CN104200229A - SAR (Synthetic aperture radar) target discrimination method combining sparse feature selection - Google Patents
SAR (Synthetic aperture radar) target discrimination method combining sparse feature selection Download PDFInfo
- Publication number
- CN104200229A CN104200229A CN201410446516.9A CN201410446516A CN104200229A CN 104200229 A CN104200229 A CN 104200229A CN 201410446516 A CN201410446516 A CN 201410446516A CN 104200229 A CN104200229 A CN 104200229A
- Authority
- CN
- China
- Prior art keywords
- training
- projection
- sar
- image
- features
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000012850 discrimination method Methods 0.000 title abstract 4
- 238000012549 training Methods 0.000 claims abstract description 240
- 239000013598 vector Substances 0.000 claims abstract description 71
- 238000012360 testing method Methods 0.000 claims abstract description 62
- 239000011159 matrix material Substances 0.000 claims abstract description 43
- 230000009467 reduction Effects 0.000 claims abstract description 22
- 238000000034 method Methods 0.000 claims description 44
- 230000009466 transformation Effects 0.000 claims description 32
- 230000011218 segmentation Effects 0.000 claims description 17
- 230000000877 morphologic effect Effects 0.000 claims description 14
- 238000001914 filtration Methods 0.000 claims description 13
- 230000003044 adaptive effect Effects 0.000 claims description 9
- 238000010606 normalization Methods 0.000 claims description 9
- 230000000694 effects Effects 0.000 abstract description 8
- 238000004364 calculation method Methods 0.000 abstract description 6
- 239000011800 void material Substances 0.000 abstract 1
- 238000004422 calculation algorithm Methods 0.000 description 8
- 238000002474 experimental method Methods 0.000 description 7
- 238000004088 simulation Methods 0.000 description 6
- 238000001514 detection method Methods 0.000 description 5
- 238000004458 analytical method Methods 0.000 description 4
- 230000002068 genetic effect Effects 0.000 description 4
- 238000012545 processing Methods 0.000 description 4
- 238000000605 extraction Methods 0.000 description 3
- 102100024506 Bone morphogenetic protein 2 Human genes 0.000 description 2
- 101000762366 Homo sapiens Bone morphogenetic protein 2 Proteins 0.000 description 2
- 239000000654 additive Substances 0.000 description 2
- 230000000996 additive effect Effects 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 230000006870 function Effects 0.000 description 2
- 238000003384 imaging method Methods 0.000 description 2
- 230000010287 polarization Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000009877 rendering Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000010187 selection method Methods 0.000 description 2
- 230000002776 aggregation Effects 0.000 description 1
- 238000004220 aggregation Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000007429 general method Methods 0.000 description 1
- 238000005286 illumination Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Landscapes
- Radar Systems Or Details Thereof (AREA)
- Image Analysis (AREA)
Abstract
The invention discloses an SAR (Synthetic aperture radar) target discrimination method combining sparse feature selection and relates to the field of radar automatic target recognition. The SAR target discrimination method includes steps of 1 getting a suspected target zone in n SAR training images, 2 extracting training samples from the suspected target zone, 3 obtaining a normalized training sample matrix, 4 getting a projection dimensionality reduction model under the 11 norm sparse restraint to obtain a projected vector fai, 5 obtaining training projection features, 6 getting the average of the training projection features of n1 targets and getting the training projection features of n2 clutters, 7 determining the suspected target zone in the SAR testing images, 8 extracting the training samples, 9 obtaining normalized training samples, 10 obtaining the projection features of the testing samples, and 11 judging the testing images. The SAR target discrimination method removes the negative effect of void features and redundant features in discrimination, reduces the calculation amount and improves the target discrimination performance.
Description
Technical Field
The invention belongs to the field of automatic target identification of radars, relates to the research of a target identification method in target identification, and particularly relates to an SAR target identification method combining sparse feature selection.
Background
The synthetic aperture radar SAR can provide a target high-resolution image, and SAR imaging is not limited by conditions such as weather and illumination, so the synthetic aperture radar SAR is widely applied to the fields such as military reconnaissance, wherein an automatic target identification technology based on the SAR image is one of important research subjects. The automatic target recognition of the SAR image generally adopts a three-level processing flow of the American Lincoln laboratory: detection stage, identification stage and identification stage. Firstly, carrying out pixel level detection on the whole SAR image, and removing areas which are obviously not targets to obtain a suspected target area; then, extracting identification characteristics from the suspected target area, and removing natural clutter areas and artificial clutter areas which are obviously larger than or smaller than the target by using the identification characteristics; and finally, carrying out target classification and identification on the target area reserved in the identification stage.
In the identification stage, a large number of SAR target identification characteristics are proposed in the existing literature, although theoretically each characteristic is proposed based on a certain physical meaning and reflects information such as scattering strength, structure size and the like of a target and clutter, not every characteristic has strong identifiability, and even some characteristic combined actions can obtain opposite identification effects. If all the extracted features are used for target identification, information redundancy and dimension disaster are easily caused, the calculation amount is increased, and the identification performance is seriously influenced. Therefore, the target identification stage is generally subdivided into three aspects of identification feature extraction, identification feature dimension reduction and identifier design. Most of the existing documents adopt a feature selection method to achieve the purpose of feature dimension reduction, and the feature selection method such as an exhaustion method, a genetic algorithm and the like aims to search and find an optimal feature combination. However, in practice, for high-dimensional SAR identification features, the operation amount of the exhaustive method is too large to be advisable, and the operation amount of the genetic algorithm is almost equivalent to the exhaustive method when the genetic algorithm is required to obtain a global optimal solution. From the viewpoint of reducing the amount of computation and improving the performance of the discriminator, a supervised dimensionality reduction method such as Fisher linear decision analysis (FDA) may be used. However, although the supervised dimension reduction method can transform the original high-dimensional feature projection into the low-dimensional projection feature projection and ensure the separability of the projection feature, the projection feature obtained by the supervised dimension reduction method such as FDA is still the combination of all the features, so that the negative influence of the invalid feature and the redundant feature on the identification can be weakened but not eliminated.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an SAR target identification method combining sparse feature selection. The invention adds l in the projection dimension reduction model1And 4, norm sparse constraint, namely, the feature selection is fused into the solution of the optimal projection vector, so that the optimal projection feature of the optimal feature combination is obtained, the negative effects of invalid features and redundant features in identification are eliminated, and the target identification performance is improved.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A SAR target identification method combining sparse feature selection is characterized by comprising the following steps:
step 1, taking N SAR training images, wherein the N SAR training images comprise N1SAR training image containing target and N2A SAR training image containing clutter, N, N1And N2Are respectively natural numbers, and N1+N2＝N；
For the jth SAR training image S in the N SAR training imagesjSequentially carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filtering to obtain a binary image FjJ is largeEqual to or greater than 1 and equal to or less than N;
step 2, passing the binary image FjThe pixel regions with continuous pixel amplitude values of 1 are geometrically clustered to judge the binary image FjWhether or not to contain the suspected target area Tj；
If the binary image FjDoes not contain the suspected target area TjAnd discarding the jth SAR training image Sj；
If the binary image FjContaining a suspected target area TjFrom the suspected target area TjExtracting p features, and combining the p features into a training sample xjTraining sample xjIs a column vector with dimension size p × 1, p represents the number of features, j is greater than or equal to 1 and less than or equal to N;
step 3, from N, according to steps 1 to 21Obtaining n from SAR training image containing target1Training samples of individual targets, from N2Obtaining n from SAR training image containing clutter2Training samples of each clutter; n is1≤N1，n2≤N2，N1Total number of SAR training images targeted, N2Total number of SAR training images which are clutter;
n1training samples and n for each target2Forming a training sample matrix X by the training samples of the clutter; the training sample matrix X contains n training samples, n being n1+n2N is less than or equal to N, and N is the total number of SAR training images;
for the ith training sample xiNormalizing i to be more than or equal to 1 and less than or equal to n to obtain a normalized training sample Where μ represents a row mean vector formed by the mean of each row of the training sample feature matrix X, and σ representsTraining a row standard deviation vector formed by the standard deviation of each row of the sample characteristic matrix X; and then for n1Normalizing the training samples of the targets to obtain n1Normalized target training samples, pair n2Obtaining n after normalization of training samples of each clutter2Training samples of the normalized clutter;
n1normalized target training samples and n2Forming n normalized training samples by the training samples of the normalized clutter, wherein n is n1+n2；
The n normalized training samples form a normalized training sample matrix Is the normalized training sample of the ith;
step 4, construct l1Normalized training sample matrix under norm sparsity constraintThe projection dimension reduction model of (1) is solved1Obtaining a projection vector phi by a projection dimension reduction model under norm sparse constraint;
step 5, utilizing the projection vector phi to normalize the ith training samplePerforming the following projective transformation to obtain the training projection characteristics <math>
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>‾</mo>
</mover>
<mi>i</mi>
<mi>T</mi>
</msubsup>
<mi>Φ</mi>
<mo>;</mo>
</mrow>
</math>
Step 6, for n according to step 51Carrying out projection transformation on the normalized target training sample to obtain n1Training projection characteristics containing targets, and solving n1Mean of training projection features of individual objects
For n according to step 52Carrying out projection transformation on the normalized clutter training sample to obtain n2Training projection characteristics containing clutter and solving n2Mean of training projection features of individual clutter
Step 7, SAR test image S*Carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filtering to obtain a binary image F*；
Step 8, the binary image F*The pixel areas with continuous pixel amplitude values of 1 are geometrically clustered to judge whether the suspected target area T is contained*；
If the binary image F is tested*Does not contain the test suspected target area T*Then test image S*Is determined to be a clutter;
if the binary image T is tested*Containing test suspected target area T*From the suspected target area T*In the method, p features are extracted and form a test sample x*；
Step 9, for the test sample x*Normalization is carried out to obtain a normalized test sample
Wherein, mu represents a vector formed by the mean value of each row of the training sample feature matrix X, and sigma represents a vector formed by the standard deviation of each row of the training sample feature matrix X;
step 10, utilizing the projection vector phi to carry out normalization on the test samplePerforming the following projection transformation to obtain a test sampleProjection feature of
Step 11, calculating projection characteristicsMean of training projection features with targetIs a distance ofAnd projection featuresMean of training projection features with clutterIs a distance ofIf d is1≤d2Then test image S*Is judged as a target, otherwise the image S is tested*Is determined to be a clutter.
The technical scheme has the characteristics and further improvement that:
(1) step 1 comprises the following substeps:
1a) for the jth training image SjCarrying out logarithmic transformation to obtain a training image G after the logarithmic transformationjTraining image G after logarithmic transformationjAmplitude G at pixel point (x, y)jThe expression of (x, y) is:
Gj(x,y)＝10×ln[Sj(x,y)+0.001]+30
wherein S isj(x, y) is SAR training image SjAmplitude at pixel point (x, y), Gj(x, y) is a training image G after logarithmic transformationjThe amplitude at pixel point (x, y);
1b) for training image G after logarithmic transformationjPerforming adaptive threshold segmentation and morphological filtering to obtain a binary image FjThe pixel point with the pixel amplitude of 1 in the binary image is a suspected target pixel, the pixel point with the pixel amplitude of 0 in the binary image is a non-suspected target pixel, and the binary image FjAmplitude F at pixel point (x, y)jExpression of (x, y):
(2) the step 4 specifically comprises the following steps:
l1the projection dimension reduction model under the norm sparse constraint is as follows:
wherein,is a matrix of training samples after being normalized,is of dimension p × n; y is a category information vector, the dimension of Y is n multiplied by 1, and Y only contains two values of {0,1 }; theta represents fitting projection featuresAnd a fitting quantity of the category information quantity Y; i | · | purple wind1Express to ask for l1A norm; i | · | purple wind2To representCalculating l2A norm; λ is a regularization parameter.
Compared with the prior art, the invention has outstanding substantive characteristics and remarkable progress. Compared with the prior art, the method has the following advantages:
the method has the advantages that the characteristic selection of SAR target identification is fused into the solution of the optimal projection vector, the characteristic selection and projection dimension reduction are simultaneously carried out, the identification accuracy is improved, and the calculation amount of the independent characteristic selection or projection dimension reduction is avoided:
in the face of a plurality of SAR target identification characteristics, if all identification characteristics are directly used, not only is the calculated amount increased, but also invalid characteristics and redundant characteristics often interfere with an identifier to influence the identification performance; if the optimal characteristic combination is searched by adopting searching methods such as an exhaustion method and the like, the operation cost is too high. Aiming at the problems of high dimension and different performance of identifying the features of the SAR target, the invention selects the features as l1Fusing the norm sparse constraint form into a projection dimension reduction model through l1And carrying out sparse constraint on the projection vectors by the norm to obtain the projection vectors with zero partial elements having the characteristic selection function, carrying out projection dimensionality reduction on the original characteristics through the projection vectors, and finally obtaining the optimal projection characteristics of the optimal characteristic combination. Compared with the method of directly using all the identification features and the method of directly projecting and reducing dimensions on all the identification features, the method improves the identification accuracy and reduces the calculation amount compared with search methods such as a genetic algorithm and the like.
Drawings
The invention is further described with reference to the following figures and detailed description.
FIG. 1 is a flow chart of the present invention.
FIG. 2(a) is a gray scale of an original image of an SAR image during a training phase in the present invention;
FIG. 2(b) is a binary image after adaptive threshold segmentation of SAR images in the training phase of the present invention;
FIG. 2(c) is a morphologically filtered binary image of a SAR image during a training phase in accordance with the present invention;
fig. 2(d) is a binary image containing a suspected target region after geometric clustering of the SAR images at the training stage in the present invention.
Detailed Description
Referring to fig. 1, a method for identifying an SAR target in combination with sparse feature selection, which is applicable to identification of a target in an SAR image, is described.
First, training phase
Step 1, taking N SAR training images, wherein the N SAR training images comprise N1SAR training image containing target and N2A SAR training image containing clutter, N, N1And N2Are respectively natural numbers, and N1+N2＝N；
For the jth SAR training image S in the N SAR training imagesjSequentially carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filtering to obtain a binary image FjJ is 1 or more and N or less;
it should be noted that, in the present invention, the jth SAR training image S is subjected tojIs of N1Whether the SAR training image of each target belongs to N2The SAR training images of each clutter are known, the training projection characteristics of the SAR training images of the target and the solving process of the training projection characteristics of the SAR training images of the clutter are the same, and the j-th SAR training image S is used as the training image SjThat is, any training image is exemplified for illustration, and the applicability of the method is not limited.
A large amount of background clutter and speckle noise exist in the SAR image, and subsequent feature extraction and identification are seriously interfered. Therefore, before extracting the features, the SAR image needs to be subjected to logarithmic transformation, adaptive threshold segmentation, morphological filtering and geometric clustering to obtain a suspected target region, and then relevant features are extracted for the suspected target region.
The specific pretreatment steps are as follows:
1a) for jth SAR training image SjCarrying out logarithmic transformation to obtain a training image G after the logarithmic transformationjTraining image G after logarithmic transformationjAmplitude G at pixel point (x, y)jThe expression of (x, y) is:
Gj(x,y)＝10×ln[Sj(x,y)+0.001]+30
wherein S isj(x, y) is SAR training image SjAmplitude at pixel point (x, y), Gj(x, y) is a training image G after logarithmic transformationjThe amplitude at pixel point (x, y);
through 1a) SAR training image SjThe multiplicative speckle noise in (1) is converted into additive noise. According to the imaging principle of the SAR image, a plurality of non-Gaussian and non-uniformly distributed multiplicative speckle noises exist in the SAR image, and the multiplicative speckle noises can be converted into additive noises more suitable for Gaussian distribution description through logarithmic transformation, so that the influence caused by the multiplicative speckle noises is effectively inhibited.
1b) For training image G after logarithmic transformationjPerforming adaptive threshold segmentation and morphological filtering to obtain a binary image FjThe pixel point with the pixel amplitude of 1 in the binary image is a suspected target pixel, the pixel point with the pixel amplitude of 0 in the binary image is a non-suspected target pixel, and the binary image FjAmplitude F at pixel point (x, y)jExpression of (x, y):
self-adaptive threshold segmentation firstly adopts a self-adaptive double-parameter constant false alarm detection method (see section 6.2 of radar target detection and constant false alarm processing) to carry out pixel-level detection on an SAR image to obtain a detected binary image; and then performing thresholding segmentation on the detected binary image (refer to section 7.4 of digital image processing) to obtain a final segmentation result. The morphological filtering technique is referred to in subsection 8.7 of digital image processing.
Step 2, passing the binary image FjThe pixel regions with continuous pixel amplitude values of 1 are geometrically clustered to judge the binary image FjWhether or not to contain the suspected target area Tj；
If the binary image FjDoes not contain the suspected target area TjAnd discarding the jth SAR training image Sj；
If the binary image FjContaining a suspected target area TjFrom the suspected target area TjExtracting p features, and combining the p features into a training sample xjTraining sample xjIs a column vector with dimension size p × 1, p represents the number of features, j is greater than or equal to 1 and less than or equal to N; the feature types of the features include, but are not limited to, spatial features, polarization features, and the like.
By means of binary images FjThe pixel regions with continuous pixel amplitude values of 1 are geometrically clustered to judge the binary image FjWhether or not to contain the suspected target area TjThe method specifically comprises the following steps:
the length of the maximum side length of the geometric shape of the target is set to be L, the range (0.8 xL/rho, 2.0 xL/rho) of a pixel clustering region judgment threshold D is set according to the length L of the maximum side length of the target, and rho represents the resolution of n SAR training images. If the pixel clustering area discrimination threshold D is less than 0.8 xL/rho, the suspected target area obtained through geometric clustering contains too many suspected target small areas, and if the pixel clustering area discrimination threshold D is more than 2.0 xL/rho, the suspected target area obtained through geometric clustering omits small suspected target small areas.
Obtaining a binary image FjIf the number of pixel points in the pixel area with each continuous pixel amplitude value of 1 is more than or equal to the pixel clustering area discrimination threshold D, the pixel area is considered to be suspectedThe target sub-area, otherwise, the pixel area is not considered as the suspected target sub-area;
statistical binary image FjT suspected target sub-regions are included. If T is larger than 0, setting the T suspected target sub-areas as suspected target areas Tj(ii) a If t is equal to 0, i.e. the binary image FjIf the number of pixel points in the pixel region with all the continuous pixel amplitudes being 1 is less than the pixel clustering region discrimination threshold D, the binary image F is representedjDoes not contain the suspected target area TjAnd discarding the jth SAR training image Sj。
Fig. 2 is a SAR image at an azimuth angle of 17 ° and a pitch angle of 5.5 ° using the target BMP2 in the MSTAR dataset: FIG. 2(a) is an original grayscale image; FIG. 2(b) is a binary image obtained by adaptive threshold segmentation of an original gray-scale image, wherein white pixels represent suspected target pixels and black pixels represent non-suspected target pixels; fig. 2(c) is a binary image obtained by adaptive threshold segmentation and morphological filtering on an original gray-scale image, wherein white pixels in the image represent suspected target pixels, and black pixels represent non-suspected target pixels; FIG. 2(d) is a binary image containing a suspected target region obtained by adaptive threshold segmentation, morphological filtering and geometric clustering on an original gray-scale image, wherein a white region in the image represents the finally obtained suspected target region; as can be seen from comparing fig. 2(b) and fig. 2(c), the morphological filtering can filter out a large amount of false suspected target pixels.
The main function of the geometric clustering is to eliminate the small clutter pixel areas which still exist in large quantity after the steps 1a) and 1 b). Since these smaller clutter pixel areas may occur anywhere in the image, the true target area is severely dilated if these smaller clutter pixel areas are retained as suspect target areas. Therefore, the small clutter pixel areas can be eliminated through geometric clustering, and the obtained suspected target area can reflect the shape and the size of the target more truly.
If the binary image FjDoes not contain the suspected target area TjIf yes, then the jth SAR is discardedTraining image Sj；
If the binary image FjContaining a suspected target area TjFrom the suspected target area TjExtracting p features, and combining the p features into a training sample xjTraining sample xjIs a column vector with dimension size p × 1, p representing the number of features.
The feature types of the features extracted by the invention include, but are not limited to, spatial features, polarization features, time domain features, frequency domain features, and the like.
In the SAR target identification problem, the scattering intensity of a target, the proportion of the intensity to the total image intensity, and the size, structure and other information of a suspected target area determined by geometric clustering can be used as identification features to distinguish the target from clutter.
The p features of the invention can extract at least one of the following 23 features, listed below: 14 lincoln features, namely a standard deviation feature, a fractal dimension feature, an arrangement energy ratio feature, an aggregation feature, a diagonal feature, a rotational inertia feature, a maximum constant false alarm feature, a mean constant false alarm feature, an intensity percentage feature, a counting feature and 4 spatial boundary attribute features; 6 adjacent features; the characteristics of the 3 noble doctor papers are respectively mean signal-to-noise ratio characteristic, peak signal-to-noise ratio characteristic and strong point percentage characteristic.
It should be noted that the p features may be extracted according to actual image requirements, and the p features are not specifically limited in the present invention.
Step 3, from N, according to steps 1 to 21Obtaining n from SAR training image containing target1Training samples of individual targets, from N2Obtaining n from SAR training image containing clutter2Training samples of each clutter; n is1≤N1，n2≤N2，N1Total number of SAR training images targeted, N2Total number of SAR training images which are clutter;
n1each eyeTarget training sample and n2Forming a training sample matrix X by the training samples of the clutter; the training sample matrix X contains n training samples, n being n1+n2N is less than or equal to N, and N is the total number of SAR training images;
training sample matrix X ═ X1,x2,...,xi,...xn]X is a matrix with dimension size p × n; x is the number ofiIs the ith training sample, xiIs a column vector having a dimension size of p × 1, p represents the number of features, and i is equal to or greater than 1 and equal to or less than n. For the ith training sample xiNormalizing i to be more than or equal to 1 and less than or equal to n to obtain a normalized training sample Wherein, mu represents a row mean vector formed by the mean of each row of the training sample feature matrix X, and sigma represents a row standard deviation vector formed by the standard deviation of each row of the training sample feature matrix X; and then for n1Normalizing the training samples of the targets to obtain n1Normalized target training samples, pair n2Obtaining n after normalization of training samples of each clutter2Training samples of the normalized clutter;
note that, the row mean vector μ obtained from p rows in total of the training sample matrix X is a column vector having a dimension of p × 1, σ is a vector formed by a standard deviation for each row of the training sample feature matrix X, and the row standard deviation σ obtained from p rows in total of the training sample matrix X is a column vector having a dimension of p × 1.
n1Normalized target training samples and n2Forming n normalized training samples by the training samples of the normalized clutter, wherein n is n1+n2；
The n normalized training samples form a normalized training sample matrix Is the normalized training sample of the ith;is a matrix with dimension size p n,is a column vector having a dimension size of p × 1, p represents the number of features, and i is equal to or greater than 1 and equal to or less than n.
Step 4, construct l1Normalized training sample matrix under norm sparsity constraintThe projection dimension reduction model of (1) is solved1And obtaining a projection vector phi by a projection dimension reduction model under norm sparse constraint.
Establishment of l1The projection dimension reduction model under the norm sparse constraint is as follows:
wherein,is a matrix of training samples after being normalized,the dimension of (a) is p × n; y is a category information vector, the dimension of Y is n multiplied by 1, Y only contains {0,1} two values, if the ith row value of Y is 1, the ith normalized training sample is representedFor training the target sample, if the ith row of Y takes a value of 0, the ith normalized training sample is representedTraining clutter samples; theta represents fitting projection featuresAnd a fitting amount of the category information amount Y, and the fitting amount theta is set to 1 in the present invention; i | · | purple wind1Represents the calculation of l1A norm; i | · | purple wind2Represents the calculation of l2A norm; λ is a regularization parameter used to balance the fitting error termAnd l1Norm term | | Φ | | | luminance1The regularization parameter λ takes a value greater than zero.
In the present invention, Y is a category information vector, and the limitation of the dimension of the column of the category information vector Y is performed according to Linear Discriminant Analysis (LDA), i.e., the category information vector Y should not exceed the category number K minus 1 (reference "elements of statistical learning" section 12.5). Since the SAR target identification problem only comprises two types of images, namely an SAR target image and an SAR clutter image, namely K-2, the dimension of the column of Y in the invention is K-1-2-1. Since there are n normalized training samples, the dimension of the row of Y is n. As can be seen, the dimension of Y is n × 1.
In the present invention, Φ is a projection vector, and the limitation of the dimension of the column of the projection vector Φ by LDA, that is, the projection vector Φ must not exceed the number of classes K minus 1 (section 12.5 of the reference of elements of static learning), that is, the dimension of the column of the projection vector must not exceed the number of classes K minus 1. Since the SAR target identification problem only comprises two types of images, namely a SAR target image and a SAR clutter image, namely K is 2, the dimension of the column of the projection vector phi is K-1 or 2-1 or 1 at most. According to the projection vector phiThe matrix multiplication of (c) has a requirement on the size of the matrix dimension, so the dimension of the row of the projection vector phi is equal to the normalized training sample matrixThe dimension of the line of (b), i.e. the dimension of the line of the projection vector Φ, is the number of features p. Thus, the projection vector Φ has a dimension of p × 1.
In the invention, theta is a fitting quantity to satisfy the condition of fitting error termIn the requirement of the dimension size of the matrix, the dimension size of the fitting quantity theta is 1 multiplied by 1, and the fitting quantity theta is set to be 1 in the invention.
The invention utilizes a basis tracking algorithm in1And solving a projection vector phi in a projection dimension reduction model under norm sparse constraint. The method of solving the projection vector in any model by the basis pursuit algorithm is introduced in section 2 of the document "rendering and rendering the projection vectors adaptive algorithms".
The invention is not limited to the method for solving the projection vector, and can also be realized by an orthogonal matching pursuit algorithm and the like.
In the prior art, the regression model of LDA is one of the general methods for solving the projection vector (section 12.5 of the reference "elements of statistical learning"), and the regression model of LDA is:
wherein,the normalized training sample matrix is obtained, Y is a category information vector, theta is a fitting quantity, and phi is a projection vector to be solved.
In the above-described regression model of LDA, l is not present for the projection vector Φ1And under the norm sparse constraint condition, elements in the projection vector phi obtained by solving are generally not zero, so that the projection characteristics obtained after projection transformation of the projection vector phi are still the combination of all the characteristics. The invention carries out l on the projection vector on the regression model of LDA1Norm sparsity constraint,/1The norm sparse constraint has the effect of enabling part of elements of the projection vector phi to be zero, and the features corresponding to the positions of the zero elements in the projection vector represent invalid features and redundant features which are irrelevant to classification, so that the finally obtained projection features are combinations of the features corresponding to the positions of the non-zero elements in the projection vector, namely the projection features are combinations of valid features containing classification information, and the projection features do not contain the invalid features and the redundant features any more.
Step 5, utilizing the projection vector phi to normalize the ith training sampleCarrying out projection transformation, wherein the projection formula is as follows:
obtaining training projection featuresTraining projection featuresThe dimension size is 1 × 1.
It is emphasized that, since the dimension of the column of the projection vector Φ is equal to 1 in the present invention, the projection features after projection change are no matter how many features p are selected in the present inventionAre all one-dimensional projection features.
Step 6, for n according to step 51Carrying out projection transformation on the normalized target training sample to obtain n1Training projection characteristics containing targets, and solving n1Mean of training projection features of individual objects
For n according to step 52Carrying out projection transformation on the normalized clutter training sample to obtain n2Training projection characteristics containing clutter and solving n2Training projection device containing clutterMean value of sign
Second, testing stage
Step 7, SAR test image S*Carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filtering to obtain a binary image F*。
Step 8, the binary image F*The pixel areas with continuous pixel amplitude values of 1 are geometrically clustered to judge whether the suspected target area T is contained*；
If the binary image F is tested*Does not contain the test suspected target area T*Then test image S*Is determined to be a clutter;
if the binary image T is tested*Containing test suspected target area T*From the suspected target area T*In the method, p features are extracted and form a test sample x*. It should be noted that the suspected target area T is tested in the testing stage*The p features extracted in (2) are necessarily consistent with the p features extracted in step (2) of the training phase.
The binary image F*The pixel areas with continuous pixel amplitude values of 1 are geometrically clustered to judge whether the suspected target area T is contained*The method specifically comprises the following steps:
obtaining a binary image F*If the number of pixel points in each pixel area with continuous pixel amplitude values of 1 is more than or equal to a pixel clustering area judgment threshold D, the pixel area is considered to be a suspected target sub-area, otherwise, the pixel area is not considered to be the suspected target sub-area;
statistical binary image F*T suspected target sub-regions are included. If T is larger than 0, setting the T suspected target sub-areas as suspected target areas T*(ii) a If t is equal to 0, i.e. the binary image F*Pixels in which all the pixel amplitudes are continuously 1If the number of the pixel points of the region is less than the discrimination threshold D of the pixel clustering region, the binary image F is represented*Does not contain the suspected target area F*Binary image F*And does not participate in subsequent feature extraction and identification.
Step 9, for the test sample x*Normalization is carried out to obtain a normalized test sample
Where μ denotes a vector formed by the mean of each row of the training sample feature matrix X, and σ denotes a vector formed by the standard deviation of each row of the training sample feature matrix X.
Step 10, using the projection vector phi to normalize the test sampleCarrying out projection transformation, wherein the projection transformation formula is as follows:
obtaining a test sampleProjection feature of
Since the dimension of the column of the projection vector phi is equal to 1 in the invention, the projection features after projection change are no matter how many features p are selected in the inventionAre all one-dimensional projection features, i.e. projection featuresIs 1 × 1.
Step 11, calculating projection characteristicsMean of training projection features with targetIs a distance ofAnd projection featuresMean of training projection features with clutterIs a distance ofIf d is1≤d2Then test image S*Is judged as a target, otherwise the image S is tested*Is determined to be a clutter.
The effect of the present invention will be further explained with the simulation experiment.
1. Introduction of simulation experiment data:
the simulation experiment used was the published MSTAR dataset. The data set used in this experiment included ten military vehicle targets with pitch angles at 15 °, 17 °, 30 °, and 45 °: the SAR target images of BMP2, BTR70, T72, BTR60, 2S1, BRDM2, D7, T62, ZIL131 and ZSU23-4 and the SAR clutter image with a pitch angle of 15 degrees. 11425 SAR target images are used in the experiment, 2746 SAR target images with the pitch angle of 17 degrees are used in the experiment, and 8679 SAR target images with the pitch angle of 15 degrees, 30 degrees and 45 degrees are used in the experiment. The SAR clutter images used in the experiment are 3008 in total.
2. The simulation experiment process is as follows:
a) selecting a training image: uniformly selecting 100 images of each of ten types of targets from 2746 target images with the pitch angle of 17 degrees according to different azimuth angles to form 1000 training images of the targets; simultaneously, randomly selecting 1000 clutter images from the 3008 clutter images as a training image of the clutter;
b) extracting 23 features from 1000 target images to form a training sample of a target; extracting 23 features from 1000 clutter training images to form clutter training samples; the training samples of the target and the training samples of the clutter form a training sample matrix.
c) Carrying out normalization matrix on the training samples to obtain a normalized training sample matrix;
d) giving a regularization parameter lambda equal to 1.2, and substituting the normalized training sample matrix into l1A projection dimension reduction model under norm sparse constraint is used for solving a projection vector phi corresponding to a regularization parameter lambda which is 1.2;
e) utilizing projection vector phi to perform projection transformation on a training sample of the target to obtain training projection characteristics of the target, and calculating the mean value of the training projection characteristics of the targetTraining of clutter using projection vector phiThe samples are subjected to projection transformation to obtain the training projection characteristics of the clutter, and the mean value of the training projection characteristics of the clutter is calculated
f) Selecting a test sample: 8679 total images of ten types of target images with the pitch angles of 15 degrees, 30 degrees and 45 degrees are taken as test images of the target; simultaneously obtaining 2008 clutter images as test images of the clutter by using the training images without 1000 clutter from all 3008 clutter images;
g) extracting 23 features from 8679 target test images and 2008 clutter test images to form a test sample;
h) normalizing the test sample to obtain a normalized test sample;
i) projecting and transforming the test sample by using the projection vector phi to obtain the projection characteristics of the test sample;
j) calculating a mean of the projected features of the test sample to the training projected features of the targetDistance d of1Simultaneously calculating the mean of the projection characteristics of the test sample to the training projection characteristics of the clutterDistance d of1. If d is1≤d2The test sample is judged as a target, otherwise, the test sample is judged as a clutter.
3. Simulation experiment results and analysis:
three prior art methods are used to determine the test sample, including:
the method comprises the following steps: directly using a training sample containing 23 features, calculating the mean value of the training sample of the target and the mean value of the training sample of the clutter, if the distance from the test sample to the mean value of the training sample of the target is smaller than the distance from the test sample to the mean value of the training sample of the clutter, judging the test sample as the target, otherwise, judging the test sample as the clutter; the authentication results obtained directly using the signature containing 23 features are shown in table 1;
in the second method, a Fisher linear decision analysis (FDA) is used to perform projection transformation on the training sample containing 23 features, so as to obtain one-dimensional projection features of the FDA. And calculating the mean value of the training projection features of the FDA of the target and the mean value of the training projection features of the FDA of the clutter, and judging the test sample as the target if the distance from the test sample to the mean value of the training projection features of the FDA of the target is smaller than the distance from the test sample to the mean value of the training projection features of the FDA of the clutter, otherwise judging the test sample as the clutter. The discrimination results obtained from one-dimensional FDA projection features are shown in table 1;
method three, adopting an exhaustion method, and taking 2 of 23 characteristics23Different characteristics are combined to form 223Training samples, calculating the 223And (3) if the distance from the test sample to the mean value of the training target is less than the distance from the test sample to the mean value of the training clutter, judging the test sample as the target, otherwise, judging the test sample as the clutter. The table shows this 223Under the combination of species characteristics 223Optimal discrimination of seed discrimination.
The 23 features used in the simulation are specifically the 23 features set in step 2.
Table 1 shows the identification results of the above experiments according to the present invention, wherein the error rate is calculated by the following formula:
TABLE 1
As can be seen from table 1, although the 23 SAR target identification features extracted in the experiment should theoretically reflect separable information such as the scattering intensity, the structure size and the like of the target and the clutter, due to the problems of high feature dimension, redundant features and the like, the effect is not ideal when all features are directly used for identification. Through FDA projection transformation, high-dimensional features are projected and transformed into one-dimensional projection features, so that the effects of reducing data dimension and reducing storage capacity are achieved, but because all the features participate in projection transformation, the identification error rate is equivalent to the effect of directly using 23 features. In addition, Table 1 compares our method to pass 223Optimal discrimination results of exhaustive methods of combinations of species characteristics. Experimental results show that the identification performance of the SAR target identification method combining sparse feature selection is superior to that of projection features subjected to FDA projection transformation, and meanwhile, the identification performance of the SAR target identification method is superior to that of the optimal feature combination not subjected to projection transformation, and the effectiveness of the SAR target identification method is proved.
Claims (3)
1. A SAR target identification method combining sparse feature selection is characterized by comprising the following steps:
step 1, taking N SAR training images, wherein the N SAR training images comprise N1SAR training image containing target and N2A SAR training image containing clutter, N, N1And N2Are respectively natural numbers, and N1+N2＝N；
For the jth SAR training image S in the N SAR training imagesjSequentially carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filteringWave to obtain a binary image FjJ is 1 or more and N or less;
step 2, passing the binary image FjThe pixel regions with continuous pixel amplitude values of 1 are geometrically clustered to judge the binary image FjWhether or not to contain the suspected target area Tj；
If the binary image FjDoes not contain the suspected target area TjAnd discarding the jth SAR training image Sj；
If the binary image FjContaining a suspected target area TjFrom the suspected target area TjExtracting p features, and combining the p features into a training sample xjTraining sample xjIs a column vector with dimension size p × 1, p represents the number of features, j is greater than or equal to 1 and less than or equal to N;
step 3, from N, according to steps 1 to 21Obtaining n from SAR training image containing target1Training samples of individual targets, from N2Obtaining n from SAR training image containing clutter2Training samples of each clutter; n is1≤N1，n2≤N2，N1Total number of SAR training images targeted, N2Total number of SAR training images which are clutter;
n1training samples and n for each target2Forming a training sample matrix X by the training samples of the clutter; the training sample matrix X contains n training samples, n being n1+n2N is less than or equal to N, and N is the total number of SAR training images;
for the ith training sample xiNormalizing i to be more than or equal to 1 and less than or equal to n to obtain a normalized training sample Where μ represents a row mean vector formed by the mean of each row of the training sample feature matrix X, and σ is a row standard deviation formed by the standard deviation of each row of the training sample feature matrix XVector quantity; and then for n1Normalizing the training samples of the targets to obtain n1Normalized target training samples, pair n2Obtaining n after normalization of training samples of each clutter2Training samples of the normalized clutter;
n1normalized target training samples and n2Forming n normalized training samples by the training samples of the normalized clutter, wherein n is n1+n2；
The n normalized training samples form a normalized training sample matrix Is the normalized training sample of the ith;
step 4, construct l1Normalized training sample matrix under norm sparsity constraintThe projection dimension reduction model of (1) is solved1Obtaining a projection vector phi by a projection dimension reduction model under norm sparse constraint;
step 5, utilizing the projection vector phi to normalize the ith training samplePerforming the following projective transformation to obtain the training projection characteristics <math>
<mrow>
<msub>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
<mi>i</mi>
</msub>
<mo>=</mo>
<msubsup>
<mover>
<mi>x</mi>
<mo>‾</mo>
</mover>
<mi>i</mi>
<mi>T</mi>
</msubsup>
<mi>Φ</mi>
<mo>;</mo>
</mrow>
</math>
Step 6, for n according to step 51Carrying out projection transformation on the normalized target training sample to obtain n1Training projection characteristics containing targets, and solving n1Mean of training projection features of individual objects
For n according to step 52Carrying out projection transformation on the normalized clutter training sample to obtain n2Training projection characteristics containing clutter and solving n2Mean of training projection features of individual clutter
Step 7, SAR test image S*Carrying out logarithmic transformation, self-adaptive threshold segmentation and morphological filtering to obtain a binary image F*；
Step 8, the binary image F*The pixel areas with continuous pixel amplitude values of 1 are geometrically clustered to judge whether the suspected target area T is contained*；
If the binary image F is tested*Does not contain the test suspected target area T*Then test image S*Is determined to be a clutter;
if the binary image T is tested*Containing test suspected target area T*From the suspected target area T*In the method, p features are extracted and form a test sample x*；
Step 9, for the test sample x*Normalization is carried out to obtain a normalized test sample
Wherein, mu represents a vector formed by the mean value of each row of the training sample feature matrix X, and sigma represents a vector formed by the standard deviation of each row of the training sample feature matrix X;
step 10, utilizing the projection vector phi to carry out normalization on the test samplePerforming the following projection transformation to obtain a test sampleProjection feature of
Step 11, calculating projection characteristicsMean of training projection features with targetIs a distance ofAnd projection featuresMean of training projection features with clutterIs a distance ofIf d is1≤d2Then test image S*Is judged as a target, otherwise the image S is tested*Is determined to be a clutter.
2. The SAR target identification method combining sparse feature selection as claimed in claim 1, wherein step 1 comprises the following sub-steps:
1a) for the jth training image SjCarrying out logarithmic transformation to obtain a training image G after the logarithmic transformationjTraining image G after logarithmic transformationjAmplitude G at pixel point (x, y)jThe expression of (x, y) is:
Gj(x,y)＝10×ln[Sj(x,y)+0.001]+30
wherein S isj(x, y) is SAR training image SjAmplitude at pixel point (x, y), Gj(x, y) is a training image G after logarithmic transformationjThe amplitude at pixel point (x, y);
1b) for training image G after logarithmic transformationjPerforming adaptive threshold segmentation and morphological filtering to obtain a binary image FjThe pixel point with the pixel amplitude of 1 in the binary image is a suspected target pixel, the pixel point with the pixel amplitude of 0 in the binary image is a non-suspected target pixel, and the binary image FjAmplitude F at pixel point (x, y)jExpression of (x, y):
3. the SAR target identification method combining sparse feature selection according to claim 1, wherein the step 4 specifically comprises:
l1the projection dimension reduction model under the norm sparse constraint is as follows:
wherein,is a matrix of training samples after being normalized,is of dimension p × n; y is a category information vector, the dimension of Y is n multiplied by 1, and Y only contains two values of {0,1 }; theta represents fitting projection featuresAnd a fitting quantity of the category information quantity Y; i | · | purple wind1Express to ask for l1A norm; i | · | purple wind2Express to ask for l2A norm; λ is regularizationAnd (4) parameters.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410446516.9A CN104200229B (en) | 2014-09-03 | 2014-09-03 | A kind of SAR target discrimination methods of combination sparse features selection |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410446516.9A CN104200229B (en) | 2014-09-03 | 2014-09-03 | A kind of SAR target discrimination methods of combination sparse features selection |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104200229A true CN104200229A (en) | 2014-12-10 |
| CN104200229B CN104200229B (en) | 2017-09-01 |
Family
ID=52085518
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410446516.9A Active CN104200229B (en) | 2014-09-03 | 2014-09-03 | A kind of SAR target discrimination methods of combination sparse features selection |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104200229B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104537384A (en) * | 2015-01-21 | 2015-04-22 | 西安电子科技大学 | SAR (synthetic aperture radar) target identification method combined with likelihood ratio decision |
| CN105608425A (en) * | 2015-12-17 | 2016-05-25 | 小米科技有限责任公司 | Method and device for sorted storage of pictures |
| CN106778870A (en) * | 2015-12-22 | 2017-05-31 | 中国电子科技集团公司第二十研究所 | A kind of SAR image Ship Target Detection method based on RPCA technologies |
| CN111680593A (en) * | 2020-05-29 | 2020-09-18 | 西安电子科技大学 | SAR image target identification method based on self-adaptive one-class SVM model |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101526995A (en) * | 2009-01-19 | 2009-09-09 | 西安电子科技大学 | Synthetic aperture radar target identification method based on diagonal subclass judgment analysis |
| CN102184408A (en) * | 2011-04-11 | 2011-09-14 | 西安电子科技大学 | Autoregressive-model-based high range resolution profile radar target recognition method |
| CN102628938A (en) * | 2012-04-29 | 2012-08-08 | 西安电子科技大学 | Combined Gaussian model radar target steady recognition method based on noise apriority |
| CN103984966A (en) * | 2014-05-29 | 2014-08-13 | 西安电子科技大学 | SAR image target recognition method based on sparse representation |
-
2014
- 2014-09-03 CN CN201410446516.9A patent/CN104200229B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101526995A (en) * | 2009-01-19 | 2009-09-09 | 西安电子科技大学 | Synthetic aperture radar target identification method based on diagonal subclass judgment analysis |
| CN102184408A (en) * | 2011-04-11 | 2011-09-14 | 西安电子科技大学 | Autoregressive-model-based high range resolution profile radar target recognition method |
| CN102628938A (en) * | 2012-04-29 | 2012-08-08 | 西安电子科技大学 | Combined Gaussian model radar target steady recognition method based on noise apriority |
| CN103984966A (en) * | 2014-05-29 | 2014-08-13 | 西安电子科技大学 | SAR image target recognition method based on sparse representation |
Non-Patent Citations (1)
| Title |
|---|
| ROBERT TIBSHIRANI: "Regression Shrinkage and Selection via the Lasso", 《JOURNAL OF ROYAL STATISTICAL SOCIETY. SERIES B (METHODOLOGICAL)》 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104537384A (en) * | 2015-01-21 | 2015-04-22 | 西安电子科技大学 | SAR (synthetic aperture radar) target identification method combined with likelihood ratio decision |
| CN104537384B (en) * | 2015-01-21 | 2017-09-01 | 西安电子科技大学 | A kind of SAR target discrimination methods of combination likelihood ratio judgement |
| CN105608425A (en) * | 2015-12-17 | 2016-05-25 | 小米科技有限责任公司 | Method and device for sorted storage of pictures |
| CN105608425B (en) * | 2015-12-17 | 2019-02-15 | 小米科技有限责任公司 | The method and device of classification storage is carried out to photo |
| CN106778870A (en) * | 2015-12-22 | 2017-05-31 | 中国电子科技集团公司第二十研究所 | A kind of SAR image Ship Target Detection method based on RPCA technologies |
| CN106778870B (en) * | 2015-12-22 | 2020-05-15 | 中国电子科技集团公司第二十研究所 | SAR image ship target detection method based on RPCA technology |
| CN111680593A (en) * | 2020-05-29 | 2020-09-18 | 西安电子科技大学 | SAR image target identification method based on self-adaptive one-class SVM model |
| CN111680593B (en) * | 2020-05-29 | 2023-03-24 | 西安电子科技大学 | SAR image target identification method based on self-adaptive one-class SVM model |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104200229B (en) | 2017-09-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Huang et al. | Learning-based vertebra detection and iterative normalized-cut segmentation for spinal MRI | |
| CN105809198B (en) | SAR image target recognition method based on depth confidence network | |
| Hu et al. | Automatic plankton image recognition with co-occurrence matrices and support vector machine | |
| Yoon et al. | LFIQ: Latent fingerprint image quality | |
| CN107808383B (en) | Rapid detection method for SAR image target under strong sea clutter | |
| CN101950364A (en) | Remote sensing image change detection method based on neighbourhood similarity and threshold segmentation | |
| Tombak et al. | Pixel-based classification of SAR images using feature attribute profiles | |
| CN104200229B (en) | A kind of SAR target discrimination methods of combination sparse features selection | |
| CN104680183B (en) | SAR target discrimination methods based on scattering point and the centers K oneclass classification device | |
| CN106326938B (en) | SAR image target discrimination method based on Weakly supervised study | |
| CN113674308B (en) | SAR image ship target rapid detection method based on image enhancement and multiple detection | |
| CN104239895B (en) | SAR target identification method based on feature dimension reduction | |
| CN110163182A (en) | A kind of hand back vein identification method based on KAZE feature | |
| Gao et al. | Biologically inspired progressive enhancement target detection from heavy cluttered SAR images | |
| US9547914B2 (en) | Techniques for feature extraction | |
| CN104537384A (en) | SAR (synthetic aperture radar) target identification method combined with likelihood ratio decision | |
| Dawood et al. | Texture image classification with improved weber local descriptor | |
| DE102014108492A1 (en) | Method for detecting a viewing-angle-dependent feature of a document | |
| US20230069960A1 (en) | Generalized anomaly detection | |
| CN109766899A (en) | Physical features extract and the SAR image vehicle target recognition methods of SVM | |
| Yuankui et al. | Automatic target recognition of ISAR images based on Hausdorff distance | |
| Gao et al. | Hierarchical Feature‐Based Detection Method for SAR Targets Under Complex Environment | |
| Johansson | Small vessel detection in high quality optical satellite imagery | |
| CN104091152A (en) | Method for detecting pedestrians in big data environment | |
| Tadros et al. | A contrario oil tank detection with patch match completion |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |