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A Hybrid Automatic Endmember Extraction Algorithm Based on a Local Window Huali Li and Liangpei Zhang
Abstract—Anomaly endmembers play an important role in the application of remote sensing, such as in unmixing classification and target detection. Inspired by the iterative error analysis (IEA), a hybrid endmember extraction algorithm (HEEA) based on a local window is proposed in this paper, which focuses on improving the accuracy of endmember extraction. HEEA uses the spectral-information-divergence–spectral-angle-distance metric to measure the similarity and the orthogonal subspace projection (OSP) method to search for the endmembers, which can decrease the correlation between extracted endmember spectra. Moreover, it is based on a local window which integrates both spatial and spectral aspects to extract endmembers. A synthetic image and Airborne Visible/Infrared Imaging Spectrometer data were tested with the HEEA method, classical IEA, OSP, simplex growing algorithm, sequential maximum angle convex cone, and spectral spatial endmember extraction automatic endmember extraction method. Experimental results indicated that HEEA manifested a slightly better improvement in the rmse and spectrum information than the other methods. The effect was investigated with various SNRs and different window sizes. The robustness of HEEA is better than the classical IEA, even with lower SNR. Index Terms—Automatic endmember extraction, hybrid endmember extraction algorithm (EEA) (HEEA), iterative error analysis (IEA).
I. I NTRODUCTION
H
YPERSPECTRAL sensors supply a higher spectral resolution than multispectral sensors. However, if the spatial resolution of the sensor is not high enough to separate each different material, these can jointly occupy a single pixel, and the resulting spectral measurement will be of a mixed pixel, which is a composite of the individual pure spectra (i.e., endmembers) and their corresponding fractional abundances [1], [2]. Endmembers are useful in many applications of remote sensing, providing prior information of pure materials for unmixing [3], [4], classification [5], [6], detection [7]–[10], such as in monitoring of environmental and urban processes or risk prevention and response, and so on [11]. The methods of acquiring endmembers can be divided into two groups: One selects from field data or laboratory data, while the other selects directly from the image data [2]. Selections Manuscript received September 30, 2010; revised March 3, 2011 and June 2, 2011; accepted June 27, 2011. Date of publication August 15, 2011; date of current version October 28, 2011. This work was supported in part by the National Basic Research Program of China (973 Program) under Grant 2011CB707105 and in part by the National Natural Science Foundation of China under Grants 40930532 and 41061130553. The authors are with the State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, 430079 Wuhan, China (e-mail:
[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/TGRS.2011.2162098
from available library and field spectra are not necessarily acquired under the same conditions as airborne or satellite image data, whereas the selection of image endmembers that are good representations of surface components is necessary for accurate unmixing and is easier to execute. During the past few decades, a great number of endmember extraction algorithms (EEAs) have been proposed [12]–[14], and EEAs are grouped into automatic methods and interactive methods. The interactive methods of selecting endmembers find it hard to acquire the whole endmember spectra; they also consume more processing time compared to the automatic methods. Over recent decades, several algorithms have been developed for automatic or semiautomatic extraction of spectral endmembers. These algorithms are designed based on different philosophies, of which three major criteria are of interest [15], [16]. One is convex-geometry-based methods [17], which include finding extreme points of convexity via orthogonal projection, such as the pixel purity index [18]–[20], vertex component analysis [21], and finding a simplex with the minimum volume that embraces all data samples, such as minimum volume transform [22]–[24], convex cone analysis [25], sequential maximum angle convex cone (SMACC) [26], and sparsitypromoting prior iterated constrained endmembers (ICEs) [27], [28]; alternatively, a simplex with the maximum volume that includes as many data samples as possible, such as the N finder algorithm [29] and the simplex growing algorithm (SGA) [30], [31], is used. Another is orthogonal subspace projection (OSP)-based methods [32]–[35], such as the automatic target generation process [36]. The third is by the least-squares-errorbased constrained spectral unmixing methods, such as iterative error analysis (IEA) [37] and the fully constrained least squares (FCLS) method [38]–[40]. However, these endmember extraction methods do not fully integrate the spatial information and spectral information. An automated morphological endmember extraction (AMEE) method [12], [41], [42] extracts the spatial spectral information, which employs a scalar factor that is intimately related to the spatial similarity between the pixel and its spatial neighbors and then uses the scalar factor to spatially weight the spectral information associated with the pixel. Nevertheless, the processing time of AMEE may increase significantly as the maximum size of the spatial neighborhood becomes large [10], [41]. Spectral spatial endmember extraction (SSEE) [43] projects the data to the singular value decomposition (SVD) to determinate the endmember with spatial constraints. A major limitation of SSEE [43] and spatial purity-based endmember extraction [44] is that many parameters need to be finely tuned
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to identify endmembers. SSEE [45] finds endmembers with purity of pixels, presented in a spatial neighborhood that is combined with SVD. So far, most endmember extraction methods do not consider the correlation and similarity between endmembers. To decrease the correlation and similarity between endmembers, a new automatic hybrid EEA (HEEA), inspired by IEA and the OSP method, which integrates the spatial and spectral information, is proposed in this paper. Sometimes, scale is a problem, taking the spatial information such as the window size into consideration. Experiments show its use in the application of remote sensing and its optimal window size. Compared to the current automatic endmember extraction methods, the proposed HEEA in this paper has three improvements. To amplify the separability of spectral vectors, the spectral angle distance (SAD) and spectral information divergence (SID) are combined as the SID-SAD mixed measure metric, which can make two similar spectral signatures more similar, while two dissimilar spectral signatures become more distinct. What is more, for better accuracy, spatial information is integrated with spectral information based on a local window to determine the endmember. OSP is employed as a supplement to search for the potential endmember. Since, with the IEA method, the minimum error of unmixing can be achieved, the redundancy and correlation between endmembers are neglected. However, the OSP method can suppress the unexpected information. To minimize the unmixing error and decrease the correlation, IEA is combined with OSP in the proposed HEEA. This paper is organized as follows. Section II describes our proposed HEEA. Section III reports and discusses experimental results on both synthetic and hyperspectral data sets with our proposed HEEA and some classical EEAs. In Section IV, we draw our conclusion. II. M ETHODOLOGY Since the classical IEA endmember algorithm has the previously mentioned advantages and deficiencies, a new automatic HEEA inspired by IEA is proposed in this paper. The HEEA inherits the advantages of IEA and combines with the OSP method, which alleviates the correlation between endmembers. The HEEA integrates the spatial and spectral information to determine endmembers, considering different spatial information with a discriminatory spatial weight, which improves the accuracy of the extracted endmember. While SID is more effective in preserving spectral properties and SAD is better for separability, the similarity metric of HEEA integrates both the SAD and the SID as the SID-SAD mixed measure. A. SID-SAD Similarity Metric Several discriminations of spectral characterization are employed. The classical SAD is widely used, which measures spectral similarity by finding the angle between two spectra, but many concepts in information theory are now readily applied to spectral characterization based on probability theory; in [46], the SID views each pixel spectrum as a random variable and then measures the discrepancy of probabilistic behaviors be-
Fig. 1.
Weight of each pixel in the 5 ∗ 5 window neighborhood.
tween two spectra [47], [48]. A new SID-SAD measure method [47] based on the two methods is proposed, which is a mixture of the widely used SAD metric and the recently developed information measure SID metric, which can make two similar spectral signatures more similar, while two dissimilar spectral signatures become more distinct. SID measures the variability in the pixel, while SAD just measures the similarity of pixels in the images. SID-SAD combines the advantages of both methods. For pixel a, its spectral vector is xa = (x1a , x2a , . . . , xLa ), and for pixel b, its spectral vector is xb = (x1b , x2b , . . . , xLb ), where L is the number of bands. The well-known SAD between pixels a and b is given by xa · xb sam(xa , xb ) = cos−1 (1) xa · xb where xa and xb are the norms of xa and xb , respectively. With spectral vector xa , the normalized probability pi of band i for pixel a is given by xia pi = L (2) xia i=1
where i = 1, 2, . . . , L. Every pi can be calculated by (2), so the spectral probability vector pλ for pixel a is pλ = (p1 , p2 , . . . , pL ). In the same way, with spectral vector xb , the normalized probability p˜i of band i is given by xib p˜i = L (3) xib i=1
where i = 1, 2, . . . , L. Every p˜i can be calculated by (3), so the spectral probability vector p˜i for pixel b is p˜λ = (˜ p1 , p˜2 , . . . , p˜L ). According to the spectral probability vectors pλ and p˜λ , the SID metric is given by pλ p˜λ sid(xa , xb ) = (pλ ) ln (˜ pλ ) ln + p˜λ pλ λ λ p˜λ = (pλ − p˜λ ) ln . (4) pλ λ
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Fig. 3. Original synthetic hyperspectral image. TABLE I C OMPOSITION OF D IFFERENT R EGIONS
Fig. 2.
Flowchart of the algorithm.
Combining (1) and (4), the SID-SAD mixed similarity measure is given by sid(tan) = sid(xa , xb ) ∗ tan (sam(xa , xb )) .
(5)
In (5), by taking the product of SAD and SID, the spectral discriminability of the new SID-SAD mixed measure is increased considerably because it makes two similar spectral signatures even more similar and two dissimilar spectral signatures more distinct [46], by which the discrimination is amplified. In the proposed HEEA, a tangent function is used instead of the sine function, because the tangent function widens the dissimilarity of two spectral signatures. B. Spatial Neighborhood Weight Normally, when the endmember spectrum is estimated, its spatial information is ignored, and all the neighbors are treated as being the same. In the proposed HEEA, spatial information is considered within a local window, according to the pixels’ different distances to the potential center of homogeneous regions in geometric space, as shown in Fig. 1. When the weights
Fig. 4. Library spectra of four signatures.
in spectral space for each homogeneous pixel are different, their contributions are different. The closer the pixel to the potential endmember center, the more the weight that it contributes to decide the potential endmember, while the farther the distance between the pixel and the weighted center, the less the weight that it contributes to deciding the potential endmember. The spatial weights are multiplied by the spectral information to decide on the endmember. For a pixel p with location (i, j) and the potential homogeneous centric p0 with location (i0 , j0 ), the Euclidean distance d(i, j) between p and p0 is given by d(i, j) = sqrt (i − i0 )2 + (j − j0 )2 . (6)
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Fig. 5. Spectrum of four minerals with different methods. (a) Kaolinite. (b) Alunite. (c) Calcite. (d) Muscovite.
Moreover, the weight for every pixel with a local window is given by w(i, j) =
1, 1/d(i, j),
while
d(i, j) = 0 d(i, j) = 0.
(7)
To eliminate the absolute numerical value of w, the normalization weight is given by wr (i, j) w(i, j) = n wr (i, j)
(8)
r=1
where n is the number of homogeneous pixels in the neighborhood. Therefore, within a local window, the endmember spectrum s is estimated by s=
n
w(i, j)sx (i, j)
x=1
where sx (i, j) is the homogeneous pixel (i, j) spectrum.
(9)
C. Workflow of HEEA As with the IEA algorithm, the proposed HEEA extracts the endmember according to the resident error of linear unmixing. However, in the process of searching for the endmember, the proposed HEEA is adaptively searching for potential homogeneous signatures, where the OSP and IEA methods are automatically interchanged. As the potential endmember is obtained by the IEA method, with an above threshold similarity, the correlation between the potential endmember and spectrum in the endmember set is already very high. The classical IEA neglects this situation. However, the OSP method, which suppresses the undesired correlation information, can reduce the correlation through searching for the maximum norm of the subspace, combined with a search for the maximum error in the HEEA. The number of endmembers is predicted by the virtual dimension (VD) [49]–[54]. 1) Determining the first endmember. Input the hyperspectral image, and set the total average value of the hyperspectral image as the initial value for the first endmember. Divide the image into nine approximately equal subimages, and then, search for the maximum spectral distance between every pixel and the initial first endmember in each
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TABLE II C ORRELATION C OEFFICIENT B ETWEEN THE L IBRARY S PECTRUM AND THE E XTRACTED E NDMEMBER S PECTRUM AT SNR = 40
2)
3)
4)
5)
subimage; calculate the maximum of the nine subimages, and put them in the backup set B in descending sort order. Locate the maximum value t in the backup B set in the whole image, comparing the similarity of SAD-SID within a local window; if the similarity condition is not met, choose the next s from the backup B, also comparing the similarity, and perform the cycle of choosing candidates until obtaining an s value that meets the condition. Then, based on the local window of s, the spatial information and spectral information areintegrated to determine the first endmember. Use s = nx=1 ws (i, j)sx (i, j) to renew the first endmember spectrum, where the weighted w depends on the spatial distance between each pixel and the potential endmember; n is the number that meets the similarity condition within the window. Build the endmember set P . Unmixing and renewing the resident error image and search for the potential endmember. Unmix the hyperspectral data with the achieved endmember. Find the maximum of the entire error image and nine subimages, renew the backup set B, and locate the pixel with the maximum t; take it as a potential endmember, and check whether it meets the conditions. If it does, put it into the endmember potential sets, or if not, choose another s from the set B as a potential endmember. Deciding the potential endmember and endmember set correlation. Compare the correlation coefficient between the potential endmember and each one in the endmember set P . If the similarity is below the threshold, which means that the selected point can be taken as a potential endmember, go to step 5). If all in set B fail to meet the conditions, which means that the potential endmember spectrum is highly similar to the one in the previous endmember set P , perform step 4). OSP to suppress correlation between endmembers. Use the previous endmember set P as the undesired background to execute the OSP to the entire hyperspectral data. Search for the maximum norm of the subspace with the entire image and the nine subimages. Put them in the backup set B. Renew B. To decide endmembers. Select the potential endmember z from the B set. Execute a window filter to the potential endmember z, and calculate the similarity and discrimination between each pixel with the window and the potential endmember pixel z. With the SID-SAD measure similarity metric, by means of the weighted value to contain spatial information, the final endmember spectrum s = nx=1 ws (i, j)sx (i, j) (∗) depends on the geometric weight (the spatial information) and the spec-
tral vector, where the weight w depends on the spatial distance between each pixel and potential endmember and m is the number that meets the similarity condition T n, within the window. Put the potential endmember into the endmember set P . Renew P . 6) FCLS unmixing the hyperspectral image with the endmember set P . Unmix the hyperspectral image with endmember set P to obtain the error image. 7) Repeat the cycle in 2)–6). Perform the cycle until the number of endmembers N is achieved or the error threshold T e is achieved. The cycle is then finished. 8) Change various filter window sizes to obtain the endmember sets and fraction abundance images, and also calculate the spectral angle and correlation coefficient of each endmember. The flowchart of the algorithm is shown in Fig. 2. III. E XPERIMENTS AND A NALYSIS In this section, the proposed HEEA is applied to both a synthetic hyperspectral image and real hyperspectral images in the Matlab environment. Because all endmembers in a simulated image are known in advance, it is easy to manipulate the parameters precisely. Synthetic images, with various SNRs and various filter window sizes, were tested with HEEA. To ensure a fair comparison, several automatic endmember extraction methods, without any prior knowledge, are investigated, for which the input parameters for the EEA are the number of endmembers and the error threshold. Other classical EEAs, such as IEA, OSP, SGA, and SMACC, are also used for comparison. Additionally, SSEE is compared to HEEA. However, OSP, SGA, and SMACC only need the number of endmembers and the error threshold input parameters. HEEA, classical IEA, and SSEE require an extra window size. In addition, a real subimage of Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data with various filter window sizes is also tested by the aforementioned methods. A. Synthetic Hyperspectral Image The synthetic image has a size of 100 ∗ 100 pixels and consists of spectral signatures (i.e., endmembers) of four minerals (kaolinite, alunite, calcite, and muscovite) from the ENvironment for Visualizing Images (ENVI) spectral library [U.S. Geological Survey (USGS)]. The spectral resolution of endmembers in the spectral library is 0.002 μm, with spectral coverage from 0.39510 to 2.56000 μm. After sampling the spectrum into 45 approximately equal intervals, the spectral resolution became 0.7 μm. The mean of these 45 bands of the original synthetic image, shown in Fig. 3, ranges from 0.44 to 0.87, and the variable standard deviation is around
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TABLE III SID-SAD B ETWEEN THE L IBRARY S PECTRUM AND THE E XTRACTED E NDMEMBER S PECTRUM AT SNR = 40(∗10−5 )
TABLE IV C ORRELATION C OEFFICIENT B ETWEEN E NDMEMBER S PECTRA U NDER D IFFERENT SNRs
0.1. This synthetic image contains 12 regions, and each region contains fixed endmembers and abundances in Table I, i.e., the fifth region contains four endmembers. Endmembers and their corresponding abundances can be described as follows: S5 = 0.2 ∗ kaolinite + 0.16 ∗ alunite + 0.37 ∗ calcite + 0.27 ∗ muscovite. To test its robustness, the Gauss noise of various sequential SNRs was added. For the synthetic image, endmembers were added with and without Gauss noise. Various SNR levels of 10, 20, 30, 40, 80, and 160 were considered. Then, the results with various window sizes were investigated with the proposed HEEA and classical IEA methods. The results with various window sizes were also investigated. The USGS library spectra of the synthetic image are shown in Fig. 4. The extracted endmember spectra of the synthetic image are executed with the proposed HEEA, classical IEA, OSP, SGA, SMACC, and SSEE methods. Most of the extracted endmember spectra from those methods in Fig. 5(a)–(d) are similar in shape to the library spectra in Fig. 4, except for the extracted spectrum of calcite, which is slightly different from the library spectra, in which a trough is seen at 1.2–1.5 μm. The unexpected trough in Fig. 5(c) leads to the extracted calcite spectrum, in slight contrast to the library spectra, which may be interfered by the noise. According to the results in the experiments, kaolinite is the first extracted endmember, which implies its primacy in the image. Due to the troughs in kaolinite, alunite, and muscovite from 1.2 to 1.5 μm, the mixed pixels also have a trough at this interval, which may result in an unexpected tough in the calcite spectrum. In the experiment, calcite was extracted first by HEEA. Since there are some pixels with a high fraction of muscovite in the synthetic image, each of the previously mentioned methods shows better results. The correlation coefficient and the SID-SAD metric are used to compare the similarity between each extracted endmember spectra and the library spectra. The correlation coefficient between the library spectrum and the extracted spectrum with
Fig. 6.
False-color subimage of AVIRIS data.
HEEA, IEA, OSP, SGA, SMACC, and SSEE, is shown in Table II. The more the similarity is, the larger the correlation is. However, in Table III, the more the similarity is, the less the SID-SAD (∗10−5 ) is. Both Tables II and III reveal that the HEEA results are similar to the IEA and OSP results. Since the HEEA extracts endmembers based on the error image, which is similar to the classical IEA, the spectra are similar to those of IEA. However, HEEA shows a better performance than the others, particularly SMACC and SGA. In Table II, the correlation coefficient of HEEA is clearly higher than those of SGA and SMACC. In Table III, with the SID-SAD metric, which exaggerates the similarity and dissimilarity, HEEA shows better results than IEA and OSP. Also, HEEA shows better results than SSEE for alunite, calcite, and muscovite. In Table II, the lowest correlation coefficient between the extracted calcite spectrum and library spectrum also reveals the noise effect, and HEEA did better than the others for calcite. With different SNRs, the correlation coefficient is different. To test the robustness of HEEA, various SNR interferences were considered, and the HEEA results and the classical IEA results were compared. In Table IV, the correlation coefficient between the library spectrum and HEEA spectrum is compared
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Fig. 7.
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Spectrum of extracted endmember. (a) Mizzonite. (b) Hematite. (c) Kaolinite. (d) Alunite. (e) Analcime. TABLE V C ORRELATION C OEFFICIENT OF E ACH E NDMEMBER W ITH VARIOUS A LGORITHMS
with the correlation coefficient between the library spectrum and the classical IEA spectrum. At a lower SNR = 10, the noise strongly interfered with the signal power, which led to both methods working poorly. The correlation coefficient is nearly 0.3, which implies an incredible result. As the SNR increases, the noise interference is alleviated, and the performances of both methods were better.
TABLE VI SID-SAD OF E ACH E NDMEMBER W ITH VARIOUS A LGORITHMS (∗10−5 )
The correlation coefficient value increased with the increase in the SNR. With SNR above 20, the muscovite correlation with HEEA is higher than that for the classical IEA, and even the calcite correlation with HEEA is higher than that for the classical IEA. The average of the correlation coefficient with HEEA is higher than that for the classical IEA, which reveals that the HEEA method gives a better performance. As the SNR grows, noise interference is alleviated, and both methods show
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Fig. 8. Fraction abundance image of mizzonite. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
Fig. 9. Fraction abundance image of hematite. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
Fig. 10. Fraction abundance image of kaolinite. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
Fig. 11. Fraction abundance image of alunite. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
Fig. 12. Fraction abundance image of analcime. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
Fig. 13. Unmixing error image. (a) HEEA. (b) IEA. (c) OSP. (d) SGA. (e) SMACC. (f) SSEE.
LI AND ZHANG: HYBRID AUTOMATIC ENDMEMBER EXTRACTION ALGORITHM BASED ON A LOCAL WINDOW
Fig. 14. RMSE of various EEAs.
Fig. 15. Subimage of AVIRIS data.
better results. When the SNR is above 80, the noise interference is not so important, so both the proposed HEEA and classical IEA methods show better performance. It is shown in Table IV that, even with SNR = 30, the spectra with the proposed HEEA are more similar to the laboratory spectra than to those with IEA and they are not sensitive to noise and therefore have a better robustness, even with lower SNR. HEEA shows a better performance than the classical IEA; its better performance is attributed to the integration with spatial information and amplified discrimination with the SID-SAD similarity metric. B. Real Hyperspectral Data Set The real image is a subimage of the well-known AVIRIS data, from the Cuprite Mining District in Nevada. This image had already been atmospherically corrected with 50 reflectance bands in the range of 1.9908–2.479 μm. To reduce calculation, in this experiment, the original hyperspectral image cube was cut into 100 ∗ 100 pixels, as shown in Fig. 6, and 200 ∗ 200 pixels in Fig. 15. According to the VD method [49] (Pf = 10−3 ), second moment linear (SML) [50], Harsanyi–Farrand–Chang (HFC) with likelihood methods [51], HySime [52], [53], modified maximum orthogonal complement analysis (MMOCA) [54], and the reference map [55], five endmembers are included in Fig. 6. The extracted spectra use the previously mentioned methods shown in Fig. 7(a)–(e). With reference to the USGS
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library spectrum, kaolinite, hematite, alunite, mizzonite, and analcime are included in the subimage cube. Since the extracted endmember spectrum, which is usually obtained from the image, is different to the library spectra, it is hard to label the endmember. With prior experience and knowledge of its distinctive spectrum, kaolinite can be labeled. However, the other four endmembers can be labeled only with the benefit of considerable prior knowledge. In this experiment, the USGS mineral spectral library is used as reference spectra. The spectra of each extracted endmember with those previously mentioned algorithms in Fig. 7(a)–(e) are similar in shape, except for the spectra of the SMACC method. The spectra of HEEA, IEA, OSP, and SSEE are smoother than those of the SMACC and SGA, particularly in Fig. 7(a) and (e). The HEEA spectrum is similar to the OSP and IEA spectra, although the reflectance is always higher than those of the other two methods. Because the HEEA searches for potential endmembers, based on the previous unmixing error, which is essentially similar to IEA, this leads to the similar spectra. However, the HEEA decreases the correlation between endmembers, which tends to make its results similar to those of the OSP. What is more, due to spatial weight, the smoothness of the spectra with HEEA was still kept. To quantitatively compare the endmember spectrum with those previously mentioned methods, the correlation coefficients of each extracted endmember spectrum with various algorithms are shown in Table V. HEEA is the correlation coefficient between the spectrum of HEEA and laboratory spectra. Likewise, IEA, OSP, SGA, SMACC, and SSEE are the correlation coefficients between the spectra of extracted endmembers and laboratory spectra for those methods. The spectra of HEEA are more similar to those of IEA and OSP, when compared to the SSEE results. Also, in Table VI, the smaller SID-SAD of HEEA reveals more similarity. The corresponding fraction abundance images in Figs. 8–12 demonstrate that those results with the SGA method are more seriously affected by noise interference. With similar spectra, the abundance images of HEEA, IEA, OSP, and SMACC are visually similar. With dissimilar spectra, SMACC abundance images are different from the others, because SMACC has an extra shadow endmember to execute unmixing, while others do not, leading to the difference. HEEA, IEA, OSP, SGA, SMACC, and SSEE methods are sequential EEAs. For those methods, even similar spectra cannot make sure that their corresponding abundance images are similar because these already obtained endmember spectra interfere the next endmember extraction. Previously extracted endmember sets are different and renew endmembers sets with the similar spectra, but these updated endmember sets still are different. Then, unmixing with different endmember sets leads to different abundance images of the subsequence endmember. The error images are shown in Fig. 13. HEEA had a better performance, with an amplified discrimination similarity metric and the minimum error constraint. HEEA can classify the mixed pixels more exactly and execute unmixing better than the other methods. In Fig. 14, comparing the rmse of the unmixing error of the previously mentioned EEA, HEEA shows a better performance
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Fig. 16. Extracted spectrum of endmembers. (a) Mizzonite. (b) Hematite. (c) Kaolinite. (d) Alunite. (e) Analcime. (f) Beryl. (g) Clinoptilolite.
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TABLE VII C ORRELATION C OEFFICIENT OF E ACH E NDMEMBER
TABLE VIII SID-SAD OF E ACH E NDMEMBER (∗10−5 )
with an rmse of less than 0.002, whereas the SGA method shows the worst result with a value above 0.12. The rmse of HEEA is lower than those of IEA, OSP, and SSEE, with an amplified discrimination similarity metric and the minimum error constraint. HEEA can classify the mixed pixels more exactly and execute unmixing better than the other methods. SSEE showed better results than IEA and OSP, with a smaller rmse. The 200 ∗ 200 pixel subimage of AVIRIS data in Fig. 15, in which seven endmember signatures are extracted, was tested with VD [49] (Pf = 10−3 ), SML [50], HFC with likelihood methods [51], HySime [52], [53], and MMOCA [54]. The spectra of each endmember with those EEAs are shown in Fig. 16. The spectra extracted by HEEA, classical IEA, OSP, and SSEE are similar in shape, except for the spectrum by the SMACC method. In Table VII, the spectrum correlation coefficient with the proposed HEEA is similar to those with the OSP and IEA methods, with a slight difference to that with SMACC. In Table VIII, the SID-SAD between the extracted endmember and library spectra is shown. Since the library spectra are not unique for each endmember, the closest one in the library is selected to label it. With these two similarity metrics, the HEEA method shows better results than the other methods. With these endmembers, fully constrained unmixing was executed. The abundance images of each endmember in Figs. 17–24 are generally similar. However, SMACC shows differences when compared to the other methods. The five abundance images of the first endmember are similar for their similar endmember spectrum. The SMACC abundance images of the fifth, sixth, and seventh endmembers are different from the others, corresponding to the different spectra. The rmse of unmixing with each method is shown in Fig. 25. HEEA, SSEA, OSP, and IEA show a better performance than SMACC. With the ENVI software, the unmixing results contained an extra shadow endmember and its abundance, which leads to the largest error. The rmses of HEEA and IEA are lower than that of OSP, which are based on a minimum error constraint in unmixing.
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C. Sensitivity Analysis The number of endmembers is hard to estimate exactly, but it needs to be determined before endmember extraction. Therefore, synthetic images with different numbers of endmembers are investigated with the HEEA method, under two circumstances. The first circumstance is that, as the true number of endmembers varies, the estimated number is the same as the truth. The other is that, as the true number is fixed at one value, the estimated number varies. Four synthetic images are used, which are composed of between four and seven endmembers, and the same estimated number is executed with HEEA. With different numbers, the average correlation between extracted spectra and library spectra changes without direction (see Fig. 26). Because of the differing numbers of true endmembers in the synthetic images, the abundance image is different, and the result is without regularity. In Fig. 27, the true endmember number is fixed at five, while the estimated number of endmembers varies from three to seven. In Fig. 27, the average correlation coefficient obtains its maximum at the true number five, which reveals that the estimated number reaches the true number and the extracted endmembers are the optimal endmembers. If the estimated number is less than five, kaolinite is not extracted, which causes the average correlation coefficient to decrease. If the estimated number is greater than five, some mixed pixels are regrouped to a new endmember, such as alunite and calcite, which decreases the average correlation coefficient. However, the HEEA, with overestimation of the number of endmembers, can obtain the smaller rms with redundant endmembers; the HEEA, with underestimation of the number of endmembers, obtained the limited endmember and larger rms. Not only the SNR influences the accuracy of endmember spectra but also the parameter of window size contributes to the HEEA. The optimal size of the window is now addressed; HEEA without and with various SNR levels is investigated. The rmse in Fig. 28(a) is decreasing while the window size increases from a smaller window size; however, it shows an ascending trend after the size of nine. Because the window size increases, more pixels are participating in potential endmember determination, producing a more precise endmember spectrum. With a precise endmember, the rmse has a descending tendency. However, as the window size is increased after nine, the rmse increases. With a relatively large window, some pixels with a farther spatial relation also are contained, which should have been clustered into another mixed-cluster group. Due to these mixed-clustered pixels, rmse shows a slight pulse. There should be an optimal window size at the trough of the rmse curve. Even with noise, Fig. 28(b) and (c) also shows a descending tendency and an ascending tendency after one window size. With the stronger noise, Fig. 28(b) shows two troughs at five and nine. Fig. 28(c) shows a trough at about nine, which is similar to Fig. 28(a). The rmse manifests better results at a window size of nine. The optimal window size should be located at about nine for this synthetic image. Considering the correlation coefficient of the extracted endmember spectrum, it verified the tendency, with the trough at
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Fig. 17. Abundance image of mizzonite. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 18. Abundance image of hematite. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 19. Abundance image of kaolinite. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 20. Abundance image of alunite. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 21. Abundance image of analcime. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
nine in Fig. 29, because, at a window size of nine, the average correlation coefficient obtained the maximum of 0.97175 while, at a window size of 17, it is 0.97085.
In Fig. 29, at a window size of three, the average correlation coefficient is low at nearly 0.93. Because the noise interferes with the initial value for the potential endmember and there
LI AND ZHANG: HYBRID AUTOMATIC ENDMEMBER EXTRACTION ALGORITHM BASED ON A LOCAL WINDOW
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Fig. 22. Abundance image of beryl. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 23. Abundance image of clinoptilolite. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 24. Error image. (a) HEEA. (b) IEA. (c) OSP. (d) SMACC. (e) SSEE.
Fig. 25. RMSE of various EEAs.
Fig. 26. Correlation coefficients with varying numbers of true endmember.
Fig. 27. Correlation coefficients with varying estimated numbers of endmembers.
are fewer pixels in the window to contribute to the endmember determination, the extracted endmember spectrum is a little different from the library spectra. As the window size increases, the correlation coefficient reveals that an optimal window size exists. The peak of the correlation coefficient at a window size of nine in Fig. 29 indicates that the proper size is nine for calcite and kaolinite. For the 200 ∗ 200 pixel AVIRIS subimage, the rmse also shows a similar tendency (see Fig. 30). As the window size is increasing, the rmse decreases. When the window size is above seven, the rmse increases. The trough is located at seven, revealing the optimal window size for this image.
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Fig. 28. RMSE and the window size with various SNRs. (a) No noise. (b) SNR = 30. (c) SNR = 80.
The window size should be the proper one: A proper increase of window size is necessary for accuracy. If it is too small, the pixels, which are potentially used to calculate the endmember pixel, are limited, so the endmember spectrum is a bit far from the other window sizes, and the error increases. As the size becomes larger, more pixels participate in deciding the endmember. Nevertheless, some pixels that should be clustered into another mixed-cluster group are also included, leading to an increased unmixing error. IV. C ONCLUSION Fig. 29. Correlation coefficient between each endmember and the library spectra at SNR = 80.
Fig. 30. RMSE of the unmixing result with AVIRIS data.
In this paper, a HEEA based on a local window and inspired by IEA has been proposed. Based on the framework of the IEA algorithm, the proposed HEEA not only can automatically extract the endmembers and the corresponding abundance image of each endmember but also can minimize its unmixing error. The spatial information of potential endmembers is taken into consideration, combined with the spectral information. In the experiments, both a synthetic hyperspectral image and real AVIRIS data were tested with the HEEA method and the classical IEA, OSP, SGA, SMACC, and SSEE automatic endmember extraction methods. Experimental results of HEEA manifested a slightly better improvement in the rmse and spectrum information as compared to other methods. The effect of various SNRs has also been investigated. Moreover, HEEA presents a higher robustness with low SNR. In HEEA, the SID-SAD similarity metric, which can make two similar spectral signatures more similar, while two dissimilar spectral signatures become more distinct, can increase the separability of endmembers.
LI AND ZHANG: HYBRID AUTOMATIC ENDMEMBER EXTRACTION ALGORITHM BASED ON A LOCAL WINDOW
The proposed HEEA considers spatial information through a local window, which delivers a better performance even with low SNR. OSP has been introduced as an auxiliary method to determine the potential spectra, which decreased the correlation coefficient between extracted endmember spectra. However, the proposed HEEA considered spatial information through a local window, so the optimal window size is a problem. Investigation of various window sizes revealed that an optimal window size hardly existed in smaller window sizes. This will be the focus of our future work. R EFERENCES [1] N. Keshava and J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag., vol. 19, no. 1, pp. 44–57, Jan. 2002. [2] D. M. Rogge, B. Rivard, J. Zhang, and J. Feng, “Iterative spectral unmixing for optimizing per-pixel endmember sets,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 12, pp. 3725–3736, Dec. 2006. [3] M. Zortea and A. Plaza, “Improved spectral unmixing of hyperspectral images using spatially homogeneous endmembers,” in Proc. IEEE ISSPIT, Dec. 16–19, 2008, pp. 258–263. [4] C.-I. Chang, Hyperspectral Imaging: Techniques for Spectral Detection and Classification. New York: Kluwer, 2003. [5] A. Zare and P. Gader, “Hyperspectral band selection and endmember detection using sparsity promoting priors,” IEEE Geosci. Remote Sens. Lett., vol. 5, no. 2, pp. 256–260, Apr. 2008. [6] X. Huang, L. Zhang, and P. Li, “Classification and extraction of spatial features in urban areas using high-resolution multispectral imagery,” IEEE Geosci. Remote Sens. Lett., vol. 4, no. 2, pp. 260–264, Apr. 2007. [7] L. Zhang, B. Du, and Y. Zhong, “Hybrid detectors based on selective endmembers,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 6, pp. 2633– 2646, Jun. 2010. [8] B. Du and L. Zhang, “Random selection based anomaly detector for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 5, pp. 1578–1589, May 2011. doi:10.1109/TGRS.2010.2081677. [9] J. Broadwater and R. Chellappa, “A hybrid algorithm for subpixel detection in hyperspectral imagery,” in Proc. IEEE IGARSS, 2004, vol. 3, pp. 1601–1604. [10] Q. Du, “Band selection and its impact on target detection and classification in hyperspectral image analysis,” in Proc. IEEE Workshop Adv. Techn. Anal. Remotely Sensed Data, Oct. 27–28, 2003, pp. 374–377. [11] M. Zortea and A. Plaza, “Spatial preprocessing for endmember extraction,” IEEE Trans. Geosci. Remote Sens., vol. 47, no. 8, pp. 2679–2693, Aug. 2009. [12] A. Plaza, P. Martinez, R. Perez, and J. Plaza, “A quantitative and comparative analysis of endmember extraction algorithms from hyperspectral data,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 3, pp. 650–663, Mar. 2004. [13] A. Plaza and C.-I. Chang, “Impact of initialization on design of endmember extraction algorithms,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 11, pp. 3397–3407, Nov. 2006. [14] P. J. Martínez, R. M. Pérez, A. Plaza, P. L. Aguilar, M. C. Cantero, and J. Plaza, “Endmember extraction algorithms from hyperspectral images,” Ann. Geophys., vol. 49, no. 1, pp. 93–101, Feb. 2006. [15] Q. Du, L. Zhang, and N. Raksuntorn, “Improving the quality of extracted endmembers,” in Proc. WHISPERS, Aug. 26–28, 2009, pp. 1–4. [16] C.-C. Wu and C.-I. Chang, “Does an endmember set really yield maximum simplex volume?” Proc. IEEE IGARSS, Jul. 23–28, 2007, pp. 3814–3816. [17] J. W. Boardman, “Geometric mixture analysis of imaging spectrometry data,” in Proc. Int. Geosci. Remote Sens. Symp., 1994, pp. 2369–2371. [18] J. Boardman, F. Kruse, and R. Green, “Mapping target signatures via partial unmixing of AVIRIS data,” in Proc. Summaries JPL Airborne Earth Sci. Workshop, 1995, pp. 23–26. [19] C.-I. Chang and A. Plaza, “A fast iterative algorithm for implementation of pixel purity index,” IEEE Geosci. Remote Sens. Lett., vol. 3, no. 1, pp. 63–67, Jan. 2006. [20] C.-I. Chang, C.-C. Wu, and H.-M. Chen, “Random pixel purity index,” IEEE Geosci. Remote Sens. Lett., vol. 7, no. 2, pp. 324–328, Apr. 2010. [21] J. M. P. Nascimento and J. M. Bioucas-Dias, “Vertex component analysis: A fast algorithm to unmix hyperspectral data,” IEEE Trans. Geosci. Remote Sens., vol. 43, no. 4, pp. 898–910, Apr. 2005. [22] M. Craig, “Minimum-volume transforms for remotely sensed data,” IEEE Trans. Geosci. Remote Sens., vol. 32, no. 3, pp. 542–552, May 1994.
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Huali Li received the B.S. degree in remote sensing science and technology from Wuhan University, Wuhan, China, in 2007, where she is currently working toward the Ph.D. degree in the State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing. Her major research interests include hyperspectral image processing, signal processing, and pattern recognition.
Liangpei Zhang received the B.S. degree in physics from Hunan Normal University, Changsha, China, in 1982, the M.S. degree in optics from the Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, China, in 1988, and the Ph.D. degree in photogrammetry and remote sensing from Wuhan University, Wuhan, China, in 1998. He is currently the Head of the Remote Sensing Division with the State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University. He is also a “Chang-Jiang Scholar” Chair Professor appointed by the Ministry of Education, China. He has more than 200 research papers and is the holder of five patents. He is currently the Principal Scientist for the China State Key Basic Research Project (2011–2016) appointed by the Ministry of National Science and Technology of China to lead the remote sensing program in China. He also serves as an Associate Editor of the International Journal of Ambient Computing and Intelligence, International Journal of Image and Graphics, International Journal of Digital Multimedia Broadcasting, Journal of Geospatial Information Science, and Journal of Remote Sensing. His research interests include hyperspectral remote sensing, high-resolution remote sensing, image processing, and artificial intelligence. Dr. Zhang is a Fellow of the Institution of Electrical Engineers, an executive member (Board of Governor) of the China National Committee of International Geosphere–Biosphere Programme, an executive member of the China Society of Image and Graphics, and others. He regularly serves as a Cochair of the series SPIE Conferences on Multispectral Image Processing and Pattern Recognition, Conference on Asia Remote Sensing, and many other conferences. He edits several conference proceedings, issues, and the Geoinformatics Symposiums.