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Target Recognition of SAR Images via Matching Attributed Scattering Centers with Binary Target Region Jian Tan 1,2 , Xiangtao Fan 1,2 , Shenghua Wang 3, * and Yingchao Ren 2 1 2 3

*

Hainan Key Laboratory of Earth Observation, Sanya 572029, China; [email protected] (J.T.); [email protected] (X.F.) Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100094, China; [email protected] School of Public Administration and Mass Media, Beijing Information Science and Technology University, Beijing 100093, China Correspondence: [email protected]

Received: 25 July 2018; Accepted: 5 September 2018; Published: 10 September 2018







Abstract: A target recognition method of synthetic aperture radar (SAR) images is proposed via matching attributed scattering centers (ASCs) to binary target regions. The ASCs extracted from the test image are predicted as binary regions. In detail, each ASC is first transformed to the image domain based on the ASC model. Afterwards, the resulting image is converted to a binary region segmented by a global threshold. All the predicted binary regions of individual ASCs from the test sample are mapped to the binary target regions of the corresponding templates. Then, the matched regions are evaluated by three scores which are combined as a similarity measure via the score-level fusion. In the classification stage, the target label of the test sample is determined according to the fused similarities. The proposed region matching method avoids the conventional ASC matching problem, which involves the assignment of ASC sets. In addition, the predicted regions are more robust than the point features. The Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset is used for performance evaluation in the experiments. According to the experimental results, the method in this study outperforms some traditional methods reported in the literature under several different operating conditions. Under the standard operating condition (SOC), the proposed method achieves very good performance, with an average recognition rate of 98.34%, which is higher than the traditional methods. Moreover, the robustness of the proposed method is also superior to the traditional methods under different extended operating conditions (EOCs), including configuration variants, large depression angle variation, noise contamination, and partial occlusion. Keywords: synthetic aperture radar (SAR); target recognition; attributed scattering center (ASC); region matching; score fusion

1. Introduction Owing to the merits of synthetic aperture radar (SAR), interpreting high-resolution SAR images is becoming an important task for both military and civilian applications. As a key step of SAR interpretation, automatic target recognition (ATR) techniques are employed to decide the target label in an unknown image [1]. Typically, a general SAR ATR method is comprised of two parts: feature extraction and a decision engine. The former tries to obtain low-dimensional representations from the original images while conveying the original discrimination capability. In addition, the high dimensionality of the original image is reduced significantly, which helps improve the efficiency of the following classification. Different kinds of features are adopted or designed for SAR target recognition in the previous literature. The Sensors 2018, 18, 3019; doi:10.3390/s18093019

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features describing the physical structures or shape of the target are extracted for SAR ATR, e.g., binary target region [2–4], target outline [5,6], target’s radar shadow [7], local texture [8], etc. Park et al. [2] design several descriptors from the binary target region for SAR target recognition. In [3], a SAR ATR method is designed through the matching of binary target regions, where the region residuals are processed by the binary morphological operations to enhance divergences between different classes. In [4], the binary target region is first described by the Zernike moments, and a support vector machine (SVM) is employed for classification afterwards. The target outline is taken as the discriminative feature in [5], which is approached by the Elliptical Fourier Series (EFS). Then, SVM is used to classify the outline descriptors. Yuan et al. use the local gradient ratio pattern to describe SAR images with application to target recognition [8]. The projection features are also prevalent in SAR ATR. Principal component analysis (PCA) [9], linear discriminant analysis (LDA) [9], and non-negative matrix factorization (NMF) [10] are often used to extract the projection features. Based on the idea of manifold learning, other projection features are designed to exploit the properties of the training samples [11–13]. In the high frequency area, the total backscattering of a whole target can be regarded as the summation of several individual scattering centers [14]. In this way, the scattering center features are discriminative for SAR target recognition. Several SAR ATR methods have been proposed using the attributed scattering centers (ASCs) which achieve good effectiveness and robustness [15–19]. In the classification stage, the classifiers (decision engines) are adopted or designed according to the properties of the extracted features. For features with unified forms, e.g., feature vectors extracted by PCA, classifiers like SVM [4,5,20,21], adaptive boosting (AdaBoost) [22], sparse representation-based classification (SRC) [21,23,24], etc., can be directly used for classification tasks. The deep learning method, i.e., convolution neural network (CNN), is also demonstrated to be notably effective for image interpretation [25–29]. In CNN, the hierarchical deep features are learned by the convolution layers with a softmax classifier to perform the multi-class regression at the end. However, for features with no specific orders, e.g., ASCs, the former classifiers cannot be directly employed for classification. Usually, a similarity measure between these features is defined [16–18]. Afterwards, the target label is assigned as the template class achieving the maximum similarity. This paper proposes an efficient and effective method for SAR ATR via matching ASCs with binary target regions. In previous works [16–18] using ASCs for SAR ATR, a complex one-to-one correspondence is often built for the following similarity evaluation. In [16], Chiang et al. solve the assignment problem between two ASC sets using the Hungarian algorithm and evaluate the similarity as the posterior probability. Ding et al. exploit the line and triangle structures in the ASC set during the similarity evaluation based on the one-to-one correspondences between two ASC sets [17,18]. However, it is still a difficult and complex task to precisely build the correspondence between the ASCs for the following reasons [30]. First, there are always missing or false alarms caused by the extended operating conditions (EOCs) such as occlusion, noises, etc. Second, the ASCs cannot be extracted with no errors. As a result, the extraction errors also cause problems. Lastly, as point features, the ASCs lack of high stability, especially because SAR images change greatly with variations in the target azimuth [31]. As a remedy, in this study, each of the extracted ASCs from the test image is represented by a binary region. In detail, the backscattering field of the ASC is first calculated based on the ASC method, and then transformed to the image domain. Afterwards, a global threshold is used to segment the reconstructed images of individual ASCs as binary regions. In the image domain, the spatial positions of the ASCs can be intuitively observed. For ASCs with higher amplitudes, they tend to produce regions with larger areas because their images contain more pixels with high intensities. In addition, the distributed ASCs with lengths could also maintain their attributes at proper thresholds. Hence, the predicted binary regions actually embody the attributes of the ASCs such as the spatial positions, relative amplitudes, and lengths. The binary regions of individual ASCs are matched to the extracted binary target region from the corresponding template samples. The overlap and differences during the region matching reflect the correlations between the test image and corresponding templates from various classes. Based on the region matching results, three matching scores are defined. To combine

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the strengths of different scores, a score-level fusion is performed to obtain a unified similarity. Finally, the target label is determined according to the calculated similarities. In the remainder of this study, we do the following: in Section 2, we introduce the extraction of binary target region and ASCs. The main methodology of matching ASCs with the binary target region is presented in Section 3. In Section 4, experiments are conducted on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset. Finally, in Section 5, we draw conclusions according to the experimental results, and outline some future work. 2. Extraction of Binary Target Region and ASCs 2.1. Target Segmentation We first obtain the binary target region using the target segmentation algorithm. In this study, the detailed target segmentation algorithm consists of the following steps: (1): Equalize the original image intensities into the range of 0 to 1 by the standard histogram equalization algorithm [32]. (2): Perform mean filtering on the equalized image with a 3 × 3 kernel [32]. (3): Preliminarily segment the “smoothed” image using the normalized threshold of 0.8. (4): Remove false alarms caused by the noises using the Matlab “bwareaopen” function, which is capable of removing regions with a few pixels. (5): Perform the binary morphological closing operation [32] to fill the possible holes and connect the target region. Figure 1 illustrates the implementation of target segmentation with a SAR image of BMP2 tank in the MSTAR dataset shown as Figure 1a. The equalized and smoothed images from Step 2 and Step 3 are displayed in Figure 1b,c, respectively. After the preliminary segmentation, the result is shown in Figure 1d, in which there are some false alarms brought by the noises or clutters. In this step, the threshold is set to be 0.8 mainly according to the repetitive observations at different thresholds, as well as referring to the previous works [22]. The pixel number for the “bwareaopen” function is set to 20; thus, the isolated regions with less than 20 pixels can be eliminated. The result is obtained as Figure 1e. The morphological closing operation is conducted using the 7 × 7 diamond structuring element shown as Figure 2. Finally, the intact binary region is obtained as Figure 1f. The binary target region describes the physical structures and geometrical properties of the target. Actually, it is a continuous region connecting the images of individual scattering centers on the target. From this aspect, the binary target region can be used as the reference for ASC matching.

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Figure 1. Illustration of of the target segmentation algorithm: (a)(a) original SAR image of of BMP2 tank; (b) Illustration ofthe the target segmentation algorithm: (a) original SAR image of BMP2 tank; Figure 1. Illustration target segmentation algorithm: original SAR image BMP2 tank; (b) equalized image; (c) smoothed image after mean filtering; (d) preliminary segmentation result; (e)(e) (b) equalized image; (c) smoothed image after mean filtering; preliminary segmentation result; equalized image; (c) smoothed image after mean filtering; (d) (d) preliminary segmentation result; result after the opening operation; (f)(f) result after the closing operation. (e) result after the opening operation; (f) result after the closing operation. result after the opening operation; result after the closing operation.

Figure 2. The The structuring elements used in the closing operation. Figure 2. The structuring elements used in in thethe closing operation. Figure 2. structuring elements used closing operation.

2.2. ASC Extraction 2.2. ASC Extraction 2.2. ASC Extraction 2.2.1. ASC Model 2.2.1. ASC Model 2.2.1. ASC Model SAR images reflect the target’s electromagnetic characteristics in the high frequency region, which SAR images reflect thethe target’s electromagnetic characteristics in in thethe high frequency region, SAR images reflect electromagnetic characteristics high frequency region, can be quantitively modeled astarget’s a summation of local properties, i.e., scattering centers [14]. The target’s which can be quantitively modeled as a summation of local properties, i.e., scattering centers [14]. which can be quantitively modeled as summation of local properties, i.e., scattering centers [14]. backscattering field can be expressed asafollows: The target’s backscattering field can be expressed as follows: The target’s backscattering field can be expressed as follows: K

K

K θ) = ∑ Efi (, f ;, θ φ; θ ) EE (Ef((,ff, ;,φ; θ Ei (E  ;)θ)   ( f ,  i;)θii ) i

(1) (1)(1)

i 1i =1 i 1

K Knumber In In Equation (1), frequency angle, respectively. is is thethe In Equation (1), φdenotes thethe frequency andand aspect angle, respectively. K is the fand denotes Equation (1),ff and and denotes the frequency andaspect aspect angle, respectively. of the ASCs in the radar measurement. For a single itsASC, backscattering field canfield be calculated number of of thethe ASCs in in thethe radar measurement. For aASC, single itsits backscattering can bebe number ASCs radar measurement. For a single ASC, backscattering field can according to ASC model [14] Equation (2). calculated according to ASC model [14] Equation (2). calculated according to ASC model [14] Equation (2). − j4π f f αi · exp(j 4π f ff cos φ + y sin φ)) j 4π EEi ((f f, φ; , ;θθi ))= AAi( ·j ( j )fαi) αexp(   yi sin  )) )) c ( x(i(xcos i E ( f ,  i; θ ) i A  ( j f c ) i  exp( xii cos yii sin (2) i i i f 2π f c c c f ·sinc( cc Li sin(φ − φi )) · exp(−2π f γi sin φ) (2)(2) 2π2π f f sinc( L sin(   )) exp(-2πfγ sin ) i  ))  exp(-2πifγ sin )  sinc( i i wave and θ where c denotes the propagation velocity of electromagnetic = { θi } = c c i Li sin( [ Ai , αi , xi , yi , Li , f i , γi ](i = 1, 2, · · · , K ) represents the attribute set of all the ASCs in a SAR image. where the propagation velocity electromagnetic c c denotes where denotes propagation velocity ( xof,of electromagnetic wave wave and and In detail, for the ith ASC, the Ai is the complex amplitude; i yi ) denote the spatial positions; αi is represents the attribute set of all the ASCs in a SAR θθ {θi{}θ } [A[i A , αi, ,αxi,,xyi, ,yLi, ,Lfi,, fγi, ]( i 1, 2, , K ) γ i ]( i  1, 2,  , K ) represents the attribute set of all the ASCs in a SAR i i i i i i i image. image.InIndetail, detail,forforthetheithithASC, ASC,Ai Ais isthethecomplex complexamplitude; amplitude; xi,xyi, y denote denotethethespatial spatial i

i

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the frequency dependence; for a distributed ASC, Li and φi represent the length and orientation, respectively; and γi denotes the aspect dependence of a localized ASC. 2.2.2. ASC Extraction Based on Sparse Representation The characteristics of a single SAR image can be approximated by only a few ASCs. So, the ASCs to be extracted are actually sparse in the model-parameter domain, which discretize the parameter space to form an overcomplete dictionary [33,34]. Therefore, the sparse representation can be employed to estimate the ASC parameters. The ASC model in Equation (1) is first expressed as Equation (3). s = D (θ ) × σ

(3)

where s is obtained by reformulating the 2-D measurement E( f , φ; θ ) into a vector; D (θ ) represents the overcomplete dictionary. In detail, each column of D (θ ) stores the vector form of the electromagnetic field of one element in the parameter space θ; σ denotes a sparse vector and each element in it represents the complex amplitude A. In practical situations, the noises and possible model errors should also be considered. Therefore, Equation (3) is reformulated as follows: s = D (θ ) × σ + n

(4)

In Equation (4), n denotes the error term, which is modeled as a zero-mean additive white Gaussian process. Afterwards, the attributes of the ASCs can be estimated as follows: σˆ = argminkσ k0 , s.t. ks − D (θ ) × σ k2 ≤ ε

(5)

σ

In Equation (5), ε = knk2 represents the noise level; k•k0 denotes l0 -norm and σˆ is the estimated complex amplitudes with respect to the dictionary D (θ ). As a nondeterministic polynomial-time hard (NP-hard) problem, the sparse representation problem in Equation (5) is computationally difficult to solve. As a remedy, some greedy methods, e.g., the orthogonal matching pursuit (OMP), are available [33,34]. Algorithm 1 illustrates the detailed procedure of ASC extraction based on sparse representation. Algorithm 1 ASC Extraction based on Sparse Representation Input: The vectorized SAR image s, noise level ε, and overcomplete dictionary D (θ ). Initialization: Initial parameters of the ASCs θˆ = ∅, reconstruction error r = s, counter t = 1. 1. while kr k22 > ε do 2. Calculate correlation: C (θ ) = D H (θ ) × r, where (•) H represents conjugate transpose. 3. Estimate parameters: θˆt = argmaxC (θ ), θˆ = θˆ ∪ θˆt . θ

4. Estimate amplitudes: σˆ = D † (θˆ) × s, where (•)† represents the Moore-Penrose pseudo-inverse, D (θˆ) ˆ denotes the overcomplete dictionary from the parameter set θ. ˆ 5. Update residual: r = s − D (θ ) × σˆ . 6. t = t + 1 ˆ Output: The estimated parameters set θ.

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3. 3. Matching Matching ASCs ASCs with with Binary Binary Target Target Region 3.1. Region Region Prediction Prediction by by ASC ASC 3.1. As point point features, features,the thematching matchingofoftwo twoASC ASCsets setsis is a complex and difficult task, analyzed As a complex and difficult task, as as analyzed in in previous research [30]. a remedy, thisstudy, study,the theextracted extractedASCs ASCsfrom fromthe the test test image image are are previous research [30]. As As a remedy, in in this represented as as binary binary regions regions using using a thresholding thresholding method. method. The The backscattering backscattering field field of of each each ASC ASC is is represented first calculated thethe ASCASC model in Equation (2). Afterwards, the imaging performed first calculatedbased basedonon model in Equation (2). Afterwards, the process imagingis process is to transform the backscattering field to the image domain. In this study, the imaging process is performed to transform the backscattering field to the image domain. In this study, the imaging consistent with the MSTAR including windowing (−35 dB Taylor window), process is consistent with theimages MSTAR images zeropadding, including zeropadding, windowing (−35 dB Taylor and 2D fast Fourier transform The (FFT). detailed operating of MSTAR SAR imagesSAR can window), and 2D fast Fourier (FFT). transform The detailedparameters operating parameters of MSTAR be referred to [32]. Denoting the maximum intensity of the images from individual ASCs as m, the images can be referred to [32]. Denoting the maximum intensity of the images from individual ASCs global threshold region for prediction is set to beism/α, is ,the scaleαcoefficient larger than 1. as global for threshold region prediction set towhere be mα/ α where is the scale coefficient m , the Figure 3 shows the predicted binary regions of three ASCs with different amplitudes at α = 30. The larger than 1. Figure 3 shows the predicted binary regions of three ASCs with different amplitudes at images from ASCs with higher amplitudes tend to have higher pixel intensities, as shown in Figure 3a α 30 . The images from ASCs with higher amplitudes tend to have higher pixel intensities, as (from left right).3aTheir predicted binary Their regions are shown in Figure 3b, correspondingly. It shows shown in to Figure (from left to right). predicted binary regions are shown in Figure 3b, that the stronger ASCs produce binary regions with larger areas. Figure 4 shows the predicted binary correspondingly. It shows that the stronger ASCs produce binary regions with larger areas. Figure 4 region the of apredicted distributed ASC. As shown, the lengthASC. of the canofbe the shows binary region of a distributed Asdistributed shown, theASC length themaintained distributedinASC predicted region at the proper threshold. Therefore, the predicted binary region can effectively convey can be maintained in the predicted region at the proper threshold. Therefore, the predicted binary the discriminative attributes of the the original ASC, such as spatial positions, relative and region can effectively convey discriminative attributes of the original ASC, amplitudes, such as spatial lengths. Figure 5 illustrates the target’s image reconstructed alltarget’s the extracted ASCs, as wellby as positions, relative amplitudes, and lengths. Figure 5 illustratesby the image reconstructed the predicted regions. Figure 5a shows a SAR image of BMP2 tank. The ASCs of the original image all the extracted ASCs, as well as the predicted regions. Figure 5a shows a SAR image of BMP2 tank. are extracted based on sparse and used to reconstruct the target’s image, as shown The ASCs of the original imagerepresentation are extracted based on sparse representation and used to reconstruct in Figure 5b. The reconstruction result5b. shows the extracted ASCs can remove background the target’s image, as shown in Figure The that reconstruction result shows that the the extracted ASCs interference, while the target’s characteristics can be maintained. Figure 5c shows the overlap of all can remove the background interference, while the target’s characteristics can be maintained. Figure 5c the predicted regions. predicted regionsClearly, can convey geometrical shape and scattering shows the overlap ofClearly, all the the predicted regions. the the predicted regions can convey the center distribution of the original center image.distribution of the original image. geometrical shape and scattering

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(b) Figure 3. 3.Images Imagesand andbinary binaryregions regionsof ofASCs ASCswith withdifferent differentamplitudes: amplitudes:(a) (a)images; images;(b) (b)binary binaryregions. regions. Figure

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Figure 4. Image and binary region of a distributed ASC: (a) image; (b) binary region. Figure 4. Image and binary region of a distributed ASC: (a) image; (b) binary region. Figure 4. Image and binary region of a distributed ASC: (a) image; (b) binary region.

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Figure 5. Illustration of ASC extraction and region (a) (b) prediction: (a) original image; (b) (c)reconstructed Figure 5. Illustration of ASC extraction and region prediction: (a) original image; (b) reconstructed image using ASCs; (c) overlap of all the predicted regions. image using ASCs; (c) overlap of all the predicted regions. Figure 5. Illustration of ASC extraction and region prediction: (a) original image; (b) reconstructed 3.2. Region Matching image using ASCs; (c) overlap of all the predicted regions.

3.2. Region Matching regions of individual ASCs are mapped to the target region from the corresponding The predicted template samples. is assumed that the template are always obtained some cooperative The predicted of individual ASCs samples are mapped to the target in region from the 3.2. Region MatchingItregions conditions. Hence, the template images contain the properties of the intact target at high corresponding template samples. It is assumed that the template samples are alwayssignal-to-noise obtained in The predicted regions ofofindividual ASCs arebetween mapped to the target region from the ratios (SNR). Theconditions. detailed steps the region matching sample and its corresponding some cooperative Hence, the template images containthe thetest properties of the intact target corresponding template samples. It is assumed that the template samples are always obtained in sample can be summarized as follows: attemplate high signal-to-noise ratios (SNR). The detailed steps of the region matching between the test someStep cooperative conditions. Hence, the template images contain the properties of the intact target extracted ASCs fromsample the testcan sample are converted to binary regions according to sample and 1: itsThe corresponding template be summarized as follows: at high 3.1. signal-to-noise ratios (SNR). The detailed steps of the region matching between the test Section Step 1: The extracted ASCs from the test sample are converted to binary regions according sample and corresponding template regions sample can summarized as region follows: Step 2: its Map each of the predicted ontobe the binary target from the corresponding to Section 3.1. Step 1: The extracted ASCs from the test sample are converted to binary regions according template Step 2:sample. Map each of the predicted regions onto the binary target region from the corresponding to Section 3.1. Step 3: The overlapped region between all the predicted regions and the binary target region template sample. Stepthe 2: correlation Map each ofbetween the predicted onto thesample; binary target region from the corresponding reflects thebetween testregions andall template and the unmatched regions Step 3: The overlapped region the predicted regions and the binary targetrepresent region template sample. their differences. reflects the correlation between the test and template sample; and the unmatched regions represent Step 3: 6The overlapped region the predicted regions and the binary Figure displays the results of between the regionallmatching between the predicted regionstarget of theregion BMP2 their differences. reflects the correlation between the test and template sample; and the unmatched regions represent SAR image6 in Figure the 5a and binary target regions from the template of BMP2, andBMP2 BTR70 Figure displays results of the region matching between thesamples predicted regionsT72, of the their differences. targets in the MSTAR dataset. The white regions represent the overlap between the predicted regions SAR image in Figure 5a and binary target regions from the template samples of BMP2, T72, and Figure 6 displays the results of the region matching betweentemplates, the predicted regions of theregions BMP2 of the test ASCs target region fromwhite the corresponding grey BTR70 targets in and thebinary MSTAR dataset. The regions represent the whereas overlap the between the SAR image in Figure 5a and binary target regions from the template samples of BMP2, T72, and predicted regions of the test ASCs and binary target region from the corresponding templates, BTR70 targets in the MSTAR dataset. The white regions represent the overlap between the whereas the grey regions reflect their differences. Clearly, the region overlap with the correct class predicted regions of the test ASCs and binary target region from the corresponding templates, has a much larger area than those of the incorrect classes. Three scores are defined to evaluate the whereas the grey regions reflect their differences. Clearly, the region overlap with the correct class matching results, as follows. has a much larger area than those of the incorrect classes. Three scores are defined to evaluate the matching results, as follows.

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reflect their differences. Clearly, the region overlap with the correct class has a much larger area than RMthe matching results, as follows. those of the incorrect classes. Three scores M are definedRMto evaluate G2 G3 (6) G1 Rt , RN N , M R R (6) G1 = , G2 = M , G3 = M RN where N is the number of predictedN regions, Ri.e., the number of all the extracted ASCs. M t denotes the number of predicted regions, which are assumed to be matched with the template’s where N is the number of predicted regions, i.e., the number of all the extracted ASCs. M denotes target region. RM denotes the total area of all the matched regions; RN and Rt are the areas of the number of predicted regions, which are assumed to be matched with the template’s target region. the predicted regions and target region, respectively. predicted is judged Rall denotes the total area of allbinary the matched regions; R N and Rt For are athe areas ofregion, all the itpredicted M to be matched only if the overlap between itself and the template’s binary region is larger regions and binary target region, respectively. For a predicted region, it is judged to be matchedthan onlyhalf if of its area. the overlap between itself and the template’s binary region is larger than half of its area. Tocombine combinethe theadvantages advantagesofofthe thethree threescores, scores,a alinear linearfusion fusionalgorithm algorithmisisperformed performedtotoobtain obtain To the overall similarity as Equation (7) [35]. the overall similarity as Equation (7) [35].

S

ωG

ωG

ωG

(7) (7)

S = ω1 G11 +1 ω2 G2 2 2+ ω33G33

where ω1 , ω2 and ω3 denote the weights; S represents the fused similarity. With little prior where ω1 , ω 2 and ω3 denote the weights; S represents the fused similarity. With little prior information information oniswhich is more important, equal weights are assigned to the three this on which score more score important, equal weights are assigned to the three scores in thisscores study,ini.e., ω ω ω 1/ 3 . ωstudy, = ω3 1= 1/3. 2 3 1 = ω2i.e.,

(a)

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Figure Region matching results between a BMP2 imageimage and three classes being: BMP2; Figure6. 6. Region matching results between a BMP2 and template three template classes(a) being: (a) (b) T72; (c) BTR70. BMP2; (b) T72; (c) BTR70.

3.3. 3.3.Target TargetRecognition Recognition The Theproposed proposedmatching matchingscheme schemefor forthe theextracted extractedASCs ASCsand andbinary binarytarget targetregion regionisisperformed performed with application to SAR target recognition. The basic procedure of our method is illustrated in Figure 7,in with application to SAR target recognition. The basic procedure of our method is illustrated which can summarized as follows. as follows. Figure 7, be which can be summarized (1) (1) (2) (2) (3) (3) (4) (4) (5) (5)

The TheASCs ASCsofofthe thetest testimage imageare areestimated estimatedand andpredicted predictedasasbinary binaryregions. regions. Theazimuth azimuthofofthe thetest testimage imageisisestimated estimatedtotoselect selectthe thecorresponding correspondingtemplate templateimages. images. The Extractthe thebinary binarytarget targetregions regionsofofall allthe theselected selectedtemplate templatesamples. samples. Extract Matchedthe thepredicted predictedregions regionstotoeach eachofofthe thetemplate templateregions regionsand andcalculate calculatethe thesimilarity. similarity. Matched Decide the target label to be the template class, which achieves the maximum similarity. Decide the target label to be the template class, which achieves the maximum similarity.

Specifically, the azimuth estimation algorithm in [22] is used, which also uses the binary target Specifically, the azimuth estimation algorithm in [22] is used, which also uses the binary target region. So, it can directly perform on the target region from Section 2 to obtain the estimated region. So, it can directly perform on the target region from Section 2 to obtain the estimated azimuth. azimuth. The estimation precision of the method is about ±5°. Accordingly, in this study, the The estimation precision of the method is about ±5◦ . Accordingly, in this study, the template samples template samples with azimuths in the interval of [−3°: 1°: 3°] around the estimated one are used as with azimuths in the interval of [−3◦ : 1◦ : 3◦ ] around the estimated one are used as the potential the potential templates. In addition, to overcome the 180° ambiguity, the template selection is templates. In addition, to overcome the 180◦ ambiguity, the template selection is performed on performed on the estimated azimuth and its 180° symmetric one, and the average of the similarities the estimated azimuth and its 180◦ symmetric one, and the average of the similarities from all the from all the candidate template samples is adopted as the final similarity for target recognition. The candidate template samples is adopted as the final similarity for target recognition. The scale coefficient scale coefficient to determine the global threshold is set as α 30 according to the experimental to determine the global threshold is set as α = 30 according to the experimental observations for observations for parameter selection. parameter selection.

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Estimated azimuth

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Template database

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Estimated azimuth

Template database Target 1 Binary region Target 1 Binary region

Test image Test image

ASC extraction ASC extraction

Region prediction Region prediction

Target 2 Binary region Target 2 Binary region

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Target C Binary region Target C Binary region

Region matching Region matching

Similarities Similarities

Maximum similarity Maximum similarity

Target type Target type

Figure 7. The basic procedure of target recognition. Figure7.7.The Thebasic basic procedure procedure ofoftarget recognition. Figure target recognition.

4. Experiment Experiment on on MSTAR Dataset 4. on MSTAR Dataset 4. Experiment MSTAR Dataset 4.1. Experimental Setup 4.1. Experimental Setup MSTAR Dataset 4.1.1.4.1.1. MSTAR Dataset Dataset widely used benchmarkdataset dataset for for SAR ATR methods, i.e., i.e., MSTAR dataset, is The The used benchmark dataset forevaluating evaluating SAR ATR methods, i.e., MSTAR dataset, widely used benchmark evaluating SAR ATR methods, MSTAR dataset, is adopted for experimental evaluation in this paper. The dataset is collected by the Sandia National is adopted experimentalevaluation evaluationininthis thispaper. paper.The Thedataset datasetisis collected collected by by the Sandia National adopted forforexperimental Laboratory airborne SAR sensor platform, working at X-band with HH polarization. There are ten Laboratory airborne SAR sensor platform, working at X-band with HH HH polarization. polarization. There are ten classes of ground targets with approaching physical sizes, whose names and optic images are classes targets with approaching physical sizes, sizes, whosewhose names and optic images presented classes ofofground ground targets with approaching physical names and opticareimages are presented in Figure 8. The collected SAR images have resolutions of 0.3 m × 0.3 m. The detailed in Figure 8. The collected SAR images have resolutions of 0.3 m × 0.3 m. The detailed template and presented in Figure 8. The collected SAR images have resolutions of 0.3 m × 0.3 m. The detailed template and test sets are given in Table 1, where samples from 17° depression angle are adopted as ◦ depression angle are adopted as the templates, test sets are given in Table 1, where samples from 17 template and test whereas sets are images given in where samples from 17° depression angle are adopted as the templates, at Table 15° are1, classified.

whereas imageswhereas at 15◦ are classified. the templates, images at 15° are classified.

Figure 8. Optic images of the ten targets to be classified.

Figure 8. Optic images of the ten targets to be classified. classified.

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Table 1. The template/training and test sets for the experiments. Target

Serial

Template/Training Set Depr.

Test Set

Number

Depr.

Number

15◦

BMP2

9563 9566 c21

17◦ 17◦ 17◦

233 232 233

15◦ 15◦

195 196 196

BTR70

c71

17◦

233

15◦

196

132 812 S7

17◦ 17◦ 17◦

232 231 228

15◦ 15◦ 15◦

196 195 191

17◦ 17◦ 17◦ 17◦ 17◦ 17◦ 17◦

299 299 299 256 299 298 299

15◦ 15◦ 15◦ 15◦ 15◦ 15◦ 15◦

274 274 273 195 274 274 274

T72

ZSU23/4 D08 ZIL131 E12 T62 A51 BTR60 k10yt7532 D7 92v13015 BDRM2 E71 2S1 B01

Depr. is abbreviation of “depression angle”; the picture of each target is given in Figure 8.

4.1.2. Reference Methods In order to reflect the merits of the proposed method, several prevalent SAR target recognition methods are taken as the references, as described in Table 2. For the SVM method, the classifier is performed by the LIBSVM package [36] on the feature vectors extracted by PCA, whose dimensionality is set to be 80 according to previous works [21,24]. In SRC, the OMP algorithm is chosen to resolve the sparse representation tasks of the 80-dimension PCA features. The A-ConvNet is a taken as a representative SAR ATR method using CNN. The designed networks in [25] is used for training and testing based on the original image intensities. The target recognition method based on ASCs in [28] is compared, in which a similarity measure between two ASC sets is formed for target recognition. The region matching method in [3] is also compared. The target region of the test sample is matched with the regions from different classes of templates and the similarities are calculated to determine the target label. All the methods are implemented on a PC with Intel i7 (Intel, Hanoi, Vietnam) 3.4 GHz CPU and 8 GB RAM. In the following tests, we first perform the experiment to classify the ten targets under SOC. Then, several EOCs including the configuration variants, large depression angle variation, noise contamination, and partial occlusion, are used for further evaluation of the performance of our method. Table 2. Methods to be compared with the proposed one. Method

Feature

Classifier

Reference

SVM SRC A-ConvNet ASC Matching Region Matching

Feature vector from PCA Feature vector from PCA Image intensities ASCs Binary target region

SVM SRC CNN One-to-one matching Region matching

[20] [24] [28] [18] [3]

4.2. Experiment under SOC At first, the recognition task is conducted under SOC based on the template and test sets in Table 1. Specifically, for BMP2 and T72 with three configurations, only “9563” for BMP2 and “132” for T72 are used in the template samples. Table 3 displays the confusion matrix of our method on the ten targets, in which the percentage of correct classification (PCC) of each class is illustrated. Clearly,

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the PCCs of these targets are over 96%, and the average PCC is calculated to be 98.34%. Table 4 displays the average PCCs, as well as the time consumption (for classifying one MSTAR image) of all the methods. Our method achieves the highest PCC, indicating its effectiveness under SOC. Although CNN is demonstrated to be effective for SAR ATR, it cannot work well if the training samples are insufficient. In this experimental setup, there are some configuration variants between the template and test sets of BMP2 and T72. As a result, the performance of A-ConvNet cannot rival the proposed method. Compared with the ASC Matching and Region Matching methods, our method performs much better, indicating that the classification scheme in this study can better make use of ASCs and target region to enhance the recognition performance. As for the time consumption, the classifiers like SVM, SRC, and CNN perform more efficiently than the proposed method because of the unified form of the features used in these methods. The ASC matching consumes the most time because it involves complex one-to-one matching between ASC sets. Compared with the region matching method in [3], the proposed method is relatively more efficient. The method in [3] needs to process the region residuals between two binary target regions, which is more time-consuming than the proposed region matching method. Table 3. Confusion matrix of the proposed method on the ten targets under SOC. Target

BMP2

BTR70

T72

T62

BDRM2

BTR60

BMP2 BTR70 T72 T62 BDRM2 BTR60 ZSU23/4 D7 ZIL131 2S1 Average

553 0 6 0 0 1 1 1 0 0

6 196 4 0 0 0 0 0 2 4

7 0 562 0 0 0 0 0 0 0

0 0 0 274 0 0 1 0 0 0

0 0 0 0 274 0 1 0 1 0

3 0 0 0 0 193 0 1 0 1

ZSU23/4 D7 2 0 2 0 0 0 269 0 2 0

0 0 5 0 0 1 0 271 0 0

ZIL131

2S1

PCC (%)

1 0 3 0 0 0 1 0 269 0

2 0 0 0 0 0 1 1 0 269

96.44 100 96.73 100 100 98.94 98.16 98.88 98.18 98.18 98.34

PCC: percentage of correction classification.

Table 4. Average PCCs of all the methods under the standard operating condition. Method

Proposed

SVM

SRC

A-ConvNet

ASC Matching

Region Matching

PCC (%) Time consumption (ms)

98.34 75.8

95.66 55.3

94.68 60.5

97.52 63.2

95.30 125.3

94.68 88.6

4.3. Experiment under EOCs The template/training samples are usually collected or simulated under some cooperative conditions. EOCs refer to those conditions occurred in the test samples, which are not included in the template/training set, e.g., configuration variants, depression angle variance, noise contamination, etc. To improve the robustness, it is desirable that the ATR methods work robustly under different types of EOCs. In the following paragraphs of this subsection, we evaluate the proposed method under several typical EOCs. 4.3.1. EOC 1-Configuration Variants The ground military target often has different configurations. Figure 9 shows four different configurations of a T72 tank, which have some locally structurally modifications. In practical applications, the configurations of the test samples may not be included in the template set. Table 5 lists the template and test samples for the experiment under configuration variants. The configurations of BMP2 and T72 to be classified are different to their counterparts in the template sets. Table 6 displays the classification results of different configurations by our method. The test configurations can be

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be 98.64%. Table 7 compares the average PCCs of different methods under configuration variants. recognized with PCCs works highermost than robustly 96%, andunder the average PCC isvariants calculated to the be 98.64%. Table 7 The proposed method configuration with highest average compares the average PCCs of different methods under configuration variants. The proposed method PCC. For targets of different configurations, they share similar physical sizes and shape with some works most robustly In under variants highest average PCC. For targets of different local modifications. this configuration case, the target regionwith and the local descriptors can provide more robustness configurations, they share similar physical sizes and shape with some local modifications. In this case, than the global features, like image intensities or PCA features; that’s why the ASC Matching and the target region and local descriptors can provide more robustness than the global features, like image Region Matching methods outperform the SVM, SRC, and CNN methods in this situation. intensities or PCA features; that’s why the ASC Matching and Region Matching methods outperform the SVM, SRC, and CNN methods in thisand situation. Table 5. Template test sets with configuration variants. Table 5.Depr. Template andBMP2 test sets withBDRM2 configurationBTR70 variants.

Template set Template set

Test set Test set

17°

233 (9563)

Depr.

298

233

BMP2

BDRM2

BTR70

17◦

233 (9563)

298

233

15°, 17°

428 (9566) 429 (c21) 428 (9566) 429 (c21)

15◦ , 17◦

0 0

T72 232 (132) T72 426 (812) 232573 (132) (A04) 426 (812) 573 (A05) 573573 (A04) (A07) 573 (A05) (A10) 573567 (A07)

0 0

567 (A10) Table 6. Classification results of different configurations of BMP2 and T72. Table 6. Classification of BMP2 and(%) T72. Target Serial results BMP2of different BRDM2configurations BTR-70 T72 PCC Target BMP2 BMP2

T72 T72

Average

9566 Serial

412 BMP2

11 BRDM2

c21 9566 812 c21 A04 812 A05 A04 A05 A07 A07 A10

420 412 18 420 5 18 15 31 3 7

4 11 14 81 18 21 2 0

A10

7

0

2 BTR-70 T723 2 2 20 00 00 03 3 2 2

96.26 PCC (%)

3 3 3407 560 407 571 560 571 565 565 558 558

Average

97.90

96.26 95.54 97.90

97.73 95.54 99.65 97.73 99.65 98.60 98.60 98.41 98.41 98.58

98.58

Figure 9. Four Four different configurations of T72 tank. Table 7. PCCs of of all all the the methods Table 7. PCCs methods under under configuration configuration variants. variants. Method Method PCC PCC(%) (%)

Proposed Proposed 98.58 98.58

SVM SVM 95.67 95.67

SRC A-ConvNet A-ConvNetASC ASC Matching Region Region Matching SRC Matching Matching 95.44 96.16 97.12 96.55 95.44 96.16 97.12 96.55

4.3.2. EOC 2-LargeDepression DepressionAngle AngleVariation Variation EOC 2-Large The platform heights. Consequently, the platform conveying conveying SAR SARsensors sensorsmay mayoperate operateat atdifferent different heights. Consequently, depression angle of the measured image is likely to to bebe different the depression angle of the measured image is likely differentwith withthose thoseofofthe thetemplate templatesamples, samples, or few few depression depression angles. angles. The which are often collected at only one or The template template and and test test sets in the Table 8, 8, where where three three targets targets (2S1, (2S1, BDRM2, BDRM2, and andZSU23/4) ZSU23/4) are present experiment are showcased in Table ◦ are classified. Images 45° Images at at 17° 17◦ are are adopted adopted as as the the template template samples, samples, whereas whereas those those at 30° 30◦ and 45 classified. SAR SAR images images of of 2S1 2S1 target target at at 17°, 17◦ , 30° 30◦ and and 45° 45◦ depression depression angles angles are are shown shown in in Figure Figure 10, 10, respectively. showsthat thatthe thelarge large depression angle variations notably change the appearances respectively. ItIt shows depression angle variations notably change the appearances and and scattering patterns the target. The results from our method under large depression angle scattering patterns of theof target. The results from our method under large depression angle variation variation are displayed in Table 9. It achieves the average PCCs of 97.80% and 76.16% at 30° and 45°

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are displayed in Table 9. It achieves the average PCCs of 97.80% and 76.16% at 30◦ and 45◦ depression angles, respectively. performances of all the methods a large depression angledepression variation depression angles, The respectively. The performances of allunder the methods under a large ◦ are displayed in Table 10. All the a 45 fall depression mainly becauseangle, the angle variation are displayed in PCCs Tablefall 10.sharply All theatPCCs sharply angle, at a 45° depression test images have significant differences with the training ones,with as shown in Figure 10. as In shown the ASCin mainly because the test images have significant differences the training ones, matching method, similarity evaluation performed based on the correspondence of twoon ASC Figure 10. In the the ASC matching method,isthe similarity evaluation is performed based the sets. So, some stable ASCs under still help correct angle target variance recognition. correspondence of two ASC sets.large So, depression some stableangle ASCsvariance under large depression still Therefore, it achieves a higher average PCC than SVM, SRC, CNN, and region methods at a help correct target recognition. Therefore, it achieves a higher average PCCmatching than SVM, SRC, CNN, ◦ ◦ ◦ 45 angle. Inmethods comparison, our depression method obtains theInhighest accuracies both 30obtains and 45the anddepression region matching at a 45° angle. comparison, our at method depression angles, validating highest robustness in thisvalidating case. highest accuracies at both 30°its and 45° depression angles, its highest robustness in this case.

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◦ ; (b) 30◦ ; (c) 45◦ . Figure Figure10. 10.SAR SARimages imagesfrom fromdepression depressionangles anglesof:of:(a) (a)1717°; (b) 30°; (c) 45°.

Table 8. Template and test sets with large depression angle variation. Table 8. Template and test sets with large depression angle variation. Depr.

Depr. Template set set 17◦ 17° Template 30◦ 30° Test set set Test 45◦ 45°

2S1

2S1 BDRM2 BDRM2 299 298 299° 298° 288 287 288 287 303 303 303 303

ZSU23/4

ZSU23/4 299 299° 288 288 303 303

◦ and 45◦ depression angles. Table Table9.9.Classification Classificationresults resultsofofthe theproposed proposedmethod methodatat3030° and 45° depression angles.

Depr. Depr.

Target Target

◦ 30 30°

2S1 2S1 BDRM2 BDRM2 ZSU23/4 ZSU23/4

◦ 45 45°

2S1 2S1 BDRM2 BDRM2 ZSU23/4

ZSU23/4

Classification Results Classification Results 2S1 BDRM2 ZSU23/4 ZSU23/4 2S1 BDRM2 278 66 44 278 11 285 1 285 44 4 280 4 280 229 48 26 229 48 26 10 242 51 10 242 51 54 31 218 54 31 218

PCC (%) PCC (%)

96.53 96.53 99.30 99.30 97.22 97.22 75.58 75.58 79.87 79.87 71.95 71.95

Average (%) Average (%)

97.68 97.68

75.82 75.82

Table 10. PCCs of all the methods at 30◦ and 45◦ depression angles. Table 10. PCCs of all the methods at 30° and 45° depression angles. Method Method Proposed Proposed SVM SVM SRC SRC A-ConvNet A-ConvNet ASC Matching Region Matching ASC Matching Region Matching

PCC (%)

PCC (%) ◦ 4545° 30° 97.68 75.82 97.68 75.82 96.87 65.05 96.87 65.05 96.24 64.32 96.24 64.32 97.16 66.27 97.16 66.27 96.56 71.35 95.82 64.72 96.56 71.35 95.82 64.72 30◦

4.3.3. EOC 3-Noise Contamination Noise contamination is a common situation in the practical application of SAR ATR because of the noises from the environment or SAR sensors [37–39]. To test the performance of our method under possible noise contamination, we first simulate noisy images by adding Gaussian noises to

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4.3.3. EOC 3-Noise Contamination the test samples in Table 1. In detail, the original SAR image is first transformed into the frequency domain. Afterwards, the complex Gaussian noisesinare to application the frequency spectrum according Noise contamination is a common situation theadded practical of SAR ATR because of to the preset SNR. Finally, the noisyor frequency data is transformed back into image to obtain the noises from the environment SAR sensors [37–39]. To test the performance of our domain method under Sensors 2018, 18, x FOR PEER REVIEW 14 of 18 possible noise contamination, we firstthe simulate adding Gaussian noises to theaddition. test the noisy SAR image. Figure 11 shows noisy noisy SAR images imagesby with different levels of noise samples in Tableof1.all In the detail, the original SAR image is first transformed into the The average PCCs methods under noise contamination are plotted as frequency Figure 12.domain. As shown, the test samples in Table 1. In detail, the original SAR image is firstspectrum transformed into thetofrequency Afterwards, the complex Gaussian noises are added to the frequency according the our method achieves the highest PCC at each noise level, indicating the best robustness preset regarding domain. Afterwards, the complex Gaussian noises are added to the frequency spectrum according to SNR. Finally, the noisy frequency data is transformed back into image domain to obtain the noisy SAR possiblethe noise contamination. lowfrequency SNRs, the distribution greatly. However, preset SNR. Finally, theAt noisy dataintensity is transformed back into changes image domain to obtain image. Figure 11 shows the noisy SAR images with different levels of noise addition. The average the ASCs keep properties so thatthethey can beimages precisely by sparse thecan noisy SARtheir image. Figure 11 shows noisy SAR withextracted different levels of noiserepresentation. addition. PCCs of all the methods under noise contamination are plotted as Figure 12. As shown, our method The average PCCs region of all thestill methods underpixels noise contamination plotted as than Figurethe 12. background As shown, In addition, the target contains with higher are intensities or achieves the highest PCC at each noise level, indicating the best robustness regarding possible noise our method achieves the highest PCC at each noise level, indicating the best robustness regarding shadow pixels. Then, the target region can also be segmented properly. This is alsothe theASCs reason why contamination. low SNRs, the distribution changes greatly. However, can possible noiseAt contamination. Atintensity low SNRs, the intensity distribution changes greatly. However, the ASC method Region method perform better than SVM, SRC, and CNN. keepMatching their properties so and that they canMatching be precisely extracted by sparse representation. In addition, the ASCs can keep their properties so that they can be precisely extracted by sparse representation. the In target regionthe still contains pixels with higher intensities than the background or shadow pixels. addition, target region still -6 contains pixels with higher intensities -6 than the background or Then, the target region can also be segmented properly. This is also the reason why the Matching shadow pixels. Then, the target region can also be segmented properly. This is also theASC reason why -4 -4 -4 method andMatching Region Matching method perform better thanperform SVM, SRC, and CNN. the ASC method and Region Matching method better than SVM, SRC, and CNN.

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Figure 12. Performance comparison of all the methods under noise contamination.

Figure Performance comparisonof of all all the noise contamination. Figure 12. 12. Performance comparison the methods methodsunder under noise contamination.

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4.3.4. EOC 4-Partial Occlusion 4.3.4. EOC 4-Partial Occlusion In fact, the target may be occluded by the obstacles; thus, a certain proportion of the target may In the target may be occluded by the obstacles; thus, a certain proportion of the target not be fact, captured by SAR sensors. In this experiment, the occluded SAR images are generated as the may not be captured by SAR sensors. In this experiment, the occluded SAR images are generated as occlusion model in [40,41]; then, the performance of different methods is evaluated at different the occlusion model in [40,41]; then, proportion the performance different methods is evaluated at different occlusion levels. In detail, a certain of the of binary target region from the original image is occlusion levels. In detail, a certain proportion of the binary target region from the original image is first occluded from different directions. Afterwards, the remaining target region and background are first occluded from different directions. Afterwards, the remaining target region and background are filled with the original pixels, while the occluded region is filled with the randomly picked filled with the pixels. originalIn pixels, while different the occluded region is filled with the randomly pickedfrom background background this way, levels of partially occluded SAR images different pixels. In this way, different levels of partially occluded SAR images from different directions can bein directions can be generated for target recognition. In Figure 13, some occluded images are shown, generated for target recognition. In Figure 13, some occluded images are shown, in which 20% ofof the which 20% of the target regions are occluded from different directions. Figure 14 plots the PCCs all target regions are occluded from differentOur directions. 14 the plotshighest the PCCs of all methods under the methods under partial occlusion. methodFigure obtains PCCs at the different occlusion partial methodeffectiveness obtains the highest PCCs atocclusion. different The occlusion levels, indicating its levels,occlusion. indicatingOur its highest under partial predicted regions of ASCs highest under occlusion. The apredicted regions reflect the local features reflect effectiveness the local features ofpartial the target. Although part of the targetofisASCs occluded, the remaining parts ofcan the still target. Although a part of the target is occluded, the remaining parts can still keep stable. In the keep stable. In the proposed method, the ASCs are extracted to describe the local proposed method, the ASCs are extracted to describe the local characteristics of the original image. characteristics of the original image. The predicted regions can effectively convey the The predicted regions effectively convey theare discrimination of the remainingthe parts, which are not discrimination of thecan remaining parts, which not occluded. By matching predicted regions occluded. By matching the predicted regions with the intact target region of the template samples, the with the intact target region of the template samples, the proposed method can keep robust under proposed method can keep robust under partial occlusion. Similar to the conditions of noise corruption, partial occlusion. Similar to the conditions of noise corruption, the ASC Matching, and Region the ASC Matching, Region Matching methods perform better than theglobal classifiers performed on Matching methodsand perform better than the classifiers performed on the features, i.e., SVM, the global features, i.e., SVM, SRC and CNN. SRC and CNN.

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14. Performance comparisonof of all all the under partial occlusion. FigureFigure 14. Performance comparison themethods methods under partial occlusion.

5. Conclusions 5. Conclusions In this study, we propose an effective method for SAR ATR by matching ASCs to binary target

In this study, we propose an effective method for SAR ATR by matching ASCs to binary target region. Instead of directly matching the points features, i.e., ASCs, to the target region, each ASC is region. predicted Instead of directly matching the points features, i.e., ASCs, to the target region, each ASC is as a binary region using a thresholding method. The binary regions of individual ASCs predicted as ainbinary region a thresholding method. The binary individual ASCs vary vary the areas and using shapes, which reflect their attributes such asregions spatial of positions, relative in the areas and shapes, which Afterwards, reflect theirthe attributes as spatial positions, amplitudes, and amplitudes, and lengths. predictedsuch regions of the test sample relative are mapped to the binary target region from the corresponding templates. Finally, a similarity measure is defined lengths. Afterwards, the predicted regions of the test sample are mapped to the binary target region to the region matching Finally, results, and the target label is determined according to the highest from theaccording corresponding templates. a similarity measure is defined according to the region similarity. The MSTAR dataset is employed for experiments. Based on the experimental results, matching results, and the target label is determined according to the highest similarity. The MSTAR conclusions are drawn as follows. dataset is employed for experiments. on for thethe experimental results, conclusions are drawn (1) The proposed method works Based effectively recognition task of ten targets under SOC as follows. with a notably high PCC of 98.34%, which outperforms other state-of-the-art methods. Under different of effectively EOCs (including configuration depression angle (1) The (2) proposed methodtypes works for the recognitionvariants, task of large ten targets under SOC with variation, noise contamination, and partial occlusion), the proposed performs more robustly than a notably high PCC of 98.34%, which outperforms other state-of-the-art methods. reference methods owing to the robustness of the region features as well as the designed (2) the Under different types of EOCs (including configuration variants, large depression angle classification scheme. variation, noise contamination, and partial occlusion), the proposed performs more robustly than (3) Although not superior in efficiency, the higher effectiveness and robustness make the the reference methods the robustness of the features well conditions. as the designed proposed method a owing potentialto way to improve the SAR ATR region performance in the as practical classificationFuture scheme. work is as follows. First, as basic features in the proposed target recognition method, extraction of in binary target region and ASCs should be and further improvedmake by adopting (3) the Although notprecision superior efficiency, the higher effectiveness robustness the proposed or developing more robust methods. Some despeckling algorithms [42–44] can be first used to method a potential way to improve the SAR ATR performance in the practical conditions. improve the quality of the original SAR images before the feature extraction. Second, the similarity Future work is as follows. First, as basic features in the proposed target recognition method, measure based on the region matching results should be further improved to enhance the ATR the extraction precision target region andofASCs should be by adopting or performance, e.g., of thebinary adaptive determination the weights for further differentimproved scores. Third, the developing more robust methods. Some despeckling algorithms [42–44] can be first used to improve proposed method should be extended to the ensemble SAR ATR system to handle the condition the quality the original images the feature extraction. Second,should the similarity measure that of several targets areSAR contained in abefore SAR image. Lastly, the proposed method be tested on other dataset from the airborne or be orbital SAR improved sensors to further validatethe its ATR effectiveness based on theavailable region matching results should further to enhance performance, robustness. e.g., the and adaptive determination of the weights for different scores. Third, the proposed method should be extended toContributions: the ensemble system to condition that targets are the contained Author J.T.;SAR X.F.; ATR S.W. conceived andhandle worked the together to achieve thisseveral work. Y.R. performed in a SAR image. Lastly, the method should be tested on other available dataset from the experiments. J.T. wrote the proposed paper. airborneFunding: or orbital sensors to further validate effectiveness and robustness. This SAR research was funded by Beijing Municipalits Natural Science Foundation (Grant No. Z8162039), the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDA19080100, the Hainan

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Author Contributions: J.T.; X.F.; S.W. conceived and worked together to achieve this work. Y.R. performed the experiments. J.T. wrote the paper. Funding: This research was funded by Beijing Municipal Natural Science Foundation (Grant No. Z8162039), the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDA19080100, the Hainan Provincial Department of Science and Technology (Grant No. ZDKJ2016021), the Natural Science Foundation of Hainan (Grant No. 20154171) and the 135 Plan Project of Chinese Academy of Sciences (Grant No. Y6SG0200CX). And the APC was Funded by Beijing Municipal Natural Science Foundation (Grant No. Z8162039). Acknowledgments: The authors thank the anonymous reviewers for their constructive suggestions. Conflicts of Interest: The authors declare no conflict of interest.

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