Automatic target recognition based on SAR images and Two-Stage 2DPCA features

2-dimensional principal component analysis (2DPCA) has received more and more attentions in recent years, since it can evaluate the covariance matrix more accurate than PCA in extracting features from 2-dimensional images. However, a drawback of 2DPCA is that it needs more features than PCA because 2DPCA only eliminates the correlations between rows. In this paper, two-stage 2DPCA is proposed to extract features from synthetic aperture radar (SAR) images to further compress the dimension of features and decrease the recognition computation. Experimental results based on MSTAR data indicate that two-stage 2DPCA can decrease feature dimensions significantly, and the target recognition performance can be improved at the same time.


Introduction
In recent years, radar Automatic Target Recognition (ATR) based on target synthetic aperture radar (SAR) images has received more and more attentions. So far, many literatures based on MSTAR public dataset are released, which focus on the SAR target recognition related techniques including target segmentation, feature extraction, classifier design, and so on. A template matching was proposed (Ross et al., 1998). Support Vector Machine (SVM) has been applied to SAR ATR (Zhao & Principe, 2001;. The drawbacks of them are that none of them have any pre-processing and feature extraction. However, efficient pre-processing and feature extraction may help to improve recognition performance. Principal Component Analysis (PCA) is a classical feature extraction technique. But when PCA is used for images feature extraction, 2D image matrices must be previously transformed into 1D image vectors. This usually leads to a high dimensional vector space, where it is difficult to evaluate the covariance matrix accurately. To solve this problem, 2-dimensional PCA (2DPCA) for image feature extraction is proposed (Yang et al., 2004). As opposed to PCA, 2DPCA constructs the covariance matrix directly using 2D image matrices rather than 1D vectors, and evaluates the covariance matrix more accurately. Moreover, the size of the covariance matrix is much smaller. A drawback of 2DPCA is that it only eliminates the correlations between rows. So it needs more features, and this will lead to large storage requirements and cost more time in classification phase. To further compress dimension of features, two-stage 2DPCA is applied in this chapter.
The remainder of this chapter is organized as follows: in Section 2, the SAR images preprocessing method is described. 2DPCA is first reviewed, and two-stage 2DPCA is described in Section 3. In Section 4, classifiers are described. In Section 5 and 6, experimental results based on Moving and Stationary Target Acquisition and Recognition (MSTAR) data and conclusions are presented.

Logarithmic transformation
We transform the original images using logarithm conversion, which can convert speckles from multiple model to additional model and make the image histogram more suitable be approximated with a Gaussian distribution. The logarithmic transformation is given by where F denotes the magnitude matrix of the original SAR image. Since the logarithm is not defined at 0, we add an arbitrary constant (for example 0.001) to the original image before the logarithm. To ensure the pixel values to be nonnegative, we add a corresponding constant (30).

Adaptive threshold segmentation
In order to obtain the target image, the adaptive threshold segmentation method is adopted.
First of all, estimating the mean  and the variance  of the current image G , for each x y x y if x y c xy xy e l s e Where ar T , ac B denote the target and the background respectively, c can be obtained statistically from training samples.

Morphological filter and geometric clustering operation
Due to the presence of speckles, the result of threshold segmentation contains not only target, but smaller objects inevitably, as shown in Fig. 1 (b). To remove these small objects and obtain smoothing the target image, morphological filter (Gonzalez &Woods, 2002) and geometric clustering operation (Musman & Kerr, 1996) are adopted to ar T .
Morphological filter aims to smooth boundary, remove sharp protrusions, fill small concaves, remove small holes, joint gaps, and so on.
In general, filtered image ar T may also contain some non-target regions, which are much smaller than target itself, as shown in Fig. 1 (c). To remove small regions, we apply geometric clustering operation: firstly, detect and label all the independent connected regions in ar T . Then, compute areas for each region. The largest region is of our interest. In this way, we obtain the resulting ar T , as shown in Fig. 1

Image enhancement and normalization
Image enhancement (Gonzalez &Woods, 2002) can weaken or eliminate some useless information and give prominence to some useful information, which aims to enhance image quality by adopting a certain technology for a specific application. Here, we apply the power-law transformation to enhance the target image where H , K denotes the former and latter transformed image respectively,  is an constant.
In practice, due to the difference of the distance between a target and radar, the intensity of echoes differs greatly. Thus, it is necessary to normalize the image. Here, a normalized method adopted is where J , K denotes the former and latter normalized image respectively.
Due to the uncertainty of target location in a scene, 2-dimensional fast Fourier transform (2DFFT) is applied. Only half of the amplitude of Fourier is used as inputs of feature extraction due to its translation invariance and symmetric property, so that it can decrease the dimension of samples and reduce computation.

Feature extraction
Feature extraction is a key procedure in SAR ATR. If all pixels of an image are regarded as features, this would result in large requirements, high computation and performance loss. Therefore, it is necessary to extract target features.

Feature extraction based 2DPCA
So, equation (6) is the set of eigenvectors of t G corresponding to the r largest eigenvalues.
For each training image i I , its feature matrix is

Feature extraction based two-stage 2DPCA
2DPCA only eliminates the correlations between rows, but disregards the correlations between columns. So it needs more features. This will lead to large storage requirements and cost much more time in classification phase. To further compress the dimension of feature matrices, two-stage 2DPCA is applied in this chapter. Its detailed implementation is described as follows (shown in Fig.4): (1) Training images

Classifier design
In this chapter, the nearest neighbor classifier based Euclid distance is used. Compute distances of feature matrices between unknown and all training samples. Then, the decision is that this test belongs to the same class as the training sample, which minimizes the distance.
are written the following form

Experimental results
Experiments are made based on the MSTAR public release database. There are three distinct types of ground vehicles: BMP, BTR70, and T72. Fig.5 gives the optical images of the three classes of vehicles, and Fig.6 shows their SAR images.
There are seven serial numbers (i.e., seven target configurations) for the three target types: one BTR70 (sn-c71), three BMP2's (sn-c21, sn-9593, and sn-9566), and three T72's (sn-132, sn-812, and sn-s7). For each serial number, the training and test sets are provided, with the target signatures at the depression angles 17  and 15  , respectively. The training and test datasets are given in Table 1. The size of target images is converted 128 128  into 128 64  by our pre-processing described in section 2.

The effects of logarithm conversion and power-law transformation with different exponents on the recognition rates in our pre-processing method
Let us illustrate the effects of logarithm conversion and power-law transformation with different exponents in our pre-processing using an image of T72, shown in Fig.7. From Fig.7 (a), we see that the total gray values are very low, and many details are not visible. On the one hand, logarithmic transformation converts speckles from multiple to additional model and makes image histogram more suitable be approximated with a Gaussian distribution. On the other hand, it enlarges the gray values and reveals more details.
However, image contrast in the target region decreases as shown in Fig.7 (d). Therefore, it is necessary to enhance image contrast, which can be accomplished by power-law transformation with 1   . The values of  corresponding to Fig.7 (e) ~ (h) are 2, 3, 4, and 5.
We note that as  increases from 2 to 4, image contrast is enhanced distinctly. But when  continues to increase, the resulting image become dark and lose some details. By comparisons of these resulting images, we think that the best image enhancement result is at  taking 4 approximately.

Comparisons of different pre-processing methods
In SAR recognition system, pre-processing is an important factor. Let us evaluate the performance of several pre-processing approaches as follows.
Method 1: the original images are transformed by logarithm. Then, half of the amplitudes of the 2-dimensional fast Fourier transform are used as inputs of feature extraction.
Method 2: overlaying the segmented binary target ar T on the original image F gets target image, normalize it. Half of the amplitudes of 2-dimensional fast Fourier transform are used.
Method 3: overlaying ar T on F obtains target image. First, enhance it using power-law transformation with an exponent 0.6. Then normalize it. Half of the amplitudes of 2dimensional fast Fourier transform are used.

Method 4: overlaying ar
T on the logarithmic image G obtains target image, normalize it. Half of the amplitudes of 2-dimensional fast Fourier transform are used.
Method 5 (our pre-processing method in section 2): That is, overlaying ar T on G obtains target image. First, enhance it using power-law transformation with an exponent 3.5. Then normalize it. Half of the amplitudes of 2-dimensional fast Fourier transform are used. Fig. 9. Performances of 2DPCA with five pre-processing methods.
We can see that the performance of method 1 is the worst, because it does not segment the target from background clutters, which disturb recognition performances.
Comparing method 3 with 2 and 5 with 4, we easily find that image enhancement based on power-law transformation is very efficient.
The difference between method 3 and method 5 (our pre-processing method) is that the former is obtained by overlaying . ar T . on the original image F , and then enhanced by power-law transformation with a fractional exponent 0.6. The latter is obtained by overlaying ar T on the logarithm image G , and then enhanced by power-law transformation with an exponent 3.5. Due to the effects of logarithm in our method, the performance of method 5 (our pre-processing method) is better than that of method 3.
All the five experimental results testify that our pre-processing method is very efficient.

Comparisons of 2DPCA and PCA
To further evaluate our feature extraction method, we also compare 2DPCA with PCA. The flow chart of experiments is given in Fig.10. For all the training and testing samples in Table 1, Fig.11 gives the variation of recognition rates of PCA with feature dimensions, that is, the number of principal components. PCA achieves the highest recognition rate when the number of principal components (d) equal 85. For all the training and testing samples in Table 1, Fig.12 gives the variation of recognition rates of 2DPCA with the number of principal components. 2DPCA achieves the highest recognition rate when the number of principal components (r) equal 8.   Fig.11 with Fig.12, we find that recognition performance of 2DPCA is better than PCA. This is due to the facts that 2-dimensional image matrices must be transformed into 1-dimensional image vectors when PCA used in image feature extraction. The image matrix-to-vector transformation will result in some problems: (1) This will destroy 2dimensional spatial structure information of image matrix, which brings on performance loss; (2) This leads to a high dimensional vector space, where it is difficult to evaluate the covariance matrix accurately and find its eigenvectors because the dimension of the covariance matrix is very large ( mn mn  ). 2DPCA estimates the covariance matrix based on 2-dimensional training image matrices, which leads to two advantages: (1) 2-dimensional spatial structure information of image matrix is kept very well; (2) the covariance matrix is evaluated more accurately and the dimensionality of the covariance matrix is very small ( nn  ). So, the efficiency of 2DPCA is much greater than that of PCA. ) . F r o m t h i s t a b l e , w e s e e t h a t although the storage requirements are comparative, the computation complexity of 2DPCA is much smaller than that of PCA when seeking the projection vectors. So, we think that 2DPCA is much greater than PCA in computation efficiency.  Table 3. Comparisons of the computation complexity and storage requirements of PCA and 2DPCA From Table 2 and Table 3, we can conclude that 2DPCA is better than PCA in computation efficiency and recognition performance.
From Table 2, we also see that feature matrix obtained by 2DPCA is considerably large. This may lead to massive memory requirements and cost too much time in classification phase. So, we proposed two-stage 2DPCA to reduce feature dimensions.

Comparisons of 2DPCA and two-stage 2DPCA
2DPCA only eliminates the correlations between rows, but disregards the correlations between columns. The proposed two-stage 2DPCA can eliminate the correlations between images rows and columns simultaneously, thus reducing feature dimensions dramatically and improving recognition performances. Table 4 shows the highest recognition rates of 2DPCA and two-stage 2DPCA. From Table 4, we see that two-stage 2DPCA achieves the highest recognition performance with smaller feature matrices.
From Table5, we find that the storage requirements of two-stage 2DPCA are smaller than those of 2DPCA.
From Table 4 and Table 5, we can conclude that two-stage 2DPCA is better than 2DPCA in recognition performance and storage requirements.
From Table 4, we also see that the results of two-stage 2DPCA are comparative no matter how the distance between two features is defined and the recognition performance of the way of the distance along row and column is slightly better.   Table 5. Comparisons of storage requirements of 2DPCA and Two-stage 2DPCA.

Comparisons of 2DPCA and two-stage 2DPCA under different azimuth intervals
In some cases, we can obtain target azimuth. Using it, recognition performances may be improved. Group training samples with equal intervals for each class within 0~360  , then extract features within the same azimuth range for the three types of training samples in the phase of training. In the phase of testing, the test sample is chosen to be classified in the corresponding azimuth range according to its azimuth. In this experiment, training samples of each class are grouped with equal intervals by 180  ,90  , 30  respectively.
Recognition results of 2DPCA and two-stage 2DPCA under different azimuth intervals ( 180  , 90  , and 30  ) are given in Table 6. From it, we obtain that performances of the twostage 2DPCA method is better than those of 2DPCA. Moreover, two-stage 2DPCA is robust to the variation of azimuth. This

Comparisons of two-stage 2DPCA and methods in literatures
The recognition rates of two-stage 2DPCA and methods in literatures are listed in Table 7.
Recognition approaches Recognition rate (feature dimension) Template matching (Zhao & Principe, 2001) 40.76 SVM  90.92 PCA+SVM  84.54 KPCA+SVM  91.50 KFD+SVM  95.75 (2D) 2 PCA [9]  We see that performances of literatures (Zhao et al., 2001; are the worst, since they do not have any pre-processing and feature extraction. However, efficient pre-processing and feature extraction can help to improve recognition performances. In literatures Han et al., 2004), PCA, KPCA, or KFD is employed. These feature extraction methods seek projection vectors based on 1-dimensional image vectors. In our ATR system, target is firstly segmented to eliminate background clutters. Then, enhanced by power-law transformation to stand out useful information and strengthen target recognition capability. Moreover, feature extraction is based on 2-dimensional image matrices, so that the spatial structure information is kept very well and the covariance matrix is estimated more accurately and efficiently. Therefore, two-stage 2DPCA combining with our proposed pre-processing method can obtain the best recognition performance.
By comparisons of two-stage 2DPCA and the similar techniques, such as (2D) 2 PCA (Zhang & Zhou, 2005), G2DPCA (Kong et al., 2005), we can conclude that our pre-processing method is very efficient and two-stage 2DPCA is comparable to (2D) 2 PCA and G2DPCA in performance and storage requirements. Table 8 gives the results of two-stage 2DPCA, and other approaches in literatures under different azimuth intervals. From it, we obtain that performances of our method is better than those of literatures. This table further validates that two-stage 2DPCA combining with our pre-processing method is the best.