensional feature of sample set characteristic Relation, and normalized by dimensional characteristics；

1.2.1 uncoupling relation

Analyze the relation distribution between every two dimensional feature of sample space, it can be seen that the linear relationship between every two dimensional feature is not Substantially, it is believed that be nonlinear correlation.We use Schmidt orthogonalization process, remove the coupled relation between feature.This In use eigenmatrix Z={ Z₁,Z₂,...,Z_mRepresent sample set m dimensional features.

If vector Z₁,Z₂,...,Z_mLinear independence, reference vector b₀=(1,0 ..., 0)^T, order

Then b₁, b₂..., b_mPairwise orthogonal, turn into Orthogonal Vectors, by its unitization matrix X, wherein X={ X₁, X₂..., X_m}；

It is referred to as then Schmidt orthogonalizations to matrix X process from matrix Z.Initial data is being based on Schmidt just by above-mentioned After the processing of friendshipization, the coupled relation between each dimensional feature of sample can be removed, and there is identical reference vector, after being easy to Face is on considering influence of the change of certain one-dimensional characteristic to matching accuracy.

1.2.2 each dimensional characteristics normalization

If after uncoupling, the m dimensional feature set representations of n sample are：

In above formula, x_ijThe jth dimensional feature vector value of i-th of sample is represented, sample is normalized by dimension, if sample i jth Dimensional feature x_ijIt is y after normalization_ij, then x → y mapping relations are as follows：

[y_min,y_max] for setting normalization section, x_max=max (x_1j,x_2j,…x_nj)^T, x_min=min (x_1j,x_2j,… x_nj)^T。

Then the sample set eigenmatrix after normalization is

In above formula, y_nmThe m dimensional feature vector values of n-th of sample after normalizing are represented, after present invention normalization, are owned Data are in the range of [0,1].

1.3 each dimensional characteristics belong to the probability of positive/negative sample

1.3.1 SVM is trained

Due to the otherness between sample, the sample set data after processing are divided into study collection L₁Collect L with study₂, use Practise collection L₁Sample training SVMs (Support Vector Machine, SVM), to gaussian kernel function c and punishment in SVM Coefficient g carries out parameter optimization, chooses optimal parameter c and g, trains SVM models.Collect L with study₂Test sample grader Can, statistics is by the category attribute after obtained SVM classifier category of model, with reference to given positive and negative category attribute information, The classification accuracy rate of positive/negative two class is obtained, as study collection L₁Positive/negative sample class heart feature belongs to positive/negative sample probability P₊、P_-。

If study collection L₂Quantity with positive attribute sample is n₁, the quantity of the negative attribute sample of band is n₂, collect L through study₁Training SVM classifier classification after, have k₁Individual positive attribute sample is divided into negative sample, there is k₂Individual negative attribute sample is divided into positive sample, fixed Justice study collection L₁The characteristic vector of the positive sample class heart isStudy collection L₁The feature of the negative sample class heart isWherein, x_i ⁺、x_i ^-Respectively study collection L₁The feature of positive negative sample, then study collect L₁Positive/negative sample class heart feature Belong to positive and negative sample probability P₊、P_-For：

1.3.2 L₂Sample belongs to the Probability p of positive sample per one-dimensional characteristic_j ⁺

If study collection L₁The characteristics of mean of the positive attribute sample class heart isThe corresponding positive sample probability that belongs to is P₊, wherein x_i ⁺=(x_i1,x_i2,…x_ij) it is positive sample, sample characteristics Gaussian distributed x₊~N (μ⁺,σ⁺²).It is assumed that study collection It is in mapping relations that sample characteristics belong to the probability of positive sample with it, according to positive sample Gaussian Profile, can obtain L₂Sample jth dimensional feature Belong to positive sample Probability p_j ⁺For：

Wherein,For the average of positive sample jth dimensional feature,For the side of positive sample jth dimensional feature Difference, C₁、C₂For linear coefficient；

As x=μ_jWhen, corresponding is the probability P that the positive class class heart belongs to positive sample₊；

As x=+ ∞, now belong to the probability highest of positive sample, it is believed that be now 1；

As x=- ∞, the probability for now belonging to positive sample is minimum, it is believed that is now 0.

By this function with x=μ_jSegmentation, brings above formula into and obtains

1.3.3 L₂Sample belongs to the probability of negative sample per one-dimensional characteristic

Similarly such as 1.3.2, if study collection L₁The feature of the negative attribute sample class heart isIt is corresponding to belong to negative sample This probability is P_-, wherein x_i ^-=(x_i1,x_i2,…x_ij) it is negative sample, sample characteristics Gaussian distributed x_-~N (μ^-,σ^-2).It is false It is in mapping relations that fixed study collection sample characteristics belong to the probability of negative sample with it, according to negative sample Gaussian Profile, can be learnt Collect L₂Sample jth dimensional feature belongs to the probability of negative sampleFor

Wherein,For the class heart of negative sample jth dimensional feature,For negative sample jth dimensional feature Variance, C₁'、C₂' it is linear coefficient；

As x=μ_-When, corresponding is the probability P that the negative class class heart belongs to negative sample_-；

As x=- ∞, now belong to the probability highest of negative sample, it is believed that be now 1；

As x=+ ∞, the probability for now belonging to negative sample is minimum, it is believed that is now 0.

By this function withSegmentation, brings above formula into

1.3.4 L₂Fitting percentage p of the sample per one-dimensional characteristic_j：

L is obtained by this step₂Sample jth dimensional feature belongs to the probability P of positive/negative sample_j ⁺、P_j ^-, and L₂Sample is each The fitting percentage p of dimensional feature_{j_match}。

The sensitivity of 1.4 each dimensional characteristics

Pass through control variate method and corresponding SVM categories of model study collection L₂Classification accuracy rate P_(j,k), calculate study collection L₂Sensitivity of each dimensional characteristics of sample to suitability；

Consider that effect of the different sample characteristics to matching performance is different, we introduce the concept of " sensitivity ", specific as follows：

Change study collection L₂Sample matrix jth dimensional feature vector x_j, while control remaining m-1 dimensional feature vector constant, work as x_j =(k, k, k ... k)^T, its sample matrix is

1.0 changes that k is successively from 0,0.1,0.2 ..., after sample matrix is pre-processed, with SVM training patterns before to X' points Class, it is n to obtain correct classification samples number_(j,k)If total sample number is n, then classification accuracy rate now Record the maximum P of its classification accuracy rate_jmaxWith 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 }

Numerical value after m dimension normalization, as the sensitivity of its corresponding dimensional characteristics fitting percentage, i.e., final fitting percentage Contribution accuracy or weights.

Wherein, W_jFor weights corresponding to jth dimensional feature vector.

1.5 calculate sample i fitting percentage

The study collection L obtained according to step 1.3₂The each dimensional characteristics vector of sample belongs to the probability and step of positive/negative sample Rapid 1.4 obtained study collection L₂The sensitivity of each dimensional characteristics vector of sample, is calculated study collection L₂The adaptation of each sample Rate, and learn collection L₂The fitting percentage of sample and the new study collection L of its each dimensional characteristics information structure₂Sample information；

The study collection L then finally given₂The matching accuracy of middle sample is

A+b=1

Wherein, m represents the dimension of sampling feature vectors, W_jRepresent sample matches performance to the sensitive of jth dimensional feature vector Degree, P_j ⁺Represent that sample j dimensional feature vectors belong to the probability of positive sample, P_j ^-Represent that sample jth dimensional feature vector belongs to negative sample Probability, work as P_j ⁺When → 1, P_j ^-→0；Work as P_j ⁺When → 0, P_j ^-→1；A=0.5, b=0.5 are can be calculated, then

1.6 regression function models

The new study collection L obtained by step 1.5₂Sample set information, fitting recurrence obtain image suitability anticipation function Model.

Collect sample for study, we utilize study collection L₂The feature x of each sample_iThe adaptation being calculated with step 1.5 Rate P_iForm new study collection L₂Sample, sample point attribute information can be expressed as (x_i, P_i).Use step 1.3.1 method pair SVM parameters c and g carry out parameter optimization, choose parameter c and g when making SVM classifier classification performance optimal.Used here as Taiwan The libsvm built-in functions of Lin Zhiren professors aid in realizing the foundation of sample fitting percentage forecast model, new using what is be previously obtained Study collection L₂Sample training SVM classifier model, you can to obtain study collection L₂The suitability forecast model F (x) of sample.

We use Mean Square Error (mean squared error, MSE) and squared correlation coefficient (squared Correlation coefficient, r²) verify the performance of forecast model.

Wherein, y_iRepresent training sample i input adaptation rate, f (x_i) fitting percentage that training sample i is predicted is represented, l is represented Training sample number.

2 forecast periods

Utilize regression function model prediction SAR subgraphs fitting percentage to be assessed.

As shown in figure 3, it is part SAR image to be assessed in the embodiment of the present invention, for SAR image to be assessed, according to The method for practising stage etch 1.1, the light and shade target density and the notable strength characteristic of structure of extraction extraction SAR training images, then press Data prediction, the sample fitting percentage regressive prediction model that the data after processing pass through step 1.6 are carried out according to the method for step 1.2 The fitting percentage of SAR image to be assessed is predicted, i.e.,：

P_{MatchProbability}=F (x₁,x₂,…,x_m)

Wherein, P_{MatchProbability}Represent the fitting percentage of sample, x_mRepresent the m dimensional features of sample.

As shown in figure 4, it is the fitting percentage prediction result of SAR image to be assessed in the embodiment of the present invention, wherein sample 1~12 For matching performance poor (0≤p ＜ 0.4) SAR image；Sample 13~20 is schemed for the SAR of matching moderate (0.4≤p ＜ 0.7) Picture；Sample 21~31 is the SAR image of matching strong (0.7≤p≤1).Fig. 5 be in the embodiment of the present invention fitting percentage predicted with Corresponding SAR image the result, wherein Fig. 5 (a) are the fitting percentage (0≤p ＜ 0.4) of the poor SAR image of matching performance and prediction, That is the fitting percentage of sample 1~12 and corresponding SAR image the result, Fig. 5 (b) are the moderate SAR image of matching performance and prediction Fitting percentage (0.4≤p ＜ 0.7), i.e. the fitting percentage of sample 13~20 and corresponding SAR image the result, Fig. 5 (c) is matching The strong SAR image of performance and the fitting percentage (0.7≤p≤1) of prediction, the i.e. fitting percentage of sample 21~31 are tested with corresponding SAR image Demonstrate,prove result.

Claims

1. a kind of SAR image suitability Forecasting Methodology based on support vector regression, it is characterised in that methods described includes：

(1) the light and shade target density and the notable strength characteristic of structure of SAR training images are extracted, by characteristic set and is given positive and negative Category attribute forms sample information corresponding to each SAR image, and sample information corresponding to all SAR training images forms study Collection；

(2) characteristic for learning to concentrate is pre-processed, i.e., every two dimensional feature for the characteristic concentrated to study removes Coupled relation, and the feature after removal coupled relation is normalized by dimensional characteristics；

(3) the study collection after data prediction is divided into study collection L₁Collect L with study₂, collect L using study₁In sample training branch Vector machine is held, obtains the SVM classifier model of positive/negative two generic attributes sample and the Gaussian Profile of positive/negative two classes sample characteristics Characteristic；Collect L with study₂Test sample classifier performance, count each sample and pass through the classification after SVM classifier category of model Attribute, according to given positive and negative category attribute information, calculate study collection L₁In positive/negative sample class heart feature belong to positive/negative sample Probability P₊、P_-；

(4) study collection L is utilized₁Positive/negative sample class heart feature and the probability and study collection L for belonging to positive/negative sample corresponding to it₁ In the positive/negative each dimensional characteristics of two classes sample Gaussian distribution feature, obtain study and collect each sample belonging to positive/negative per dimensional feature The mapping relations of sample probability, thus calculate each study collection L₂The each dimensional characteristics of sample belong to the Probability p of positive/negative classification_j ⁺、p_j ^-, then calculate study collection L₂The fitting percentage p of each dimensional characteristics in sample_{j_match}, wherein, j represents the dimension of characteristic vector Number sequence number, its value are 1 to m, and m represents the dimension of sampling feature vectors；

(5) control variate method and corresponding SVM categories of model study collection L are passed through₂Classification accuracy rate P_(j,k), calculate study collection L₂ Sensitivity of each dimensional characteristics to suitability, wherein, k represents the value of each element in jth dimensional feature vector, k successively from 0, 0.1,0.2 ... 1.0 change；

(6) the study collection L obtained according to step (4)₂The study collection L that each dimensional characteristics fitting percentage and step (5) obtain₂Sample The sensitivity of each dimensional characteristics, study collection L is calculated₂The fitting percentage of sample；Study collection L₂Sample fitting percentage and its each dimension Spend characteristic information and form study collection L₂New sample information；

(7) the new study collection L obtained by step (6)₂Sample information, fitting recurrence obtain image suitability anticipation function model；

(8) for SAR image to be assessed, according to the method for step (1) (2), extract feature corresponding to SAR image to be assessed and Data prediction is carried out, the data after processing predict the suitable of SAR image to be assessed by the suitability forecast model of step (7) With rate.

2. the method as described in claim 1, it is characterised in that in the step (2) to study concentrate characteristic it is every Two dimensional features remove coupled relation：

If eigenmatrix Z={ Z₁,Z₂,...,Z_mRepresent the m dimensional features that study collects, reference vector b₀=(1,0 ..., 0)^T, Order

...

Then b₁, b₂..., b_mPairwise orthogonal, turn into Orthogonal Vectors, by its unitization matrix X, wherein X=X1, X2 ..., Xm }, n is total sample number；

<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. method as claimed in claim 1 or 2, it is characterised in that to the feature after removal coupled relation in the step (2) It is specially by dimensional characteristics normalization：

If sample i jth dimensional features x_ijIt is y after normalization_ij, then x → y mapping relations are as follows：

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

Then the sample set eigenmatrix after normalization is

Wherein, y_nmRepresent the m dimensional feature vector values of n-th of sample after normalizing.

4. method as claimed in claim 1 or 2, it is characterised in that numerology practises collection L in the step (3)₁Positive/negative sample class Heart feature belongs to the probability P of positive negative sample₊、P_-, it is specially：

If study collection L₂Quantity with positive attribute sample is n₁, the quantity of the negative attribute sample of band is n₂, collect L through study₁The SVM of training After grader classification, there is k₁Individual positive attribute sample is divided into negative sample, there is k₂Individual negative attribute sample is divided into positive sample, orismology Practise collection L₁The feature of the positive sample class heart isN represents total sample number, study collection L₁The feature of the negative sample class heart isWherein, x_i ⁺、x_i ^-Respectively study collection L₁The feature of positive negative sample, then study collect L₁Positive/negative sample class heart feature Belong to positive and negative sample probability P₊、P_-For：

5. method as claimed in claim 1 or 2, it is characterised in that obtain study collection in the step (4) as follows L₂The fitting percentage of each dimensional characteristics of sample：

(4.1)L₂Sample belongs to the Probability p of positive sample per one-dimensional characteristic_j ⁺；

If L₁The characteristics of mean of the positive attribute sample class heart isThe corresponding positive sample probability that belongs to is P₊, wherein x_i ⁺= (x_i1,x_i2,…x_ij) it is positive sample, sample characteristics Gaussian distributed x₊~N (μ⁺,σ⁺2)；It is assumed that study collects sample characteristics and its The probability for belonging to positive sample is in mapping relations, according to positive sample Gaussian Profile, can obtain L₂It is general that sample jth dimensional feature belongs to positive sample Rate p_j ⁺For：

<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>

Wherein,For the average of positive sample jth dimensional feature,For the variance of positive sample jth dimensional feature, C₁、C₂For linear coefficient；

As x=- ∞, the probability for now belonging to positive sample is minimum, it is believed that is now 0；

By this function with x=μ_jSegmentation, brings above formula into and obtains

<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)L₂Sample belongs to the probability of negative sample per one-dimensional characteristic

If L₁The feature of the negative attribute sample class heart isThe corresponding negative sample probability that belongs to is P_-, wherein x_i ^-=(x_i1, x_i2,…x_ij) it is negative sample, sample characteristics Gaussian distributed x_-~N (μ^-,σ^_-2)；It is assumed that study collection sample characteristics belong to it The probability of negative sample is in mapping relations, according to negative sample Gaussian Profile, can obtain L₂Sample jth dimensional feature belongs to the general of negative sample RateFor：

<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,For the average of negative sample jth dimensional feature,For the variance of negative sample jth dimensional feature, C₁'、C₂' it is linear system Number；

As x=+ ∞, the probability for now belonging to negative sample is minimum, it is believed that is now 0；

By this function withSegmentation, brings above formula 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> <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)L₂Fitting percentage p of the sample per one-dimensional characteristic_j：

L is obtained by this step₂Sample jth dimensional feature belongs to the probability P of positive/negative sample_j ⁺、P_j ^-And L₂Sample is per one-dimensional spy The fitting percentage P of sign_{j_match}。

6. method as claimed in claim 1 or 2, it is characterised in that the step (5) as follows, is calculated Practise collection L₂Sensitivity of each dimensional characteristics of sample to suitability：

Change study collection L₂Sample matrix jth dimensional feature vector x_j, while control remaining m-1 dimensional feature vector constant, work as x_j= (k,k,k,…k)^T, 1.0 changes that k is successively from 0,0.1,0.2 ..., its sample matrix is

<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 sample matrix is pre-processed, X' is classified with SVM training patterns before, obtaining correct classification samples number is n_(j,k)If total sample number is n, then classification accuracy rate nowRecord the maximum of its classification accuracy rate P_jmaxWith 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 }

Numerical value after m dimension normalization, the sensitivity as its corresponding dimensional characteristics fitting percentage；

<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_jFor the sensitivity of jth dimensional feature vector fitting percentage.

7. method as claimed in claim 1 or 2, it is characterised in that the step (6) as follows, obtains study collection L₂ In i-th of sample fitting percentage P_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

Wherein, m represents the dimension of sample characteristics, W_jRepresent the sensitivity of jth dimensional feature vector fitting percentage, P_j ⁺Represent L₂Sample jth Dimensional feature belongs to the probability of positive sample, P_j ^-Represent L₂Sample jth dimensional feature belongs to the probability of negative sample,

Work as P_j ⁺When → 1, P_j ^-→ 0, P_i→1；

Work as P_j ⁺When → 0, P_j ^-→ 1, P_i→0；

A=0.5, b=0.5 are can be calculated, 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. method as claimed in claim 1 or 2, it is characterised in that the feature of extraction is in the step (1)：

Light and shade target density：Ratio shared by light and shade target pixel points, it is complete that bright target pixel points represent that gray value is more than SAR image The point of figure gray value 2/3, dark target pixel points represent that gray value is less than the point of SAR image full figure gray value 1/3；

The notable intensity of structure：Binary edge extraction is carried out to radar image, and utilizes connected component labeling method, is removed few as number connects After the noise of logical field mark, mark sum of all pixels and the ratio of the wide wide average of height of image.