Spatial-Aware Collaborative Representation for Hyperspectral Remote Sensing Image Classification

Transcription

1 Spatial-Aware Collaborative Representation for Hyperspetral Remote Sensing Image ifiation Junjun Jiang, Member, IEEE, Chen Chen, Member, IEEE, Yi Yu, Xinwei Jiang, and Jiayi Ma Member, IEEE Representation-residual based lassifiers have attrated muh attention in reent years in hyperspetral image (HSI) lassifiation. How to obtain the optimal representation oeffiients for the lassifiation task is the key problem of these methods. In this letter, spatial-aware ollaborative representation (SaCR) is proposed for HSI lassifiation. In order to make full use of the spatial-spetral information, we propose a losed-form solution, in whih the spatial and spetral features are both utilized to indue the distane-weighted regularization terms. Different from traditional ollaborative representation based HSI lassifiation algorithms, whih model the spatial feature in a preproessing or post-proessing stage, we diretly inorporate the spatial information by adding a spatial regularization term to the representation objetive funtion. Experimental results on three HSI datasets verify that our proposed approah outperforms the state-of-the-art lassifiers. Index Terms Hyperspetral image lassifiation, ollaborative representation (CR), spatial regularization, spetral spatial information. I. INTRODUCTION Hyperspetral remote sensing (HRS) allows the simultaneous aquisition of full portrayal of eah material s spetral refletane and inreases the possibility of disriminating ground objets more aurately [], [2], [3], [4]. Reently, representation-based lassifiation methods are of great interest in hyperspetral image (HSI) lassifiation due to their exellent performanes [5], [6], [7], [8], [9], [0], [], [2]. The ommon idea is to represent a test sample by the training samples and assign the lass that provides the lowest reonstrution residual. We term this strategy as representationresidual based lassifiation in this letter. For example, sparse representation (SR) lassifiation was first proposed in [3], and has been suessfully applied in various appliations [4], [5], [6], [7], [8], [9], [20]. Chen et al. [5] introdued SR to HSI lassifiation based on the assumption that HSI pixels that belong to the same lass approximately lie in a low-dimensional subspae. In [2], Zhang et al. argued that it is the ollaborative representation The researh was supported by the National Natural Siene Foundation of China (65043, , ), and by the Fundamental Researh Funds for the Central Universities, China University of Geosienes (Wuhan) under Grant CUGL6042. J. Jiang and X. Jiang are with the Shool of Computer Siene, China University of Geosienes, Wuhan 4074, China (junjun0595@63.om, ysjxw@hotmail.om). C. Chen is with the University of Central Florida, Orlando, USA (henhen87073@gmail.om). Y. Yu is with the Digital Content and Media Sienes Researh Division, National Institute of Informatis, Tokyo 0-84, Japan (yiyu@nii.a.jp). J. Ma is with the Eletroni Information Shool, Wuhan University, Wuhan 4072, China ( jiayima@whu.edu.n). (CR) rather than the omputationally expensive SR onstraint that atually determines the lassifiation performane. Inspired by this observation, Li et al. [8] developed a joint CR (JCR) lassifiation method with spatial and spetral features from surrounding pixels, and they further extended JCR to the kernel version and the weighted version in [9] and [0], respetively. In addition to the raw pixel feature, Gabor feature [] or multi-feature [7] has been proposed to improve the performane of JCR. Instead of exploring the neighbor pixels, Li et al. [6] onstruted a joint matrix using the nonloal pixels of a test pixel, and proposed a nonloal joint ollaborative representation lassifiation method. The essential of utilizing the spatial information of these ollaborative representation methods is to onstrut a joint vetor [8], [], [9], or matrix [5], [6] before performing sample representation. By inorporating the spatial information of HSI, one an expet to obtain a better representation than using spetral information only [22], [23], [24], [25]. To simultaneously inorporate the spetral and spatial information to the representation framework, in this letter we propose a spatial-aware ollaborative representation (SaCR). In SaCR, we design two expliit regularization terms: one is for modeling the spetral similarity onstraint and the other is for the spatial similarity onstraint. Based on these two regularization terms, we develop a losed-form solution to effetively fuse the spetral and spatial information. Experimental results on three HSI datasets demonstrate the proposed method outperforms the state-of-the-art spetral-spatial based CR lassifiation tehniques. II. RELATED WORK Suppose there are N training HSI pixels x i IR d (d dimensional feature spae), i =, 2,, N, hosen from C different lasses. The training set an be also denoted by a matrix X = [x, x 2,, x N ] IR d N. Let w i {, 2,, C} be the label of the i-th pixel and n l be the number of available training samples from the l-th lass, thus C l= n l = N. Given a test pixel y IR d, CR based methods utilize all the training samples to represent it: J(α) = y Xα λω(α). () Here, the regularization parameter λ balanes the trade-off between the reonstrution residual and the prior of α. After solving the optimal representation oeffiients α = arg min J(α), the lass label of the test pixel y is determined α aording to the minimum residual, lass(y) = arg min y X l α l 2 2, (2) l=,2,...,c

2 2 where X l and α l are the subsets of X and α, respetively. Different priors Ω(α) have been proposed to regularize the least squares problem. In SR lassifiation, a test sample is sparsely represented by an l 0 norm regularization. In [2], Zhang et al. argued that it is the CR nature (i.e., using all the training samples) rather than the sparsity that improves lassifiation auray. To make the representation more flexible, nearest regularized CR method [26] introdues a loality onstraint to regularize the solution of () by giving different freedom to training samples aording to their Eulidean distanes from y: J(α) = y Xα λ Γα 2 2 (3) where Γ is a biasing Tikhonov matrix defined by with Γ ii = y x i 2, i =, 2,..., N. If the distane between a training sample x i and the test sample y is large, x i will be given a small ontribution (i.e., the orresponding representation oeffiient α i is small), and vie versa. In HSI, neighboring pixels usually onsist of similar materials with high probability. Thus, their spetral harateristis are highly orrelated. The spatial orrelation aross neighboring pixels an be indiretly inorporated through a joint model. For example, Xiong et al. [8] proposed to simultaneously represent a test pixel and its neighbors by spatially averaging the test and training pixels: J(α) = ỹ X l α l λ Γ l α l 2 2 (4) where ỹ denotes the average spetral features for the test pixel y entered in a window with m neighbors, and X l is the averaged value for eah element in matrix x l. In [0], they further developed an improved version to utilize more appropriate weights for surrounding pixels. A. SaCR III. THE PROPOSED METHOD In this setion, we introdue our proposed CR model by expliitly modeling the spetral and spatial feature. Speifially, we develop a losed-form solution based on spatial-aware ollaborative representation (SaCR), in whih the spetral and spatial information is used together to indue regularization terms. Different from traditional CR models, whih use neighbor pixels to onstrut a joint vetor by averaging [8], [0] or matrix by ombing [7], [6], [5] (they all an be seen as a predefining stage), we diretly inorporate the spatial feature into the objetive funtion (6) by adding a spatial feature indued regularization term: J(α) = y Xα λ Γα γ diag(s)α 2 2, (5) where s = [s, s 2,, s N ], s i is assoiated with eah training samples whih enourages representation oeffiients that are spatially oherent with respet to the training data, and diag(s) returns a square diagonal matrix with the elements of vetor s on the main diagonal. Here, the regularization parameters λ and γ ontrol the ontributions of the loality prior (seond term) and spatial prior (third term), respetively. For more details about the effets of these two parameters, please refer to the Setion IV-B. Analogous to the role of the Tikhonov matrix Γ, diag(s) ats similar effets. If one training sample x i is neighbor to the test pixel, i.e., s i is small (the penalty on representation oeffiient α i is small), then α i is likely to be a relatively large value and x i ontributes signifiantly to the reonstrution of the test pixel, and vie versa. Denoting the pixel oordinate of sample x i and y as (p i, q i ) and (p y, q y ) respetively, the spatial oherent between x i and y an be measured as s i = [dist((p i, q i ), (p y, q y ))], (6) where dist( ) denotes Eulidean distane and is a smooth parameter adjusting the distane deay speed for the spatial prior. Usually we further normalize s to be between (0, ] by dividing max(s) from s. The introdution of the smooth parameter gives the model more flexibility. It allows to emphasize more on neighbor pixels with better disriminability. When the value of is very large, our proposed model will heavily penalize pixels that are far away from the test pixel y by assigning weights lose to 0 to them. From Eq. (5), we learn that the proposed SaCR model onsists of three parts: the first part is the data reonstrution term to ensure the reonstruted sample (xα ) being similar to y, the seond part is the spetral indued penalty term that enfores similar training pixels to the test pixel to have large representation oeffiients and vie versa, and the last part is the spatial indued penalty term that enfores the neighbor training pixels of the test pixel (i.e., training pixels that are spatially lose to the test pixel) to have large representation oeffiients and vie versa. λ and γ are two regularization parameters to balane the ontributions of the three terms. The optimization of (5) is similar to (4), whih an be derived analytially as: B. α = (x T X+λΓ + γdiag(s))x T y. (7) To take into onsideration of the ontextual information of enter pixels, we further extend our SaCR method to a joint version (named for short): J(α) = ỹ Xα λ Γα γ diag( s)α 2 2, (8) where ỹ is defined as in JCR [], X is the average value for eah element in matrix x, i.e., x j = (/m) m i= x i, j =, 2,, N, Γ and s are defined by X and ỹ. When ompared with SaCR and, we learn that an be summarized as the following two steps: (i) average filtering and (ii) performing SaCR on the filtered image. Note that the average filtering usually an smooth the random noise in HSI image, so an be expeted to have better results than SaCR. C. Relation to Existing Methods It is worth mentioning that our proposed method aims to simultaneously inorporate the spetral and spatial information to the HSI lassifiation task, where spatial and

3 3 TABLE I THE PARAMETER SETTINGS OF OUR PROPOSED SACR AND JSACR METHODS FOR THE THREE HSI DATASETS. Parameters Pine University of Pavia SaCR SaCR SaCR e-06 e+04 e+06 e spetral features are both utilized to indue the distaneweighted regularization terms, and this makes different from the existing spetral and spatial features based HSI lassifiation methods. Speifially, CR [2] an be seen as a speial ase of the proposed SaCR method when we set Γ to the identity matrix and γ to zero (see Eq. () and Eq. (5)); When we set γ to zero, the proposed SaCR method will redue to WCR [0] (see Eq. (3) and Eq. (5)); Our proposed method will redue to JCR [8] when we set γ to zero, please refer to the objetive funtions (4) and (8). When ompared with the traditional CR based methods, e.g., WCR and JCR, our proposed SaCR and both have the spetral penalization fator and spatial penalization fator, thus the proposed algorithm will take muh time to alulate the similarity. IV. EXPERIMENTS AND ANALYSIS In this setion, we investigate the effetiveness of the proposed SaCR lassifiation algorithm and its joint version () using three HSI datasets. The lassifiers inluding support vetor mahine (SVM) [27], [28], SVM with omposite kernel that ombines the spetral and spatial information via a weighted kernel summation (denoted by SVM-CK) [28], SR lassifiation [3], JSR lassifiation [5], CR lassifiation [2], weighted ollaborative representation (WCR) lassifiation [0] and JCR lassifiation [8] are used for omparison in this letter. The lassifiation performane is measured by overall auray () on the three HSI datasets. A. Experimental Datasets The first HSI dataset is the Pine, aquired by National Aeronautis and Spae Administrations (NASA) Airborne Visible/Infrared Imaging Spetrometer (AVIRIS) sensor, whih generates pixels and 220 bands in the m region, of whih 20 noisy bands are removed before lassifiation. It ontains 6 ground-truth lasses, and the lass-speifi numbers of test and training samples are shown in Table I. The seond dataset is the University of Pavia, whih is olleted by the Refletive Optis System Imaging Spetrometer (ROSIS) sensor and ontains a spatial overage of pixels. It generates 5 spetral bands, of whih 2 noisy bands are removed. There are nine ground-truth lasses of the dataset. The third dataset is the, olleted by the 224-band Airborne Visible Infrared Imaging Spetrometer (AVIRIS) sensor over Valley, California, whih generates pixels is the number of orretly predited pixel/total of pixel to predit SaCR SaCR Fig.. ifiation auray with varying regularization parameters λ and γ of SaCR and on Pine (top row), University of Pavia (middle row), and ( bottom row), respetively Fig. 2. ifiation auray with varying regularization parameter of SaCR and on Pine (left olumn), University of Pavia (middle olumn), and (right olumn), respetively. and 204 bands over m with spatial resolution of 3.7 m, of whih 20 water absorption bands are removed before lassifiation. For the above three datasets, the test and training data is randomly seleted from the available ground truth maps. The lass-speifi numbers of test and training samples are shown in Table II, Table III, and Table IV. To avoid any bias, all the experiments are repeated 0 times, and we report the average lassifiation auray. B. Parameter Settings To demonstrate the effetiveness of our proposed approah, we study the effet of the three regularization parameters λ, γ and. In general, the fivefold ross-validation strategy based on training samples is onsidered for parameter tuning. Fig. plots the urves of the values on the three HSI datasets as a funtion of the regularization λ and γ. It is worth noting that eah left subfigure shows the values aording to γ when λ is set to the optimal value, and eah right subfigure presents the values aording to λ when

4 4 TABLE II CLASSIFICATION ACCURACY (%) FOR THE INDIAN PINE DATASET. Alfalfa Corn-notill Corn-mintill Corn Grass-pasture Grass-trees Grass-pasture-mowed Hay-windrowed Oats Soybean-notill Soybean-mintill Soybean-lean Wheat Woods Buildings-Grass-Trees-Drives Stone-Steel-Towers # samples ifiation Algorithms Train Test SVM SVM-CK SR JSR CR WCR JCR SaCR Overall Auray (%) γ is set to the optimal value. From Fig., we an see that: i) by setting proper values of λ or γ, is better than SaCR, whih implies the effetiveness of utilizing ontextual information of enter pixels; ii) when γ is set to the optimal value, the inrease of λ brings small gains. However, when λ is set to the optimal value, the inrease of γ brings relatively large gains. This indiates that the spatial indued penalty term plays a relatively more important role than the spetral indued penalty term does in the sample representation; iii) when γ = 0, the proposed SaCR method redues to the WCRC method, the performane of SaCR is restrited. This an be explained by that the spatial indued onstraint is essential for HSI lassifiation task. Table I tabulates the parameter settings for the three HSI datasets when our proposed SaCR and ahieve the best performanes. In addition to the analysis of λ and γ, we also evaluate the performane of our proposed method with different smooth parameter (as shown in Fig. 2). The smooth parameter has an important influene on the lassifiation auray. It annot apture the spatial struture information if the smooth parameter is set too large or too small. To obtain the best performanes, the Pines and University of Pavia datasets employ larger values of than the dataset. This is mainly beause that the former two datasets have a lot of disonneted lasses, while the latter exhibits more spatial homogeneity. From the objetive funtion (5), we learn that large values of γ and mean that spatial onstraint aount for main ontribution, and SaCR method tends to selet a small number of neighbor pixels. This point ould be learned from Table I. SaCR uses relatively small values of parameters γ and for the Pine dataset and the dataset (γ is e+4 or 0, is 4 or 2), and large values for the dataset (γ is e+6 and is 9). C. ifiation Performane The performanes of SaCR and are shown in Table II, Table III and Table IV. From these results, we an onlude that the introdution of the ontextual information greatly improves the performane of the original pixel based method, e.g., as for the Pine dataset, SVM-CK has 23.48% gain over SVM, JSR has 9.8% gain over SR, JCR has 35.23% gain over CR, and has.03% gain over SaCR. Similar results an be also observed from the other two datasets. The differene between JCR and our proposed is that additionally imposes a spatial feature indued regularization term. From the reported results, we an see that this spatial regularization is important in the representation residual based HSI lassifiation method. The improvements of over JCR are 0.5%, 5.9%, and 3.63% on the Pine dataset, the University of Pavia dataset and the dataset, respetively. V. CONCLUSIONS In this letter, we proposed a novel CR HSI lassifiation method based SaCR. It has a losed-form solution to inorporate the spatial and spetral information simultaneously. Meanwhile, we further developed a joint SaCR () modeling that takes into onsideration of the ontextual information of the enter pixel. Extensive experimental results on three benhmark HSI datasets verified the effetiveness of inorporating the spatial feature indued regularization term. Comparison results demonstrated that our proposed algorithm an obtain better performane than the state-of-the-art spetralspatial HSI lassifiation methods. REFERENCES [] J. Lin, Q. Wang, and Y. Yuan, In defense of iterated onditional mode for hyperspetral image lassifiation, in ICME, July 204, pp. 6. [2] Q. Wang, J. Lin, and Y. Yuan, Salient band seletion for hyperspetral image lassifiation via manifold ranking, IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 6, pp , June 206. [3] C. Chen, W. Li, H. Su, and K. Liu, Spetral-spatial lassifiation of hyperspetral image based on kernel extreme learning mahine, Remote Sensing, vol. 6, no. 6, pp , 204. [4] B. Du, M. Zhang, L. Zhang, R. Hu, and D. Tao, Pltd: Path-based lowrank tensor deomposition for hyperspetral images, IEEE Transations on Multimedia, vol. 9, no., pp , Jan 207. [5] Y. Chen, N. M. Nasrabadi, and T. D. Tran, Hyperspetral image lassifiation using ditionary-based sparse representation, IEEE Trans. Geosi. Remote Sensing, vol. 49, no. 0, pp , 20.

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