Proceedings of the 11th European Radar Conference
Enhanced ATR by jointly using Coherent and Incoherent Target Decomposition Theorems on Polarimetric ISAR images Stefano Lischi1,2 , Alberto Lupidi2 , Elisa Giusti1,2 , Marco Martorella1,2 1
2
Department of Information Engineering, University of Pisa, Via G. Caruso 16 - 56122 Pisa - Italy Radar and Surveillance System (RaSS) National Laboratory, CNIT, Galleria G.B. Gerace 18 - 56124 Pisa - Italy
[email protected], phone +39 050 3820810
the autofocusing algorithm effectiveness, etc. The idea that is investigated is based on the jointly used of CTD and ICTD features with the aim to overcome the weaknesses of each method separately. To assess the performance of the proposed algorithm, a dataset collected in an anechoic chamber is considered. This paper is organized as follows. Section II deals with features vectors definition. A features analysis is described in Section III that can be used to identify the features with the greatest discrimination power. The classifiers used to assess the performance in terms of recognition capability are presented in Section IV. Results obtained by processing data acquired in an anechoic chamber are shown in Section V. Finally, conclusions are drawn in Section VI.
Abstract—An Automatic Target Recognition (ATR) algorithm is presented in this paper that is based on the use of polarimetric ISAR (Pol-ISAR) images and Target Decomposition (TD) theory. Specifically both Coherent Target Decomposition (CTD) and InCoherent Target Decomposition (ICTD) methods are used here to extract features from Pol-ISAR images. The two methods are used here jointly to overcome their weaknesses when used separately. Keywords—Automatic target recognition, Pol-ISAR images, polarimetric target decomposition
I.
I NTRODUCTION
Pol-ISAR images have been largely exploited in the literature for ATR. To be effective, an ATR system must be able to extract a suitable set of features from the available data. Many different kinds of feature can be extracted from a Pol-ISAR image, such as geometrical (target size, target shape, etc...) and polarimetric information. The geometrical interpretation of an ISAR image is strongly dependent on the target’s own motion, which is usually unknown. A 2DISAR image is in fact a filtered projection of the 3D target’s reflectivity function onto a 2D plane, which is called Image Projection Plane (IPP). Such plane is dependent on the radartarget geometry and kinematics. The use of the polarimetric information alone should, therefore, provide a more robust ATR system with respect to the IPP orientation. However, it should be pointed out that the IPP orientation does not depend on the target orientation and that the polarimetric features are robust with respect to the former and not to the latter. Several TD theorems have been proposed in literature. These methods can be categorized into CTD methods and ICTD methods. Although the CTD is able to carefully characterize the polarimetric properties of each scattering centers composing the target, it can be effectively applied when a scatterer exhibits a high degree of coherency, which is however difficult to be assessed. Moreover, the number of scattering centers may change significantly among different ISAR images thus determining feature vectors of different size. On the contrary, ICTD methods allow for the target to be characterized in a more compact way as they provide feature vectors of fixed size. As a drawback, they are able to characterize the target polarimetric behavior from a global perspective only. In a real application it may difficult to assess what method to be used, as the global ATR performance would depend on several factors, such as the spatial resolution, the target’s own motions,
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II.
F EATURES E XTRACTION
A. Coherent Target Decomposition A number of scattering centers are first extracted from the Pol-ISAR image via the Pol-CLEAN algorithm [1]. Each scattering center is then decomposed according to the Cameron’s decomposition [2]. Cameron’s decomposition algorithm has been in fact proven to be effective to characterize a single scatterer scattering mechanisms and therefore to be useful for man-made targets classification. According to Cameron’s method, each scattering centers can be characterized by means of a complex value, z = zR + jzI , which represents the polarimetric property of the scattering center, and the angle φ which represents the scatterer orientation around the radar LoS. The CTD feature vector can then be defined as follows, xCT D = (zR , zI , φ)
(1)
where zR = zI = φ =
(zR,1 , zR,2 , . . . , zR,Ns ) (zI,1 , zI,2 , . . . , zI,Ns ) (φ1 , φ2 , . . . , φNs )
(2)
and Ns is the number of dominant scatters extracted by the Pol-CLEAN technique. B. Incoherent Target Decomposition Differently from CTD methods, ICTD ones are able to characterize the target globally. Once the Pol-ISAR image is formed, an area containing the target of interest is cropped
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1) Fisher Discriminant Ratio: The first step is to look at each of the available features independently and test their discrimination capability. Although, to look at each feature separately is far from optimal, it helps us to discard easily features with a low discriminating power. The Fisher’s discriminant ratio defined in [5] is commonly adopted to evaluate the class-separability of singular features:
from the image and the coherency matrix is computed as follows: K K† Σ= (3) Np where K is a 3×Np matrix containing the scattering vectors of each of the Np resolution cells. In this paper the Cloude-Pottier eigenvalue-eigenvector algorithm [3] is used to decompose Σ. Then, the following feature vector can be defined: xICT D = (H, A, p1 , p2 , α1 , α2 , αM L )
F DR =
(4)
i
σi2 + σj2
(7)
2) Scatter Matrices: The second step aims at assessing the discriminating power of different vectors of features. In particular, we adopted a simple criteria based on the so-called scatter matrices illustrated in [5]. This criteria is built upon information related to the way feature vector samples are scattered in the L-dimensional feature space:
(5)
C. Feature vector definition For many years CTD has been identified as the most qualified method to polarimetrically characterize a man-made target from a single-scatterer point of view. However, this is difficult to be assessed as coherent image formation, such as ISAR imaging, has the disadvantage of concentrating a superposition of effects due to multiple scatterers within a single resolution cell. Therefore, what may appear like a single-scatterer may instead be a superposition of multiple scatterers. Recently the possibility to use ICTD method to classify man-made targets has been investigated in [4]. Although, ICTD method is always been used to classify distributed targets, results in [4] show that it can also be used to characterize man-made targets. It may therefore be interesting to investigate what is the most suitable set of feature to recognize a man-made target. In a real application it could be however difficult to assess what method provides the best classification performance. To obtain the best classification performance, the idea proposed in this paper explores the possibility to fuse together the two set of features. According to this idea the new feature vector can be defined as x = (xCT D , xICT D ) . (6) III.
j6=i
where µi and σi are respectively the mean and standard deviation of the feature under investigation for the ith class.
where H is the polarimetric entropy, A is the polarimetric anisotropy, pi is the probability of the ith eigenvalue, αi is the angle representing the polarimetric behavior of the ith eigenvalue. The mean angle αM L is defined as αM L = α1 p1 + α2 p2 + α3 p3 .
M X M 2 X (µi − µj )
J2 =
|Sm | = |S−1 w Sm | |Sw |
(8)
where Sw and Sm are the within-class scatter matrix and the mixture scatter matrix respectively as defined in [5]. IV.
C LASSIFICATION M ETHODS
Two kind of classifiers have been tested in this work: Support Vector Machines (SMV) and Normal-Based Bayesian Classifier (BC). A. Support Vector Machines SVM were introduced initially in [6] and they represent an efficient technique for non-linear classification. The idea behind SVMs is to estimate a separation hyperplane between two classes in the L-dimensional feature space. The training dataset is composed of the couples {xi , yi }, where the ith input vector xi belongs to the features space and the output is yi ∈ {−1, 1}, where 1 indicates the positives and -1 the falses. From the combination of various binary SVM, a k-class classification can be obtained. The one-against-one approach was chosen, where, after evaluating k(k − 1)/2 binary classifiers (all possible combinations), we can obtain k(k − 1)/2 hyperplanes separating the classes. Classification on the test set is made through a max-wins voting scheme.
F EATURE ANALYSIS
A. Features Pre-Processing Feature pre-processing is an important step in any machine learning problem. Irrelevant information, such as for example feature value outside of the range, redundancy or noisy and unreliable data can damage the knowledge discovered during the training phase. In this work we followed essentially the procedure illustrated in [5] which includes outliers removal, features normalization and missing values removal.
B. Bayesian Classifier The Bayesian Classifier [7] needs the knowledge of some a-priori information, namely the class probability P (ci ) and the probability of observing a specified feature vector x given the class, P (x|ci ). If we had such information, the BC would be the optimum classifier with the minimum probability of error. In practice, we need to estimate these quantities from the training dataset, having then a sub-optimal classifier. The method aims at maximizing the a-posteriori probability, which according to Bayes theorem can be written as follows:
B. Features analysis The feature analysis is carried out before the classification step in order to identify the features that allow for a better discrimination of the targets. In this work, the constructed feature dataset has been analyzed following the two main steps illustrated in [5] and shown below.
P (ci |x) =
90
P (x|ci )P (ci ) . P (x)
(9)
The maximum a posteriori (MAP) hypothesis is given by P (ci |x) = argmax {P (x|c)P (c)}
(10)
c∈C
where P (x) and P (c) can be omitted as the first does not depend on c and the classes are assumed to be equiprobable. A decision hyper-surface can be easily computed in the case of Normal distributed features. V.
R ESULTS
(a) Target A
(b) Target B
(c) Target C
(d) Target D
(e) Target E
(f) Target F
(g) Target G
(h) Target H
A. Setup description The data was collected in an anechoic chamber at the University of Adelaide, Australia. The transmitted signal was a stepped frequency pulsed waveform with center frequency equal to 10 GHz and 401 frequencies equally spaced by 10 MHz. The targets were on a turntable that was rotated of 0.1◦ after each radar sweep. A set of 101 radar sweep was collected for each radar acquisition. Each target was made of 4 simple scatterers, specifically trihedrals, dihedrals and flat planes of various size and orientation. More details and pictures of the targets can be found in [8]. Each target represents a class. Additive Gaussian White Noise was added to the raw data in order to asses the algorithm performance at different Signal to Noise Ratio (SNR). The Pol-ISAR images are shown in Fig.1.
B. Results Figure 2 shows the FDR defined in (7) for all the features extracted from the dataset, both CTD and ICTD, against the SNR. As the targets are composed of 4 elementary scatterers, Ns has been set equal to 4. As a result, the size of x is equal to 19. By observing Fig.2, we can notice that as the SNR decreases, the FDR generally decreases as well. This is due to the fact that the different classes become more and more confused and therefore less separable. By focusing on SNR=5 dB, we can see that the most discriminating CTD feature is zR,1 , while the most discriminating ICTD one is αM L . Figure 3 shows an estimate of the probability density function (PDF) relative to zR,1 and αM L for all the classes. From Fig.3(a) and Fig.3(b), we can notice that in these two feature spaces the different classes are visibly well separated. Moreover, we can also qualitatively verify the hypothesis of Gaussian PDF. Figure 4 shows the log(J2) defined in (8). Both the two full CTD and ICTD feature vectors, as well as the fusion vector, have been considered. By observing Fig.2, we can notice that as the SNR increases, log(J2) increase as well and this is in accordance with the FDR analysis. Figure 2 shows that, in terms of log(J2), the CTD feature vector performs better than the ICTD feature vector for all the SNRs. Moreover, the fusion of the two vector always improves the class separability. Figure 5 shows the results of classification with both classifiers in term of Probability of Correct Classification (PCC). Both the classifiers were trained on the dataset with 0 dB of SNR. Results obtained show how the joint use of CTD and ICTD feature set can enhance classification performance. For both classifiers, as the targets are composed of small geometrical objects, the CTD dataset performs better than the ICTD dataset. In both cases, we have PCC over 80% at SNR greater or equal to -5 dB. Fusion technique, applied for now without feature vector optimization, shows performance equal or greater than
Fig. 1: Pol-ISAR images of the targets.
both CTD or ICTD taken separately. Especially at SNR over -5 dB, preliminary results show an improvement between 3% and 5%. This is clear with SVM, while BC for now does not show appreciable improvements, while the PCC is slightly higher. By observing Fig.4, we would have expected a general higher PCC using the fusion vector instead the CTD and ICTD vector separately. However, Fig.5 shows that the classification performance was not in general increased when the fusion vector was used. This fact can be explained by the so called the curse of dimensionality [5]. Basically, the fusion of the CTD and ICTD feature vectors defines a higher dimensionality feature space (12 for CTD, 7 for ICTD and 19 for the fusion). In machine learning problems, it is well known that a higher dimensionality feature space requires a grater number of observations, but in this work the number of observations was fixed by the number (101) of the collected
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Fig. 4: log(J2) for the different feature vectors against the SNR.
Fig. 2: FDR for all the features against the SNR.
(a) SVM classifier
(b) Bayesian classifier
Fig. 5: Total probability of correct classification.
(a) zR,1
proposed CTD and ICTD features fusion method for PolISAR images on different dataset. Moreover, features selection algorithms [5] will be implemented in order to define a robust polarimetric features vector for ATR of man-made targets.
(b) αM L
Fig. 3: Histogram of two normalized CTD and ICTD features for all the classes at SNR=5 dB.
R EFERENCES [1] M. Martorella, A. Cacciamano, E. Giusti, F. Berizzi, B. Haywood, and B. Bates, “CLEAN technique for polarimetric ISAR,” International Journal of Navigation and Observation, Special issue on Modelling and Processing of Radar Signals for Earth Observation, vol. 2008, pp. 1–12, 2008. [2] W. L. Cameron, N. N. Youssef, and L. K. Leung, “Simulated polarimetric signatures of primitive geometrical shapes,” IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 3, pp. 793–803, 1996. [3] S. Cloude and E. Pottier, “An entropy based classification scheme for land applications of polarimetric SAR,” IEEE Tr. On Geoscience and Remote Sensing, vol. 35, pp. 68–78, 1997. [4] R. Paladini, M. Martorella, and F. Berizzi, “Classification of manmade targets via invariant coherency-matrix eigenvector decomposition of polarimetric sar/isar images,” Geoscience and Remote Sensing, IEEE Transactions on, vol. 49, no. 8, pp. 3022–3034, Aug 2011. [5] S. Theodoridis and K. Koutroumbas, Pattern Recognition, 3rd ed. San Diego, CA, USA: Elsevier, 2006. [6] C. Cortes and V. Vapnik, “Support-vector networks,” vol. 20, no. 3, 1995, pp. 273–297. [7] T. Mitchell, “Machine learning.” New York, NY, USA: McGraw-Hill, Inc., 1997. [8] M. Martorella, E. Giusti, L. Demi, Z. Zhou, A. Cacciamano, F. Berizzi, and B. Bates, “Target recognition by means of polarimetric isar images,” Aerospace and Electronic Systems, IEEE Transactions on, vol. 47, no. 1, pp. 225–239, January 2011.
radar sweeps. If the number of observations is not enough for the considered feature space dimensionality, the classification performance is not increased by adding more feature, even if the added features exhibit a strong class separability power. The curse of dimensionality problem can be overcome by using a greater number of observation in the classification performance analysis, or by selecting the minimum number of features that guarantees the optimal classification results for the given number of observations [5]. VI.
C ONCLUSION
In this paper an Automatic Target Recognition Method which makes a jointly use of coherent and incoherent target feature set has been presented. The class separability power of CTD and ICTD features, together with their fusion, was evaluated in terms of FDR and J2. The classification performance of different feature vectors was analyzed by means of two kind of classifiers, namely the SVM and a Bayesian classifier. It was shown that the fusion of the CTD and ICTD features is never worse than the two different feature sets used separately. In the case of SVM classifier, the overall classification performance is enhanced by a 5%. Further work will see the test of the
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