Physics Procedia 24 (2012) 1431 – 1436
1875-3892 © 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee. doi:10.1016/j.phpro.2012.02.212
Physics
Procedia
Physics Procedia 00 (2011) 000–000www.elsevier.com/locate/procedia
2012 International Conference on Applied Physics and Industrial Engineering
SAR Target Feature Extraction and Recognition Based on
2D-DLPP
Ping Han, Jingxian Wu, Renbiao Wu
Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300,China
Abstract
In this paper, a new feature extraction algorithm named 2D-DLPP (Two-dimensional Discriminant Locality Preserving Projections) is used for SAR ATR (Synthetic Aperture Radar Automatic Target Recognition). First, SAR target images are preprocessed by log-transformation and 2D FFT, then 2D-DLPP is applied to extract target feature which can not only preserve local information by capturing the local geometry of manifold but also implement sample dimension reduction effectively. Finally, classification with SVM (Support Vector Machine) is performed to get the good recognition rate. Experimental results based on MSTAR (Moving and Stationary Target Acquisition and Recognition) SAR data demonstrate that 2D-DLPP can obtain more effective target feature and improve the recognition rate obviously compared with 2D-LDA (Two-dimensional Linear Discriminant Analysis).
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer]
Keywords: synthetic aperture radar; automatic target recognition; feature extraction; two-dimensional discriminant locality preserving projections
1. Introduction
Due to all weather and all time work capability, synthetic aperture radar (SAR) is widely used in military and civil fields. It is important for SAR applications that a target is correctly recognized from the corresponding SAR images. Hence, automatic target recognition (ATR) based on SAR becomes an interest problem in current radar community[1][2].
As a key step in ATR, the feature extraction plays an important role in the recognition task. In order to obtain a good performance, the extracted features should maximize the between-class distance and minimize the within-class distance, such as the features extracted by Linear Discriminant Analysis (LDA)[3] and Two-dimensional Linear Discriminant Analysis (2D-LDA) [4]. The objective of the LDA is
to find the optimal projection for the samples so that the discrimination ratio of between-class scatter matrices to within-class scatter matrices reaches its maximum. 2D-LDA benefits from LDA, it is based on 2D image matrices rather than column vectors so the image matrix does not need to be transformed into a
© 2011 Published by Elsevier B.V. Selection and/or peer-review under responsibility of ICAPIE Organization Committee.
Open access under CC BY-NC-ND license.
long vector before feature extraction. The advantage arising in this way is that the Small Sample Size (SSS) problem[5] does not exist any more. LDA is a linear dimensionality reduction method. But nonlinear
structure usually exists in images and plays an important role in classification[6]. The general linear
dimensionality reduction methods do not take into account whether the nonlinear structure of samples is preserved.
Two-dimensional Discriminant Locality Preserving Projections[7] (2D-DLPP) is a novel method for
feature extraction. It has a stronger ability to manifold learning. When nonlinear structure exists in data set, the lower dimensional subspace obtained by this method can preserve the essential characteristics of samples. In this paper, 2D-DLPP is applied to extract SAR target features. Experimental results based on MSTAR SAR data show that the 2D-DLPP is more effective compared with 2D-LDA.
2.Two-dimensional Linear Discriminant Analysis(2D-LDA)
Let X represent a training sample of m rows and n columns, Vdenotes projection matrix. L
G is the between-class scatter matrix and GHis the within-class scatter matrix. The objective function of 2D-LDA is defined as:
= L T T H Max VG V J1 VG V (1) L
G andGHare computed as:
1 1 C ( ) (T ) L i i i i n N = = ∑ − − G m m m m (2) 1 1 1 C ni ( j ) (T j ) H i i i i i j N = = = ∑ ∑ − − G X m X m (3)
WhereCis the sample classes, niand midenote the number and mean value of training samples in class i respectively, Nis the total number of the training samples. j
i
X denotes the jthsample in the th
i class, mis the mean matrix of allNtraining samples.
The optimal projection matrix Voptis obtained by the eigenvectors v v1, , ,2" vl corresponding to the l largest eigenvalues of 1
H− L
G G .i.e. Vopt=[ , , , ]v v1 2"vl .
3. Two-dimensional Discriminant Locality Preserving Projections(2D-LPP)
2D-DLPP is based on LPP. The aim of LPP is to seek a subspace that can best describe the essential manifold and preserve the local structure of samples.
Suppose X represents a training image with m rows and n columns. Udenotes projection matrix. We project the sample matrix directly onto U to obtain the feature matrix Y :
=
Y XU (4)
The objective function of 2D-DLPP is defined as:
2 1 , 1 2 , 1 = k n C k k k i j ij k i j C i j ij i j W Min B = = = − ∑ ∑ − ∑ Y Y J2 f f (5) Where k k i， j
respectively, and accordingly, ,f fi j are their mean feature matrix. i.e., 1 i n i i k i k= n = ∑ f Y . • means L2 norm. k ij
W and Bij will be described in next paragraph. Returning (4) in (5), we can get the following equation:
2 1 , 1 2 , 1 = k n C k k k i j ij k i j C A i j ij i j W Min B = = = − ∑ ∑ − ∑ X U X U J2 m U m U (6) Where k ij
W is the similarity between the image k i
X and k j
X , it is defined as:
2
exp( / ), both and
belong to th class 0,otherwise k k i j i j k ij t W k ⎧ − − ⎪⎪ = ⎨ ⎪ ⎪⎩ if X X X X (7) ij
B is the similarity between mi and mj, it is defined as:
2
exp( / )
ij i j
B = − m m− t (8)
Where t is the window width determining the decay rate of the similarity, and it is empirically pre-specified.
By algebra formulation, the numerator of (6) can be reduced to:
2 1 , 1 1 , 1 1 2 1 ( ) ( ) 2 [( ) ] ( ) k k n C k k k i j ij k i j n C T k k T k k k i j i j ij k i j T T m T T m W W = = = = − ∑ ∑ = ∑ ∑ − − = − ⊗ = ⊗ X U X U U X X X X U U X D W I XU U X L I XU (9) Where 1 11 1 1 [( ) , ,( ) , ,( ) , ,( C) ] T T T C T C T n n = " " "
X X X X X , Dk is a diagonal matrix, and
k k
j ii = ∑ ij
D W .Wkis composed of k
ij
W .D and W are separately composed of Dk and Wk.
= −
L D W is a Laplacian matrix. Imis an identity matrix of order m, and operator ⊗ is the Kronecher product of the matrices.
Similarly, the denominator of (6) can be reduced to:
2 , 1 , 1 1 2 1 ( ) ( ) 2 [( ) ] [ ] C i j ij i j C T T i j i j ij i j T T m T T m B B = = − ∑ = ∑ − − = − ⊗ = ⊗ m U m U U m m m m U U Μ E B I MU M H I MU Υ (10)
WhereMT =[( ) , ,( ) , ,(m1 T " mi T " mC) ]T ,Eis a diagonal matrix, Eii = ∑jBij ，H E B= − . According to (6), (9) and (10), the objective function can be reduced to:
( ) [ ] T T T m L T T T m H Min ⊗ =Min ⊗ U X L I XU U S U U M H I MU U S U (11) where 1 , 1 1 ( ) ( ) 2 k n C k k T k k k L i j i j ij k i j= = W = ∑ ∑ − − S X X X X (12) , 1 1 ( ) ( ) 2 C T H i j i j ij i j= B = ∑ − − S m m m m (13)
Then minimizing the objective function can be solved from the following generalized eigenvalue problem:
L =λ H
S U S U (14)
As we know, the main idea of 2D-DLPP is to find a optimal projection matrix Uoptwhich
minimizes the objective function. It is a well-known fact that the eigenvector corresponding to the minimum eigenvalue of 1
H− L
S S is the optimal projection. Generally, as it is not enough to have only one optimal projection, we usually go for d projections u u1, , ,2" ud , which are the eigenvectors corresponding to the d smallest eigenvalues of 1
H− L
S S .i.e.Uopt =[ , , , ]u u1 2" ud is the optimal projection matrix. d is usually selected according the following rules:
1 1 d i i N i i λ τ λ = = ∑ ≤ ∑ (15)
Where λi is the eigenvalue corresponding to the eigenvector ui, in this paper, τ =5%.
4. Experiments and Analysis
In the experiment, MSTAR SAR image database is employed. We select three types of SAR target image (T72, BMP, BTR) for training and testing. Each image has the size of 128 by 128. Every kind of target images covers 0 to 360 degree of orientation. The training samples are collected at a depression angle of 17°, and the testing samples’ depression angle is 15°.
In the preprocessing, each original image is cut into 65*65 chips first, then log-transformation, 2D FFT and magnitude-normalization are performed.
SAR images of a same target often show different appearance at different azimuths. In order to improve the recognition rate, we divide all the processed training samples into several groups at equal aspect ranges or bins, i.e. windowing the sample in azimuth, then extract the features of training samples in the same window with 2D-DLPP and train SVM classifier. In this paper, four
Training
sam ples preprocessing projection spaceSolving Triaining SVM classifier Store projection m atrix Project in corresponding space Orientation estim ation preprocessing Testing sam ples classification output
different window sizes are considered in order to test the robustness to the azimuth. They are 30°, 60°, 90° and 180°, and the classification performance is analyzed under different azimuth windows.
In testing process, after preprocessing and orientation estimation, we classify the test samples with the corresponding SVM classifier according to their pose information. Multi-class SVM classifier is used to finish classification, and the kernel function we select is the radial base function
( , ) exp( ), 5
k u v = −γ u v− γ = . Table.1 lists the experimental results with 2D-DLPP feature extraction under different azimuth windows. We also list the experimental results achieved by 2D-LDA to compare with the proposed method.
Table.1 average recognition rate with different feature extraction methods window width targets methods 30° 60° 90° 180° T72 2D-LDA 98.46% 98.80% 98.97% 96.92% 2D-DLPP 98.80% 99.32% 99.48% 98.80% BMP 2D-LDA 89.10% 89.27% 85.69% 72.07% 2D-DLPP 93.19% 93.02% 93.19% 87.57% BTR 2D-LDA 98.98% 97.45% 98.98% 97.96% 2D-DLPP 99.49% 99.49% 99.49% 98.98%
Table.2 total average recognition rate with different feature extraction methods window width
methods 30° 60° 90° 180°
2D-LDA 94.52% 94.53% 93.28% 86.42%
2D-DLPP 96.49% 96.64% 96.79% 94.01%
From table.1 and table.2, we can see the target feature extracted by 2D-DLPP can be classified more correctly compared with that of 2D-LDA, especially for BMP2, whose target image is more blur than other two kinds of target pictures. The recognition rate of BMP2 is improved more obviously.
Additionally, it also shows that the recognition rate of 2D-LDA changes remarkably when the window size become larger especially such as 1800, whereas 2D-DLPP is not very sensitive to the
changes of pose information.
Table.3 The number of feature extraction with different methods window width
methods 30° 60° 90° 180°
2D-LDA 23 23 24 22
We also studied the target feature number extracted with the two methods and compared which is more effective in dimension reduction. The results with different window size are listed in table.3. We can see from table.3 that the number of extracted feature with 2D-DLPP is half less than that with 2D-LDA. In other words, 2D-DLPP performs better in dimensionality reduction.
5. Conclusions
A matrix-based feature extraction method called 2D-DLPP is applied to SAR ATR. It remains the locality preserving characters and can reflect the underlying nonlinear manifold structure. Although 2D-DLPP and 2D-LDA are all linear matrix-based dimensionality reduction methods and can reduce the complexity of algorithm, 2D-DLPP can preserve the underlying nonlinear manifold structure. Experimental results on MSTAR show that it can improve the recognition rate better as well as achieve an effective dimension reduction.
6. Acknowledgement
This work is supported in part by the co-funded project of National Natural Science Foundation and Civil Aviation Administration of China under grant 60979002.
References
[1] Duan Rong, Chen Ling , Man Hong. Adaptive SAR ATR in likelihood space. Algorithms for Synthetic Aperture Radar Imagery XII. Proceedings of SPIE 2005, 5808:294-305.
[2] Sun Yijun, Liu Zhi-peng, Todorovic Sinisa, et al. Synthetic Aperture Radar Automatic Target Recognition Using Adaptive Boosting. SPIE The International Society for Optical Engineering, San Diego, 2005, 5:282-293.
[3] Yinan Yang, Yuxia Qiu and Chao Lu. Automatic Target Classification Experiments on the MSTAR SAR Images. Proceedings of the Sixth International Conference on SNPD/SAWN’05, 2005: 2-7.
[4] Jian-Gang Wang, Hui Kong and Wei-Yun Yao, 2D FDA vs. 1D FDA: Stereo Face Recognition[J].
[5] SANQUANASAT P, ASDORNWISED W, JITAPUNKUL S,et al. Two-dimensional linear discriminant analysis of principal component vectors for face recognition[C]. IEEE International Conference on A coustics, Speech and Signal Processing. New York: IEEE, 2006:2164-2170.
[6] Lu Ke, Zhao Jidong, Wu Yue and He Xiaofei. Relevance Feedbacks Algorithm Based on Locality Preserving Projections [J]. Journal of Computer-Aided Design & Computer Graphics, 2007, 19(1): 20-24.
[7] Yu Weiwei, Face Recognition using Two-dimensional Discriminant Locality Preserving Projections[J], 2009 Asia-Pacific Conference on Information Processing,2009:3-6.
