Abstract: Reference spectral signature selection is a fundamental workfor automatic oil spill detection. To address this issue, a new approach isproposed here, which employs the density-based cluster to select a specificspectral signature from a hyperspectral image. This paper first introducesthe framework of oil spill detection from hyperspectral images, indicatingthat detecting oil spill requires a reference spectral signature of oil spill,parameters of background, and a target detection algorithm. Based on theframework, we give the new reference spectral signature selection approachin details. Then, we demonstrate the estimation of background parametersaccording to the reflectance of seawater in the infrared bands. Next, theconventional adaptive cosine estimator (ACE) algorithm is employed toachieve oil spill detection. Finally, the proposed approach is tested viaseveral practical hyperspectral images that are collected during the HorizonDeep water oil spill. The experimental results show that this new approachcan automatically select the reference spectral signature of oil spills fromhyperspectral images and has high detection performance.
OCIS codes: (010.0280) Remote sensing and sensors; (010.4450) Oceanic optics; (100.2960)Image analysis; (280.4788) Optical sensing and sensors.
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1. Introduction
Oil spill occurs frequently because of drilling accident, transportation leakage, and natural leak-ing from ocean floor, etc. According to the European Space Agency (1998), 45% of the oilpollution comes from operative discharges from ships [1]. Especially, after the BP DeepwaterHorizon oil spill [2, 3], great attentions are attracted from all around the world about the de-structive effect of oil spill [4]. Hence, the detecting of oil spills becomes an urgent and desiredwork.
Currently, more attentions are focused on the use of satellite-based synthetic aperture radar(SAR) images to detect oil spills [5, 6]. In SAR images, the capillary waves backscattering ofoil spill is different from that of sea background. When oil is spilled on the sea surface, it formsa thin layer on the sea surface. This layer decreases microwaves and thereby generates darkareas in the SAR images [7, 8]. The merit of SAR images is that they have very high groundresolution, which can as high as that of panchromatic remote sensing images. But SAR imagesmay also have dark areas that are generated by other floating materials, which will lead tohigh false alarm of detection [9, 10]. Moreover, the pattern of oil spill may have very differentfeatures under different wind speed, and it is difficult to model. In addition, SAR remote sensingcannot find oil spills as wind speed is under or up a specific value [1].
Optical remote sensing is believed to have good performance in detecting oil spills undervarious conditions. Otremba et al. did extensive fundamental works about the optical char-acteristics of oil spill in seawater [11–15]. Lu et al. propose remarkable approaches to esti-mate oil slick thickness by optical remote sensing [16–19]. Hu et al. present excellent methodsto detection oil spills by using visible infrared imaging radiometer (VIIRS) [20–22]. Amongthe airborne or satellite-borne remote sensing sensors, hyperspectral sensor acquires both thespatial and spectral information of a pixel, having high ability in discriminating different ob-jects [23,24]. Hence, it has outstanding performance in detecting oil spills from seawater back-ground [25–27]. To detect oil spill pixels from hyperspectral images, a reference spectral sig-nature should be obtained at first. Unfortunately, the selection of reference spectral signature
from hyperspectral images is still a challenge issue. In [28], Clark et al. measure the reflectanceof oil in laboratory that is collected from the sea after oil spill, and utilize the measured spectralreflectance as a reference spectral signature. The reference spectral signature is then matchedwith the spectra of hyperspectral images that are corrected by atmosphere model. However, themeasured spectral signature may be different from the spectra that are corrected by atmospherecorrection model. Because atmosphere effect is so complicated that it cannot be modeled ac-curately. In some strong absorption bands, the compensated spectra have large deviation fromits original spectral reflectance. Therefore, it is reasonable to extract reference spectral signa-tures directly from hyperspectral images. In [29, 30], the researchers use an un-mixing methodto obtain the spectral signature of oil spills from hyperspectral images. The drawback of theapproach is that the number of end-members should be given first [31, 32]. Moreover, after theun-mixing procedure the extracted end-members must be tested manually to examine whichspectral signature comes from oil spills.
Recently, Rodriguez and Laio proposed a density-based cluster algorithm, published on Sci-ence [33], which can find clusters automatically and shows great adaptation under extremeconditions. This algorithm characterizes elements by their density and relative distance. Theelements with high density and large relative distance are spotted as cluster centers. And theirneighbors are clustered to the nearest cluster center automatically. The uniquely and profoundlyimportant advantages of the algorithm are its simpleness and high efficiency. The algorithm isimmediately applied in many practical applications, resulting in remarkable fruitions and muchhigher performance than conventional cluster algorithms [34–36]. For oil spill pixels, they closeto each other in spectral domain, and are far away from the seawater pixels. This characteris-tic fits the requirement of the density-based cluster. Therefore, we introduce the density-basedcluster algorithm to select a reference spectral signature from a hyperspectral image. After ob-tained the reference spectral signature of oil spill, the detection of oil spills can be achievedeasily by introducing the framework of target detection in hyperspectral images.
This paper is organized as follows. In section 2, the framework of oil spill detection is given.In Section 3, the density-based cluster algorithm is modified to meet the requirement of oil spilldetection. The background estimation procedure is shown in section 4. The execution of theproposed approach is illustrated in Section 5. In Section 6, the proposed approach is evaluatedand discussed. Finally, the conclusion is provided in Section 7.
2. Framework of oil spill detection from hyperspectral images
The main task of an oil detection algorithm is to determine whether a pixel under test is an oilpixel or a seawater pixel. The mathematical framework of oil spill detection algorithm can beapplied by that of target detection algorithms, which is primarily based on binary hypothesistesting. The optimum decision strategy of the binary hypothesis testing is to maximize theprobability of detection (PD) while keeping the probability of false alarm (PFA) under a fixedvalue, which is known as the Neyman-Pearson criterion and is embodied in the likelihood ratiotest [37, 38].
Λ(x) =f (x;θ1|H1 = oil)
f (x;θ0|H0 = seawater)≷H1
H0η (1)
As shown in Eq. (1), the probability of observing x under the null hypothesis is f (x|H0), andthe probability of observing x under the alternative hypothesis is f (x|H1). The desired PFA isachieved by setting the threshold η to an appropriate level.
For target detection, the parameters used for conventional algorithms are commonly the ref-erence spectral signature of targets, mean and covariance of background, and target detectionalgorithms. Thus, for oil spill detection, it is necessary to estimate the reference spectral signa-
ture of oil spills, the mean vector and covariance of seawater background, and an appropriatedetection algorithm.
3. Extraction of reference spectral signature of oil spill
3.1. Density-based cluster algorithm
Density-based cluster algorithm is a very simple and high efficient cluster algorithm, havingexcellent adaption in many applications. It is proposed based on the idea that cluster centershave a higher density than their neighbors, and the cluster centers are isolated from each other.It can automatically identify cluster centers, and assign every element to its closest center.Density-based cluster algorithm only depends on the distance between each two elements. Sinceoil spill and seawater have different spectral signatures, a proper distance between each twospectral signatures can be designed to make that the reference spectral signature of oil spillshas the highest density in all oil spill spectral signatures.
In hyperspectral images, the reference spectral signature of oil spill appears on the vertexof the convex polygon in spectral space. It cannot fit the requirement of density-based clus-ter algorithm, a new distance measurement should be designed to make the reference spectralsignature close to all spectral signatures of the oil spill pixels.
Let x(m,n) = [x(m,n,1),x(m,n,2), · · · ,x(m,n,k), · · · ,x(W,H,Nd)] denote a spectral signa-ture of a pixel in position (m,n). Nd denotes the number of spectral channels. The width andheight of a hyperspectral image are W and H respectively. Let i = nW +m, the distance of twospectral signatures is designed as follows
d(i, j) =x(i) ·x( j)
‖x(i)‖‖x( j)‖ (2)
This definition is based on the assumption that the reference spectral signature of oil spill hassmall distance from the oil contaminated pixels and has large distance from the seawater pixels.
In [33], Rodriguez and Laio define a local density ρ(i)
ρ(i) = ∑j
χ [(d(i, j)] (3)
where χ(x) is
χ(x) =
{1, x < dc
0, otherwise(4)
dc is called cutoff distance. It is found by sorting all the distances. The distance that poses onthe 2% of the distances is the cutoff distance. For practical applications, the authors suggestthat
χ(x) = exp
[−(
xdc
)2]
(5)
In [33], Rodriguez and Laio also define another parameter called δ (i). It is measured by com-puting the minimum distance between element i and any other elements with higher density:
δ (i) = minj:ρ( j)>ρ(i)
[d(i, j)] (6)
For the element that has highest density, δ (i) = max j[d(i, j)]. δ (i) is much larger than the typ-ical nearest neighbor distance only for elements that are local or global maxima in the density.
Therefore, cluster centers are recognized as elements for which the value of δ (i) is anomalouslylarge.
3.2. Down-sampling hyperspectral scene
The density-based cluster algorithm is designed based on the distances of each two elements.For a hyperspectral image with the size of W ×H, the distances, required to be calculated, isW ×H×(W ×H−1)/2. Usually, the size of a hyperspectral image is very large, so the numberof distances required to be calculated is much larger. Suppose the size of a hyperspectral imageis 800× 400, the number of distances required to be calculated is 1.152× 1011. This is a verylarge number, which will cost much time to process the cluster procedure.
To save time consuming, we first down-sample hyperspectral images to reduce the numberof distances required to calculate, and extract a rough reference spectral signature in low reso-lution. Then refine the rough result to the original resolution.
For a hyperspectral image, it is down-sampled to a small size. Let x(md ,nd) denotes a spectralsignature in low resolution.
x(md ,nd) =1
W 2d
Wd ,Wd
∑lm=1,ln=1
x(m+ lm,n+ ln) (7)
Where md = �m/Wd�, nd = �n/Wd�, (md ,nd) denotes pixel position in low resolution. Wd isthe width of down-sample window. It is suggested that down-sampling a hyperspectral scene tothe size of 2000 pixels is suitable.
3.3. Band feature extraction
The density-based cluster algorithm defines a density and a delta parameter to find clustercenters. The delta parameter represents the gap of different clusters. However, oil diffuses inseawater, thus the transition region of oil and seawater is not clear, which makes the deltaparameter becomes invalid. To address the issue, we replace the delta parameter with a newdesigned parameter based on the spectral features of oil spill. Fig. 1 is the spectral signature ofoil spill, cloud, and seawater.
0.5 1.0 1.5 2.0 2.50.0
0.1
0.2
0.3
0.4OilCloudSeawater
Ref
lect
ance
(0-1
)
Wavelength (�m)
Fig. 1. Reflectance of oil, cloud, and seawater.
As shown in Fig. 1, oil spill has some obvious features in 1.2μm and 1.73μm that are gen-erated by C-H bond. Whereas, cloud has high reflectance in both visible and infrared bands.
Seawater only has high reflectance before 0.8μm. In [39], Clark et al. proposed a band featureextraction method that has been shown excellent performance in identifying planet materials.In this paper, the band feature extract method is introduced to extract the band features of oilspectral signatures.
Suppose the spectral signature of oil in the selected band is denoted by xbo(k). The contin-uum of xbo(k) is denoted by xcbo(k), as shown in Fig. 1. The continuum-removed oil spectralsignature in the band is
xnbo(k) =xbo(k)xcbo(k)
(8)
Similarly, a continuum-removed observed spectral signature in the band is
xnb(k) =xb(k)xcb(k)
(9)
where xcb(k) is the continuum of the observed spectral signature in the band.A strength factor of the oil spectral signature and the observed spectral signature is
b =∑xnbxnbo − (∑xnb ∑xnbo)/Nf
∑x2nbo − (∑xnbo)2/Nf
(10)
where Nf denotes the number of spectral channels in the feature band. Another strength factoris
bg =∑xnbxnbo − (∑xnb ∑xnbo)/Nf
∑x2nb − (∑xnb)2/Nf
(11)
Thus, the correlation coefficient of the oil spectral signature and the observed spectral signatureis
α = bbg (12)
Let the slope of the continuum of the observed spectral signature is denoted by ks, we defineda slope factor
β =1
1+
(ks − kos
kt
)4 (13)
where kos is the slope of the continuum of the oil spectral signature in the feature band. kt is thecutoff slope of the continuum of oil spectral signature.
Therefore, the band feature of an observed spectral signature is
fm = αβ (14)
For a spectral signature, the integral band feature fb can be calculated by multiplying all theband feature in each selected spectral band.
fb = ∏m
fm (15)
where fb ≤ 1. The larger the fb is, the larger probability the spectral signature is an oil spectralsignature.
For the Airborne Visible / Infrared Imaging Spectrometer (AVIRIS) hyperspectral images,the selected bands are 1.2μm and 1.73μm.
Therefore, a decision graph can be generated by using the density and band feature of aspectral signature. As indicated in Eq. (14), if a spectral signature is an oil spectral signature,
Fig. 2. A decision graph and its corresponding spectral signature.
the fm of the spectral signature is large. Combing with the characteristic of ρ(i) , the oil spectralsignatures appear on the top right of the decision graph. In contrast, the points of seawaterappear on the bottom left of the decision graph. Fig. 2 is a decision graph.
As shown in Fig. 2, the points that have large density and large fb correspond to the spectralsignatures that have obvious absorption bands which are formed by oil spill. So the point onthe top right of the decision graph can be extract as a rough reference spectral signature.
3.4. Identification of spectral signature of oil spill
Normalize ρ(i)
ρn(i) =ρ(i)−ρmin
ρmax −ρmin(16)
where ρmax and ρmin are the maximum and minimum of ρ(i), respectively.The point on the top right corner of the decision graph can be identified as reference spectral
signature.In [33], Rodriguez and Laio suggest a integrated parameter to identify cluster centers by
multiplying ρ and δ . Thusfc(i) = ρn(i) fb (17)
fm = max fc(i) (18)
fos =
{1, fm ≥ τsp
0, fm < τsp(19)
The pixel that fos corresponds is the selected pixel in low resolution.To select the spectral signature in original resolution, the pixel that is selected in the low
resolution is enlarged to the original resolution. It will correspond to some pixels in originalresolution. The final reference spectral signature is extracted by calculating the density of thepixels in original resolution. The selected pixel in original resolution is
ρm =Wd ,Wdmax
lm=1,ln=1[ρ(m f + lm,n f + ln)] (20)
Where m f = ml ×Wd , n f = nl ×Wd , (ml ,nl) is the selected pixel position in the low resolution.The pixel that has the largest density is the extracted pixel. The spectral signature that the pixelcorresponds is the final selected reference spectral signature.
As discussed in Section 2, the detection of oil spill requires the parameters of background. Inmany target detection algorithms, the parameters of background are estimated using a wholehyperspectral image, the disturbance of targets is neglected. This does not lead to large devia-tions, because targets only occupy a few pixels in a hyperspectral image. However, for oil spilldetection, oil spills may cover the large part of a hyperspectral scene. Using the whole scene toestimate the parameters of background will lead to large deviations. Hence, the estimation ofbackground parameters should be restricted on the seawater regions.
As shown in Fig. 1, the reflectance of seawater is much smaller than that of clouds and oilin 1.0-2.5μm bands. Thus, the seawater can be segmented by thresholding reflectance in thebands
rb =1
Kr −Kl +1
Kr
∑k=Kl
x(k) (21)
lb =
{1, rb ≥ τr
0, rb < τr(22)
where τr is set to be about 0.1. Here, the threshold should be select as low as possible. Thiscan make the segmented region are only water regions, even the transition regions of oil andseawater are also excluded.
After thresholding, the parameter of seawater regions can be calculated.
mb =1
Nb∑
lb(i)=1
x(i) (23)
Cb =1
Nb −1 ∑lb(i)=1
[x(i)−mb][x(i)−mb]T (24)
where Nb denotes the number of pixels of seawater background.In marine environment, seawater regions occupy the main part of a hyperspectral image, it is
easy to segment seawater regions from a hyperspectral image.
5. Oil spill detection
The oil detection algorithm used here is borrowed from the target detection algorithms thatare designed and evaluated in the last two decades. In [38, 40, 41], Manolakis et al evaluatedmany conventional target detection algorithms and suggested that the adaptive cosine estimator(ACE) algorithm [42,43] had better detection performance than the other evaluated algorithms.In this paper, we introduce the ACE algorithm for the oil spill detection.
Every pixel in a hyperspectral image relates to an area of sea surface. The reflectance of thatpixel is the function of the reflectance of the materials in the area. This process is denoted bythe very famous model called linear mixture model. The model assumes that the reflectance ofa pixel is linearly mixed with the reflectance of the materials covered by the pixel. A reasonableassumption is that the abundance of each material is approximately the fraction of the pixel thatthe material occupies.
where αp denotes the abundant of the pth materials. This model means that the αp must satisfytwo constraints for all pixels:
Np
∑p=1
αp = 1 (26)
αp ≥ 0 (27)
This two equation are known as the sum-to-one and non-negativity constraints.Consider a pixel that is completely filled by a target material. Under the mixing constraints,
the reflectance of the pixel are generated by a target. This type of target is called a full pixeltarget. Whereas a pixel that is not completely filled by a target material. This type of target iscalled a subpixel target. The pixel contains some combination of the target signature and othermaterial signatures.
Based on the discussion in Section 2, the detection of oil spill can be processed as a hypoth-esis testing problem where there are two competing hypotheses [42, 43].{
H0 : x = nb
H1 : x = sα +σnb(28)
Here σ denotes the amount of background covered area in H1 hypotheses. nb corresponds tothe background modeled as a multivariate normal distribution with zero mean and covariancematrix
nb ∼ N(0,Cb) (29)
Consider s an Nd dimension vector (lexicographically ordered) of reference spectral signa-ture. The test statistic of ACE algorithm is [42, 43]
T 2ACE =
(sT C−1b x)2
(sT C−1b s)(xT C−1
b x)(30)
If T 2ACE > η , the pixel under test is oil spill, otherwise background. Where η is determined by
probability of false alarm. Cb is the covariance of seawater background. To fit the requirementof Eq. (29), a demean process should be executed before applying of Eq. (30) [37, 38].
After extracted the reference spectral signature, each spectral signatures of a hyperspectralimage is tested by using Eq. (30) to determine whether it comes from oil or not.
The procedure of our approach is executed as shown in Fig. 3.1. For a hyperspectral image, it is first down-sampled to a small size of between 2000 and
5000 pixels. This number is not a necessary requirement. It is determined by the performance ofthe used computer. The down-sampling process is to reduce the number of spectral signaturesto make the following clustering process can be applied.
2. The improved density-based cluster is applied on the down-sampled image. Distancesof each two spectral signatures of the down-sampled image are calculated using Eq. (2), withwhich the density parameter is obtained. The physical feature parameter of every spectral signa-ture is calculated by using Eq. (14). Using the density and physical feature parameter, a decisiongraph is generated. The point on the top right of the graph is selected as the rough result.
3. After clustering, a rough spectral signature is identified. And the corresponding pixel isfound. The down-sampled image is enlarged to the original resolution. Thus the identified pixelrelates to some pixels in original resolution. All related pixels are tested using the densityparameter, the pixel that has the largest density is the final selected pixel, hence the final selectedspectral signature is identified.
Fig. 3. Execution of the proposed reference spectral signature selection approach.
4. A reflectance threshold for background segmentation is estimated according to the phys-ical property of clear water. To ensure the segmented regions only come from seawater, thereflectance threshold should be selected as small as possible.
5. The reflectance of each pixel is calculated by averaging reflectance in bands between1.5μm and 2.5μm. If the reflectance of the pixel is below the reflectance threshold, the pixel islabeled 1, or else it is labeled 0.
6. For all pixels that are labeled 1, we calculate their mean vector and covariance matrix.7. Use the selected spectral signature as prior signal, substitute the reference spectral signa-
ture and the covariance matrix into Eq. (30), the oil spill detection result can be obtained.
6. Experimental result and discussion
To validate our proposed reference spectral signature selection approach, AVIRIS data is usedas test samples. AVIRIS is a proven instrument in the realm of earth remote sensing. It is aunique optical sensor that delivers calibrated images of the upwelling spectral radiance in 224contiguous spectral channels with wavelengths from 400 to 2500 nanometers [44]. In this paper,six hyperspectral subimages are select to test the performance of the proposed approach. Fourhyperspectral subimages have oil spills that were captured by AVIRIS after Gulf oil spill onMay 18, 2010, overflying on the ER-2 aircraft at an altitude of 9,000 m. Two hyperspectralsubimages has no oil spills that are also selected to test the reliability of our approach. The datais downloaded from the website of Jet Propulsion Laboratory. The six hyperspectral imagesare shown in false color generated using the 5th, 24th, 38th band of the images. The AVIRISradiance data were converted to surface reflectance data using the FLAASH model in ENVIsoftware. The data in strong absorption bands is discarded. The false color images of the dataare shown in Fig. 4.
As shown in Fig. 4(a), oil spills spread in seawater on the top of the scene. The bright areasrelates to the high content of oil. The dark areas are the transition of oil spills and seawater.
Fig. 4. False color images of test hyperspectral images. (a) Scene 1, (b) Scene 2, (c) Scene3, (d) Scene 4, (e) Scene 5, (f) Scene 6.
In Fig. 4(b), there are some clouds in the scene. This is a disturbance for oil spill detection.In Fig. 4(c), the oil spills are covered by heavy smoke, which is a strong interference for oilspill detection. Figure 4(d) has strong sun glint belt on the top of the scene. Fig. 4(e) only hasclear water and seashore. Figure 4(f) has heavy algae bloom along the island. Without priorinformation of oil, it is difficult to detection oil spills from the hyperspectral images.
The scenes were first down-sampled to the 1/64 of original resolution to apply the improveddensity-based cluster algorithm. After down-sampling, the number of pixels in the six imagesbecomes to 5000. This can highly reduce the burden of the following clustering procedure. We
then calculate the distances of each two spectral signatures. By using the distances, the densityparameter is obtained. Next, the band feature of oil spill is calculated. By using the density andband feature, decision graphs are generated. Rough spectral signatures can be extracted fromthe top right of the decision graphs. The decision graphs and the selected points are shown inFig. 5.
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Fig. 5. Decision graphs and selected points. (a) Scene 1, (b) Scene 2, (c) Scene 3, (d) Scene4, (e) Scene 5, (f) Scene 6.
The red points in Figs. 5(a)-5(d) are the selected points in low resolution. They are on thetop right of the decision graph and are distinct from the others points, which make them easilyto extract. While, Fig. 5(e)-5(f) have points only on the bottom left of the graphs. By using the
integral equation, no point are extracted as oil spectral signature. Although there are differenceinterferences in the scenes 1-6, our approach can extract the true oil spill spectral signature. Theextracted oil pixels are indicated by a white arrow in Fig. 4. The selected oil spectral signaturesare shown in Fig. 6.
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The oil spectral signatures are the solid line in Fig. 6. Their waveform are similar to that ofthe oil spectral signature in Fig. 1. Both of them have obvious absorption bands in 1.2μm and1.73μm. This results indicated the selected pixels are the oil pixels in the scenes.
To estimate the parameters of background, the seawater regions are segmented by using theradiance in bands of 1.0μm-2.5μm. The regions that have oil spills and clouds are excludedfrom the scene. Seawater are labeled as background. The parameters of background are calcu-lated by using the segmented areas. We next use ACE detector to detect oil spills. The resultsare shown in Fig. 7
Fig. 7(a) shows that the oil spills on the top of the scene have high response. The thicker theoil spill is, the higher the response is. In contrast, seawater background has low response. Theresult in Fig. 7(b) is similar to that in Fig. 7(a). Figure 7(c) only has high response on the thickoil spills, because oil spills are covered by thick smoke, which severely reduce the detectionperformance. Figure 7(d) has high response on the oil spills area, while the sun glint areas havelow response. The results show the proposed reference spectral signature selection approachhas high performance in extracting oil spectral signatures. By using a proper threshold, the oilspill area can be obtained.
Fig. 7. Oil spill detection results. (a) Scene 1, (b) Scene 2, (c) Scene 3, (d) Scene 4.
7. Conclusion
In this paper, we propose an reference spectral signature selection approach for automatic oilspill detection. Based on the framework of target detection algorithm in hyperspectral image.We first employ the density-based cluster to select specific spectral signature from hyperspectralimages. We then estimate the parameter of background according to the reflectance of seawaterin the infrared band. And the conventional ACE algorithm is adopted to achieve oil spill de-tection. Finally, the proposed approach is tested via two practical hyperspectral images that arecollected during the Horizon Deepwater oil spill. The experimental results show that our newapproach can automatically detect oil spill from hyperspectral images and has good detectionperformance.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (61301290) andthe Fundamental Research Funds for the Central Universities (NSIY151410, NSIZ011401).
