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Remote Sens. 2017, 9(10), 1085; https://doi.org/10.3390/rs9101085
Letter
MultiLayer Model Based on MultiScale and MultiFeature Fusion for SAR Images
^{1}
Key Laboratory of Computer Vision and System, Ministry of Education, Tianjin University of Technology, Tianjin 300384, China
^{2}
Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, China
^{3}
School of Computer Science and Technology, Tianjin University, Tianjin 300072, China
^{*}
Authors to whom correspondence should be addressed.
Received: 16 August 2017 / Accepted: 18 October 2017 / Published: 24 October 2017
Abstract
:A multilayer classification approach based on multiscales and multifeatures (ML–MFM) for synthetic aperture radar (SAR) images is proposed in this paper. Firstly, the SAR image is partitioned into superpixels, which are local, coherent regions that preserve most of the characteristics necessary for extracting image information. Following this, a new sparse representationbased classification is used to express sparse multiple features of the superpixels. Moreover, a multiscale fusion strategy is introduced into ML–MFM to construct the dictionary, which allows complementation between sample information. Finally, the multilayer operation is used to refine the classification results of superpixels by adding a threshold decision condition to sparse representation classification (SRC) in an iterative way. Compared with traditional SRC and other existing methods, the experimental results of both synthetic and real SAR images have shown that the proposed method not only shows good performance in quantitative evaluation, but can also obtain satisfactory and cogent visualization of classification results.
Keywords:
sparse representation classification (SRC); multilayer structure; multifeature fusion; multiscale; SAR image1. Introduction
Synthetic aperture radars (SAR) can obtain stable image data as we are observing the planet Earth. It is not affected by light conditions and can be used day and night under various conditions [1,2]. In recent years, SAR image classification has received more attention as an important part of image understanding and interpretation. A considerable number of image classification algorithms have been proposed, such as support vector machine (SVM) [3], neural network (NN) [4], wavelet decomposition, and sparse representation classification (SRC) [5], etc. Among these existing methods, the traditional SVM and NN methods show high reliability in pattern recognition. However, the relevant computation cost is expensive, and they are easily affected by the selection of features. SRC, which is based on sparse representation and was proposed by Mallat and Zhang [6], has been proven to be an extremely powerful tool in image processing and can obtain good performance in the final processing results [7,8,9,10,11,12,13,14,15].
The basic ideas of SRC are the linear description hypothesis and spatial joint representation mechanism. This is based on the minimum residual between the original and the reconstruction signal. The sparse coefficients associated with the different classes are selected to reconstruct the original signal. Actually, SRC cannot be directly applied to SAR image classification due to the imaging mechanisms of SAR being different to those of nature imagery. However, if an SAR image is transformed into a specific feature space, the SRC can be efficiently used in SAR image classification. A joint sparsity model (JSRM) is proposed based on SRC [16], in which the small neighborhood around the test pixel are represented by linear combinations of a few common training samples. Furthermore, the features cannot be represented well on a single scale, which results in the low accuracy of classification results. Neighboring regions of different scales correspond to the same test pixel and they should offer complementary and correlated information for classification. Different sizes of textures in an image have different performance in different scales. The hierarchical sparse representationbased classification (HSRC) [17] can solve the problem in a previous reference [16] to a certain extent, but the HSRC belongs to classification based on each pixel, which only depends on the selection of features in the spatial domain and the selected scale for each layer. This may lead to a loss or misrepresentation of information, resulting in poor classification accuracy and timeconsuming training requirements.
In this paper, aiming to overcome the abovementioned problems, we proposed a novel approach, which is called the multilayer with multiscale and multifeature fusion model (ML–MFM), for SAR image classification. This maintains high accuracy and robustness in addition to having reduced time requirements. Firstly, in order to fix the deficiency of using a single feature and to provide more textural and gray statistical level information [5,12,16], we extracted three types of features of a SAR image for different classes and different scales, which are respectively the graylevel histogram, graylevel cooccurrence matrix (GLCM), and Gabor filter [18,19,20,21]. In other words, a discriminative feature vector is composed of the graylevel histogram, GLCM and Gabor filter for each class, while the feature matrix is constructed by the column vector composed of discriminative feature vectors of all classes and row vectors composed of discriminative feature vectors of all scales. Moreover, motivated by the fusion of characteristics from multiple frames in reference [22], a multiscale fusion strategy was used to construct the dictionary. Thus, the extracted features under different scales can be merged together to construct the column vectors of the dictionary (see Figure 1), which can allow complementation between sample information and reduce the time complexity. Following this, we should segment an SAR image into a host of homogeneous regions called superpixels, with the structural information captured by a discriminative feature vector extraction for each superpixel. Finally, inspired by the idea of layers in the spatial pyramid in reference [21], the multilayer operation is utilized to refine the classification results by adding a threshold decision condition to SRC in an iterative way. If a superpixel meets the condition as the new atoms in the dictionary, the category is recorded. Otherwise, it will be used as the testing sample for the next layer (Figure 3 depicts the abovementioned basic framework). Compared with other methods, the final classification results of the proposed method have higher accuracy.
The remainder of this paper is organized as follows. In Section 2, we briefly review the SRC, while the procedure of our novel model regarding the use of ML–MFM for SAR image classification is explored. The experimental results for synthetic and real SAR images are presented and compared with others in Section 3. Comparison with the HSRC [17] and the major innovation points are provided in Section 4. Finally, conclusions are drawn and future research directions are described in Section 5.
2. Materials and Methods
2.1. SRC
We assume an SAR image contains $K$ classes. ${D}_{K}$ is the kth class of the subdictionary constructed by concatenating feature vectors of the kth class. We can define a dictionary $D$ constructed by $[{D}_{1},{D}_{2},\dots ,{D}_{K}]$ for an SAR image. The testing sample $y$ can be formulated by a series of training samples as follows:
where $\psi (\cdot )$ is an Eigen function which can be used to realize the transformation from pixel to feature space and $x=[0,\dots ,0,{x}_{i,1},\dots ,{x}_{i,{n}_{i}},0,\dots ,0]\in {R}^{n}$ is a sparse coefficient vector whose entries are zeros except those associated with the ith class. A sparse coefficient $x$ indicates that it will be easier to estimate the identity of the testing sample $y$. A sparse coefficient $x$ can be obtained by solving the following errorconstrained Equation (2) or the sparsityconstrained Equation (3):
where $\sigma $ is the error tolerant limit and $sl$ is the sparsity level which can represent the maximum number of selected atoms in the dictionary. Moreover, ${\Vert \cdot \Vert}_{0}$ and ${\Vert \cdot \Vert}_{2}$ denote ${l}_{0}$ and ${l}_{2}$ norms, respectively. Usually, the problem of solving sparse coefficients can be performed using the orthogonal matching pursuit (OMP) method [23].
$$y=\psi (y)=Dx\in {R}^{M}$$
$$\widehat{x}=\mathrm{arg}\mathrm{min}{\Vert x\Vert}_{0}\text{}\mathrm{subject}\text{}\mathrm{to}\text{}{\Vert yDx\Vert}_{2}\le \sigma $$
$$\widehat{x}=\mathrm{arg}\mathrm{min}{\Vert yDx\Vert}_{2}\text{}\mathrm{subject}\text{}\mathrm{to}\text{}{\Vert x\Vert}_{0}\le sl$$
After obtaining the sparse coefficient $\widehat{x}$, the class label $\widehat{k}$ of the test pixel $y$ can be determined by the minimal error between $y$ and its approximation from the subdictionary of each class:
where ${\widehat{x}}_{k}$ represents the coefficients in $\widehat{x}$ belonging to the kth class. In order to demonstrate the drawback of the SRC algorithm clearly, a simple experiment was performed on two real SAR images (the original SAR image is in Figures 10a and 12a), observed in Figure 2. We can see that the final SRC results are unacceptable from Figure 2a,b. This is mainly because the SRC algorithm extracts features of SAR images only by using the pixelbypixel method, resulting in a lack of complementation between sample information. Therefore, to solve this problem, superpixels and more complete features need to be taken into account.
$$\widehat{k}=\mathrm{arg}\underset{k}{\mathrm{min}}{\Vert yD{\widehat{x}}_{k}\Vert}_{2},\text{}k=1,\dots ,K$$
2.2. Proposed MultiLayer and MultiFeature Model (ML–MFM)
In this section, the multilayers and multifeature model (ML–MFM) based on the SRC algorithm is proposed. The basic framework of the proposed method is shown in Figure 3.
Figure 3 can be understood in four parts: superpixel generation, multifeature extraction, multiscale with fusion strategy and multilayer sparse representation classification. In the first stage, the oversegment algorithm is used. The initialization dictionary is subsequently used in different scales, before being fused by the fusion strategy, which is introduced in Section 2.2.2. The first classification is performed using the initialization dictionary and the superpixels. Finally, SRC is used in multilayers through iterations to obtain the final result.
2.2.1. Multilayer SRC
There are some difference between SAR image classification and face recognition, the training samples of which can be controlled by a human in a standard data set. SAR images contain various complex terrains. It is difficult to guarantee enough training samples to represent each pixel. To deal with the challenge, reference [17] developed a hierarchical sparse representation classifier to improve the classification of the SAR image, which we called the multilayer SRC.
In this classifier, $h\text{}(1\le h\le H)$ represents the layer of classification. Sparse representation is used for each layer. Thus, we performed sparse representation $h$ times. As the number of layers $h\text{}(1\le h\le H)$ increases, the classification map becomes closer to the final result. Finally, the number of $h$ is analyzed in Section 3.1.
2.2.2. Multiscale FusionBased Dictionary
In the application of sparse representation, a dictionary is first constructed. To counter the existence of speckle and the complex appearance in the SAR image, we transform the pixel value space into a feature space, which reduces the computational complexity and extracts the discriminative features from the SAR image. The graylevel histogram, GLCM and Gabor filter features are extracted to capture statistical properties in the SAR image. We concentrated on these three types of features to form a feature vector for representing each pixel or superpixel. This nonlinear feature will provide competitive performance by representing statistical information and capturing texture information in adjacent areas.
Moreover, different texture features of images show different performances in different scales [24]. In the classification of the image, many experiments have proved that different scales correspond to the same test sample $y$. The information from different scales complements each other, which is useful to classify each pixel.
We selected ${n}_{i}$ vectors of the lth scale training samples from the ith class in the hth layer as columns to construct a matrix ${A}_{i,l}^{h}=[{f}_{i,l,1}^{h},{f}_{i,l,2}^{h},\dots ,{f}_{i,l,{n}_{i}}^{h}]\in {R}^{m\times {n}_{i}}$, where $m$ denotes the dimension of the extracted feature vector. Scale $l$ means the scale sizes $(2l+1)\times (2l+1)$ of the extracted features. Therefore, $l=1$ is the finest scale and $l=L$ is coarsest scale, which depends on the resolution of the image. This can be calculated by $L=floor(resolution*3/2)$. We constructed a matrix by the concatenation of the ${n}_{i}$ training sample vectors of all $K$ defined classes and all $L$ scales in the fixed hth layer as follows:
$${A}^{h}=\left[\begin{array}{cccc}{A}_{1,1}^{h}& {A}_{1,2}^{h}& \cdots & {A}_{1,L}^{h}\\ {A}_{2,1}^{h}& {A}_{2,2}^{h}& \cdots & {A}_{2,L}^{h}\\ \vdots & \vdots & \cdots & \vdots \\ {A}_{K,1}^{h}& {A}_{K,2}^{h}& \cdots & {A}_{K,L}^{h}\end{array}\right]$$
Following the dictionary ${D}^{h}$ in the fixed hth layer is defined by row element using the average fusion strategy in matrix ${A}^{h}$. This is shown as follows:
$${D}^{h}=\left[\begin{array}{c}{D}_{1,fusion}^{h}\\ {D}_{2,fusion}^{h}\\ \vdots \\ {D}_{K,fusion}^{h}\end{array}\right]\stackrel{{D}_{i,fusion}^{h}=\frac{1}{{n}_{1}+{n}_{2}+\cdots +{n}_{L}}{\displaystyle \sum _{l=1}^{L}{\displaystyle \sum _{j=1}^{{n}_{L}}{f}_{i,l,j}^{h}}}}{\leftarrow}\left[\begin{array}{cccc}{A}_{1,1}^{h}& {A}_{1,2}^{h}& \cdots & {A}_{1,L}^{h}\\ {A}_{2,1}^{h}& {A}_{2,2}^{h}& \cdots & {A}_{2,L}^{h}\\ \vdots & \vdots & \cdots & \vdots \\ {A}_{K,1}^{h}& {A}_{K,2}^{h}& \cdots & {A}_{K,L}^{h}\end{array}\right]={A}^{h}$$
2.2.3. MultiLayer and MultiFeature Model
It is wellknown that pixels are not natural entities but a result of the discrete representation of an image, with structural information captured in a region rather than a pixel. Furthermore, the computational complexity increases rapidly with an increase in the scale of pixels used. Therefore, we first divided the SAR image into superpixels to integrate the contextual information of neighboring pixels and to reduce computational complexity. In our method, the operation of superpixel generation uses the TurboPixel algorithm [25]. Furthermore, in order to encode gray, textural and spatial information into superpixels, we described each superpixel $s{p}_{t}\in sp=\left\{s{p}_{t}1\le t\le N\right\}$ by a $m$ dimensional feature vector ${f}_{s{p}_{t}}=[{f}_{t,1},{f}_{t,2},\dots ,{f}_{t,m}]$, in which $N$ is the maximum number of superpixels.
Unlike other recognition methods, SAR image classification lacks training samples to effectively represent each pixel. To deal with the challenge, inspired by the idea of the hierarchical sparse representation [17], we proposed a multilayer operation based on SRC and the multifusion scale dictionary for SAR image classification.
Based on dictionary construction and the superpixel $s{p}_{t}$, we used Equation (2) with the ${l}_{0}$ norm to ensure a sparse solution. The sparse coefficient can be solved by OMP to obtain $\widehat{x}$. We define the hth layer of the minimum residual error and class as Equations (7) and (8), respectively.
where the ${res}_{i}^{h}(\psi (s{p}_{t}))$ is the residual error in the hth layer under the fusion scale; ${r}^{h}$ is the minimum residual error; and ${c}^{h}$ is the category of $s{p}_{t}$. Different from Equation (4), we introduce a parameter $\Delta \mathrm{T}$ as the threshold value to limit the superpixel and judge whether it belongs to this class instead. If the ${r}^{h}$ is within the specified tolerance limit, the pixel belongs to the current class $i$. Otherwise, the uncertain samples are classified again in the next layer. Following this, the class of superpixels in hth ($1\le h<H1$, where $H$ is layer number) layer are expressed as:
where ${r}^{h}\le \Delta \mathrm{T}$ is a restricted condition to ensure that the superpixel belongs to the category. In fact, the choice of the threshold value $\Delta \mathrm{T}$ will influence our final results to some extent and it will be further discussed in Section 3.1.
$${r}^{h}={res}_{\mathrm{min}}^{h}(\psi (s{p}_{t}))=\underset{i=1,\dots ,K}{\mathrm{min}}{res}_{i}^{h}(\psi (s{p}_{t}))$$
$${\widehat{k}}^{h}=\mathrm{arg}\underset{i}{\mathrm{min}}{\Vert \psi (s{p}_{t}){D}^{h}{\widehat{x}}_{i}\Vert}_{2},i=1,2,\dots ,K$$
$$label(s{p}_{t})=\{\begin{array}{c}\mathrm{arg}\underset{i}{\mathrm{min}}{\Vert \psi (s{p}_{t}){D}^{h}{\widehat{x}}_{i}\Vert}_{2},i=1,2,\dots ,K;{r}^{h}\le \Delta \mathrm{T}\\ uncertain,\text{\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}}otherwise\end{array}$$
The uncertain superpixels in the (h + 1)th ${A}_{i}^{h}=[{f}_{i,1}^{h},{f}_{i,2}^{h},\dots ,{f}_{i,{n}_{i}}^{h}]\in {R}^{m\times {n}_{i}}$ $(1\le h<H)$ layer will be classified by Equations (7)–(9). We selected superpixels from each class, which are labeled as the new training samples in the hth layer. Following this, we extract the feature vector at the hth layer. Arranging these vectors as the columns vector ${A}_{sp}^{h}=[{A}_{1}^{h},{A}_{2}^{h},\dots ,{A}_{K}^{h}]$, we define the dictionary ${D}^{(h+1)}$ in the fixed (h + 1)th layer based on the dictionary ${D}^{h}$ in the fixed hth layer.
$${D}^{(h+1)}=\left[\begin{array}{c}{D}_{1,fusion}^{(h+1)}\\ {D}_{2,fusion}^{(h+1)}\\ \vdots \\ {D}_{K,fusion}^{(h+1)}\end{array}\right]=Average\left(\left[\begin{array}{c}{D}_{1,fusion}^{h}\\ {D}_{2,fusion}^{h}\\ \vdots \\ {D}_{K,fusion}^{h}\end{array}\right],\left[\begin{array}{c}{A}_{1}^{h}\\ {A}_{2}^{h}\\ \vdots \\ {A}_{K}^{h}\end{array}\right]\right)=Average({D}^{h},{A}_{sp}^{h})$$
In fact, the uncertain superpixels decrease with an increase of layers. When $h=H$, there is still a small number of uncertain points (marked by yellow in Figure 3). However, the dictionary ${D}^{H}$ is modified by Equation (10), before the remaining pixels will be classified by a traditional sparse representation classifier until it outputs the final result. The whole ML–MFM for the SAR image classification algorithm is summarized as follows:
Algorithm 1. ML–MFM for synthetic aperture radar (SAR) Image Classification 
Input: SAR image, threshold $\Delta \mathrm{T}$, class number $K$, layer $H$. 
Output: classification map. 
1. Segment the SAR image into superpixels by [25]. 
2. Construct the initial fusion dictionary ${D}^{1}$ by Equations (5) and (6), while the fusion dictionary contains $K$ class, ${D}^{1}=[{D}_{1,fusion}^{1},{D}_{2,fusion}^{1},\dots ,{D}_{K,fusion}^{1}]$. Choosing a specified number of pixels ${n}_{i}$ from the original SAR image as the samples, each sample can be represented by the $m$ dimension extracted variety of features. 
3. Multilayer SRC and dictionary in layers are constructed. 


while $1\le h\le H$ 
if ${r}^{h}\le \Delta \mathrm{T}$ 
$\underset{i}{\mathrm{min}}{res}_{i}^{h}(\psi (s{p}_{t}));$ 
$label(s{p}_{t})\leftarrow i;$ 
updating dictionary by (10) 
${D}^{(h+1)}=Average({D}^{h},{A}_{sp});$ 
else $uncertain({s{p}_{t}}^{h})\leftarrow s{p}_{t}=\psi (s{p}_{t});$ 
$h\leftarrow h+1$; 
end while 
3. Results
In this section, the proposed model is now applied in the classification of synthetic and real SAR images. To validate the performance of the proposed method, we use both types of images in quantitative evaluation and visualization results. We mainly compare our results with the results of previous studies [3,5,16,17], in which their parameters are tuned to obtain the best results. Figures 8a, 9a and 10a are the synthetic SAR images, which are from the Brodatz database. These synthetic SAR images have three, four and five types of different textural regions, while the size of each image is 512 × 512, 335 × 335, and 512 × 512, respectively. The test images are named Syn1, Syn2 and Syn3, respectively. In addition, three real SAR images (SAR1, SAR2 and SAR3) were tested in experiments. SAR1 has a size of 256 × 256, which covers the China Lake Airport, California, with a KuBand radar with a 3m resolution. SAR2 has a size of 321 × 258, which covers the pipeline over the Rio Grande river near Albuquerque, New Mexico, with a KuBand radar with 1m resolution. SAR3 has a size of 284 × 284, which covers the XBand radar with 3m resolution. The central processing unit time was obtained by running the Matlab code on a DELL computer with Inter (R) Core (TM) i7CPU, 3.4 GHz, 16 GB RAM with MATLAB 2014(a) on Windows 10 (64bit operating system) in our experiment.
3.1. Experimental Settings
In the experiment, we used the TurboPixel [25] algorithm to oversegment the original image into homogeneous regions and to obtain the superpixels. As each superpixel has different sizes, the features of each superpixel need to be processed so that the fusion features of all superpixels have the same dimensions (i.e., m = 60 in our method). Sixteen effective distribution features and four statistical features suggested by a previous study [17] were used. Thus, the features extracted by graylevel histogram and GLCM have 16 dimensions and four dimensions for each superpixel, respectively. After calculating the convolution of the initial bank of Gabor filters, which consists of 40 filters with five scales and eight orientations, the mean value of the filter response corresponding to each superpixel was computed for every filter. Therefore, the Gabor feature of each superpixel was a 40dimension vector corresponding to 40 Gabor filters with the total number of dimensions being 60. In addition, the ranges of the radial basis function kernel width and penalty coefficients are (0.0001, 0.001, 0.01, 0.1, 1, 10) and (0.1, 1, 10, 100, 500, 1000) respectively.
3.1.1. Influence of Parameters
It is necessary to set ideal parameters to obtain satisfactory results. There are two main parameters that need to be set in our model, namely $H$ and $\Delta \mathrm{T}$ (threshold). Based on plenty of experimental data and the analysis of results, each parameter should satisfy the following condition: $1\le H\le 6$, $0.07\le \Delta \mathrm{T}\le 0.24$. We noted that the parameter $H$ is influenced by the resolution of the SAR images (similar to a previous reference [17]), as mentioned in Section 2.2. We used an experiment to show the influence of $H$, which is depicted in Figure 4. The horizontal axis represents the layer $h$, while the vertical axis represents a certain superpixel number. Here, we artificially set the total superpixel number to 1000 of SAR1. From Figure 4, it is more intuitive to find the most suitable layer range. This is because when $H>6$, the speed of the growth of certain points slow significantly in histogram and line chart. In many experiments, if we set $H=6$ as the maximum number of layers, it is the best choice with regards to time and precision. In addition, it is worth noting that $\Delta \mathrm{T}$ is the threshold to control the categories of accuracy (blue solid line) and the kappa coefficient (green dotted line) with our proposed method. From Figure 5, we can see that when $\Delta \mathrm{T}$ is too small, there are many uncertain superpixels until $h=H$. However, when $\Delta \mathrm{T}$ is too large, the finer areas cannot be placed into classes. Therefore, appropriate parameter selection is very important.
3.1.2. Analysis of MultiFeature Fusion and MultiScale Fusion
MultiFeature Fusion
In this part, the multifeature fusion is analyzed to verify its effectiveness in obtaining satisfactory results. In our paper, the fusion strategy is introduced to construct the dictionary. We perform an experiment on the original SAR1 (Figure 6a) to show the influence of multifeature fusion on the dictionary and the impact of classification results. The rectangular areas of Figure 6a–e are marked by red, yellow and green, respectively. Figure 6b shows the results of the method with the graylevel histogram; Figure 6c shows the results of the GLCM; Figure 6d shows the results of the Gabor method; and Figure 6e shows the results of the multifeatures method. We can see that Figure 6e has fewer miscellaneous points than Figure 6b–d. The reason is that the fusion features includes distribution features and four statistical features. Therefore, the dictionary ${D}^{h}$ includes more information to obtain better results, which is an advantage that is absent in the method with single features. Therefore, the multifeature fusion strategy is important.
MultiScale Fusion
In this part, multiscale fusion is analyzed to verify its effectiveness in obtaining satisfactory results. In our paper, the fusion strategy is introduced to construct the dictionary. We perform an experiment on the original SAR1 (Figure 7a) to show the influence of the fusion strategy on the dictionary after merging features under different scales. The rectangular areas of Figure 7b,c are both marked by red, yellow and green. Figure 7b shows the results method with the fusion strategy; Figure 7c shows the results method without the fusion strategy. We can see that Figure 7b has fewer miscellaneous points than Figure 7c. The reason for this is that the fusion dictionary ${D}^{h}$ includes each scale information (homogeneous and marginal regions). This has similar effects on the dictionary under multiscales, which are absent in the method without the fusion dictionary and are important to SAR image processing. Therefore, the multiscale fusion strategy is important.
3.2. Results on Synthetic SAR Images
In this section, we test the capability of the proposed algorithm by applying it to the synthetic SAR images Syn1, Syn2, and Syn3. The superpixels of Syn1, Syn2, and Syn3 are 2800, 1500 and 2800, respectively. In our method, $H=6$ and $\Delta \mathrm{T}$ is 0.221. The scale (patch) size in the support vector machine (SVM) [3], SRC [5] and JSRM [16] is fixed and we set it to be 3 × 3. The ground truth was used to calculate the accuracy of the classification results to evaluate the contrast algorithms. We can see that the proposed method can obtain a higher accuracy of classification than the results of previous studies [3,5,16] and can reduce the processing time found in reference [17]. Moreover, as shown Figure 8, Figure 9 and Figure 10, as well as Table 1, the proposed method can keep the details (edges) in a similar way to reference [17] in the visual representation. However, the results of the other methods in finer textural regions (marked with pink and yellow), such as Figure 9e–g, have significantly different degrees of error, which is caused by the lack of samples. Although our method has no significant improvement in accuracy compared to the method in reference [17], there are benefits to not requiring an extensive amount of time in pixelbypixel training and having less miscellaneous points existing in the final classification.
3.3. Results of Real SAR Images
In this section, three real SAR images are used for further analysis. The compared methods are the same as those used on synthetic SAR images. The results are shown in Figure 11, Figure 12 and Figure 13. These original real images have three, three and four types of different regions as shown in Figure 11b, Figure 12b and Figure 13b, respectively. The superpixels of SAR1, SAR2 and SAR3 are 1000, 1200 and 1100 as shown in Figure 11b, Figure 12b and Figure 13b, respectively. The evaluation of the classification method is based on the visual inspection of the classification and the run time, accuracy, as well as the kappa coefficient. The scale in SVM, SRC and JSRM is set to 7 × 7, which represents the best result in the experiments.
From Figure 11c–g, we can see that the proposed method can achieve the classification in different areas and eliminate the influence of shadows, which always leads to categories by mistake. However, when we compare Figure 11c with 11g, it is difficult to know whether our proposed method is better, as it seems that Figure 11g [17] has better visualization results, albeit with some miscellaneous points. Therefore, the accuracy of the quantitative analysis is required for further analysis. From Table 2, it can be seen that the accuracy of the previous study [17] is only slightly higher than our proposed method, but the required running time is too long, as previously seen with synthetic SAR images.
From Figure 12c–g, we can see the classification results of different methods, especially in the yellow and red rectangle regions. The yellow and red rectangles of the proposed method in Figure 12c have less miscellaneous points than Figure 12d–f. In general, a smaller number of miscellaneous points indicates a more complete extraction of information and a more stable performance of the algorithm. The different rectangle regions highlight the superiority of the proposed algorithm. However, when we compare Figure 12c with 12g, it is difficult to know whether our proposed method is better, as it seems that Figure 12g [17] has better visualization results, albeit with some miscellaneous points. Therefore, data analysis was used (accuracy, run time and kappa coefficient) for further analysis. From Table 2, it can be seen that the accuracy of the previous method [17] is only slightly higher than our proposed method, but the required running time was too long, as previously seen with synthetic SAR images.
The analysis of Figure 13 is similar to Figure 11 and Figure 12. From Figure 11, Figure 12 and Figure 13, the proposed method is shown to be suitable for the SAR image classification and obtains the optimal results. Table 2 provides the quantitative evaluation of different methods. Although the HSRC obtains higher classification accuracy compared with the others, the running time is too long among the different methods. Our method has the absolute advantage in the running time, with competitive accuracy that is only slightly lower than HSRC. Moreover, our method gets the highest robustness, which is reflected by the kappa coefficient. Above all, our method outperforms the others in terms of time consumption and robustness.
4. Discussion
Traditional SVM [3] is limited by lacking samples, which results in low classification accuracy. For instance, the number of training samples is 300, which is 0.46% of the total samples. Fewer samples affect the selection of optimal parameters by SVM for the testing samples, which will decrease the classification accuracy. In the sparse representation method, the HSRC [13] can solve the problem of reference [16] to a certain extent. It introduces the hierarchical concept and multisize patch feature to solve the problem of lacking samples. Using SRC in SAR classification for both these methods improves the accuracy and stability. However, HSRC classifies images based on each pixel, which only depends on the selection of features in the spatial domain and the selected scale for each layer. This may lead to the loss or misrepresentation of information, which requires a long time for training.
In our paper, we inherit the advantages of reference [17], such as multilayer. However, the difference is the multiscale and multifeature fusion. In the multifeature fusion stage, we take three different methods to extract the gray and texture characteristics, which are stable in the presence of noise and changes in view, and can enrich the information of images. Moreover, the strategy of the multifeature fusion was inspired by [23], which fused the different features from multiple layers. We fused the different features from different scales. This reduces the computational time and ensures a rich amount of information. Furthermore, classification based on superpixels can improve the speed of algorithms effectively. Three evaluation metrics (i.e., run time (time), average accuracy (AA) and the Kappa coefficient (K)) are adopted in these experiments to evaluate the quality of classification results. AA represents the mean of the percentage of correctly classified pixels for each class. K estimates the percentage of classified pixels corrected by the number of agreements. We performed comparative experiments with four other methods. The proposed method can solve the time redundancy problem of HSRC, but has its uncertainties. For instance, the uncertain points are always in the process of the algorithm until $h=H$. That is the reason we use the traditional SRC (this step is same as reference [17]) in the last step.
5. Conclusions
In this paper, based on superpixels, we presented a new model of classification of SAR images. It validates that adding multiple features, scales and layers can benefit the results of SRC classification and enrich the information of the images. Furthermore, using multiple layers can decrease the computational time due to the use of superpixels. The fusion strategy was introduced to merge each scale together to form a multifusion dictionary. With the added benefits, robustness was enhanced and the classification accuracy was improved significantly. The comparison experiments based on synthetic SAR images and real SAR images clearly demonstrate the efficiency and advantages of the proposed classification method. Moreover, the proposed classification method is also able to achieve lower computational costs. These added benefits are general for SAR image classification, and can be suitable for utility in more applications in the area of SAR image classification, as well as in other areas where the SRC method could be applied.
This method provides a slight improvement in calculation time for SAR image classification and application. Moreover, future research will focus on developing more efficient algorithms to cope with the largescale SAR images.
Acknowledgments
This work is supported by National Natural Science Foundation of China (No. 61472278 and 61102125). The author would like to thank numerous colleagues for their contribution to this work and three reviewers and editors for improving the manuscript.
Author Contributions
This work was prepared and accomplished by Aobo Zhai, who also wrote the manuscript. Xianbin Wen outlined the research and supported the analysis. He also revised the work in presenting the technical details. Liming Yuan, Haixia Xu both suggested the design of comparison experiments and supervised the writing of the manuscript at all stages. Qingxia Meng provided writing suggestions.
Conflicts of Interest
The authors declare no conflict of interest.
References
 Oliver, C.; Quegan, S. Understanding Synthetic Aperture Radar Images; SciTech Publishing: Raleigh, NC, USA, 2004. [Google Scholar]
 Adragna, F.; Nicolas, J. Processing of Synthetic Aperture Radar Images; Wiley: New York, NY, USA, 2010. [Google Scholar]
 Akbarizadeh, G. A new statisticalbased kurtosis wavelet energy feature for texture recognition of SAR images. IEEE Trans. Geosci. Remote Sens. 2012, 50, 4358–4368. [Google Scholar] [CrossRef]
 Xue, X.R.; Wang, X.J.; Xiang, F.; Wang, H.F. A new method of SAR image segmentation based on the gray level cooccurrence matrix and fuzzy neural network. In Proceedings of the IEEE 6th International Conference Wireless Communications Networking and Mobile Computing, Chengdu, China, 23–25 September 2010. [Google Scholar]
 Wright, J.; Yang, A.Y.; Sastry, S.S.; Ma, Y. Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 2009, 31, 210–227. [Google Scholar] [CrossRef] [PubMed]
 Mallat, S.G.; Zhang, Z. Matching pursuits with timefrequency dictionaries. IEEE Trans. Signal Process. 1993, 41, 3397–3415. [Google Scholar] [CrossRef]
 Elad, M.; Aharon, M. Image Denoising Via Sparse and Redundant Representations over Learned Dictionaries. IEEE Trans. Image Process. 2006, 15, 3736–3745. [Google Scholar] [CrossRef] [PubMed]
 Buades, A.; Coll, B.; Morel, J.M. A NonLocal Algorithm for Image Denoising. In Proceedings of the IEEE Conference Computer Vision Pattern Recognition, San Diego, CA, USA, 20–26 June 2005. [Google Scholar]
 Yue, C.; Jiang, W. An algorithm of SAR image denoising in nonsubsampled contourlet transform domain based on maximum a posteriori and nonlocal restriction. Remote Sens. Lett. 2013, 4, 270–278. [Google Scholar] [CrossRef]
 Fang, L.Y.; Li, S.T.; Mcnabb, R.P.; Nie, Q.; Kuo, A.N.; Toth, C.A.; Izatt, J.A.; Farsiu, S. Fast Acquisition and Reconstruction of Optical Coherence Tomography Images via Sparse Representation. IEEE Trans. Med. Imaging 2013, 32, 2034–2049. [Google Scholar] [CrossRef] [PubMed]
 Li, S.; Yin, H.; Fang, L. Remote Sensing Image Fusion via Sparse Representations over Learned Dictionaries. IEEE Trans. Geosci. Remote Sens. 2013, 51, 4779–4789. [Google Scholar] [CrossRef]
 Xiang, D.; Tang, T.; Hu, C.; Li, Y.; Su, Y. A kernel clustering algorithm with fuzzy factor: Application to SAR image segmentation. IEEE Geosci. Remote Sens. Lett. 2011, 7, 1290–1294. [Google Scholar]
 Wang, W.; Xiang, D.; Ban, Y.; Zhang, J.; Wan, J. Superpixel Segmentation of Polarimetric SAR Images Based on Integrated Distance Measure and Entropy Rate Method. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2017, 99, 1–14. [Google Scholar] [CrossRef]
 Liu, B.; Hu, H.; Wang, H.; Wang, K.; Liu, X.; Yu, W. SuperpixelBased Classification with an Adaptive Number of Classes for Polarimetric SAR Images. IEEE Trans. Geosci. Remote Sens. 2013, 51, 907–924. [Google Scholar] [CrossRef]
 Zhang, X.; Wen, X.; Xu, H.; Meng, Q. Synthetic aperture radar image segmentation based on edgeregion active contour model. J. Appl. Remote Sens. 2016, 10, 036014. [Google Scholar] [CrossRef]
 Chen, Y.; Nasrabadi, N.M.; Tran, T.D. Hyperspectral Image Classification Using DictionaryBased Sparse Representation. IEEE Trans. Geosci. Remote Sens. 2011, 49, 3973–3985. [Google Scholar] [CrossRef]
 Hou, B.; Ren, B.; Ju, G.; Li, H.; Jiao, L.; Zhao, J. SAR Image Classification via Hierarchical Sparse Representation and Multisize Patch Features. IEEE Geosci. Remote Sens. Lett. 2016, 13, 33–37. [Google Scholar] [CrossRef]
 Swain, M.J.; Ballard, D.H. Color indexing. Int. J. Comput. Vis. 1991, 7, 11–32. [Google Scholar] [CrossRef]
 Haralick, R.M.; Shanmugam, K.; Dinstein, I. Textural Features for Image Classification. IEEE Trans. Syst. Man Cybern. 1973, 3, 610–621. [Google Scholar] [CrossRef]
 Yan, X.; Jiao, L.; Xu, S. SAR image segmentation based on Gabor filters of adaptive window in overcomplete brushlet domain. In Proceedings of the 2nd AsianPacific Conference on Synthetic Aperture Radar, Xi’an, China, 26–30 October 2009. [Google Scholar]
 Gu, J.; Jiao, L.; Yang, S.; Liu, F.; Hou, B.; Zhao, Z. A Multikernel Joint Sparse Graph for SAR Image Segmentation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2016, 9, 1265–1285. [Google Scholar] [CrossRef]
 Zhao, S.; Liu, Y.; Han, Y.; Hong, R.; Hu, Q.; Tian, Q. Pooling the Convolutional Layers in Deep ConvNets for Video Action Recognition. IEEE Trans. Circuits Syst. Video Technol. 2015, 1. [Google Scholar] [CrossRef]
 Tan, M.; Tsang, I.W.; Wang, L.; Zhang, X. Convex Matching Pursuit for Largescale Sparse Coding and Subset Selection. In Proceedings of the AAAI Conference on Artificial Intelligence, Toronto, ON, Canada, 22–26 July 2012. [Google Scholar]
 Mo, X.; Monga, V.; Bala, R.; Bala, R.; Fan, Z.G. Adaptive Sparse Representations for Video Anomaly Detection. IEEE Trans. Circuits Syst. Video Technol. 2013, 24, 631–645. [Google Scholar]
 Levinshtein, A.; Stere, A.; Kutulakos, K.N.; Fleet, D.J.; Dickinson, S.J.; Siddiqi, K. TurboPixels: Fast Superpixels Using Geometric Flows. IEEE Trans. Pattern Anal. Mach. Intell. 2009, 31, 2290–2297. [Google Scholar] [CrossRef] [PubMed]
Figure 2.
Classification results with the sparse representation classification (SRC) algorithm of a previous study [5] on (a) SAR1 and (b) SAR2.
Figure 4.
Illustration of certain and uncertain superpixels with different layers corresponding to SAR1 (Figure 7a) in our method (the total number of superpixels is 1000).
Figure 5.
Influence of threshold $\Delta \mathrm{T}$ in classification accuracy (blue solid line) and Kappa coefficient (green dotted line) corresponding to SAR1 (Figure 7a).
Figure 6.
Comparison of (a) the original SAR1 with (b) graylevel histogram; (c) graylevel cooccurrence matrix (GLCM); (d) with Gabor; (e) with multifeatures.
Figure 7.
Comparison of (a) the original SAR1 (b) with fusion strategy; and (c) without fusion strategy.
Proposed Method  SVM [3]  SRC [5]  JSRM [16]  HSRC [17]  

SAR Image  Accuracy  Time  Accuracy  Time  Accuracy  Time (s)  Accuracy  Time  Accuracy  Time 
Syn1  98.79  120.32  80.35  51.88  76.38  101.37  91.73  161.37  98.89  230.59 
Syn2  97.76  103.96  88.73  54.89  80.83  85.74  94.78  137.49  98.12  201.14 
Syn3  96.04  124.48  73.29  48.14  70.86  106.84  89.14  153.26  96.24  243.32 
Proposed Method  SVM [3]  SRC [5]  JSRM [16]  HSRC [17]  

SAR Image  Accuracy  Time  Accuracy  Time  Accuracy  Time  Accuracy  Time  Accuracy  Time 
SAR1  96.18  102.38  89.79  48.68  85.38  98.67  93.67  147.73  96.20  238.95 
SAR2  97.57  121.35  87.68  43.19  87.33  99.24  92.48  139.58  97.62  253.48 
SAR3  97.52  124.41  83.59  51.94  79.96  102.68  91.04  160.36  96.74  258.72 
AA ^{1}  97.42  87.02  84.22  92.40  97.83  
K ^{2}  0.961  0.713  0.806  0.941  0.959 
^{1} AA is average accuracy; ^{2} K is kappa coefficient.
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