Hyperspectral image classification based on volumetric texture and dimensionality reduction

Abstract

A novel approach using volumetric texture and reduced-spectral features is presented for hyperspectral image classification. Using this approach, the volumetric textural features were extracted by volumetric gray-level co-occurrence matrices (VGLCM). The spectral features were extracted by minimum estimated abundance covariance (MEAC) and linear prediction (LP)-based band selection, and a semi-supervised k-means (SKM) clustering method with deleting the worst cluster (SKMd) band-clustering algorithms. Moreover, four feature combination schemes were designed for hyperspectral image classification by using spectral and textural features. It has been proven that the proposed method using VGLCM outperforms the gray-level co-occurrence matrices (GLCM) method, and the experimental results indicate that the combination of spectral information with volumetric textural features leads to an improved classification performance in hyperspectral imagery.

Keywords

hyperspectral imagery / image classification / volumetric textural feature / spectral feature / fusion

Introduction

Hyperspectral remote sensing plays an important role in land cover classification and mapping ( Chang, 2013). Spectral information has been widely explored in hyperspectral imagery classification, whereas related works on geometric features and textural features are still limited ( Gamba et al., 2007; Mura et al., 2011). Texture is the structure formed by regular changes in color, and potentially can be used to distinguish ground objects. This is important for feature extraction and target recognition in remote sensing because it captures the spectral distribution characteristics of the ground objects. Thus, textural features combined with spectral information can improve classification accuracy ( Yang et al., 2010; Rajadell et al., 2013; Chen et al., 2014a, 2014b). Several texture analysis approaches are currently used for hyperspectral image classification, including structural ( Benediktsson et al., 2005; Bernabe et al., 2014), statistical ( Jackson and Landgrebe, 2002), model-based ( Li et al., 2012), and transform-based methods ( Angelo and Haertel, 2003). Among the statistical methods, the gray-level co-occurrence matrices (GLCM) method is the most prevalent ( Haralick et al., 1973; Jackson and Landgrebe, 2002) and outperforms other classification approaches ( Nyoungui et al., 2002; Mokji and Bakar, 2007), although this approach is generally applied to single-band image classification.

The conventional concept of texture is normally applied to single-band grayscale or color images. It may not be accurate for hyperspectral images because the textures of the different bands vary significantly. Recently, Tsai et al. ( 2007) extended the model of GLCM to three-dimensional (3D) space and proposed a volumetric GLCM (VGLCM) model to cope with the high dimensional features of hyperspectral data. The VGLCM texture can capture the relations between neighboring spectral bands; therefore, combining volumetric textural features with spectral features is expected to improve classification performance.

In this paper, we propose a novel classification framework as well as several schemes for hyperspectral image classification by combining spectral information and volumetric textural features. In the proposed schemes, the VGLCM algorithm is combined with dimensionality reduction techniques, such as minimum estimated abundance covariance (MEAC)-based band selection, and a semi-supervised k-means (SKM) clustering method with deleting the worst cluster (SKMd)-based band clustering.

The rest of the paper is organized in the following manner. In Sections 2 and 3, the GLCM, VGLCM, and dimensionality-reduction algorithms for textural and spectral feature extraction are reviewed. In Section 4, we describe the proposed framework and combination schemes for hyperspectral image classification. In Section 5, the experimental results are presented with two hyperspectral datasets. Finally, the conclusions are presented in Section 6.

GLCM and volumetric GLCM models

GLCM model and parameter analysis

The GLCM model ( Haralick et al., 1973) is a widely used algorithm for image texture analysis. The model is a measurement of the second-order statistical changes in gray levels as well as their spatial patterns. It reflects the information of directions, neighboring spacing, and magnitude changes in gray levels, and provides a tool for analyzing local patterns and pixel arrangements in images.

Let I be an N_x×N_y image with N_g gray levels and each pixel in I corresponding to a gray level belonging to G. The co-occurrence frequencies (joint distribution) of the gray levels were calculated for the pixels in δ=(d, θ) distance intervals to form an N_g×N_g co-occurrence matrix, where d and \theta represent the distance and the angle between two pixels, respectively. The angle between different pixels was computed by the spectral angle mapper (SAM) algorithm ( Chang, 2003), which determined the spectral distance between two spectra by calculating the angle between the spectra and treating them as vectors in a space with a dimensionality equal to the number of bands. The co-occurrence probability of pairwise pixels was calculated as P(i, j)=p(i, j, d, θ), which can be normalized as

(1) p\left(i,j\right)=P\left(i,j\right)/r,

where r is the number of pairwise pixels. The statistical attributes extracted from the gray level probability matrix obtained from Eq. (1) were used to quantize the local textural features. GLCM is typically computed in four directions: θ = 0°, θ = 45°, θ = 90°, and θ = 135°. Fourteen statistical measurements, including energy, contrast, entropy, and correlation, can be computed from GLCM. Finally, a feature vector is generated by using the means and variances of all of the measures.

The texture features extracted by using GLCM were mainly affected by the quantization level, the size of the moving window, the distance and angle between pairwise pixels, and the statistical measures. The size of the moving window accounted for 90.4% of the classification variability, 7.1% was explained by the statistics used as texture measures, and only a small portion by the quantization level and the distance and the angle between the pixel pairs ( Marceau et al., 1990).

Volumetric GLCM model

For texture analysis of hyperspectral imagery, two-dimensional (2D) texture analysis algorithms were generally applied to a single band at a time, and 2D textures were collected for subsequent analysis. However, owing to the contiguous spectral sampling, a hyperspectral dataset can be considered as an image cube with volumetric characteristics, as illustrated in Fig. 1. As a result, it is possible to treat hyperspectral imagery as volumetric data and investigate texture features in 3D space. The spectral vector of a pixel in a hyperspectral image contains spectral reflection or radiation information about the land objects from multiple spectral bands. The texture of a hyperspectral image has the following characteristics: structure, randomness, spatial limitation, continuity, and anisotropy. These can be defined as follows: 1) The texture has spatial structural features because the land objects have shape structures. 2) The texture is random owing to the complexity of land objects. 3) The texture is limited to certain geometric spaces because of the area restriction of the images. 4) Pixels z(x) and z(x+h) in an image are correlated when h is within a certain range, and the correlation disappears as h exceeds the range. 5) Textural features vary in different directions; thus, textures from any single spectral band cannot represent the texture of the entire image. Moreover, the texture extracted from the remote sensing image as a cube may be able to capture the overall characteristics of the data. From a geometric point of view, the texture of a hyperspectral image is a volumetric texture.

VGLCM is another commonly used texture extraction method proposed in ( Tsai et al., 2007). As shown in Fig. 2, the procedures for texture extraction by using VGLCM and GLCM are different. The GLCM model uses a 2D moving window in 2D space. However, VGLCM applies a moving box in 3D space to calculate the texture. For a hyperspectral image cube with n gray levels, the co-occurrence matrix, M, is an n-by-n matrix. Values of the matrix elements within a moving box, W, at a given displacement d = (dx, dy, dz) are defined as ( Tsai et al., 2007)

(2) M\left(i,j\right)={\displaystyle \sum _{x=\mathrm{1}}^{Wx-dx}{\displaystyle \sum _{y=\mathrm{1}}^{Wy-dy}{\displaystyle \sum _{z=\mathrm{1}}^{Wz-dz}\{\begin{array}{ll}\mathrm{1},\hfill & W\left(x,y,z\right)=i\mathrm{and}W\left(x+dx,y+dy,z+dz\right)=j,\hfill \\ \mathrm{0},\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e},\hfill \end{array}}}}

where i and j are the values of pairwise pixels, and x, y, z represent the positions in the moving box. M(i, j) is the value of a 3D GLCM element that reflects how often the gray levels of two pixels, G(x, y, z) and G(x+dx, y+dy, z+dz), are equal to i and j, respectively, within a moving box ( Tsai et al., 2007). In a hyperspectral data cube, d is usually set to one pixel in distance. For each pixel that has 26 neighboring pixels, there are 26 combinations, or 13 if symmetry is considered, in the horizontal and vertical directions. The directions are listed in Table 1 in the form of vectors, where θ and ψ are horizontal and zenith angles, respectively.

Because not all of the statistical measures are suitable for describing the texture features ( Haralick et al., 1973), we chose variance, contrast, dissimilarity, energy, entropy, and homogeneity as the measurements to extract the texture features. It is notable that the dimension of the 2D/3D texture feature is equal to the dimension of original spectral features. To reduce the dimension of 3D texture, principal component analysis (PCA) was applied to obtain the first PC feature ( Liu et al., 2010).

As previously mentioned, the texture features extracted from VGLCM are sensitive to the box size. To obtain an optimal box size, we analyzed the texture features with various box sizes. The semi-variogram function is an efficient tool for analyzing spatial heterogeneity ( Rahman et al., 2003), which can be used for anisotropy analysis of the texture. Let A be a pixel in a hyperspectral image with value z(x); then, B is another pixel that is h pixels away from A and has a value of z(x+h), and the semi-variogram function of these two pixels is defined as

(3) \gamma \left(h\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{2}N\left(h\right)}}{\displaystyle \sum {\left[z\left(x\right)-z\left(x+h\right)\right]}^{\mathrm{2}}},

where N is the number of the pairwise pixels, z(x) and z(x+h) represent the gray levels of the pairwise pixels, and h is the Euclidean distance between the pixels. The semi-variogram function is applicable in 2D or 3D spaces. In 2D space, each spectral band generates a semi-variogram function plot, whereas in 3D space, all of the spectral band features generate only one plot, which greatly reduces the computational complexity (as shown in Fig. 3).

Dimensionality reduction methods

MEAC-based band selection

MEAC is a supervised band-selection algorithm proposed by Yang et al. ( 2011). We assume there are p classes present in an image. Based on the linear mixture model, a pixel r can be considered as the mixing result of the endmembers of the p classes. Let the endmember matrix be \mathbf{S}=\left[{\mathbf{s}}_{\mathrm{1}},{\mathbf{s}}_{\mathrm{2}},\mathrm{...},{\mathbf{s}}_p\right] . The pixel r can be expressed as

(4) \mathbf{r}=\mathbf{S}\mathbf{\alpha }+\mathbf{n},

where \mathbf{\alpha }={\left({\alpha }_{\mathrm{1}}\mathrm{}{\alpha }_{\mathrm{2}}\mathrm{}{\alpha }_p\right)}^{\mathrm{T}} is the abundance vector, n is the uncorrelated white noise with E\left(\mathbf{n}\right)=\mathrm{0} , and Cov\left(\mathbf{n}\right)={\sigma }^{\mathrm{2}}\mathbf{I} (I is an identity matrix, and σ is a least-squares estimation). Intuitively, the selected bands constrain the deviation of \widehat{\alpha } from the actual \alpha to the lowest value. If only parts of the classes are known, this is equivalent to

(5) \underset{{\mathrm{\Phi }}^S}{\arg \min }\left\{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{e}\left[{\left({\mathbf{S}}^{\mathrm{T}}{\mathrm{\Sigma }}^{-\mathrm{1}}\mathbf{S}\right)}^{-\mathrm{1}}\right]\right\},

where Φ^S is the selected band subset, and \mathrm{\sum } is the noise covariance matrix. The resulting band-selection algorithm is referred to as the MEAC method.

Even without any training sample, the MEAC method can be used as long as the class signatures are available. In addition, it is not necessary to examine the entirety of the original bands or band combinations. With forward searching and the initial band-pair selection, this method can complete band selection very quickly.

SKMd band clustering

Given a set of bands (B₁, B₂,…, B_L), where each band is arranged into an N-dimensional vector, N is the number of pixels. k-means band clustering aims to partition the L bands into k clusters C = {C₁, …, C_m, …,  C_k} ( \mathrm{1}\le m\le k ) to minimize the following objective function, expressed as

(6) \underset{\mathrm{C}}{\arg \min }{\displaystyle \sum _{m=\mathrm{1}}^k{\displaystyle \sum _{{\mathbf{B}}_l\in C_m}D\left({\mathbf{B}}_l,{\mathbf{\mu }}_m\right)}},

where μ_m is the cluster center of C_m, and D\left(•,•\right) represents a distance metric gauging the similarity between a band and the center of the cluster to which it is assigned. Its computational complexity is linearly proportional to the number of pixels N. To reduce the complexity, class signatures were used as the algorithm input; thus, the complexity becomes linearly proportional to the number of signatures S (S≪N). This approach is denoted as semi-supervised k-means (SKM).

The SKM algorithm is initialized with distinctive bands as cluster centroids. The idea of unsupervised band selection was presented in 2011 ( Yang et al., 2011). The band-selection algorithm is initialized by choosing a pair of bands, B₁ and B₂, leading to a band subset Φ = {B₁, B₂}. It then determines a third band, B₃, that is the most dissimilar to all the bands in the current Φ by using a certain criterion, resulting in an updated subset, \mathrm{\Phi }=\mathrm{\Phi }\cup {\mathbf{B}}_{\mathrm{3}} . The selection step is repeated until the number of bands in Φ is large enough. Here, the linear prediction (LP) error, i.e., the difference between an original band and its linear predicted version using bands in Φ, is employed as the similarity metric. A band with the maximum LP error is the most dissimilar band from those in Φ and should be selected.

After k-means clustering, k clusters with their centroids are ready for further analysis. However, it does not mean that all of them should be used. Some clusters may not be helpful for object classification, and they may even bring confusion. Thus, we have proposed to remove a cluster by exhaustively searching for the worst one; when it is removed, the remaining clusters provided the most similar classification maps to those by using all of the original bands. It is observed that deleting one cluster generally results in improvement, but deleting more than one cluster may not necessarily provide further improvement. Thus, only one cluster is removed hereafter. The SKM algorithm deleting the worst cluster is denoted as SKMd ( Su et al., 2011; Su and Du, 2012). In the experiment, the SKMd algorithm was used to obtain clusters for classification.

Proposed classification framework

Many applications have proved that informative texture features can be a good booster for classification improvement ( Benediktsson et al., 2005; Gamba et al., 2007; Yang et al., 2010; Mura et al., 2011). In our previous research, we proposed some dimensionality-reduction algorithms ( Su et al., 2011; Yang et al., 2011), and classification accuracy was improved significantly. Therefore, it is possible to improve classification performance by combining volumetric texture features with dimensionality reduced spectral features.

In our proposed classification framework (as shown in Fig. 4), the volumetric textural features were extracted using the VGLCM algorithm, and dimension-reduced spectral features were obtained by using a MEAC-based band selection and SKMd-based band-clustering algorithm. In the proposed spectral-textural fusion schemes, the selected band, clusters, PCA components (or PCs), and texture features are fused for classification. Each feature from VGLCM or GLCM can be viewed as a new band, thus all of the features for each scheme derived from different algorithms are fused by a vector-stacking method ( Huang et al., 2011). The fused feature vectors are then used as inputs for support vector machines (SVMs; Plaza et al., 2009), and overall classification accuracy is used for performance evaluation. Four spectral–textural fusion schemes, listed in Table 2, are designed to validate that texture features could effectively increase classification accuracy. The detailed schemes include scheme I: texture features fused with all of the bands of original data; scheme II: texture features fused with some principle components of the original data after PCA compression; scheme III: texture features fused with selected bands from the original data; and scheme IV: band-clustering centroids fused with texture features.

Experiment results and analysis

Experimental data

The first experimental image is the HYDICE subimage scene with 304 × 301 pixels over the Washington, D.C., Mall area ( Su et al., 2012). After bad band removal, 191 bands were used in the experiment. There are six classes, including roof, tree, grass, water, road, and trail, in the dataset. Six class centers were used for the band selection. The numbers of training and test samples are shown in Table 3. The other experimental image is an AVIRIS subimage scene taken over northwest Indiana’s Indian Pines with 145 × 145 pixels and 202 bands. This image consists of 16 ground-truth land-cover classes ( Chen et al., 2014a). The numbers of samples are shown in Table 4. In the experiment, five-fold cross-validation methods were used for classification. Samples from the DC Mall and Indian Pines datasets were used to evaluate the performance of the VGLCM algorithm. For experiment I, the texture features extracted by VGLCM and GLCM, respectively, were compared. For experiment II, the texture features were first extracted by VGLCM and then fused with spectral features for classification.

Texture box size analysis

Several hyperspectral texture samples of the typical surface features provided the best box size. During the experiment, two texture samples of each typical surface feature were collected from the D.C. Mall dataset. In Fig. 5, the rectangular shapes in various colors represent different objects. White, pink, yellow, and red represent roads, grass, trees, and buildings, respectively. Levels of sensitivity were then calculated as shown in Fig. 6. We can see that the curve of semi-variogram function increases until the window size is 7 for roads, trees, and buildings, which indicates that 7 has the highest frequency among all of the objects in the hyperspectral image. That is, 7 × 7 × 7 is the best box size for the DC Mall dataset.

Various window sizes were tested for GLCM using the D.C. Mall dataset, as well. As can be seen from Fig. 7, the best window size is 7 × 7.

Experiment I: HYDICE Washington Mall

In these experiments, the box size for VGLCM is 7 × 7 × 7 and the angle is (135°, 135°), while the window size for GLCM is 7 × 7 and angle is 135°. Figure 8 shows the comparison of the texture features, including variance, contrast, difference, energy, entropy, and homogeneity from these two algorithms. The plots on the right show the results of the VGLCM algorithm (different colors represent different intensities of textures). These figures indicate that the features derived from VGLCM are better than those of GLCM.

To further evaluate the performance of the proposed method, features extracted by using VGLCM and GLCM, respectively, were combined with the spectral features. These spectral features are 191 bands of the original data, the first five components after PCA compression, five selected bands from the original data (i.e., 62, 110, 25, 95, and 152), and the five clustering centroids extracted by the SKMd algorithm, respectively. The classification results of the D.C. Mall by VGLCM and GLCM are reported in Table 5. Specifically, for the two cases of VGLCM features fused with five selected bands and five clustering centroids, the overall classification accuracy was improved and even reached 96.10%. The other four cases also showed improvement in the classification rate when VGLCM rather than GLCM was used. As shown in Table 5, the classification accuracies increased after the fusion of texture features and spectral data. Figure 9 illustrates the classification maps by using GLCM and VGLCM textures. In the maps, the classification results of the fusion of spectral data and VGLCM texture features are better than those of the fusion of GLCM texture and spectral data.

Experiment II: AVIRIS Indian Pines

For the Indian Pines dataset, the experiments showed that the best box (window) sizes to describe this dataset are 9 × 9 × 9 and 9 × 9 for VGLCM and GLCM, respectively. The extracted texture features were then combined with the original dataset, 15 selected bands from the MEAC algorithm and 15 cluster centroids from the SKMd algorithm. The classification results of the Indian Pines dataset by VGLCM and GLCM are reported in Table 6. It can be seen that the classification results of VGLCM with six texture features outperformed those of GLCM.

An improved view of classification comparison by using spectral and textural features is presented in Fig. 10. From left to right, the first and fourth bar groups represent the four combination schemes in Table 6. After the fusion with texture information, the image classification accuracy was considerably improved. It also shows that texture extraction by using the VGLCM algorithm can lead to a more robust classification.

Conclusions

Volumetric texture features with spectral information derived from dimensionality reduction were investigated in hyperspectral image classification. A novel classification framework and four schemes combining volumetric texture features with reduced spectral features for hyperspectral image classification were proposed. The experimental results demonstrated that by extracting texture features in 3D space, the classification VGLCM outperforms that by extracting texture features in 2D space. Different from the GLCM algorithm, which is generally applied to a single band at a time, VGLCM applies a moving box in 3D space, thereby leading to more informative texture features. Moreover, the results indicate that texture features combined with the original data or the dimension-reduced data resulted in an improved classification rate, and the performance of VGLCM was better than that of GLCM.

However, the performance improvement from the VGLCM was just approximately 2%, compared with the GLCM method, in addition to being achieved at a higher computational cost. For future research, advanced fusion schemes such as classifier ensemble methods will be investigated. In addition, with high-performance computing facilities available, VGLCM can be easily implemented in parallel mode to reduce computational time ( Liu et al., 2012).

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