1562 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013

Ship Classification in TerraSAR-X Images WithFeature Space Based Sparse Representation

Xiangwei Xing, Kefeng Ji, Huanxin Zou, Wenting Chen, and Jixiang Sun

Abstract—Ship classification is the key step in maritime surveil-lance using synthetic aperture radar (SAR) imagery. In this let-ter, we develop a new ship classification method in TerraSAR-Ximages based on sparse representation in feature space, in whichthe sparse representation classification (SRC) method is exploited.In particular, to describe the ship more accurately and to reducethe dimension of the dictionary in SRC, we propose to employ arepresentative feature vector to construct the dictionary instead ofutilizing the image pixels directly. By testing on a ship data setcollected from TerraSAR-X images, we show that the proposedmethod is superior to traditional methods such as the templatematching (TM), K-nearest neighbor (K-NN), Bayes and SupportVector Machines (SVM).

Index Terms—Ship classification, sparse representation classifi-cation (SRC), synthetic aperture radar (SAR) image.

I. INTRODUCTION

SYNTHETIC aperture radar (SAR) is an effective mea-sure for large area maritime monitoring in contrast to

other alternatives such as visible light, infrared, and multi-/hyperspectral imagery, as SAR is independent of meteorologi-cal conditions [1]. In order to successfully implement maritimesurveillance with SAR imagery, ship classification is one ofthe most important steps, which has attracted a lot of interestrecently.

There have been a handful of prior works in the literaturestudying the ship classification in SAR images (see e.g., [2]–[5], [7], and references therein). The authors in [2] proposedusing a back propagation neural network classifier, whoseperformance was demonstrated on simulated data set. In [3],Margarit et al. designed fuzzy logic decision rules to iden-tify ships’ category, and analyzed the signature of ships onENVISAT 30 m resolution SAR imagery using the numericaltool GRECOSAR. However, the ship classifications in [2], [3]were only carried on simulated or relatively medium resolutionSAR imageries. Meanwhile, exploiting the polarimetric SAR(PolSAR) and polarimetric interferometric SAR (PolInSAR)for ship classification was considered in [4] and [5]. In [4],Touzi et al. investigated ship characterization with coherenttarget decompositions (CTD) on PolSAR imagery. In [5], the

Manuscript received January 1, 2013; revised April 1, 2013; accepted May 3,2013. Date of publication July 9, 2013; date of current version October 10,2013. This work is supported by the National Natural Science Foundation ofChina under Grant 61240058.

The authors are with the School of Electronic Science and Engineer-ing, National University of Defense Technology, Changsha 410073, China(e-mail: xingxiangwei@nudt.edu.cn; jikefeng@nudt.edu.cn; hxzou@163.com;yuting07290301@163.com; jxsun@gmail.com).

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.2013.2262073

authors retrieved the height information from PolInSAR dataand categorized ships from the retrieved 3-D ship geometryrepresentation. Despite the encouraging results utilizingPolSAR and PolInSAR, there still exist some technical chal-lenges for practical implementation. The Pol/PolIn SAR needsrestrictive system requirements (such as full-pol and multi-pass) that are not available in most of the satellite sensors [6]. Totackle these challenges, implementing ship classification withsingle polarimetric imagery can be a practical alternative, dueto the increased resolution for the images from TerraSAR-X,RADARSAT-2, and Cosmo-SkyMed, etc. Although there hasbeen a preliminary work [7] studying the ship recognition withhigh-resolution TerraSAR-X images, it was limited to very fewclassified targets.

On the other hand, sparse representation [8] has found greatsuccess on face recognition [9], [10], hyperspectral imageclassification [11] and SAR automatic target recognition (ATR)[12]. Through representing the test sample as the combina-tion of training samples, sparse representation classification(SRC) determines the class of the test sample based on theresulted sparsest coefficients. The sparsest coefficients containdiscriminatory information of the samples in a low-dimensionalsubspace and are robust to noise, occlusion as well as incom-plete observation [8]–[10]. Due to these characteristics, SRCmethod would be an efficient tool for ship categorization inSAR images.

In this letter, we investigate the ship classification on a largedata set to evaluate the performance of single polarizationTerraSAR-X images, for which SRC method is applied. Morespecifically, we employ the extracted features to constructthe dictionary for sparse representation instead of directlyutilizing the image pixels, due to the following two reasons.First, SAR images are very sensitive to target’s articulationor configuration, as well as the sensor’s frequency, grazingangle and resolution. Thus, even for the same type of ships,the appearance of SAR image presents large difference, andas a consequence, directly categorizing ships using the imagepixels will lead to disperse results. Second, due to the highdimensionality of the original image space, using the imagepixels directly will bring heavy computational burdens for re-solving the sparse representation. Therefore, with the extractedfeatures, we can describe ships in SAR images more accuratelyand simultaneously decrease the computational burdens. Wevalidate our proposed method by testing on a real ship dataset collected from TerraSAR-X images. It is shown that theproposed SRC method is superior to traditional methods suchas the template matching (TM), K-nearest neighbor (K-NN),Bayes, and Support Vector Machines (SVM).

1545-598X © 2013 IEEE

XING et al.: SHIP CLASSIFICATION IN TERRASAR-X IMAGES 1563

Fig. 1. Procedure of ship classification based on sparse representation classification.

The remainder of this letter is organized as follows. Section IIprovides a brief review of the sparse representation. Section IIIproposes to construct a feature based dictionary and classifiesships with the SRC method. Then, Section IV validates themethod by testing on real data sets collected from TerraSAR-Ximages. Finally, Section V concludes this letter.

II. BRIEF REVIEW ON SPARSE REPRESENTATION

In this section, we give a brief review on the sparse represen-tation, i.e., how to represent a test sample as the combination oftraining samples from a dictionary [8]. Note that the test samplecan represent a ship or other objects such as a face, etc. In thisletter, we focus on ships.

Suppose that there are K distinct classes of ships and thelabeled training samples for the K classes are known a priori,then our objective is to correctly determine the class of a newtest ship sample. Assume that the number of training samplesfor the ith class is ni, the dimension of each sample is m, anddenote φi,j ∈ R

m×1 as the jth training sample for class i. Thenthe matrix for class i containing all ni training samples isgiven by

Φm×ni

i = [φi,1, φi,2, . . . , φi,ni] . (1)

Accordingly, all training samples for the K classes are concate-nated into a dictionary matrix Φ ∈ R

m×N , i.e.,

Φm×N = [Φ1,Φ2, . . . ,ΦK ] (2)

where N =∑K

i=1 ni denotes the total number of training sam-ples. With the dictionary Φ at hand, we consider an observednew test ship sample denoted by y ∈ R

m×1. If this samplebelongs to class i, then it can be well approximated by a linearcombination of the training samples in the ith class, i.e.,

ym×1 = ci,1φi,1 + ci,2φi,2 + · · ·+ ci,niφi,ni

(3)

in which the scalar ci,j is the weighted coefficient associatedwith the jth training sample of class i to reconstruct the sampley. Correspondingly, the linear representation of y using alltraining samples in the dictionary can be denoted as

[y]m×1 = [Φ]m×N [x]N×1 (4)

with x = [0, . . . , 0, ci,1, . . . , ci,ni, 0, . . . , 0]T being a sparse

weighted coefficient vector whose entries are all zero exceptthose associated with the ith class.

With a sufficiently large number of samples for each class,the coefficient vector x is expected to be very sparse. Based onthe recent development in the theory of sparse representationand compressive sensing, the solution of x can be recoveredvia solving the following �1-norm minimization problem[9], [10]:

minx

‖x‖1 subject to y = Φx (5)

where ‖x‖1 denotes the �1-norm of x, which sums up theabsolute values of all entries in x. Moreover, the equalityconstraint in (5) can be relaxed to allow noise, i.e., problem(5) can be relaxed as

minx

‖x‖1 subject to ‖y −Φx‖ ≤ ε (6)

where ε is the allowed error tolerance. Problems (5) and (6)can be recast as linear programs (LP) and second-order coneprograms (SOCP), respectively. Thus, they are both convex andcan be solved by existing convex optimization software [13].It is worth noting that the complexity of solving the SOCP isO(m2N2), where m and N are the dimension of the sampleand the total number of training samples, respectively [cf. (1)and (2)].

III. PROPOSED SHIP CLASSIFICATION METHOD

In order to employ the above sparse representation in shipclassification for a dedicated test ship sample, we need toconstruct a dictionary of the training samples and design aclassification strategy based on the obtained sparse weightedcoefficient vector for this test sample. In this section, wefirst propose to construct a feature based dictionary, and thenclassify the test ship sample by obtaining the coefficient vectorbased on the dictionary. The procedure of this method is shownin Fig. 1.

A. Feature-Based Dictionary Construction

Before we proceed to construct the feature based dictionary,we assume that the ships have been reliably detected by apply-ing the ship detection technique and thereby separated from thesurroundings. Specifically, in this letter we first detect the shipsfrom TerraSAR-X images by implementing our previouslyproposed constant false alarm rate (CFAR) method [14]. Next,we utilize a window with a size of 256 × 256 to extract thedetected ships from the background, where the ship is centeredat the window. Then we can acquire the binary image of eachship based on precise segmentation procedures.

1564 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013

We are ready now to present the feature-based dictionaryconstruction. Note that in the face recognition, the most com-monly utilized dictionary is to use the image pixels directly, forwhich the dictionary Φ is set as the image pixels of the trainingsamples. In contrast, however, in SAR imagery the image pixelbased dictionary is not desirable due to the variety of shipappearances and the high dimensionality of the image space.Thus, we construct the dictionary of sparse representation withship features. More specifically, we propose to use both geo-metric features and electromagnetic scattering characteristic inthe feature based dictionary, which are illustrated in detail asfollows.

1) Geometric Features: Geometric features include shiplength, length to width ratio, shape complexity, centroid, andthe covariance coefficient, which have been widely utilized forship recognition in SAR imagery [15] and thus are utilized asthe features here.

First, the ship length and length to width ratio are obtainedfrom the minimum enclosing rectangle, denoted by Len and R,respectively.

Next, the shape complexity, centroid, and the covariancecoefficient can be calculated from the back scattering intensityof the target area. Specifically, the shape complexity is de-fined as

C = P 2/4πS (7)

with P being the perimeter of the ship and S being the area ofship pixels. Centroid reflects the distribution of strong scattersof the ship. Since we concentrate on the scatter distributionalong the premier axis, the centroid is defined as

X =∑m

∑n

I(m,n) ·m/∑

m

∑n

I(m,n) (8)

where I(m,n) is the intensity of the pixel with position (m,n).The covariance coefficient is represented by the ratio of meansquare covariance to the mean value μ, given by

V =

√∑m

∑n

(I(m,n)− μ)2/

μ. (9)

It is worth noting that the above geometric features derivedfrom SAR images may be different from the real features(due to the inversion process applied to SAR images), whichwould affect the performance of classification. Fortunately, itis shown in [16] that the above estimated ship features havegood correlations with the corresponding real features. Thus, byapplying the feature extraction procedure, we can achieve goodestimations of the features. As a consequence, we utilize theseestimations in the dictionary, while the effect of the estimationinaccuracy is not considered here.

2) Local Radar Cross Section Density: Besides the geo-metric features, electromagnetic scattering characteristic is theinherent characteristic of targets on SAR imagery. However,the typical attributed scattering model [17] for depicting thescattering characteristic is inapplicable here due to its extremecomputing power and model fidelity requirements. Thus, anovel feature is proposed in the following to describe the ships’scattering characteristic on SAR imagery.

Fig. 2. Division and local RCS density features of typical ships.

The radar cross section (RCS) of ship on SAR imageryconsists of numerous scatterers that come from the ship’s localphysical structure. The local physical structures of differenttypes of ships are distinct due to their functionality. Take thecontainer (cf. Fig. 3) as an example. It can be observed that theengine room is located at the stern, and thus the back scatteringintensity is strong at the stern; it can also be observed that deckcontainers are located at the superstructure of the containership, and correspondingly there exist bright edges in the SARimage. Therefore, by considering the various backscattering in-tensity of the local physical structures, we can divide the wholeship into several parts along the premier axis and accordinglypropose a novel feature, namely local RCS density, as follows.Suppose the ship is divided into L parts. Then we can formallydefine the local RCS densities as

LRCSi = (Mi/Ai)/ max1≤i≤N

(Mi/Ai), i = 1, . . . , L (10)

where Mi and Ai are the total intensity and the area of parti, respectively. Accordingly, we define LRCS as a vectorconsisting of the L local RCS densities, i.e.,

LRCS = [LRCS1, LRCS2, . . . , LRCSL]. (11)

In this letter, we choose L = 3 to emphasize on the backscattering heterogeneity of the bow, middle, and stern. Fig. 2illustrates the local RCS density features of samples fromcontainer, oil tanker, and bulk (cf. Fig. 3).

In summary, the above geometric and local RCS densityfeatures carry discriminatory information for different classesof ships. Therefore, we extract these features according to thestructure characteristic of the three typical ships, and accord-ingly denote the feature vector f of each ship sample as

f = [Len,R,C,X, V,LRCS]T (12)

based on which the feature based dictionary as well as thefeature of the test ship sample can both be obtained.

Towards this end, we have extracted the features from theship samples and also obtained the dictionary, i.e., y and Φhave been obtained. Based on the sparse representation theoryin Section II, the sparsest coefficient, denoted as x1, can beobtained by solving the convex optimization problem (6).

XING et al.: SHIP CLASSIFICATION IN TERRASAR-X IMAGES 1565

Fig. 3. Samples of the bulk (top), container (middle), and oil tanker (bottom)on TerraSAR-X imagery.

B. Classification Based on Sparse Representation

With the sparsest coefficient x1 at hand, we determine theclass of the test sample y in the following. Ideally, if all thenonzero entries in the estimate x1 are associated with one singleship class i, then we can easily determine the ith class thatthe test sample belongs to. However, due to modeling errorand noise, small nonzero entries associated with multiple otherclasses may exist. To tackle this challenge, we employ theclassification strategy in [9] as follows to harness the subspacestructure of x1 for ship classification.

For each class i, let δi : Rn → Rn be the characteristic func-

tion that selects the coefficients associated with the ith class.That is, for any vector x ∈ R

n, δi(x) ∈ Rn is a new vector

whose nonzero entries are only the entries in x associatedwith class i. Then, we can reconstruct the test sample as yi =Φδi(x1) and recognize y as the ship class that has the minimumresidual between y and yi, i.e.,

argmini

r(y).= ‖y −Φδi(x1)‖2 . (13)

IV. EXPERIMENT RESULTS AND DISCUSSION

In this section, we present experiment results on a collectedTerraSAR-X SAR ship data set to demonstrate the effectivenessof the proposed algorithm. In the experiment, the ship dataset is collected from six TerraSAR-X stripmap-mode SARimages with 2.0 m × 1.5 m resolution in azimuth and rangedirections. The image acquisition dates vary from May 13, 2008to December 04, 2010. With the aid of ground truth informationsupplied by AIS, it is known a prior that there are three kindsof ships in the data set: container (C), oil tanker (OT), andbulk (B). The number of these three kinds of ships is 150, 150,and 150, respectively. Some ship samples of the data set areshown in Fig. 3. Note that we only focus on the classificationfor these three typical ships in this letter. If there are moretypes of ship samples available, the method here can be viewedas a sub-classifier and thereby can be expanded to a largerATR-based ship classifier; on the other hand, the method herecan also be extended to classify these new types of ships withtheir features extracted.

We carry out the experiments using MATLAB implementa-tions on a 3.0 GHz machine with 4 GB RAM. We compare theclassification performance of the proposed SRC algorithm withthe traditional TM, K-NN, Bayes, and SVM algorithms.

To evaluate the performance of the SRC method for shipclassification, we randomly select 40 samples of each classfor training and the rest samples for recognition test. Forcomparison, classification experiments are conducted on boththe original image pixels and the feature space. In the case ofimage pixels, the image is down sampled to a 12 × 12 matrix.In the case of feature space, all the ship images are processed toextract the geometric and local RCS density features as in (12).ε is set as 0.05 for the SOCP in (6). For implementing theK-NN (K = 3) and SVM methods, the MATLAB code avail-able at http://csie.ntu.edu.tw/~cjlin/libsvm/ is used. The radialbasis function (RBF) is adopted as a kernel function of SVM,and the RBF parameters are selected empirically to achieveoptimal performances.

Since the training samples are selected randomly, we carryout the classification experiments repeatedly for ten times andaverage the results. Table I illustrates the comparison on clas-sification accuracy and speed of the TM, K-NN, Bayes, SVM,and SRC methods in image and feature spaces. It is observedthat all the methods except the TM achieve better performancesin the feature space than that in the image space. In the featurespace, it is also observed that the SRC method outperformsthe other methods and yields the best overall classification rateas high as 92.00%. This performance gain validates that theSRC is applicable to classify ships in SAR images, and further-more, the extracted features are effective than original imagepixels.

Table I also presents the detailed classification results ofthe classifiers on the three classes of ships. For the bulk, wecan observe that all five methods achieve higher classifica-tion rate, since the bulk maintains a smaller size than the oiltanker and container. For the container, we can see that higherclassification accuracy is achieved in the feature space thanin the image space, opposite to the case with the oil tanker.The different performances indicate that the features and imagepixels maintain diverse discriminatory abilities, especially forthe container. In general, one can also observe that the SRCmethod achieves higher classification rate than the other fourmethods. This is due to the fact that the SRC reconstructsthe test sample as a linear combination of training samplesand is robust to occlusion and noises, while the other fourmethods would be seriously affected by them due to the similargeometric size between the oil tanker and container.

Regarding the time consuming, it is observed that all the fivemethods speed up in the feature space, which demonstrates thatthe reduced dimensionality significantly reduces the complexityof classification methods. It is also observed that the SVMmethod consumes the fewest time, which indicates that SVMmight be a practical alternative by considering the performance-complexity tradeoff. Although it is observed that the SRCmethod has a relatively high complexity, it is worth noting thesparse optimization algorithms are recently under very activeresearches. Thus, the SRC is expected to be more efficient andpromising.

1566 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 6, NOVEMBER 2013

TABLE ICOMPARISON ON CLASSIFICATION ACCURACY (%) AND SPEED (S) OF 1-NN, 3-NN, BAYES, RBF-SVM,

AND SRC METHODS. (a) IMAGE SPACE. (b) FEATURE SPACE

V. CONCLUSION

A ship classification method based on SRC in feature space isproposed in this letter. The method first extracts the geometricand the local RCS density features to construct the dictionary,and then applies the SRC method to recognize ships in thefeature space. It is shown by experiments that the proposedmethod outperforms the TM, K-NN, Bayes, and SVM for theclassification of container, oil tanker, and bulk on TerraSAR-XSAR images. Despite the effectiveness of the proposed method,many developments need to be further considered in the futurework, including optimization algorithms of the sparse repre-sentation, extraction of more features to describe the ships andexperiments carried on a large data set under various conditions.

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