Supervised Graph Embedding for Polarimetric SAR Image Classification

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 10, NO. 2, MARCH 2013

Supervised Graph Embedding for Polarimetric SAR Image Classification Lei Shi, Student Member, IEEE, Lefei Zhang, Student Member, IEEE, Jie Yang, Liangpei Zhang, Senior Member, IEEE, and Pingxiang Li, Member, IEEE

Abstract—This letter introduces an efficiency-manifoldlearning-based supervised graph embedding (SGE) algorithm for polarimetric synthetic aperture radar (POLSAR) image classification. We use a linear dimensionality reduction technology named SGE to obtain a low-dimensional subspace which can preserve the discriminative information from training samples. Various POLSAR decomposition features are stacked into the input feature cube in the original high-dimensional feature space. The SGE is then implemented to project the input feature into the learned subspace for subsequent classification. The suggested method is validated by the full polarimetric airborne SAR system EMISAR, in Foulum, Denmark. The experiments show that the SGE presents a favorable classification accuracy and the valid components of the multifeature cube are also distinguished. Index Terms—Classification, dimensionality reduction (DR), graph embedding, polarimetric synthetic aperture radar (POLSAR).

I. I NTRODUCTION

P

OLARIMETRIC synthetic aperture radar (POLSAR) is a new form of radar system. The change in the polarization state of electromagnetic waves reflected from the Earth’s surface characterizes the nature of the land features. The current frameworks of the classification procedures are almost identical in that they first estimate the initial cluster centers (manual or automatic) and then specify the measurement of the classifier. The proper feature will reduce the redundancy information and improve the accuracy of the classifier operator. In POLSAR classification frameworks, the common feature analyses include the H/alpha, the Yamaguchi, the Neumann, the Huynen, the Krogager, the Cameron decomposition, etc. However, there is a large information redundancy in difference features, since the Krogager rotation angle is always relative to the prevalent orientation angle compensation methods [1] and the H/alpha parameters describe the chaotic volume attribution, which is also described in the Freeman–Durden methods, etc. Moreover, the current POLSAR methods only consider the decomposition

Manuscript received December 12, 2011; accepted April 30, 2012. This work was supported in part by the Fundamental Research Funds for the Central Universities under Grant 201161902020003, by the National Natural Science Foundation under Grant 60890074, and by the National High-Technology R&D Program (863 Program) under Grant 2011AA120404. The authors are with the Remote Sensing Group, State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2012.2198612

features sparsely. The intrinsic character should be explored by the dimensionality reduction (DR) technique. In the last years, a large number of linear and nonlinear DR approaches have been proposed to project high-dimensional data into a new space of lower dimensionality. The conventional DR algorithms contain principal component analysis (PCA) [2], linear discriminated analysis [3], maximum margin criterion [4], etc. Some recently proposed manifold learning algorithms find a nonlinear low-dimensional feature representation based on preserving the specific local property, e.g., locally linear embedding (LLE) [5], isometric feature mapping (ISOMAP) [6], local tangent space alignment (LTSA) [7], Laplacian eigenmaps (LEs) [8], Hessian eigenmaps [Hessian locally linear embedding (HLLE)] [9], and multidimensional scaling [10]. In remote sensing image analysis, previous hyperspectral researchers have demonstrated that DR is useful for feature extraction and subsequent classification [11]–[13]. However, the topic of POLSAR DR is restricted. A few researchers have investigated the use of DR for POLSAR imagery, in which most of them have projected the 4-D POLSAR span images into the low dimension by PCA or independent component analysis [14]. In order to consider the local property of a data set in highdimensional feature space, the LLE and the ISOMAP have been implemented in the 9-D polarimetric covariance matrix directly [15], [16]. When carrying out the DR algorithms in radar, the dimension of original POLSAR observers is low. More potential high-dimensional features could be obtained by stacking various polarimetric decomposition results, and literature [17] introduced the LE algorithm for POLSAR multifeature classification. This method showed that the LE intrinsic feature vector is more separable than the original feature vectors for classification. However, two key issues should be discussed before using manifold-learning-based DR algorithm for POLSAR image classification: 1) The discriminative information from the given training samples should be considered into the DR step to further improve the classification performance, and 2) the linear versions of nonlinear technologies should be introduced to solve the out-of-sample extension in POLSAR image classification [18], [19]. In this letter, in order to address these two issues, we introduce the supervised graph embedding (SGE) algorithm, which can promote discriminative information in the reduced feature space for subsequent classification effectively. Furthermore, the SGE shows more stability than the other techniques as regards classification accuracy versus reduced dimensionality. The rest of this letter is organized as follows. Section II introduces the framework of POLSAR SGE, which contains the

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SHI et al.: SUPERVISED GRAPH EMBEDDING FOR POLSAR IMAGE CLASSIFICATION

Fig. 1.

Framework of polarimetric SGE classification.

noise suppression, the high-dimensional POLSAR feature cube construction, and the SGE algorithm. The experimental results of the suggested method are presented in Section III. Finally, Section IV gives the conclusion and our future work.

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the POLSAR. In literature [17], 42 decomposition features in total are spliced into a high-dimensional cube; moreover, the DR methods are implemented, and it gives better classification accuracy than the feature reduction on the original C3/T 3 data sets directly. When the DR is operated, the inner redundancy of the different decomposition methods is reduced, which gives a favorable indicator to evaluate the different decomposition algorithms. In distributed target classification, polarimetric decomposition should be implemented, such as the Neumann, the Freeman–Durden, the Yamaguchi, and the Cloude decompositions. Moreover, the Krogager, the Cameron, and the Touzi decomposition methods focus on the stationary target (pure single target). Theoretically, the dimension of feature cube is infinite, and we proposed the same 42 features of the literature [17] to verify our SGE. C. SGE

II. F RAMEWORK OF POLSAR SGE The framework of polarimetric SGE classification is shown in Fig. 1, which is composed of preprocess noise suppression, the feature cube building, and the SGE classification. A. Noise Suppression of POLSAR The original single-look complex (SLC) images of POLSAR are always at a high level of speckle noise, and the DR methods are very sensitive to the noise. The commonly used boxcar filter always causes blurring at the edges of the blocks. There have been several researchers describing advanced algorithms, such as the refined LLMMSE-LEE filter [20] and the span-driven adaptive neighborhood (SDAN) [21]. However, the refined LLMMSE-LEE is always influenced by the brightness target in local windows, and SDAN cannot be implemented in the covariance C3 or coherence T 3 matrices directly. In this letter, we combine the segmentation and the boxcar filter algorithm to better estimate the C3/T 3 matrix. First, statistical region merging (SRM) [22] is used to segment the original Pauli-red"green"blue (RGB) POLSAR images (|HH + V V | − Blue, |HH − V V | − Red, and |HV | − Green), and each segmentation object gets a label. Then, the local window pixels, which are labeled as the same segmentation object as the central window pixel, are used to estimate the C3 or T 3 matrix in the boxcar filter. B. Characteristics of Feature Cube The dimensions of the hyperspectral image are obtained by the continuous-frequency-observation sensor; however, the dimensions of POLSAR come from the reflected polarimetric attribution of the material. In general, the C3/T 3 matrix contains rare features, which only contains three real diagonal and three complex nondiagonal elements in monostatic radar. That is why there is just a small quantity of literatures about the SAR DR. When various polarimetric decomposition methods are implemented, the results could be stacked into a high-dimensional feature cube, and it is very suitable to

The SGE algorithm is based on manifold learning. For an input data set V = [v 1 , v 2 , . . . , v N ] ∈ RL×N , in which N and L denote the numbers of samples and features, the manifold learning DR algorithms try to find the low-dimensional feature representation Y = [y 1 , y 2 , . . . , y N ] ∈ Rd×N which preserves the graph constructed by the vertex matrix V at the specific local property measures using various similarity criteria. Based on the graph embedding [23], some of the manifold learning DR algorithms can be unified to a framework, including the works of LLE, LTSA, ISOMAP, LE, and HLLE which are all focused on unsupervised DR. When the supervised information is provided, i.e., we have the sample label information li |N i=1 = {1, 2, . . . , c} in c denoting the number classes, the similarity preservation property from the graph should be measured by minimizing the distances of the sample pairs of the same class as well as maximizing the distances of sample pairs of different classes in the low-dimensional feature space. This idea can be defined in the following optimization. For each sample v i , we have the following patch optimization on its low-dimensional representation y i min yi

k1 k2 y i − y + 2 − λ y i − y − 2 j

j

j=1

(1)

j=1

− in which y + j (j = 1, . . . , k1 ) and y j (j = 1, . . . , k2 ) are the − low-dimensional representations of v + j and v j , respectively. + v j is the jth sample of the same class, and v − j is the jth sample of the different classes, sorted by the Euclidean distance 2 − 2 of sample pairs v i − v + j and v i − v j , respectively. λ is a parameter to adjust the weight between minimization and maximization. Similar to the approach in patch alignment framework [24], we have the definition supervised local patch of V (i) and its low-dimensional representation Y (i) + + − − − V (i) = v i , v + 1 , v 2 , . . . , v k1 , v 1 , v 2 , . . . , v k2

Y

(i)

L×(k1 +k2 +1) ∈ R + + − − − = yi , y1 , y2 , . . . , y+ k1 , y 1 , y 2 , . . . , y k2

∈ Rd×(k1 +k2 +1)

(2) (3)

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and by defining a coefficient vector η in (4), patch optimization (1) can be reduced to (5) 1, . . . , 1, −λ, . . . , −λ η= (4) k1 k2 min Y (i)

k 1 +k2

2 (i) (i) η j Y 1 −Y j+1

j=1

T (i) −ek1 +k2 (i)T = min tr Y diag(η)[−ek1 +k2 I k1 +k2 ]Y I k1 +k2 Y (i)

(5) = min tr Y (i) Li Y (i)T . Y (i)

(i)

In (5), η j is the jth element in η, Y j is the jth column in matrix Y (i) , and T −ek1 +k2 i (6) L = diag(η)[−ek1 +k2 I k1 +k2 ] I k1 +k2 where ek1 +k2 = [1, . . . , 1]T ∈ R(k1 +k2 ) and I k1 +k2 ∈ R(k1 +k2 )×(k1 +k2 ) is an identity matrix. Then, the full optimization of SGE is obtained by summing all the patch optimizations of v i (5). Because the columns in patch Y (i) are selected from the full input data matrix Y ∈ Rd×N , which has its own index system, we introduce a selection matrix S i ∈ RN ×(k1 +k2 +1) to align all the samples in Y (i) together into a unified index system in Y Y (i) = Y S i

(7)

in which the detailed definition of S i is given by 1, if m = Φi {n} i S (m,n) = 0, else

(8)

Y

N

tr(Y S i Li S iT Y T ) = min tr(Y LY T ) Y

i=1

scales with the number of samples, i.e., when this number is increased to 104 , it requires a long time in computing L as well as the eigenvalue decomposition. As a result of these two points, the nonlinear manifold learning algorithms suffer from the out-of-sample problem. To overcome this issue, the linear version of the introduced nonlinear DR technology should be considered to solve such out-of-sample extension in POLSAR image classification. In this letter, we adopted the work of locality preserving projection (LPP) linearization [26]. We can consider Y = U T V in which U ∈ RL×d ; then, (9) is deformed as min tr(U T V LV T U ). U

where Φi = [i, i1 , . . . , i(k1 +k2 ) ] is the index vector for the samples in patch Y (i) . We then sum the patch optimizations of all the given samples to obtain the whole optimization of SGE min

Fig. 2. (a) Multilook EMISAR Pauli-RGB image. In (b) the ground truth map, Ww. is the winter wheat. (c) SRM + boxcar filter result. (d) ENL result.

(9)

in which

(12)

Similar to (9), the optimal solution for (12) is the d eigenvectors associated with d smallest eigenvalues in the decomposition problem V LV T α = γα.

(13)

III. E XPERIMENTAL R ESULTS L=

N

(S i Li S iT ) ∈ RN ×N .

(10)

i=1

The solution of (9) is obtained by solving the eigenvalue decomposition problem [25] Lα = γα.

(11)

The feature mapping given by optimization (9), i.e., V ∈ RL×N → Y ∈ Rd×N , from the original high-dimensional feature space to the low-dimensional subspace can be nonlinear and implicit. Thus, in POLSAR image classification applications, two key issues should be addressed: 1) We have no supervised information for test samples to construct alignment matrix L in the optimization, and 2) note that the size of L

A. Data Set Description and Preprocess In this section, the classification results are undertaken to evaluate the SGE classification framework. The full polarimetric airborne SAR system EMISAR has imaged the scene in April 1998. The EMISAR system is a high-resolution system (1.5-m range resolution and 0.75-m azimuth resolution) working in 1.25 GHz. The original SLC image is processed by four looks in the azimuth and three looks in the slant range to keep the squared pixel size. In Fig. 2(a), the 300 × 421 pixel image locates in Foulum, Denmark, and several vegetations are planted on the flat ground, such as the coniferous, rye, oat, and winter wheat (Ww.) in Fig. 2(b); we refer to the ground truth from the literature [27]. Before stacking the decomposition images into the feature cube, the SRM + boxcar mixture filter

SHI et al.: SUPERVISED GRAPH EMBEDDING FOR POLSAR IMAGE CLASSIFICATION

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TABLE I C LASSIFIER ACCURACY AND T IME C OST E VALUATION

Fig. 3. Primary and secondary components of various DR methods. (a) SGE. (b) LPP. (c) KPCA. (d) PCA.

Fig. 4. Classification results of DR methods. (a) NN. (b) PCA + NN. (c) KPCA + NN. (d) LPP + NN. (e) SGE + NN.

is implemented in polarimetric images. The speckle noise is filtered in a 9 × 9 window size. In Fig. 2(c), the mixture filter has a favorable performance. First, the linear features of edges are preserved well, and we do not find obvious edge blurring. In Fig. 2(d), the equal-number look (ENL) of the whole area is high, and that implies a low noise result. After the speckle suppression, multiple polarimetric decomposition results are superposed into a feature cube. Although there are a few limitations about the feature cube structure, we do not try to append too many decomposition methods. For comparing the DR effectively, we construct the same 42-D polarimetric features as those in [17], and each feature image is also unified from zero to one. B. DR Classification Test Then, the DR methods, containing the PCA, the kernel PCA (KPCA), the LE, and the SGE, are used to get the lowdimensional images and the better classification results. One should notice that there are 126 300 pixels in the image; thus, it is impossible to execute the eigenvalue decomposition of an alignment matrix of size 105 in an acceptable time consumption. So, we adopted the linear version of the LE, i.e., LPP, for comparison. The common nearest neighbor (NN) Euclid measurement classifier is used to evaluate the DR. The training and the testing areas are extracted independently; then, 300 training samples and 500 testing samples are picked randomly in each class. In Figs. 3 and 4, the dimension of polarimetric features is reduced and classified by the PCA, the KPCA, the LPP, and the SGE with the NN distance measurement. The primary 8-D

features are used to classify the EMISAR data after various DR methods. The SGE parameters k1 , k2 , and λ are set as 5, 10, and 0.04, respectively. In LPP, we experimentally set k NN size as k = 5 and the heat-kernel parameter as 1.2 × 104 , respectively. When implementing the KPCA, the radial-basisfunction kernel is used. The linear distinguish potency can be evaluated by the primary and secondary components after the DR operators. We plot the first two components of the image results in Fig. 3 with the five typical classes first. The SGE makes a distinction between several classes, and the results are suitable to the Euclid measurement, which means designable by a linear classifier. In LPP, several classes present a compaction structure, except the oat, but still better than the KPCA and PCA. Moreover, it seems that there is no too much difference between the KPCA and PCA. The various DRs show the possibility to distinguish the class features in the linear space, which may be difficult by the common POLSAR algorithms. There is no too much difference at first glance in Fig. 4, and the major land-cover blocks are distinguished well. However, the NN, the PCA + NN, the KPCA + NN, and the LPP + NN show some fragments in the water, which is confused with the winter wheat. The SGE + NN shows a better result but, still, with a little confusion with the rye. The quantitative evaluations of the overall accuracy (OA) and kappa coefficient [19] are presented in Table I. All methods have a high OA, which is higher than 0.87, and the kappa is higher than 0.84. The DR methods demonstrate the potential in improving the POLSAR classification accuracy. The SGE + NN shows the highest OA and kappa values. In Table I, the NN and PCA + NN have the lowest computational cost. It may be strange when the PCA + NN time is a little lower than the NN one. The NN explores 42-D features to classify, and the PCA + NN only uses the 8-D features after the PCA operator. That is why the time cost of PCA + low-dimensional NN is similar to the direct highdimensional NN. Moreover, the KPCA indeed costs much time when the kernel matrix is constructed, and the fast improved version should be implemented in future work. The proposed SGE seems more efficient than the LPP with high accuracy. In general, the conventional POLSAR algorithms, such as the H/alpha/Wishart, have a moderate performance in distinguishing nature land-cover types. There are some literatures talking about the general POLSAR classification accuracy [28], [29]. For the special vegetation, the precision is near 85%, and the OA is higher than 80%. In this letter, we find that the POLSAR results are improved considerably by reducing the feature cube dimensions, even in the simplest NN classifier. The dimension–OA curves in Fig. 5 present the stability of various DR algorithms, and the OA is favorable at the high dimension. When the dimension is high, the LPP shows similar

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Fig. 5. Classification OA and dimension curves by various DR methods.

accuracy with the proposed SGE, and the inner character is extracted by SGE more efficiently. IV. C ONCLUSION In this letter, a novel DR algorithm has been introduced for POLSAR image classification. At the preprocess level, we use the SRM + boxcar filter to reduce the speckle noise which disturbs the radar cross-section coefficient. Various POLSAR observers and multifarious POLSAR decomposition results are stacked into the input feature cube. Then, the SGE algorithm is adopted to obtain a low-dimensional projection in which the discriminative information of training samples can be best preserved. Finally, the classification map is achieved by using the NN Euclid measurement in the reduced subspace. The experimental results show that the introduced SGE has a potential to keep the intrinsic features of POLSAR, which could improve the subsequent classification performance favorably. Compared to other nonlinear DR technologies, the suggested SGE algorithm could deal with the out-of-sample problem, so it outperformed other methods in both classification rate and computational time. However, we can only explain the DR process as a projection of the original space to the lowdimensional feature. Our future work will be focused on the sparse representation of the DR projection matrix, which could reveal a meaningful interpretation between the original input variables and the output features which are adopted in the classification. ACKNOWLEDGMENT The authors would like to thank the handling editor and anonymous reviewers for their careful reading and helpful remarks, which have contributed in improving the quality of this letter. R EFERENCES [1] J. S. Lee and L. Ainsworth, “The effect of orientation angle compensation on coherency matrix and polarimetric target decompositions,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 1, pp. 53–64, Jan. 2011. [2] I. T. Jolliffe, Principal Component Analysis. New York: SpringerVerlag, 2002. [3] S. Mika, G. Ratsch, J. Weston, B. Scholkopf, and K.-R. Muller, “Fisher discriminant analysis with kernels,” in Proc. IEEE Signal Process. Soc. Workshop, Madison, WI, 1999, pp. 41–48.

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