locality preserving property

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268 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 2, MARCH 2013

SAR Target Configuration Recognition UsingLocality Preserving Property and

Gaussian Mixture DistributionMing Liu, Yan Wu, Peng Zhang, Qiang Zhang, Yanxin Li, and Ming Li

AbstractFeature extraction is the key step of synthetic aper-ture radar (SAR) target configuration recognition. A statisticalmodel embedding the locality preserving property is presentedto extract the maximum amount of desired information from thedata, which is of crucial help to recognition. The noise, or error,of the SAR image samples is described by a Gaussian mixturedistribution, and the locality preserving property is embeddedinto the statistical model to focus on the problem of configurationrecognition. Along with the extraction of the information of inter-est through the use of the statistical model, also, the preservation ofthe local structure of the data set is achieved. Parameter estimationis implemented through the expectationmaximization algorithm.Experimental results on the Moving and Stationary Target Acqui-sition and Recognition data set validate the effectiveness of theproposed method. SAR target configuration recognition is realizedwith satisfactory accuracy.

Index TermsConfiguration recognition, Gaussian mixturedistribution, locality preserving property, synthetic aperture radar(SAR) image.

I. INTRODUCTION

T

HE AIM of synthetic aperture radar (SAR) target configu-

ration recognition is to find the probable target in the SARscene and then recognize the configuration of the found target.

The target configuration indicates how the target is deployed,

and targets of the same type with different configurations

are called variants [1]. Traditional algorithms for SAR target

recognition focus on the recognition of target types, which

means that targets with different configurations of the same

type are regarded as the same [2][5]. However, the recognition

of the target configuration is of significance to a number of

application areas, such as detailed information capturing of

interested targets and battlefield perception.

Manuscript received January 17, 2012; revised April 6, 2012; accepted

April 30, 2012. Date of publication July 6, 2012; date of current versionOctober 22, 2012. This work was supported in part by the National NaturalScience Foundation of China under Grant 60872137, by the National DefenseFoundation of China under Grant 9140C0103071003, by the Aviation Sci-ence Foundation of China under Grant 2011018106, and by the SpecializedResearch Fund for the Doctoral Program of Higher Education under Grant20110203110001.

M. Liu, Y. Wu, Q. Zhang, and Y. Li are with the School of ElectronicEngineering, Xidian University, Xian 710071, China (e-mail: [email protected]; [email protected]; [email protected];[email protected]).

P. Zhang and M. Li are with the National Key Laboratory of Radar SignalProcessing, Xidian University, Xian 710071, China (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LGRS.2012.2198610

The key step of a recognition algorithm lies in feature ex-

traction, which not only realizes the dimensionality reduction

of the data set but also preserves the information useful for

recognition of the samples as much as possible. An algorithm

is proposed for target configuration recognition using locality

preserving property and Gaussian mixture distribution, which

extracts the maximum desired information through a statistical

model. Gaussian mixture distribution has good adaptability, and

its parameter estimation is relatively easy. It can approximateany distribution smoothly in theory, which has been widely

applied to many SAR image processing areas like segmentation

and classification [6][8]. Considering the existence of the

speckle noise in SAR images and the residual error of the

model, a mixture of Gaussian distributions is used to describe

the statistical property of the unwanted component of SAR

images. The locality preserving property can ensure that the

same configuration samples that are close to each other in

the high-dimension space are still close in the low-dimension

space. To preserve the local structure of the samples of the same

configuration, the locality preserving property is embedded into

the statistical model, which is of importance to SAR targetconfiguration recognition.

The main steps of the proposed recognition algorithm is

shown in Fig. 1. In the first step, the images are preprocessed

to enhance the recognition performance [3], [4]; in the second

step, the projection matrix is obtained by using the Gaussian

mixture distribution statistical model embedding the locality

preserving property, and the SAR image to be recognized is

projected by the projection matrix, and parameter estimation is

implemented through the expectation maximization (EM) algo-

rithm [9][11]; in the last step, a nearest neighbor classifier [12]

is applied to identify the target configuration. The effectiveness

of the proposed algorithm is verified with experimental results,

and the comparisons with other algorithms further prove theadvantages of the proposed one.

II. SAR TARGET CONFIGURATION

RECOGNITION ALGORITHM

As mentioned earlier, effective feature extraction is the

precondition of accurate recognition. For a given SAR im-

age sample yi (i = 1, 2, . . . , N ), N is the number of theSAR images which are used as the training data, and we

have [13]

yi

= Wxi

+m + ni

(1)

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LIU et al.: SAR TARGET CONFIGURATION RECOGNITION 269

Fig. 1. Flow diagram of the proposed algorithm.

where W is the projection matrix and xi (i = 1, 2, . . . , N ) isthe reduced-dimensionality representation ofyi.m is the mean

ofy, y = {y1,y2, . . . ,yN} is the original data set, and ni isthe corresponding noise, or error. As can be seen, the original

sample yi consists of both the useful component xi and the

unwanted component ni. The essential of feature extraction is

to preserve the useful information as much as possible, which

is helpful for recognition. How to achieve the elimination of

the influence ofn, n = {n1,n2, . . . ,nN}, and the preservationof the desired x, x = {x1,x2, . . . ,xN}, is the very point thatfeature extraction focuses on.

In the view of statistic, the objective function can be ex-

pressed as

argW

maxp(x|y). (2)

The marginal distribution p(y) does not give a direct in-fluence to the objective function, and through the Bayesian

equation p(x|y) = p(x)p(y|x)/p(y), we can get

p(x|y) p(x)p(y|x). (3)

Thus, the objective function in (2) can be updated as

argW

max[p(x)p(y|x)] = argW

maxp(y,x). (4)

A. Gaussian Mixture Distribution for the Likelihood Function

Taking the special statistical property of SAR images into

consideration, we describe the error (consists of the speckle

noise caused by SAR imaging and the residual error of the

model) by Gaussian mixture distribution, which can approxi-

mate any distribution smoothly in theory [6]. Utilizing (1), the

likelihood function is given as

p(yi|xi) =Cc=1

p(c)p(yi|xi, c) (5)

where C is the number of Gaussian distributions, p(yi|xi, c) N(Wxi +m +c,

2

c ), c and 2

c are the corresponding

mean and variance ofni, respectively, p(c) is the weight of the

cth part (c = 1, 2, . . . , C ), and we haveC

c=1 p(c) = 1.Substituting p(yi|xi, c) into (5), the likelihood function is

shown as

p(yi|xi) =C

c=1p(c)

1

22c

D2

exp(yiWximc)T(yiWximc)

22c

(6)

where D is the dimensionality of the original samples and thesymbol T represents the transpose of matrix.

B. Locality Preserving Property Embedded Into the Prior

As to the prior p(x) in (4), it is regarded as p(x) N(0, I) [11], and I is an identity matrix

p(x) =p(x1,x2, . . . ,xN) =N

i=1

p(xi)

=Ni=1

1

2

d2

exp

1

2xTi xi

=

1

2

Nd2

exp

1

2tr(xTx)

(7)

where d is the dimensionality ofx and tr() represents the traceof matrix.

In order to preserve the local structure of the data that is

useful for configuration recognition, here, p(x) is modified as

p(x) =p(x1,x2, . . . ,xN) =N

i=1

p(xi)

=

1

2

Nd2

exp

12

Ni,j=1

(xi xj)TSij(xi xj)

=

1

2

Nd2

exptr(xLxT)

(8)

where L = H S is the Laplacian matrix, H is a diagonalmatrix whose entries Hii =

j Sij (or Hii =

i Sij, since

S is symmetric) are column sums ofS, and S is the affinity

matrix that reflects the similarity between any two samples. It

is constructed as

Sij =

exp yiyj

2

t

yi,yj belong to the same class0 yi,yj belong to different classes

(9)

where t is a constant.Here, we take a close look at (8). The physical implication

can be seen in this way: Provided that the samples yi and

yj are close, (8) guarantees that the closer xi and xj are,

the larger p(x) will be, and vice versa. In other words, thesamples that are close in the high-dimension space are still

close in the low-dimension space through the construction of

the prior given by (8). Hence, the local structure of the data set

has been preserved, which is just as what is discussed in [14]

named locality preserving projection (LPP), or better, we havefused the objective function presented in [14] into the prior. In


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addition, as can be seen from (9), the closer yi and yj are,

the bigger Sij will be. Since we wish p(x) to be as large aspossible demanded by (4), when Sij is big implying that yi and

yj are close to each other, to be in accordance with the objective

function, the value of(xi xj)2 has to be smaller. It means that

xi and xj should be even closer after dimensionality reduction,

which is just what we expect.Note that the matrix S used here is different from that in

[14]. The S constructed here establishes relationships among

all the samples that belong to the same class, while weights of

the samples that belong to different classes are all set to zero.

The global topological structure of the data is preserved by this

improvement. Due to the full use of the given labels, both the

local and global topological properties of the data are retained.

C. Parameter Estimation Using EM Algorithm

The objective function expressed by (4) can move to

argW

maxp(y,x) argW

max [lnp(y,x)]

= argW

maxNi=1

ln [p(yi,xi)] . (10)

In this part, we come to the solution of the parameters

using the EM algorithm [9][11]. We note that Pic (missingdata in this situation) denotes indicator variable labels whose

model is responsible for generating ni, and we can derive an

EM algorithm by considering the corresponding log-likelihood

function of the complete data which takes the form

L =

Cc=1

Ni=1

Pic ln [p(c)p(yi,xi|c)] . (11)

In the expectation step, taking the expectation of L withrespect to the posterior distributions and neglecting the constant

parameters that do not give an influence to the results, we have

=Cc=1

Ni=1

Pic

lnp(c)

D

2ln2c

1

22cyi Wxi m c

2

1

2

N

j=1

(xi xj)TSij(xi xj) (12)

where Pic= (p(ni|c)p(c)/C

c=1 p(ni|c)p(c))=(p(ni|c)p(c)/p(ni)) is the posterior responsibility of component c for gen-erating ni, p(ni|c) N(c,

2

c ).Then, we calculate the expectation ofx through the deriva-

tive of the function shown in (12)

xi =

Cc=1

Pic

1

2cWTW + (Hii 1)

1

C

c=1Pic

1

2cWT(yi m c) + 0

(13)

where 0 =N

j=1,j=i xjSij .

TABLE ICONFIGURATIONS AND SIZES OF THE TRAINING AND TESTING DATA SETS

In the maximization step, is maximized with respect to c,

2

c , and W to get the updated values with the newly obtainedx. As to p(c), we can take advantage of the Lagrange multiplier; the new value of p(c) can be obtained through maximizingthe following equation:

+

1

Cc=1

p(c)

. (14)

The newly obtained parameters are

p(c) = 1N

Ni=1

Pic

c =1

Ni=1

Pic

Ni=1Pic(yi Wxi m)

2c =1

D

Ni=1

Pic

Ni=1

Picyi Wxi m c2

W =

Cc=1

Ni=1

Pic

1

2c(yi m c)x

T

i

Cc=1

Ni=1

Pic

1

2cxix

T

i

1

. (15)

The algorithm iterates these two steps until convergence.

Hereto, the parameters are obtained, which are ready for

identification of the target configuration through the use of anearest neighbor classifier [12].

III. EXPERIMENTAL RESULTS AND ANALYSIS

Experimental results on the Moving and Stationary Target

Acquisition and Recognition database supported by the

Defense Advanced Resarch Projects Agency/Air Force

Research Laboratory of the U.S. [1] verify the effectiveness

of the proposed algorithm. The armored personnel carrier

BMP2 consists of three different configurations, which are

sn-9563, sn-9566, and sn-c21; the configurations of the main

battle tank T72 are sn-132, sn-812, and sn-s7; and the armored

personnel carrier BTR70 is with only one configuration sn-c71.The SAR images obtained with the depression angle 17 are


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LIU et al.: SAR TARGET CONFIGURATION RECOGNITION 271

TABLE IIPERFORMANCE OF TARGET-T YP E RECOGNITION UNDER DIFFERENT ALGORITHMS

Fig. 2. Recognition rate of each configuration versus dimensionality.

TABLE IIIPERFORMANCE OF TARGET CONFIGURATION RECOGNITION UNDER DIFFERENT ALGORITHMS

used as the training data set, and the SAR images obtained

with the depression angle 15 are used as the testing data set

recommended by the workgroup [1]. All the images are 128128 pixels, and the aspect angles of the vehicles lie between

0 and 360. The configurations and sizes of the training and

testing data sets are given in Table I.

To validate the advantage of the proposed algorithm, the

LPP-based algorithm [14] and the principal component analysis

(PCA)-based algorithm are taken as comparisons. First, the

redundant background is excluded to get a 48 48 pixelsubimage from the center of each image, and the amplitude of

the subimage is normalized subsequently.

In the first instance, we focus on the recognition of the

target type as the existing algorithms [2][5]; the results under

different algorithms are shown in Table II. It can be seen that the

recognition rate of the proposed algorithm is the best for eachtype; ideal 100% accuracy can be obtained for the type BTR70

with only one configuration. However, the advantage is not

explicit; the total recognition rate of the PCA-based algorithm

whose performance is the worst of the three can even reach as

high as 97.00%. The reason for this phenomenon is that even

misjudging one configuration into another one of the same type

will still be regarded as the right judgment, which contributes to

the high recognition rate. However, in situations such as more

detailed information capture, the recognition of the type is not

enough as aforementioned.

Experiments are carried out on the interested target con-

figuration recognition. The curve of recognition rate versus

dimensionality is shown in Fig. 2. As can be seen, the proposed

algorithm (with red solid line) can obtain better results than

both the LPP-based algorithm (with green dashed line) and the

PCA-based algorithm (with blue dotted line) for each configu-

ration. Different from type recognition, the advantage is muchmore explicit in this situation. Table III displays the recognition


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TABLE IVCONFUSION MATRIX OF THE PROPOSED ALGORITHM

WITH THE BEST TOTAL RECOGNITION RESULT

rate of each configuration when the total recognition rate is the

highest, and Table IV is the corresponding confusion matrix

of the proposed algorithm. Inspecting Table IV, we can find

out that, in the view of type recognition, 100% accuracy can

be obtained for BTR70, which is with only one configuration.

Even to the types BMP2 and T72, both with three different

configurations, there are only two mistakes. One of them is the

misjudgment of BMP2-sn9563 into T72-sn812, and the other

one is the misjudgment of T72-snS7 into BMP2-sn9566.

In this situation, the performance of the PCA-based method

is still the worst among the three. The reason lies in the

fact that the PCA-based algorithm cannot preserve the local

structure of the data, which is of great help to recognition [14].

The LPP-based method performs better than the PCA-based

one, although worse than the proposed one, because it makes

good use of the local structure of the data; the discriminatinginformation for recognition is preserved.

As to the proposed algorithm, satisfactory performance is

achieved by using the maximum desired information for recog-

nition through the statistical model. Owing to the advantage of

the Gaussian mixture distribution model, which can describe

any distribution accurately, a mixture of Gaussian distributions

is used to describe the error precisely with the consideration of

the particular statistical property of the SAR images. Moreover,

the locality preserving property is introduced into the statis-

tical model successfully to capture the local structure of the

data as the LPP algorithm [14]. Moreover, with the modified

construction of the affinity matrix, not only the advantage ofthe local structure of the data is preserved but also the global

topological structure of the data is obtained, which is also useful

for recognition.

IV. CONCLUSION

A new way of feature extraction has been proposed for SAR

target configuration recognition in this letter. The statistical

property of the data is taken into consideration when extract-

ing feature. The maximum amount of desired information is

extracted effectively in the view of statistic. Due to the speckle

noise existed in the SAR image and the error of the model, a

mixture of Gaussian distributions is used to describe the un-

wanted component. Moreover, the locality preserving property

is embedded into the statistical model successfully, and thus,

the local structure of the data set is preserved effectively. The

parameters are estimated using the EM algorithm; promising

results are obtained.

Note that some advanced models have been proposed to

describe the statistical property of SAR images [15][17]. In-troduction of these advanced models into the proposed method

will provide the basis of future research.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers for

their helpful comments and suggestions.

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