A semi-ellipsoid-model based fuzzy classifier to map grassland in Inner Mongolia, China

ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

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A semi-ellipsoid-model based fuzzy classifier to map grassland in Inner Mongolia, China Hai Lan, Yichun Xie ⇑ Department of Geography and Geology, Eastern Michigan University, Ypsilanti, Michigan 48197, United States

a r t i c l e

i n f o

Article history: Received 10 August 2012 Received in revised form 2 July 2013 Accepted 16 July 2013

Keywords: Fuzzy classifier Grassland classification Landsat Semi-ellipsoid-model Tetragonal pyramid model Image fusion

a b s t r a c t Remote sensing techniques offer effective means for mapping plant communities. However, mapping grassland with fine vegetative classes over large areas has been challenging for either the coarse resolutions of remotely sensed images or the high costs of acquiring images with high-resolutions. An improved hybrid-fuzzy-classifier (HFC) derived from a semi-ellipsoid-model (SEM) is developed in this paper to achieve higher accuracy for classifying grasslands with Landsat images. The Xilin River Basin, Inner Mongolia, China, is chosen as the study area, because an acceptable volume of ground truthing data was previously collected by multiple research communities. The accuracy assessment is based on the comparison of the classification outcomes from four types of image sets: (1) Landsat ETM+ August 14, 2004, (2) Landsat TM August 12, 2009, (3) the fused images of ETM+ with CBERS, and (4) TM with CBERS, respectively, and by three classifiers, the proposed HFC-SEM, the tetragonal pyramid model (TPM) based HFC, and the support vector machine method. In all twelve classification experiments, the HFC-SEM classifier had the best overall accuracy statistics. This finding indicates that the medium resolution Landsat images can be used to map grassland vegetation with good vegetative detail when the proper classifier is applied. Ó 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier B.V. All rights reserved.

1. Introduction Grasslands are an ecosystem sensitive to global climate change and are also an important land cover that bears vibrant human imprints (Liang et al., 2003). Remote sensing technology has been shown to be a practical and economical approach to study land cover changes and resource monitoring and assessment, especially over large areas (Langley et al., 2001; Nordberg and Evertson, 2003). Image classification is widely used to derive land use and land cover data from remotely sensed images. However, mapping grassland with fine biotic detail over large areas has been challenging for either the coarse resolutions of remotely sensed images or the high costs of acquiring images at high-resolutions. The main challenges are that the same type of vegetation may exhibit different spectral features due to different growth conditions or environments. On the other hand, different types of vegetation may show similar spectra. It is commonly known that plant communities present mosaic-like patterns, which makes it hard to extract vegetation information from remote sensed images with acceptable accuracy (Cingolani et al., 2004; Stuart et al., 2006; Sha et al., 2008).

⇑ Corresponding author. Tel.: +1 734 487 0218; fax: +1 734 487 6979. E-mail address: [email protected] (Y. Xie).

Many researchers have tried to use Landsat images for grassland classification and mapping because these images are easily accessible and cover large areas (Table 1). The Institute of Remote Sensing Applications at the Chinese Academy of Sciences mapped land use/cover changes in the Xilin River Basin in Inner Mongolia four times: July 31, 1987, August 11, 1991, August 27, 1997 and May 23, 2000 (Chen et al., 2003). This research group applied a classic supervised classifier (the maximum likelihood classification procedure) to map the grassland using secondary classes, i.e., meadow grassland, temperate (typical) grassland, desert grassland, and non-grassland. They achieved an overall classification accuracy of 81.0% in 1987, 81.7% in 1991, 80.1% in 1997, and 78.2% in 2000. In the same study area, Sha et al. (2008) applied a hybrid fuzzy classifier (HFC) to map the grassland with a more detailed vegetative classification system of 11 plant community types and achieved an overall accuracy of 80.2% in comparison with the conventional maximum-likelihood classifier (69.0%). Sha and Xie (2010) tried a new spectral substrata classifier in the same area and obtained a comparable accuracy of 79.3%. A tempo-spatial feature evolution based classifier was explored to map the historical land cover in 1985 in the same area with the same vegetative classification system and obtained a reasonable accuracy level of 80.6% (Xie et al., 2010). Mapping grasslands using Landsat images has been reported globally (Sohn and Qi, 2005). Cingolani et al. (2004) developed a

0924-2716/$ - see front matter Ó 2013 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS) Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.isprsjprs.2013.07.011

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

Table 1 Selected case studies of mapping grassland with Landsat images. Researchers

Year

Study area

Method

Accuracy (%)

Chen et al. (2003)

Xilin river basin, inner Mongolia, China

Maximum likelihood

Same as above

Sha and Xie (2010) Xie et al. (2010) Cingolani et al. (2004)

1987 1991 1997 2000 2004 2004 2004 1985 1997

Lucas et al. (2007) Lyons et al. (2012)

2001,2002 1972–2010

Berwyn Mountains North Wales, UK Australian coast

Hybrid fuzzy classifier Maximum likelihood Spectral substrata Tempo-spatial feature evolution Maximum likelihood Discriminant classifier Numerical decision rules based fuzzy logic Object-based classifier

81.0 81.7 80.1 78.2 80.2 69.0 79.3 80.6 78.0 86.0 80.0 65.0–80.0

Sha et al. (2008)

Same as above Same as above Rangeland in central Argentina

discriminant classifier for mapping a heterogeneous mountain rangeland in central Argentina, and produced a better overall accuracy (86%) in comparison with the traditional maximum likelihood classifier method (78%). Lucas et al. (2007) used the time-series Landsat images to map semi-natural habitats and agricultural land use in the Berwyn Mountains, North Wales, United Kingdom, by applying the numerical decision rules based fuzzy logic method. They integrated their knowledge of ecology with vegetation indices derived from single and multi-date Landsat data to discriminate vegetation types. They concluded that the rule-based classification produced a better classification accuracy (exceeding 80%), especially in extensive, contiguous and homogeneous habitats. A long time-series of Landsat images (38 years, 1972–2010) were processed to map land cover and sea-grass distributions in an Australian coastal environment by applying an object-based classifier (Lyons et al., 2012). Although the in situ field data was not available, the researchers were able to develop an object-based image classifier on the basis of their field knowledge and produced sea-grass and land cover maps with an average overall accuracy of 65% for the former and 80% for the later. Other types of satellite images have also been utilized to produce grassland and land use/cover maps. Moderate Resolution Imaging Spectroradiometer (MODIS) data (the EVI time series from 2003) were used to map land use/cover on the North China Plain. A decision tree was developed based on five phonological features derived from EVI profiles, land surface temperature and topographic slope. This method achieved an overall accuracy of 75.5% (Zhang et al., 2008). Moreover, various sources of remotely sensed images were fused or synthesized to map and analyze land use/ cover changes at each of the following time intervals, Landsat ETM+ (June 30, 2001), SPOT imagery (November 21, 2003 and May 5, 2008) and CBERS02 CCD (June 5, 2006) by applying an object-oriented classification method. The classification results were then utilized to study the spatiotemporal patterns of land use/cover changes induced by excessive human activities (Wang et al., 2012). Furthermore, hyperspectral data and images were processed to map land use/cover and to detect their spatiotemporal changes. An interesting experiment in identifying optimal wavelengths of hyperspectral data for discriminating rangeland species and examining the levels of rangeland degradation was reported in Okhombe, South Africa (Mansour et al., 2012). It is worth pointing out that several image classification techniques were involved in the aforementioned literature for classifying grasslands, such as the maximum likelihood classifier (MLC, Chen et al., 2003), the discriminant classifier (DC, Cingolani et al., 2004), the rule-based classifier (RBC, Lucas et al., 2007), the hybrid fuzzy-logic-based classifier (HFC, Sha et al., 2008) and the objectbased classifier (OBC, Lyons et al., 2012). There is an increasing volume of literature focused on new approaches to classification in the context of mapping land uses and covers. These new classifiers can be categorized generally into three groups in addition to the

traditional non-supervised and supervised ones. The first group includes the algorithms derived from support vector machine (SVM), which has been recently introduced as a new technique for solving a variety of learning, classification and prediction problems (Malon et al., 2008; Guo et al., 2008; Zhao et al., 2008). SVM is built with a solid theoretical foundation in statistical learning theory (Vapnik, 1995, 1998; Su, 2009). SVM solves a binary classification problem by searching for maximal margin hyperplanes in terms of a subset of the input data (also referred to as support vectors) between different classes (Wu et al., 2008). The second group consists of object-based classifications (OBC), which are often developed to process high resolution images. The OBC method often constructs contiguous pixels with similar spectral information into objects for classification on the basis of knowledge-driven feature characteristics (Lu and Weng, 2007). The benefit of the OBC method over pixel-based classifications is that the objects contain more information such as color, shape, texture and so on (Benz et al., 2004) to facilitate the separation of different features. The third group encompasses the rule-based classifiers that usually involve some type of learning process in image classification. Typical classifiers in this group include fuzzy rules and functions, neural network algorithms, decision trees, etc. In fact, there is a new trend taking place within this category, called the advancement of hybrid or multiple classifiers (Maulik and Saha, 2010). For instance, the integration of computational intelligence into rule-based fuzzy-logic has been proposed to develop a spectral-rule-based decision tree for near-real-time automatic image classification (Baraldi, 2011). The genetic algorithm-based, selforganizing concept and the neural-network-based fuzzy-logic rule are fused to develop a multilayered classifier for land cover classification by using image textural and spectral features (Mitrakis et al., 2008). Evolutionary algorithms and the genetic fuzzy-rule based classification systems are combined to construct a threestage learning process to map land cover changes from hyperspectral images (Stavrakoudis et al., 2012). In this paper, efforts are made to improve the hybrid-fuzzyclassifier (HFC) for grassland mapping developed by Sha et al. (2008). A new semi-ellipsoid-model (SEM) is developed to replace the tetragonal pyramid model (TPM) used in Sha’s HFC, in order to more accurately assign the fuzzy memberships between the spectral classes extracted by image processing and the bio-spectral classes built from the field samples.

2. The study area and research design methodology The Xilin River Basin, situated at 43°260 –44°290 N and 115°320 – 117°120 E, is located in the eastern-central part of Inner Mongolia where grasslands are the primary natural land cover (Fig. 1). Historically, the Xilin Basin is one of the most representative steppe zones in China, which has attracted much interest for both

H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

23

Fig. 1. The study area.

managerial planning and scientific investigation (Li et al., 1988). The Xilin Breeding Stock Rangeland was established in the early 1950s. Researchers from Nanjing Agriculture University surveyed the grassland and forage grass in 1952 (The Inner Mongolia and Ninxia Survey Team of CAS, 1985). The Xilin Basin was designated as the biological research area by the University of Inner Mongolia in 1957. A large-scale scientific survey was conducted in 1964– 1965. A permanent ecosystem observation station was established there in 1979 by the Chinese Academy of Sciences (Li et al., 1988). In recent years, as the population has increased, residential areas have expanded, and grazing has intensified, grassland degradation has become a major ecological and economic problem resulting in the decrease of grassland productivity and desertification (Tong et al., 2004; He et al., 2005; Li et al., 2005). Rigorous efforts have been made by field ecologists and environmental scientists to map plant communities and their changes over time to provide scientific data to support policy making for sustainable utilization of grassland resources. Sha et al. (2008) successfully mapped the grassland in the Xilin River Basin with the finest vegetative details reported in current literature by classifying Landsat ETM+ into eleven categories of plant communities. They developed an improved classifier called the hybrid-fuzzyclassifier (HFC). HFC is a soft and statistically based classification method rather than a hard, pixel-based method, which is suitable for image classifications in complicated regions where high within-pixel variations may exist (Lo and Choi, 2004). This paper attempts to improve the classification accuracy by developing a new semi-ellipsoid-model (SEM) as a replacement to the tetragonal pyramid model (TPM) used in Sha’s HFC (2008). Our research design is depicted in Fig. 2. Steps 1 through 10 of our process are a reorganization of Sha’s HFC approach (2008). Our research area straddles two Landsat TM/ETM+ scenes: path 124/row 29 and path 124/row 30. Images in 2004 (August 14) and 2009 (August 12) were chosen because of the quality of the images and the availability of ground reference points (GRPs) from these years. Our 1–3 steps pre-processed the Landsat TM/ETM+ images. First, geometric corrections using the 1st order polynomial rectification with accuracy to a root-mean-square deviation (RMSE) of

less than one-half a pixel were carried out with the GRPs gathered on the field trips, respectively. Secondly, a strictly image-based atmospheric correction, as proposed by Chavez (1996), was followed to remove atmospheric haze impact on these images. Thirdly, roads and urban areas, heavily deserted areas, farming and man-fenced lands were removed from the images visually with the support of topographic data to avoid possible side influences, since those lands had no typical vegetative spectral signatures. The two scenes from each year were mosaicked into a complete theme. In addition, two CBERS (the China–Brazil Earth Resources Satellites) images (August 8, 2004 and August 5, 2009) were also processed and fused with their counterparts (ETM+ and TM images), respectively, to create two new images for the purpose of comparison (Table 2). The reflective bands (band 1, 2, 3, 4, 5, 7) of each of the four images were used to create Img I. The image processing was done independently for each image and for each year. This study used 482 field plant samples from 2004 and 584 from 2009 as the ground reference points. The validated samples from each year were randomly divided into training sets and testing sets using a ratio of 3 to 1. Therefore, we used 348 samples in the training set and 134 samples in the testing set in 2004, and 434 in the training set and 150 in the testing set in 2009. The training and testing sets were applied to each image and to the different years, respectively. In Step 4 of our process, the training samples were registered on Img I first, and then the spectral data of the 6 reflective bands at the training sample sites were extracted. The brightness value of each band at each training sample location was used to produce a brightness matrix. As a result, two brightness matrixes of 348  7 (sampling-id + 6 bands) were created for the two 2004 images, while two brightness matrixes of 434  7 were created for the two 2009 images. The testing samples are used in the final accuracy assessments. In Step 5, a principal component analysis (PCA) was performed on each brightness matrix created from Step 4. The principal component matrix (PCM) was built with the Statistical Product and Service Solutions (SPSS) software using maximum likelihood

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

1. Select a grassland classification system from botany point of view (Bio-class)

9. Classify (Unsupervised ISODATA) IMG II to form Spec(tral)classes (63)

10. Statistical analysis on Specclasses to form Spec Matrix (MSpec)

2. Acquire and preprocess Landsat ETM/TM image to create IMG I

3. Collect and validate ground reference points (GRPs)

4. Generate brightness matrix from Landsat ETM/ TM image and GRPs

8. Apply PCA transformation on IMG I to create IMG II

6. Hierarchical cluster on major PCs to form BioS(pectral)-classes (21)

5. PCA on the brightness matrix

11. Explore SemiEllipse-Based fuzzy membership function to match MSpec with MBio-S

7. Statistical analysis on Bio-S classes to form Bio-S Matrix (MBio-S)

13. Accuracy assessment and validation at multiple years

12. Restore Bio-S classes to Bioclasses

Fig. 2. The flow chart of HFC-SEM design and implementation.

algorithm to transform the brightness values of the 6 bands from the training samples into 2 principal components (Principal Component 1 and 2). In Step 6, a hierarchical clustering analysis was performed using SPSS with the 11 Bio-classes as priori groups, and the two principal components (from Step 5) as variables. By using Euclidean distance as the linkage distance between the unweighted pair-group centroids called the Linkage Rule (LR), 11 tree-like dendrograms were generated. An appropriate threshold was identified through many rounds of experiments so as to achieve the best separation of the clusters. This threshold was then used to intercept the axes of all 11 dendrograms to create bio-spectral (Bio-S) classes to synthesize the spectral information from Img I and the botanic information from the field samples. The aforementioned process was executed independently over the four Img I images. The principal components, the cumulative variances, the LR thresholds and the numbers of Bio-S for the four images are reported in Table 2. These parameters are also used independently on each of the four images in the following sections. In Step 7, statistical analysis was conducted on the Bio-S classes with the principal components as the variables to generate MBio-S, a matrix of n  dm. MBio-S synthesized the statistical information of the principal components for the Bio-S classes in the form of

M BioS ðCidn ; Meancompd1 ; SDcompd1 ; Meancompd2 ; SDcompd2 ; . . . ; Meancompdm ; SDcompdm Þ

ð1Þ

where n was the total number of Bio-S classes, dm was the number of principal components selected after the PCA analysis, Cid was the code of Bio-S class, Meancomp-dm was the mean value for the principal component (comp-dm), and SDcomp-dm was the standard deviation of the principal component (comp-dm). This formula also implies that our analytical design can handle more than two principal components. The decision of how many principle components chosen depends on the total information explained by the components. A critical value of 90% is strongly recommended. In Step 8, the two components were applied to Img I to transform the reflective bands of Img I into a new image (Img II) with the two principal components as the new bands. An unsupervised

method (ISODATA algorithm) was applied in Step 9 to classify Img II into a total number of 3  n spectral classes (Spec-c; 63 if 2009 TM is taken as an example). In Step 10, a statistical analysis was conducted on the 3  n Spec-c with the principal components as the variables. Similarly to Step 7, MSpec-c, a matrix of p  dm, was created to extract the statistical information of the Spec-c in the form of

MSpec-c ðCidp ; Meancompd1 ; SDcompd1 ; Meancompd2 ; SDcompd2 ; . . . ; Meancompdm ; SDcompdm Þ

ð2Þ

where p was the total number of the Spec-c, and all other annotations are the same as for MBio-S. The choice of the multiplier, 3, is to make sure that the size of the Spec-c is large enough but not too large to make the matching between MBio-S and MSpec-c impossible. Steps 11 through 12 define a semi-ellipse-based fuzzy membership function to match MSpec-c with MBio-S, which will be explained in detail in the next section. Step 13 conducts an accuracy assessment on the basis of comparison between the classification outcomes from three classifiers (the proposed HFC-SEM, Sha’s HFC-TPM, and SVM) over four types of images: (1) Landsat ETM+ August 14, 2004, (2) Landsat TM August 12, 2009, (3) the fused image of ETM+ with CBERS from August 2004, and (4) the fused image of TM with CBERS from August 2009. 3. The semi-ellipsoid-model based hybrid-fuzzy-classifier (HFCSEM) Determining how to define a fuzzy membership function is the critical step in a HFC classification. There are three types of fuzzy memberships: (1) Exact similarity – this type of membership indicates that a Spec-class has the same statistical spectral property as a Bio-S class, meaning a 100% match; (2) Absolute dissimilarity – states that a Spec-class differs significantly from a Bio-S class when the mean value of any principal component between these two classes was greater than the sum of the standard deviations of the Bio-S class and the Spec-class, indicating a 0% match; and (3) Partial similarity – reflects that two cases from a HFC Spec-class

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31 Table 2 Information explained by principal factors over 4 images in 2 years. Principal component analysis

Landsat TM, August 12, 2009

Fused TM with CBERSa in August 5, 2009

Landsat ETM+, August 14, 2004

Fused ETM+ with CBERSa in August 8, 2004

Component 1 (% of Var.) Component 2 (% of Var.) Cumulative Var. % LRb threshold # of Bio-S

7.14 (85.17%) 1.07 (12.71%) 97.88% 16.5 21

26.12 (83.51%) 3.61 (11.54%) 95.05% 12 21

5.00 (83.40%) 0.90 (14.96%) 98.37% 11.5 21

29.43 (88.37%) 2.70 (8.11%) 96.48% 13.5 22

a It is the CBERS (the China–Brazil Earth Resources Satellites) HR (High Resolution) image, which is a single band image with a spectral range 0.5–0.8 lm and the spatial resolution 2.36 m. b LR: Linkage rule for measuring the linkage distance between the unweighted pair-group centroids in a hierarchical clustering analysis.

and a HFC Bio-S class have some similarity and the fuzzy value between these two cases is larger than 0% but less than 100%. Sha et al. (2008) developed the tetragonal pyramid model in a three-dimensional space to compute a fuzzy similarity value to identify whether any two cases could be matched. One tetragonal pyramid was defined for the Bio-S class case and the other for the Spec-class case. As an example, we will examine the Bio-S case. The bottom side of the tetragonal pyramid is a rectangle. The length of this rectangle is the standard deviation of the first principal component (Stdx1) while the width is the standard deviation of the second principal component (Stdy1). As the result, two tetragonal pyramids were created for the Bio-S case and the Spec-class case, respectively. The two tetragonal pyramids have the same volume through the adjustment of the heights. The fuzzy similarity value is evaluated as the intersected volume between these two pyramids (Sha et al., 2008). The larger an intersected volume is, the more likely the similarity between the Spec-class and the Bio-S class. The core idea of the tetragonal pyramid model is to construct two volumetric 3D bodies to represent the spectral information (Spec-c) from the processed satellite image, and the combined vegetative and spectral information (Bio-S) from the training samples, respectively. TPM utilizes the volumetric sizes of the two tetragonal pyramids to assess a matching status (i.e., the fuzzy similarity) by computing the intersected volume of the two pyramids. Although it is easy to construct tetragonal pyramids computationally, the TPM method has its limitations. A tetragonal pyramid is not an optimal 3D geometrical object that can obtain a maximum volume when its outer bounding dimensions are fixed. In other word, the TPM method is not effective for creating a 3D object that can attain a maximum volume when the length and width of the primary plane are determined. It would be an improvement if a more efficient technique could be found to create a 3D object that owns a higher volumetric body than a tetragonal pyramid does. Therefore, the semi-ellipsoid model (SEM) is proposed in this paper. The shape of a semi-ellipsoid is often studied to describe shapechanges and space-filling of objects in motion, collision, rotation, and diffraction. The concepts and models of semi-ellipsoids have been applied in a wide array of scientific explorations, from the study of asteroid (Torppa et al., 2008; Jurgens, 1982), to the characteristics of solubility (McBride and Lomba, 2007; Rogosic et al., 2003), and molecular anisotropy (Lee and Kang, 2011; Faubel et al., 1985). From a surface point of view, a semi-ellipsoid model is the most effective for characterizing convex shapes of cells, molecules, particles and asteroids when they are in motion. It is this feature of the semi-ellipsoid that can produce a 3D geometrical object with an optimal volumetric body. From the perspective of preserving information for either Bio-S or Spec-c cases, a semi-ellipsoid attains more information (i.e. having a larger volume from the geometric point of view) than a tetragonal pyramid. The semi-ellipsoid is an outer ellipsoid that

Fig. 3. Geometric comparison of a tetragonal pyramid and a semi-ellipsoid.

contains four additional volumetric bodies (AVBs) in addition to the major portion of a tetragonal pyramid (Fig. 3). Each AVB is on one side of the pyramid, which is the inscribed object when a quarter of the pyramid is cut off from a quarter of the semi-ellipsoid. Although the height of the tetragonal pyramid is adjustable in order to preserve the same volume for two pyramids (Sha et al., 2008), the inscribed section of the pyramid within the semi-ellipsoid is normally larger than the outside section (Fig. 3). Therefore, geometrically, the semi-ellipsoid is more volumetric than the pyramid, and, statistically, the former contains more information than the latter. The semi-ellipsoid model is more effective than the tetragonal pyramid model. A fuzzy similarity matrix (FSM) is built on the basis of a semiellipsoid. It is an np matrix, where n is the total number of HFC Bio-S classes and p is the total number of HFC Spec-c classes. The value of each cell in this matrix shows the similarity between a Bio-S class and a Spec-c class. This value is determined by intersecting two semi-ellipsoids: one formed by the Bio-S class and the other by the Spec-c class. These two semi-ellipsoids are required to have the same volume. The construction of the semiellipsoid is as follows (TUDM, 2007):

(

Fðx; yÞ ¼ S:

ðxxÞ2 2a2

RR

þ

S

minðZ 1 ðx; yÞ; Z 2 ðx; yÞÞdS

Þ2 ðyy 2b2

¼1

ð3Þ

In Eq. (3), x is the axis of principal component 1 and y is the axis of principal component 2 in PCA space. The mean value of principal  is the mean value of principal component component 1 is x and y 2. The major axis (2stdx) of the inscribed ellipsoid is a (analogous to the long side of the rectangle in the tetragonal pyramid model) and b is the minor axis (2stdy) of the inscribed ellipsoid. So, the value of the major axis of the ellipsoid, which pffiffiffi is the bottom-side of the semi-ellipsoid model in this study, is 2a.p For ffiffiffi the same reason, the minor axis of the semi-ellipsoid model is 2b.

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

The arch surface of the semi-ellipsoid is constructed by finding heights (Z values) over the bottom-side of the semi-ellipsoid. The first step is to choose a point on the bottom-side, which is noted as (x0, y0). What needs to be done next is to find a way to compute the height of this point on the arch surface. A transect of the semiellipsoid is a semi-ellipse, which can be computed using the following equation:

 Þ2 ðx0  xÞ2 ðy0  y þ ¼1 2 2 2a 2b

ð4Þ

A second transect passing this point is also a semi-ellipse. If these two semi-ellipses are designed to be intersected, the intersection points of the two semi-ellipses can be calculated as follows:

8 < ðxx2Þ2 þ ðyy2Þ2 2a

2ab

ð5Þ

: yy0 ¼ y0 y xx0 x0 x

Fig. 4. The illustration of the semi-ellipsoid model.

8 y ¼ kx þ d > > <  k ¼ yx00 yx > > : d ¼ y  x0 ðy0 yÞ 0

ð6Þ

x0 x

The solution to Eqs. (5) and (6) is a new semi-ellipse:

 Þ2 ðx  xÞ2 ðkx þ d  y þ ¼1 2 2a2 2ab

ð7Þ

Eq. (7) can be transformed as the following: 2 2 Þ  2xx þ ½x2 þ ðd  y Þ2  2a2 b2  ð2b þ 2a2 k Þx2 þ ½2kðd  y

¼0

ð8Þ

8 2 2 2 > < A ¼ 2b þ 2a k Þ  2x B ¼ 2kðd  y > : 2 Þ2  2a2 b2 C ¼ x þ ðd  y

ð9Þ

Hence, the coordinates of the two intersection points can be computed as,

(

pffiffiffiffiffiffiffiffiffiffiffiffi 2 x1 ¼ Bþ 2AB 4AC

ð10Þ

y1 ¼ kx1 þ d (

pffiffiffiffiffiffiffiffiffiffiffiffi 2 x2 ¼ B 2AB 4AC

ð11Þ

y2 ¼ kx2 þ d Define the major axis and the minor axis of the new semi-ellipse as a0 and b0 , and the highest height as c. So, the values of a0 and b0 are obtained as follows:

8 <

a0 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Þ2 ðx1  xÞ2 þ ðy1  y

: b0 ¼ c ¼ 3 2pab

ð12Þ

Make a new two-dimensional coordinate system as that shown in Fig. 4, the axis x0 and the axis y0 . In this new coordinate system, the semi-ellipse formula is changed as,

x2 y2 þ ¼ 1ðy P 0Þ a2 b2

ð13Þ

Hence, the final solution can be obtained by Eq. (14),

8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > < x00 ¼ ðx0  xÞ2 þ ðy0  y  Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > : Zðx; yÞ ¼ y0 ¼ h ¼ a02 b02 b02 x020 0 a02

ð14Þ

The similarity between a HFC Bio-S class and a HFC Spec-c class is evaluated by the intersecting volume of the corresponding

semi-ellipsoids. A program written in .NET Framework has been developed for calculating the intersecting volume. The training samples are stored in an ArrayList. The fuzzy membership between the spectral classes and the training samples is depicted in hash tables by using a Dictionary Class. The System Drawing Library is used to construct the ellipse shapes. The function Intersect() performs an overlap between two ellipses in Region format. The function GetRegionScans() returns an array of rectangles that approximate the overlain regions. So the total area of these rectangles is an approximation to the area of the overlain region. 4. Accuracy assessment The accuracy of the SEM-based hybrid-fuzzy classification is assessed from three angles: (1) the outcome of the principal component analysis (PCA), because the key assumption of our HFC is to generalize a small number of principal components in order to remove noise and improve classification accuracy (Sha et al., 2008); (2) the comparison of the classification results from three classifiers, HFC-SEM, HFC-TPM, and SVM; and (3) the detailed examination of the fuzzy assignments between HFC-SEM and HFC-TPM, because the former is supposed to be an improvement to the latter. The outcome of the PCA is very acceptable, which synthesizes two principal components consistently over all four processed images. The cumulative variances explained by the two components all exceed 95% (Table 2). Moreover, the statistics of the overall accuracy and Kappa illustrate that there exists a clear trend (Table 3) among the classification outcomes from the three classifiers. The accuracy levels of HFC-SEM are higher than those of HFCTPM, which are also better than those of SVM. It is worth pointing out that the SVM classifier was applied to the feature space of the two principle components and used the eleven true botanical classes as the target. The performance of SVM is the least acceptable, about 6–10 percentage points lower than HFC-TMP and 10–15 percentage points lower than HFC-SEM. For this reason, SVM is dropped in the latter accuracy assessments concerning plant community types. Another finding is that the classification accuracies of HFC over the fused images are noticeably improved in comparison with the original ETM+ or TM images. However, the degree of improvement attributed to the change of image sources is relatively insignificant in comparison with the change of classification methods from TPM to SEM. For instance, the overall accuracy statistics of the SEM-based classifications are usually four percentage points higher than TMP-based classifications, while the accuracy statistics of the fused images are only 1.3 percentage points higher than the original images (Table 3). Moreover, the accuracy statistics of HFC are decreasing from 2004 to 2009 no matter what the

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31 Table 3 Comparison of HFC-SEM and HFC-TPM over 4 Images in 2 Years. Image types

HFC-SEM

Landsat TM, August 12, 2009 Unclassified area vs. total area Fused TM with CBERSb, August 5, 2009 Unclassified area vs. total area Landsat ETM+, August 14, 2004 Unclassified area vs. total area Fused ETM+ with CBERS, August 8, 2004 Unclassified area vs. total area

SVMa

HFC-TPM

Overall accuracy (%)

Kappa statistics

Overall accuracy (%)

Kappa statistics

Overall accuracy (%)

Kappa statistics

81.33 3.68 82.67 5.33 83.08 4.51 84.60 2.93

0.80

77.32 4.14 78.67 6.52 80.20c 6.29 81.53 3.98

0.76

71.33 0.00 70.15 0.00 67.69 0.00 69.14 0.00

0.69

0.81 0.81 0.83

0.78 0.77c 0.79

0.68 0.66 0.67

a The SVM classifications were processed with the SVM module provided in ENVI. Three basic functions, Linear, Polynomial, and Radial were examined. The differences between the three functions were trivial. Radial gave the best results that were report. b It is the CBERS (the China–Brazil Earth Resources Satellites) HR (High Resolution) image, which is a single band image with a spectral range 0.5–0.8 lm and the spatial resolution 2.36 m. c The accuracy statistics are taken from Sha et al. (2008), which were confirmed by our own experiments.

Table 4 Accuracy test of HFC-SEM in 2009 on TM Image. Vegetation classes

Reference totals

Classified totals

Number correct

Cleistogenes squarrosa 12 13 9 Stipa grandis 13 9 7 Achnatherum splendens 21 23 16 Stipa krylovii 17 15 15 Artemisia frigida 17 18 15 Carex pediformis 9 10 7 Carex spp. 11 9 9 Caragana microphylla 7 10 6 Leymus chinensis + stipa baicalensis 11 9 8 Leymus chinensis 25 25 24 Salsola collina (Chenopodium 5 5 4 glaucum) a Unclassified 2 4 2 Totals 150 150 122 Overall classification accuracy = 81.33%; average classification accuracy = 79.60% Overall kappa statistics = 0.80

Producers accuracy (%)

Users accuracy (%)

75.0 53.9 76.2 88.2 88.2 77.8 81.8 85.7 72.7 96.0 80.0

69.2 77.8 69.6 100.0 83.3 70.0 100.0 60.0 88.9 96.0 80.0

–

–

a Two testing samples fell into the unclassified areas. Since their bio-classes were known, the locations where two samples fell were treated as classified.

image sources or the classification methods are. This decline is attributed to fragmentation or deterioration of grasslands in the study area, which was confirmed by previous research in the same study area (Chen et al., 2003). However, it is worth pointing out that the accuracy statistics from SVM do not conform to the findings from HFC. There is no pattern that can be drawn from the outcomes of the SVM classifications over the four image sources. Furthermore, it is important to examine the accuracy statistics of different plant communities between the two classifiers (SEM and TPM) over the different image years. Our findings confirm that the patterns of change in the accuracy statistics among different plan communities between 2004 and 2009 are quite similar, although the general accuracy degrees are declining between these 2 years. As a result, the accuracy statistics in 2009 are reported in Tables 4–7 as an illustration. By analyzing the changes among the four tables, we come to the following finding; the classification accuracies vary significantly among different plant communities and there is no single classifier or image source that is superior consistently across all plant communities. For instance, HFC-SEM on the TM Image (Table 4) works best for Leymus chinensis (both producers and users accuracy statistics are around 96%), and least for Stipa grandis (the producers and users accuracy statistics are 53.9% and 77.8%, respectively). For the HFC-TPM method on the TM Image, it is the worst combination of classifier and image from the statistics of overall accuracy, average accuracy and Kappa (Table 5), but produces the second best

producers and users accuracy statistics for Achnatherum splendens (90.5% and 82.6%). However, in general, this combination produces lower accuracy statistics and, especially, the lowest for L. chinensis and Stipa baicalensis (the producers and users accuracy statistics are 63.6% and 87.5%, respectively). The HFC-SEM method used on the fused image of TM and CBERS is the best combination of the classifier and the image from the perspective of overall accuracy, average accuracy and Kappa statistic (Table 6). Although it generates several best sets of the producers and users accuracy statistics for A. splendens (95.24% and 90.91%), Stipa krylovii (94.12% and 88.89%), and Caragana microphylla (100% and 70%), it leads to the poorest accuracy statistics for Carex pediformis (66.67% and 60.00%). The TMP-HFC method on the fused image of TM and CBERS (Table 5) creates the best producers and users accuracy statistics for Cleistogenes squarrosa (91.67% and 100.00%). The differing classification accuracy degrees for plant community levels between the SEM and TPM models are caused by the mixed spectral information over the mosaic-like spatial patterns of grassland cover. The classification results in 2009 were also mapped. However, because of the page size limitation of this paper, only a small region, the highlighted study area (Fig. 1), is displayed in Fig. 5. Significant variations between the two classifiers over the two image1 1 For interpretation of color in Fig. 5, the reader is referred to the web version of this article.

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H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31 Table 5 Accuracy test of HFC-TPM in 2009 on TM Image. Vegetation classes

Reference totals

Classified totals

Number correct

Cleistogenes squarrosa 12 11 10 Stipa grandis 13 8 7 Achnatherum splendens 21 23 19 Stipa krylovii 17 15 13 Artemisia frigida 17 19 15 Carex pediformis 9 10 7 Carex spp. 11 9 6 Caragana microphylla 7 10 5 Leymus chinensis + stipa baicalensis 11 8 7 Leymus chinensis 25 28 22 Salsola collina (Chenopodium 5 6 3 glaucum) Unclassified 2a 3 2 Totals 150 150 116 Overall classification accuracy = 77.32%; average classification accuracy = 73.43% Overall kappa statistics = 0.76

Producers accuracy (%)

Users accuracy (%)

83.3 53.9 90.5 76.5 88.2 77.8 54.6 71.4 63.6 88.0 60.0

90.9 87.5 82.6 86.7 79.0 70.0 66.7 50.0 87.5 78.6 50.0

–

–

a Two testing samples fell into the unclassified areas. Since their bio-classes were known, the locations where two samples fell were treated as classified.

Table 6 Accuracy test of HFC-SEM in 2009 on the fused image of TM & CBERS. Vegetation classes

Reference totals

Classified totals

Number correct

Cleistogenes squarrosa 12 11 9 Stipa grandis 13 10 8 Achnatherum splendens 21 22 20 Stipa krylovii 17 18 16 Artemisia frigida 17 15 14 Carex pediformis 9 10 6 Carex spp. 11 14 8 Caragana microphylla 7 10 7 Leymus chinensis + stipa baicalensis 11 9 8 Leymus chinensis 25 22 22 Salsola collina (Chenopodium 5 4 4 glaucum) a Unclassified 2 5 2 Totals 150 150 124 Overall classification accuracy = 82.67%; average classification accuracy = 80.76% Overall kappa statistics = 0.81

Producers accuracy (%)

Users accuracy (%)

75.00 61.54 95.24 94.12 82.35 66.67 72.73 100.00 72.73 88.00 80.00

81.82 80.00 90.91 88.89 93.33 60.00 57.14 70.00 88.99 100.00 100.00

–

–

a Two testing samples fell into the unclassified areas. Since their bio-classes were known, the locations where two samples fell were treated as classified.

Table 7 Accuracy test of HFC-TPM in 2009 on the fused image of TM & CBERS. Vegetation classes

Reference totals

Classified totals

Number correct

Cleistogenes squarrosa 12 11 11 Stipa grandis 13 8 7 Achnatherum splendens 21 22 18 Stipa krylovii 17 14 13 Artemisia frigida 17 18 14 Carex pediformis 9 10 7 Carex spp. 11 9 6 Caragana microphylla 7 10 7 Leymus chinensis + stipa baicalensis 11 8 8 Leymus chinensis 25 28 22 Salsola collina (Chenopodium 5 6 3 glaucum) Unclassified 2a 6 2 Totals 150 150 118 Overall classification accuracy = 78.67%; average classification accuracy = 76.65% Overall kappa statistics = 0.78

Producers accuracy (%)

Users accuracy (%)

91.67 53.85 85.71 76.47 82.35 77.78 54.55 100.00 72.73 88.00 60.00

100.00 87.50 81.82 92.86 77.78 70.00 66.67 70.00 100.00 78.57 50.00

–

–

a Two testing samples fell into the unclassified areas. Since their bio-classes were known, the locations where two samples fell were treated as classified.

H. Lan, Y. Xie / ISPRS Journal of Photogrammetry and Remote Sensing 85 (2013) 21–31

(a) HFC-SEM with 2009 TM

(b) HFC-SEM with 2009 Fused Image

(c) HFC-TPM with 2009 TM

(d) HFC-TPM with 2009 Fused Image

29

Fig. 5. The maps of grassland plant communities from Landsat and CBERS images in Xilin River Basin – 2009.

sources are noticeable. There are three dominant plant communities found in the highlighted area: Artemisia frigida (magenta), S. grandis (green), and A. splendens (blue). Their distribution patterns show significant variations between the two classifiers over the two images. For instance, A. frigida is: (1) concentrated in the northern and central portions and less fragmented by HFC-SEM with TM; (2) distributed over the entire area with a relative concentration in the northern part by HFC-SEM with Fused Image and by HFC-TPM with TM; and (3) clustered in the northern part by HFC-TPM with Fused Image. It should be noted that two out of sixty-three (2/63) Spec-c classes were not matched with any Bio-S classes. Those un-matched image pixels were called the unclassified regions on the resultant classification maps. The total areas of the unclassified regions were trivial (Table 3). Over the four classification outcomes ran in 2009, two out of the 150 testing points fell within the unclassified regions (Tables 4–7). Moreover, the unclassified regions were checked with the aerial photos, these regions were located either in the areas where severe degradation occurred, or over-grazing was happening, or were in the transitional zones between different plant communities. From a spectral point of view, these regions showed mixed pixels. Moreover, because the study area was remote and had rough terrain, many of the ground reference points (GRPs) were taken closer to the transportation routes although extra attention was paid to these areas by the field researchers (Sha et al., 2008). As a result, a relatively high portion of GRPs fell within the ‘mixed pixels’. Furthermore, from the perspective of image classification accuracy, a high percentage of unclassified regions

was a bad outcome. However, from an application point of view, it beckons to identify the right classifications for these unclassified regions, because these regions were singled out.

5. Conclusion and future direction The semi-ellipsoid model is an effective algorithm for studying collision, rotation and diffraction in the fields of exploring asteroids, the characteristics of solubility, molecular anisotropy, and many others. The most salient feature of SEM is that it is most efficient for characterizing convex shapes in order to attain a maximum volume. Our study confirms that SEM is more effective than TPM for assigning the fuzzy relationships between the Specc classes and Bio-S classes. In particular, SEM is more suitable for identifying complex fuzzy memberships that are derived from the spectral information over heterogeneous areas. As discussed in the previous section, SEM performs significantly better than TPM does with the 2004 data as well as with the 2009 data no matter what the source images were (original Landsat or fused with CBERS). The hybrid approach is an important element of the hybrid method. A principal component analysis (PCA) is executed to summarize the spectral properties of the 6 selected bands into a limited number (two in this case study) of Principal Components (PC) with the vegetative classes (the ground truth training samples) chosen as priori groups. This generalization apparently eliminated some noise from heterogeneous plants, which helped extract the most

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important spectral signatures that separated the vegetative classes of interest. Hence, the outcome of PCA is an important factor that influences the accuracy of subsequent fuzzy membership assignment. Moreover, the PCA approach is extensible to higher order component dimensions. For instance, in a case of three (3) principal components, the fuzzy similarity could be computed as a weighted sum of the intersected volumes of three pairs of semiellipsoids, i.e. the semi-ellipsoid constructed from PC1 and PC2, the semi-ellipsoid from PC1 and PC3, and the semi-ellipsoid from PC2 and PC3. Another important finding was that no single classifier or any single image source performs consistently well across all plant communities. It is clear that each method has its limitation in differentiating plant communities. This paper strongly suggests that the hybrid approach is more robust than the solo method. Therefore, we recommend that higher classification accuracy could be achieved through combining several classification algorithms according to the spectral characteristics of the images used and the unique features of the study area (Li et al., 2011). The results of our many rounds of experiments with different classifiers, images, and image years also confirm that numerous factors affect the potential success of an image classification over grasslands using satellite images (Salovaara et al., 2005). Since grassland is very sensitive to human activities and environmental factors, inconsistency often occurs when grassland vegetation classifications are made either from a botanical point of view or from a spectral consideration. It is inevitable that spectral variations exist within the ground samples of the same bio-class. In other words, a bio-class may have to be sub-divided into spectrally discernible sub-classes in image classification in order to minimize spectral variations of ground samples within this bio-class (Cingolani et al., 2004; Stuart et al., 2006; Sha and Xie, 2010). Furthermore, it is apparent that the accuracy of SEM or TPM relies on several other factors. First, the size and quality of the ground reference points or field training samples have significant influence on the accuracy of a vegetation classification. It is a critical step to select an adequate number of field samples covering different classes as the training or reference points when implementing classification using remotely sensed data. In our study, 482 field samples in 2004 and 584 in 2009 were collected. Although larger numbers of samples would be preferred, it is an enormous effort to get a large number of ground reference points. In our study area, long-term observations have been maintained by several research teams. Otherwise, it is almost impossible to collect a sufficient number of samples. Second, the quality of the ground reference points is very important. The non-match of two Spec-c classes and the fall of 3–6 testing samples in the non-classified regions provide solid evidence that it is important to have high-quality field samples. Third, either grassland conditions or climate variations can have direct impact on the image processing and the performance of the fuzzy membership assignments. The images collected for this research came from August 14, 2004 and August 12, 2009, respectively. Although these two dates were very close across two different years, there were consistent declines in the classification accuracy for both the SEM and TPM methods. The differences can be explained by intensified grassland degradation (Chen et al., 2003) or annual fluctuations of climate, or both. In addition, a second candidate could exist for matching with Spec-classes on the basis of the second highest fuzzy similarity value (Sha et al., 2008). A manual check could be deployed to examine whether incorrect assignments of the field samples or fuzzy memberships could be corrected using the second highest value (Sha et al., 2008). However, we have not used the second highest values to assign the fuzzy memberships in this study for the sake of performing unbiased comparisons. Nevertheless, designing a

systematic approach to take advantage of the information contained in the second highest similarity values for more accurate classification will be one area of future improvement. Furthermore, we want to point out that the SVM classifier could take various kernel functions and use different parameters. The examinations and comparisons of SVM in this paper are limited to the common kernel functions, which could be a direction of future improvement. Finally, our study area, the Xilin River Basin, is part of the Mongol Steppe and, more importantly, is commonly recognized as a representative temperate steppe in the Eurasian Steppes (Tong et al., 2004; He et al., 2005). Therefore, the potential of applying our proposed classifier in other eco-regions of the Eurasian Steppes is very promising. However, precautions concerning various factors that have direct impacts on the SEM-HFC accuracy, such as, the size and the quality of the ground reference points, the timing of remote sensed images and corresponding grassland growing conditions, and the climate variations, should be fully examined to determine spectrally discernible bio-classes for classification. Acknowledgements This research is partially supported by a grant from the Land Cover/Land Use Program at NASA (Grant # NNX09AK87G). The authors are also grateful to The Center for Ecological Research, Institute of Botany, Chinese Academy of Sciences for assistance in collecting the ground reference samples. References Baraldi, A., 2011. Fuzzification of a crisp near-real-time operational automatic spectral-rule-based decision-tree preliminary classifier of multisource multispectral remotely sensed images. The IEEE Transactions on Geoscience and Remote Sensing 49 (6), 2113–2134. Benz, U.C., Hofmann, P., Willhauck, G., Lingenfelder, I., Heynen, M., 2004. Multiresolution, object-oriented fuzzy analysis of remote sensing data for GIS-ready information. ISPRS Journal of Photogrammetry and Remote Sensing 58 (3–4), 239–258. Chavez Jr., P.S., 1996. Image-based atmospheric corrections-revisited and improved. Photogrammetric Engineering and Remote Sensing 62, 1025–1036. Chen, S., Xiao, X., Liu, J., Zhuang, D., 2003. Observation of land use/cover change of the Xilin River Basin inner Mongolia using multitemporal Landsat images. In: Pan, X, L., Gao, W., Glantz, M.H., Honda, Y. (Eds.), Ecosystems Dynamics, Ecosystem-Society Interactions and Remote Sensing Applications for Semi-Arid and Arid Land, Proceedings of the SPIE, pp. 674–685. Cingolani, A.M., Renison, D., Zak, M.R., Cabido, M.R., 2004. Mapping vegetation in a heterogeneous mountain rangeland using Landsat data: an alternative method to define and classify land-cover units. Remote Sensing of Environment 92, 84– 97. Faubel, M., Frick, J., Kraft, G., Toennies, J.P., 1985. Determination of molecular anisotropy from diffraction and rotational inelastic scattering of He from C2H6 using two simple models. Chemical Physics Letters 116, 12–17. Guo, X.S., Sun, L.Y., Li, G., Wang, S., 2008. A hybrid wavelet analysis and support vector machines in forecasting development of manufacturing. Expert Systems with Applications 35 (1–2), 415–422. He, C., Zhang, Q., Li, Y., Li, X., Shi, P., 2005. Zoning grassland protection area using remote sensing and cellular automata modeling – a case study in Xilingol steppe grassland in northern China. Journal of Arid Environments 63, 814–826. Jurgens, R.F., 1982. Radar backscattering from a rough rotating triaxial ellipsoid with applications to the geodesy of small asteroids. Icarus 49, 97–108. Langley, S.K., Cheshire, H.M., Humes, K.S., 2001. A comparison of single date and multitemporal satellite image classifications in a semi-arid grassland. Journal of Arid Environments 49, 401–411. Lee, D.W., Kang, I.S., 2011. Minimum drag shape of a semi-ellipsoid exposed to shear flow and its possible relation to the shape of endothelial cell. Mathematical Biosciences 231 (2), 225–234. Li, B., Yon, S.P., Li, Z.H., 1988. Vegetation and its utilization in xilinhe basin. Research on Grassland Ecosystem 3, 84–183. Li, E., Zhu, S., Zhou, X., Yu, W., 2011. The development and comparison of endmember extraction algorithms using hyperspectral imagery. Journal of Remote Sensing 15 (4), 659–679. Li, F.R., Kang, L.F., Zhang, H., Zhao, L.Y., Shirato, Y., Taniyama, I., 2005. Changes in intensity of wind erosion at different stages of degradation development in grasslands of inner Mongolia, China. Journal of Arid Environments 62, 567–585. Liang, E., Vennetier, M., Lin, J., Shao, X., 2003. Relationships between tree increment, climate and above-ground biomass of grass: a case study in the typical steppe, north China. Acta Oecologica 24, 87–94.

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