Completed Extremely Nonnegative DMD for Color Texture Classification

Dense micro-block difference (DMD) has achieved good performance in gray texture representation and classification. However, its performance is not satisfactory when representing color texture. To alleviate this problem, we propose a novel color texture representation method based on Completed Extremely Nonnegative DMD (CEN-DMD) in this paper. In particular, we first use DMD to model interchannel features and interchannel features of color texture images. Considering that negative value is meaningless in a digital image, we perform a nonnegative operation during the difference process. Due to that the maximum value in a nonnegative difference patch represents a significant difference, we construct the Extremely Nonnegative DMD (EN-DMD) by fusing the maximum values of the intrachannel features and the maximum of interchannel features, and further build Completed Extremely Nonnegative DMD (CEN-DMD) by fusing EN-DMDs at five scales and the global feature of the color texture images. Finally, the Fisher Vector is used to encode the CEN-DMD to obtain a color texture descriptor. Experimental results on five published standard color texture datasets (CUReT, Colored Brodatz, VisTex, USPTex and KTH-TIPS) reveal that CEN-DMD is effective when compared to the thirteen representative color texture classification methods.


I. INTRODUCTION
Texture classification is a classic problem in the field of pattern recognition and computer vision. How to capture discriminative features from texture images is the key to solving the texture classification problem. Texture analysis and representation are also used in a variety of visual applications such as object recognition [1]- [4], face recognition [5]- [7], video classification [8], [9], image segmentation [10]- [12], and image or video retrieval [13], [14].
Since there is currently no uniform definition of textures, building an effective representation of any given texture image is always a challenging subject. This has also attracted The associate editor coordinating the review of this manuscript and approving it for publication was Donato Impedovo . a lot of scholars' attention, and various texture representation methods has been successively proposed. Texture features can be represented by the relationship between neighboring pixels and central pixels in the texture image, which is also referred to as the spatial domain method. The local binary pattern (LBP) is a method of representing a texture image by binarizing the difference between the neighborhood pixels and the center pixel [15]. It is a representative spatial domain method. In recent years, many variants of LBP have also been proposed by improving the deficiencies of the original local binary pattern [16]- [21]. The completed local binary pattern (CLBP) decomposes the image local differences into two components of sign and magnitude by a local difference sign-magnitude transform [22]. In order to enhance the robustness to rotation and noise, binary rotation invariant and noise tolerant (BRINT) [23] and median robust extended LBP (MRELBP) [24] are proposed respectively.
On the other hand, transform domain methods are to model transformation coefficients in the transformed domain. The widely used transform tools include wavelets [25], [26], contourlets [27] and shearlets [28]. Typically, Local energy histogram [25] and Heterogeneous and Incrementally Generated Histogram (HIGH) were proposed to model the wavelet coefficients for texture classification [29]. Poisson mixture model was used to model the contourlet subband coefficients [30]. Linear regression model is used to model the shearlet domain [28].
However, these texture feature extraction methods focus only on gray-scale images and ignore color information.
Color is a discriminative information in human vision, and it is also necessary to consider color information when performing texture feature extraction [31], [32]. Extracting discriminative color texture features is also a concern of many scholars who study texture classification. For color texture feature extraction, it is intuitive to use the feature extraction methods of grayscale texture on three color channels [33]. More important is to explore the features between the relative color channels. Junior et al. [33] used the theory in the data structure to view each pixel as a vertex in the graph, thereby constructing an undirected graph to represent the three color channels. The statistical moment of the shortest path between specific vertices in the undirected graph is calculated as a color texture feature. Since Improved LBP (ILBP) is conceptually simple, easy to implement and efficient LBP variant, Bianconi et al. [34] proposed to use this coding model to extract the features of intrachannels and interchannels for color texture classification. Similarly, transform domain methods are also applicable to color texture images. The analytic Gabor filters were used to analyze the color texture by calculating the first-and second-order statistics of the filtered response and using homomorphic filtering to compensate for illumination changes in the image [35]. In order to better describe the color, Chen et al. [36] designed a new color image processing tool called Complementary Color Wavelet Transform (CCWT) to make up for the gap between wavelet and complementary color. A more comprehensive study of color texture analysis can be found in [37], [38]. Furthermore, color texture analysis is also used for texture retrieval [39], pathological image analysis [40] and endoscopic and dermoscopic medical image analysis [35].
Modeling between relative color channels is a powerful trick for texture analysis. However, most of this kind of methods may ignore the global features of color texture. To alleviate this problem, in this paper, we propose a novel Completed Extremely Nonnegative DMD (CEN-DMD) texture descriptor for color texture classification. Particularly, we model color texture images using dense micro-block difference (DMD) to extract dense micro-block difference features of intrachannels and interchannels. Furthermore, the absolute values of differential features are extracted and the corresponding maximum values for the intrachannel differences and interchannel differences are selected. Multiresolution representation of color texture images is achieved by differential between different scales of micro-blocks. We named it Extremely Nonnegative DMD (EN-DMD). Subsequently, since EN-DMD only capture local features of color images, and global features are also essential for texture feature extraction. Therefore, we propose to combine the global information of the color texture image and the EN-DMD to construct an completed extremely nonnegative DMD descriptor. It contains not only intrachannel features and interchannel features, but also local features and global features of color texture. Fisher Vector (FV) is then used to encode the proposed color texture features, and support vector machines (SVM) is used to perform classification tasks. Finally, experimental results on five publicly available color texture datasets reveal the effectiveness of our proposed CEN-DMD.
The contributions of our paper are as follows: • We construct a nonnegative multiresolution DMD feature for representing texture information. This feature is a multiresolution representation of textures by performing the nonnegative operation and then concatenating micro-block features of difference sizes.
• We use the maximum values of three intrachannel difference features and the maximum values of three interchannel difference features of the color texture image to measure the significance of difference features. Intuitively, the maximum value in nonnegative difference indicates a significant difference. In addition, compared with the directly combine all intrachannel and interchannel difference features, the resulting maximum difference feature has a low dimension.
• We propose a Completed Extremely Nonnegative DMD (CEN-DMD) for representing color textures. The complete property of CEN-DMD consists of the intrachannel and interchannel information, as well as the global and local information of the color texture.
• The classification results on the five published standard texture datasets (Colored Brodatz, VisTex, CUReT, USPTex and KTH-TIPS) demonstrate that our proposed method is effective when compared with other representative color texture classification methods.
The remainder of the paper is organized as follows. Related work is shown in the Section II. In the Section III, we present the proposed Completed Extremely Nonnegative DMD for color texture representation method. Experimental results and comparison about color texture classification are presented in Section IV. Finally, Section V is the conclusion of the paper.

II. RELATED WORK
Building an effective color texture representation is a key step for performing color texture classification. As we all know, we can construct the corresponding descriptor of the three color channels by using gray-scale texture representation method, and further obtain the representation of the VOLUME 8, 2020 whole color texture image. However, for a color texture image, the three color channels are not independent. Some researchers proposed some modeling methods for building effective color texture representation methods. We now briefly review two representative methods below.
• Shortest Path in Graph for Color Texture: In order to explore the relationship among pixels of different color channels, Jarbas et al. proposed to model a color texture image as an undirected graph [33]. An image is made up of a number of pixels, each of which can be thought of as a vertex in an undirected graph. An edge connecting two vertices can be constructed between adjacent pixels, and the weight of the edge can be calculated from the pixel value of the pixel corresponding to the connected vertex. Texture features can be obtained by calculating the statistical moments of the shortest path in the undirected graph. For a color texture image, two undirected graphs can be constructed. On is to construct an undirected graph on each color channel. That is to say, a color texture image corresponds to three undirected graphs, so each shortest path belongs to only one color channel. The other is to create an undirected graph representing the entire color image. In other words, the three channels are represented as whole, so that the shortest path can explore the relationship between different color channels.
• Improved Opponent Color Local Binary Patterns: As a variant of Local Binary Pattern (LBP), Improved LBP (ILBP) is conceptually simple and easy to implement based on the point-to-average threshold method. Motivated by it, Francesco et al. proposed the use of this coding scheme for extracting intrachannel and interchannel features for color texture analysis, known as Improved Opponent Color Binary Patterns (IOCLBP) [34]. A more intuitive description of IOCLBP, the mathematical expression is as follows: where p i,v means the intensity of the ith pixel in the vth channel, n is the number of pixels in the local neighborhood. It can be easily seen from equation (1) and (2) that IOCLBP is capable of capturing intrachannel feature and interchannel feature. Although these methods achieved good performance in color texture classification, they only focus on local information and ignore the global features of color textures. Therefore, we propose an Completed Extremely Nonnegative DMD (CEN-DMD) for color texture classification. We will describe our proposed CEN-DMD in the following section in detail.

III. OUR PROPOSED COMPLETED EXTREMELY NONNEGATIVE DMD COLOR TEXTURE REPRESENTATION METHOD
In this section, we present the proposed Completed Extremely Nonnegative DMD (CEN-DMD) color texture descriptor. Particularly, we model color texture images by using dense micro-block difference (DMD) to extract dense micro-block difference features of intrachannels and interchannels. Furthermore, the absolute values of differential features are extracted and the corresponding maximum values for the intrachannel differences and interchannel differences are selected. We then present the global feature extraction of the color texture image, followed by the Fisher Vector (FV) encoding, and further we obtain the color descriptor.

A. EXTREMELY NONNEGATIVE DMD
Due to that an image texture was defined as the local spatial variations in pixel intensities and orientation [41], the difference representation is a powerful characteristic for capturing texture information. Furthermore, the individual pixels are more susceptible to noise, the dense micro-block difference in an image patch was proposed to replace the micro-block difference of a single pixel for performing gray-scale texture image classification [42], [43]. To capture local difference information for an image, pairs of micro-blocks in each image patch are used to encode the local structure of the image patch, where the average intensity of the micro-block is considered for capturing variations. In this approach, texture information of a given patch I p can be captured by utilizing smaller block, named as micro-block, in the patch instead of the individual pixel. In a given image, the pairs of micro-blocks in each image patch are used to encode the local structure of the image patch. Particularly, a given an image patch I p of size L × L and two set of sample points X = {x 1 , x 2 , . . . , x n } and Y = {y 1 , y 2 , . . . , y n }, the micro-block difference of patch I p is defined as: where where M s (x) is the average intensity of pixel in the micro-block at the position x c = (a, b) T in the I p , s is the size of the micro-block.
Since color images consist of three color channels, building a color texture descriptor is to extract intrachannel features or interchannel features. Intuitively, pairs of micro-blocks from image patches of the same color channel can be used for building intrachannel features. That is to say, the micro-block difference features within the three channels are extracted to capture intrachannel texture information. More challenging and more meaningful is to explore the relationship between color channels and extract interchannel features. We first select pairs of micro-blocks from image patches of different color channels. Due to that the channel pairs, (u, v) and (v, u) can capture the same texture information, we only use one of them to build the texture descriptor to avoid computational redundancy. Furthermore, we can extract color texture information from the combinations of three color channels.
In the image patch of each color channel of the color texture image, the selection of the pair of micro-blocks is determined by the set of two sample points X c = x c 1 , x c 2 , . . . , x c n and Y c = y c 1 , y c 2 , . . . , y c n , where c ∈ {u, v, w} represents the color channel and n represents the number of sample points. In this paper n = 80. For the image patch I c p of size L × L on the c color channel, the intrachannel difference is defined as follows: where where the size of micro-block is s×s, x c = (a, b) T represents the coordinates in the image patch on the special color channel, M c s (x c ) is the average intensity of the pixels located in the micro-block of x c = (a, b) T and || indicates absolute value operation. Since negative values are meaningless in digital images, we use absolute value operators in differential operations to make the difference features nonnegative. Therefore, the micro-block differences in the three color channels can be extracted.
More meaningful and more challenging is to explore the information between the color channels of a color texture image. Micro-block differences are used to model the relationship between the color channels of a color texture image. In the modeling process, the micro-block pairs are respectively selected from texture image patch of different color channels. In order to avoid the redundancy of calculation, only one of two combinations (u, v) and (v, u) is considered. So that there are three different combinations of color channels. Similarly, the choice of micro-block pairs is determined by the set of sample points X c and Y c . For the patch of size L × L, the interchannel difference are expressed as follows: where I c−c p is the interchannel difference of image patch between c color channel and c color channel, c ∈ {u, v, w} and c ∈ {u, v, w}. Fig. 1 shows the process of extracting intrachannel and interchannel dense micro-block difference.
The choice of micro-block pairs plays an important role in the process of feature extraction. The student t-distribution is used to sample the micro-block in the image patch. That is to say, to generate sample points in set X c and Y c . It is well known that the tail of the t-distribution FIGURE 1. The extraction process of micro-block difference of color texture including Intrachannel difference and Interchannel difference. The Intrachannel difference refer to capturing micro-block difference within a single color channel. The Interchannel difference explores the relationship between two different color channels.
is higher than the Gaussian distribution, and it is possible to capture relatively more edge information of the image block for selecting the micro-block in the image patch. The sampling points on the three color channels are different, and thus the distance or angle between the pair of micro-blocks in a single color channel or between color channels is not a constant. So this will lead to capture multi-scale information and more direction information in the image patch. We select a set of sample points in the set for selecting the pair of microblocks, and calculate the distance and consine between the sample points. Fig. 2 and Fig. 3 show the distribution histograms of distance and cosine values, respectively. We can see from Fig. 2 that the distance of the sampling points is not a specific constant. That is to say, the micro-block difference can capture different scales information. Correspondingly, It can be seen from Fig. 3 that the direction of the sampling point is not a fixed value, and thus the above micro-block difference can capture the texture information in different directions. Intuitively, the maximum value of a given set indicates a significant characteristic of the set. Moreover, negative numbers are meaningless in digital images when performing VOLUME 8, 2020 differential modeling, and thus we construct a nonnegative dense micro-block difference for further representing texture information. However, the features obtained by directly concatenating intrachannel features and interchannel features will cause the dimension of the feature to be too large. So we aim at using the maximum values of three intrachannel difference features and the maximum values of three interchannel difference features of the color texture image to measure the significance of difference features, and further combine intrachannel feature with interchannel feature as a whole for color texture analysis. At the same time, we can select different sizes of micro-blocks for differentiation and capture multiresolution information of color textures. We call this combined feature an Extremely Nonnegative DMD, abbreviated as EN-DMD. The EN-DMD is defined as follows: Note that in this paper, we use RGB color space for color texture analysis. The RGB color space based on the three basic colors of red, green and blue can be superimposed to different degrees to produce a rich and wide color. Since it is close to a nature color, the RGB color space is also a nature color mode [44].
For clarity, we randomly select two sample images from two different texture classes in the VisTex texture dateset. Fig. 4 shows the two texture images from the VisTex dataset and their dense micro-block difference histograms. In the sub-figures of Fig. 4, the x-axis of the sub-figure represents the distribution range of the difference feature, and the y-axis represents the frequency. In the histogram, each bin represented by a different color. Fig. 4(c) and (d) show their histograms of intrachannel and interchannels dense micro-block differences. Fig. 4(e) and (f) show their histogram of the maximum values of three intrachannel dense micro-block differences and the maximum values of three interchannel dense micro-block differences. That is to say, the histograms are obtained by using our proposed EN-DMD. It can be easily seen from Fig. 4 that the two histograms (c) and (d) have Finally, the Completed Extremely Nonnegative DMD (CEN-DMD) is defined as follows: For a given color texture image, our proposed descriptor CEN-DMD not only contains intrachannel features and interchannel features, but also can capture the local features and global features of color image. The completeness of CEN-DMD is also reflected here.

C. FISHER VECTOR ENCODING TO CONSTRUCT A COLOR DESCRIPTOR
In this subsection, we employ Fisher Vector (FV) to refine the above CEN-DMD and obtain the final color texture descriptor. Quantization/hard assignment was used by most early texture classification tasks, but it may lead to a quantization error. As a soft quantization, the Fisher Vector has been used to encode texture features in recent years. In the process of Fisher Vector encoding, a Gaussian mixture model is used for the probability distribution of the original features. The robust representations of the encoding is obtained by capturing the first and second order differences between the image descriptor and the GMM center. The Expectation Maximization (EM) is used to learn the training samples to obtain the parameters of the GMM. For a more detailed discussion of the Fisher Vector, please refer to [45] and [46]. After Fisher Vector encoding, we get a color texture descriptor for the color texture classification task. For simplicity, we still denote the resulting color texture descriptor by CEN-DMD. The flow chart of our proposed color texture representation method is shown in Fig. 5. The features of the color texture image include two parts, a local feature and global feature. The local features consist of maximum values of three local intrachannel features and the maximum values of three local interchannel features. Multi-resolution representation is achieved by selecting micro-blocks of different scales. We named the Extremely Nonnegative DMD (EN-DMD). Since EN-DMD ignores the global features of color texture images, we combine EN-DMD and global features into a Completed Extremely Nonnegative DMD (CEN-DMD), followed by Fisher Vector encoding. Finally, a linear SVM classifier is used to perform color texture classification. We will verify the effectiveness of our proposed method by performing a texture classification task in the following section.

IV. EXPERIMENTAL RESULTS
In this section, we perform color texture classification on five public color texture datasets to demonstrate the effectiveness of our proposed Completed Extremely Nonnegative DMD (CEN-DMD), and compared it with the other thirteen representative color texture classification methods. For local feature extraction of color texture images, we crop patches for computing local features in 2 pixel steps. The number of sampling points n in the patch is set to 80. The classification accuracy rate is calculated by 10-fold cross-validation.
In our experiments, five standard publicly available color texture datasets are used to verify the performance of our proposed CEN-DMD. The first one is Colored Brodatz as an extension of the original Brodatz from gray-scale to color texture image. It not only contains the rich texture features of the original Brodatz but also rich color information. We selected 40 representative texture classes from 112 texture classes in Colored Brodatz to verify the effectiveness of our proposed method. The samples of Color Brodatz are shown in Fig. 6, each 640 × 640 texture image is divided into 16 nonoverlapping samples of 160×160, which 8 samples are used for training and 8 samples for testing. The second is the VisTex texture dataset, which is a challenging dataset because it contains real-world texture images. In the experiment, we randomly select 40 texture classes. As shown in Fig. 7, each image of 512 × 512 is split into 16 nonoverlapping samples of 128 × 128, among which 8 images are used for training and 8 images for testing. The third is that CUReT contains 61 categories, which are composed of images taken various angles of view and illumination angles. The samples of CUReT are shown in Fig. 8. Each class contains 92 samples, of which 46 samples are used for training and the remaining 46 samples for testing. Because different illumination conditions can cause intra-class variation in appearance, it is a challenging texture dataset for classification. The third is that USPTex contains 191 classes of real-world texture images, each with 12 samples, as shown in Fig. 9, with 6 samples for training and 6 samples for testing. The last one is KTH-TIPS, as shown in Fig. 10, which consists of 10 texture categories, each with 81 samples, including changes in illumination, pose and scale. We used 40 samples for training and the remaining 41 samples for testing. The same classed are used for performing comparison with other color descriptors. The classification accuracy of all descriptors used in experiments is obtained through 10-cross validation.

A. PARAMETER SENSITIVITY INVESTIGATION AND PERFORMANCE EVALUATION 1) PATCH SIZE
In the process of micro-block difference modeling, the size of the patch and the size of the micro-block are interdependent.   If the size of patch is too small, it would lead to repetitive overlap of the micro-blocks, which will capture redundant and correlated features. On the other hand, if the size of patch is too large, the sampling of the micro-block would not insufficient, and the local structure of the texture cannot be effective captured. Therefore, the size of patch is varied from 9×9 to 15×15 with a step size of 2 and the micro-block size is varied from 1 to 5. In addition, the patch size is similar to the settings in the experiments in [42] and [43]. We test changes in experimental results for different parameters. The size of the patch is from 9 × 9 to 15 × 15 in steps of 2, and the size of the micro-block is from 1 × 1 to 5 × 5. The experiment is performed on the CUReT texture datset, and the experimental results are shown in Table 1. It can be seen from Table 1 that the classification accuracy rate almost increases with the increasing of the size of patches. The highest classification accuracy rate can almost be obtained when the patch size is

2) MULTIRESOLUTION ANALYSIS
The classification accuracy rate is different under different sizes of micro-blocks, so we can connect different sizes of micro-block to achieve multiresolution representation of texture. The number of sampling points in the patch is 80. When performing multiresolution representation, we connect the micro-block size from 1 × 1 to 5 × 5, which means that the number of micro-blocks per size is 16. We compare it to the single-scale micro-block size 5 × 5, and the experimental results on the four texture datasets are shown in Fig. 11. It is report that a single-scale and multi-scale comparison when the patch is 15 × 15. From the histogram, we can intuitively see that the multi-scale classification performance is better than the single-scale on the four different texture datasets of CUReT, VisTex, USPTex and KTH-TIPS. Especially on USPTex, the multi-scale classification accuracy rate is 1% higher than the single-scale classification accuracy rate. In summary, multiresolution analysis of color textures by connecting different sizes of micro-blocks can capture more detailed color texture information. Therefore, we select a multiresolution representation with a micro-block size from 1 × 1 to 5 × 5 in the following experiments.

3) NUMBER OF GAUSSIAN COMPONENTS
The Gaussian mixture model is used to fit the distribution of the original feature in the Fisher Vector. The number of Gaussian components is an important parameter in the Fisher Vector coding process. Similar to Mehta and Eguiazarian [42], in order to better fit the original features, we selected a different number of components from 16 to 128 and experimented on three texture datasets. The experimental results are shown in Table 2, the classification accuracy rate on the three datasets increases as the number of Gaussian components increases. According to the experimental results, we selected 128 Gaussian components in the Fisher Vector encoding process.

4) COLOR SPACE
In the following experiment, we investigate the sensitivity of color space to color texture classification performance. We test the classification performance of CEN-DMD on three VOLUME 8, 2020 texture datasets in three color space: RGB, HSV and YCbCr. The classification performance in different color space is shown in Fig. 12. Fig. 12 shows the classification of three texture datasets in different color spaces. This is because the classification accuracy in different color space on the CUReT, VisTex and USPTex datasets are quite different, which is more intuitive when displayed through histograms and is convenient for readers to read. However, the difference of classification accuracy in different color spaces is not obvious on the Colored Brodatz and KTH-TIPS datasets. Therefore, we choose the classification accuracy on the three datasets for display. Although the classification performance in the RGB color space on the VisTex texture dataset is not optimal, this may be because the heterogeneity of RGB color information of the sample picture in VisTex is weak, and thus the color distributions of picture in VisTex is relatively even. So the RGB color is not good for the VisTex dataset. The classification accuracy rate in the RGB color space on the CUReT and USPTex datasets are the best. In summary, we chose the RGB color space in the experiment.

B. EN-DMD VS CEN-DMD
As we have considered, the Extremely Nonnegative DMD (EN-DMD) extracts only the local features of intrachannel and the local features of interchannels in the color texture image, while ignoring the global features of the color texture image. To this end, we propose to combine the global features of the difference local features and the color texture image into a Completed Extremely Nonnegative DMD (CEN-DMD) for color texture analysis. We selected the patch size to be 5 × 5 and the micro-block size from 1 × 1 to 5 × 5 to compare the performance of EN-DMD and CEN-DMD on five texture datasets. The experimental results are shown in the histogram plotted in Fig. 13, and we can intuitively see that the classification performance of the color texture descriptor is not reduced after the global feature is added. The classification performance of EN-DMD and CEN-DMD on Colored Brodatz, USPTex and KTH-TIPS is comparable. The performance of CEN-DMD is slightly better on CUReT. Especially in the VisTex texture dataset, the classification result of CEN-DMD is significantly better than EN-DMD.
The CUReT texture dataset contains changes in texture image at different viewing and illumination. It can be seen from Table 3 that the classification accuracy rates of most of the comparison methods can reach 90%, and IOCLBP is the best one among the thirteen competitive methods. Compared with other classification methods, CEN-DMD has the highest classification accuracy rate on CUReT, which is about 1.5% higher than the IOCLBP. Colored Brodatz extends color information based on the original Brodatz's rich texture. It can be seen from Table 3 that the most methods can achieve higher classification accuracy rate. In comparison with these methods, the performance of CEN-DMD outweights these methods. VisTex is a challenging texture dataset that contains textures with real scenes. Among all the comparison methods, LCVBP performs best and the classification accuracy rate exceeds 79%. The experimental results of CEN-DMD on the VisTex texture dataset are superior to other comparison methods. The USPTex texture dataset consists of real-world textures, including gravel, grass, tiles, and more. It can be seen from Table 3 that the LBP + LCC performs best in the comparison methods, and the classification accuracy rate exceeds 95%, but it is still lower than CEN-DMD by about 5%. The KTH-TIPS texture dataset contains texture changes in scale and illumination. The CEN-DMD classification accuracy rate is over 2.5% higher than the other methods.
It can be seen from Table 3 that although the classification accuracy of our proposed EN-DMD and CEN-DMD are close, we can still see subtle advantage. On the VisTex texture dataset, the classification accuracy of CEN-DMD has a slight advantage. On the CUReT and USPTex, the variance of CEN-DMD is smaller. The classification accuracy and variance on the Colored Brodatz are same. On the KTH-TIPS, the classification accuracy of EN-DMD has a slight advantage, but the variance of the two methods is the same.
In order to demonstrate the effectiveness of our proposed method, we compare it with the last texture characterization method, SWOBP [57], on CUReT and KTH-TIPS texture datasets. The experimental results are shown in Table 4. It can be seen from the Table 4 that our proposed method outperforms SWOBP with three sampling radius by 1%. In addition, we compared with MICICM [58], [59] and GLCM_HSVCH [59], [60] on the more challenging texture dataset RawFoot. The RawFoot texture dataset consists of raw food samples such as meat, fish, grains and fruits, and contains changes in light direction, light source color and intensity. The RawFoot texture dataset used in the experiment contains all 69 texture classes, and each class consist 46 samples, of which 23 samples are used for training and 23 samples are used for testing. The size of each sample is 800 × 800 pixels. The experimental results are shown in Table 5. It can be seen from the Table 5 that the classification accuracy of our proposed CEN-DMD exceeds MICICM and GLCM_HSVCH on the RawFoot texture dataset. To sum up, our proposed CEN-DMD is effective and outperforms the other thirteen representative texture classification methods on the five publicly available color texture datasets.

D. COMPARISONS WITH ORIGINAL DMD
In this subsection, we compared the our proposed method with the original DMD [42] on CUReT and KTH-TIPS texture datasets. The experimental results are shown in the Table 6. It can be seen from the table 6, the classification accuracy of our proposed EN-DMD and CEN-DMD exceeds the original DMD. It is demonstrated that texture descriptor that consider color information are more discriminative than texture descriptor captured only on grayscale image. In this subsection, we compared the running time of different methods to extract one texture image feature by running MATLAB (R2014a) on a PC with Inter Core i5-7500 CPU and 8GB RAM. The experimental results are shown in Table 7. It can be seen from the Table 7 that the running time of our proposed CEN-DMD is only faster than Multilayer CCR. However, the classification performance of our proposed method is better.

V. CONCLUSION
In this paper, we propose a completed extremely nonnegative DMD (CEN-DMD) for color texture classification. CEN-DMD models the intrachannel information and interchannel information of color texture images by micro-block difference. In particular, during the difference process, we propose to nonnegative the difference features, and in order to capture the intrachannel and interchannel features simultaneously, the maximum of the intrachannel difference features and the maximum of the interchannel difference features are fused. Multiresolution representations of color texture are made by connecting micro-block difference features of different sizes. In addition, local micro-block difference features and global features of color texture are combined to construct CEN-DMD. Subsequently, the Fisher Vector is used to encode CEN-DMD to obtain a color texture descriptor. Finally, experimental results demonstrate that the proposed CEN-DMD outperforms the other thirteen representative color texture classification methods. MINGXIN