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1.IntroductionDue to the active coherent microwave imaging mechanism, synthetic aperture radar (SAR) provides high-resolution images independent from daylight, cloud coverage, and weather conditions.1 Nowadays, SAR images have become a regular and powerful information sources for many applications, including environmental monitoring, terrain classification, etc. However, the interpretation of SAR images is still a challenging task because of their special imaging mechanism. In recent years, superpixel-based methods have attracted increasing attention for SAR image understanding. The basic concept of superpixel was first presented by Ren and Malik2 as the local coherent regions using an oversegmentation algorithm. As superpixels group the pixels with similar characteristics into meaningful atomic regions, they can effectively capture image features and well adhere to object boundaries. Therefore, superpixels can achieve a better perceptual representation of images than pixels, as well as reduce the complexity of subsequent image processing tasks, such as segmentation, classification, object detection, and so on. Until now, most of the superpixel generation methods for SAR images with promising performance are specially tailored from the ones proposed in the computer vision community, such as normalized cut,3 turbopixels,4 simple linear iterative clustering (SLIC),5 etc. Normalized cut is the most classical algorithm;it treats image segmentation as a graph partitioning problem and globally minimizes the segmentation cost. However, the high computational complexity has limited the wide applicability of this algorithm. Turbopixels is an effective method for generating superpixels, and it has been applied for SAR image analysis in much research.6,7 It gradually dilates regularly distributed seeds using geometric flows and poses strong constraints on the uniformness and compactness of superpixels. Meanwhile, due to the stability and efficiency issues of the underlying level-set method, the generated superpixels present relatively lower adherence to boundaries,8 and computational results show that it runs relatively slower on real-world datasets than the other superpixel algorithms.5,9 On the contrary, SLIC5 has been widely used in SAR images because of its simple concept, easy implementation, and high efficiency in practice. SLIC assigns each pixel to a cluster of the nearest seed and iteratively updates the cluster center by computing a pixel-to-cluster distance measure. However, in the original SLIC, this measure is obtained using five-dimensional (5-D) Euclidean distance in space,5 which cannot be applied directly on SAR images due to the multiplicative speckle noise. Thus, some alternative distance measures have been proposed in the last few years. For instance, Xiang et al.10 used a distance based on pixel intensity and location similarity for SAR images that is derived from the Nakagami–Rayleigh distribution and pixel intensity ratio. Zou et al.11 combined the generalized gamma distribution-based likelihood value with spatial distance to represent the pixel-to-cluster similarity. Yu et al.12 proposed a distance of two patches based on the likelihood ratio test statistic following the exponential distribution and used it to measure the intensity dissimilarity of a pixel and a cluster center. For polarimetric SAR (PolSAR) images, Feng et al.13 directly used a complex Wishart distribution-based distance as a substitute for the feature-based distance in SLIC to generate superpixels. Song et al.14 defined a dissimilarity using the Bartlett distance, which is derived from hypothesis tests on Wishart distribution. Qin et al.15 improved the cluster center initialization and used the revised Wishart distance for local clustering. Xiang et al.16 defined a similarity measure that contains multiple cues, including polarimetric, texture, and spatial information. In summary, to relieve the speckle noise effect and make the SLIC method applicable for SAR/PolSAR images, most of the existing research follows two ideas: (1) replacing the color-based distance with statistical model based ones and making improvements and (2) combining statistical models with other features to construct a compound distance, such as . However, there is a problem with these two ideas. First, to calculate the aforementioned pixel-to-cluster distance measures, the parameters of the statistical models should be estimated accurately in each cluster. However, the initial clusters are sampled on a regular grid and will continually change during the local iterative clustering, which means the assumption of the independent and identically distribution (i.i.d.) in the clusters is usually violated, especially in heterogeneous areas. In this situation, the estimated parameters are biased, so the accuracy of distance measures will be degraded and the performance of superpixel generation will be affected. Second, combining statistical models with other features can partly improve the accuracy of the pixel-to-cluster distance measure, but the direct adding of different distances still lacks theoretical support. If there were remarkable differences in the range and distribution of values of each distance, the addition of multiple distances derived from different features would be unreliable in some cases. In this paper, we explore the issue of distance measure from another point of view. Motivated by Leung and Malik,17 edge information can be directly used to define the dissimilarity between pairwise pixels in the natural images. Additionally, in SAR images, edges are not the simple sharp changes in image brightness, but significantly reflect changes in the statistical properties of each area in the images. In other words, edge information can be considered the abstraction of the underlying statistical characteristics and a bridge to connect statistics and superpixels. Thus, the edges are more perceptual and stable to represent dissimilarity between two pixels if there is an edge located in the middle of them. Liu et al.18 computed the dissimilarity by the edge information, which is extracted by a classical region-based detector for SAR images, but the detector suffers from the scale dilemma and the orientation problem.19 Thus, the locations of edge points are unreliable and the performance of superpixels is not satisfactory. To overcome the limitation, we adopt an up-to-date detector to extract the edge information more precisely and define an edge-dominant distance to replace the statistical model-based distance. Experimental results confirm that a reliable result of superpixels can be provided using only edge information and the superpixels can well adhere to the real edges. Another problem with the model-based SLIC methods is that it is often difficult to make an appropriate selection of the relative weight between statistical similarity and spatial proximity. The weight is important for offering a balance between boundary adherence, compactness, and regularity of superpixels.5 However, it is usually set manually to a constant value by trial and error, which might still not be suitable for each iteration and is often too large to lead to undersegmentations in some areas. To solve this problem, we built an initialization step for the cluster centers with an edge-adaptive grid (EG). This grid has multiple layers that are generated based on edge information and quadtree decomposition. Experiments show that it is able to reduce the negative effect caused by a large value of the relative weight and make the performance of superpixels less sensitive to the changes of weight. The remainder of this paper is organized as follows. The proposed method is described in Sec. 2. The experiments and the performance evaluations are presented in Sec. 3. The conclusions are given in Sec. 4. 2.Superpixel Generation2.1.Edge ExtractionIn this paper, the edge information is extracted using the degenerate filter with the weight maximum likelihood estimation (DG-WMLE) proposed in Ref. 19. The DG-WMLE method can address the scale dilemma in edge extraction and provide a better performance on the estimation of the edge strength and the location of edge points, which is extremely important and necessary for generating superpixels with a good boundary adherence. The key design of the DG-WMLE method is a degenerate filter, as illustrated in Fig. 1. The edge strength of the center pixel is estimated by the dissimilarity between the two pixels adjacent to the center pixel. And the calculation of this dissimilarity needs the noise-free intensity of the two pixels. According to Refs. 20 and 21, the noise-free value can be evaluated using the WMLE, which is where means the intensity value of the SAR image with noise. The WMLE estimation on uses all the values in the search window , and the design of the window is inherited from the classic region-based filter. The weight is derived from the probabilistic patch-based dissimilarity using an exponential kernel20,21 and is calculated as follows: where denotes the patch-based dissimilarity measure of two patches and , with and as the centers, respectively, and is the kernel parameter.19Fig. 1The degenerate filter design for edge extraction: and are the length and width of the search window, respectively, is the spacing between the two pixels for calculating the edge strength at the center pixel, and is the filter orientation. This figure is adopted from Ref. 19. ![]() Considering the design of the DG filter and the WMLE-based estimation method, if and are the two adjacent pixels to the center pixel , the corresponding indicator of the edge information (i.e., the edge strength at the pixel ) at the current orientation of the filter is calculated with the use of the Bhattacharyya distance,22–24 and the edge strength at the pixel is the maximum value among all the orientations, as shown in Eqs. (3) and (4): The relative parameters are set as suggested in Ref. 19. The orientations of the filter are . The detailed information about the DG-WMLE edge extractor can be found in Ref. 19. 2.2.Edge-Dominated Local ClusteringThe SLIC5 is an effective and efficient method for superpixel generation. The basic idea of the SLIC is a local k-means clustering method, including three steps: (1) initialization of cluster centers by a regular grid (RG); (2) iterative local clustering based on a distance measure between a pixel and a cluster center; and (3) postprocessing to remove isolated pixels and enforce the connectivity of superpixels. In general, the performance of the SLIC is greatly affected by the capability of the distance measure. In the original SLIC, this measure is defined as the 5-D Euclidean distance combining the color similarity and the spatial proximity.5 Since this distance cannot be directly applied for SAR images with multiplicative speckle noise, several studies in recent years have deduced suitable measures and introduced them into the SLIC, as discussed in Sec. 1. Motivated by the work of Leung and Malik17 and Liu et al.,18 in this paper, we directly use the aforementioned DG-WMLE edge information to measure the pairwise dissimilarity of two arbitrary pixels. As shown in Fig. 2, the edge-based pairwise dissimilarity is perceptually meaningful, easy to understand, and can ensure a good boundary adherence of superpixels. Fig. 2Illustration of the pairwise dissimilarity using edge information. (a) SAR image and (b) the extraction result of DG-WMLE. Because of the high value of edge strength existing along the line , the pixels and are suggested to be divided into different clusters. On the contrary, the pixels and probably belong to the same cluster. This figure is adopted from Ref. 18. ![]() The dissimilarity of two pixels and is defined as follows: where denotes the edge strength at the pixel and is the line connecting and .Similar to Ref. 5, the distance measure for edge-dominated local clustering (EDLC) is defined as follows: where the subscript ED stands for edge-dominated, is the spatial distance of the pairwise pixels, and is the grid interval. is a relative weight introduced to control the relative importance of the edge information against the spatial distance.As mentioned in Sec. 1, the value of should be carefully determined to offer a balance between boundary adherence, compactness, and regularity of superpixels. A smaller will emphasize more and makes the generated superpixels adhere better to the real boundaries. However, a larger will emphasize and makes the superpixels more compact and regular. As shown in Figs. 3(b) and 3(c), an inappropriate choice of leads to an unsatisfactory segmentation result. More specifically, a large value of around the edges will have a fatal impact on the performance of segmentation. Fig. 3Illustration of two different initializations of cluster centers and the corresponding superpixel segmentation results. (a) initialized by a RG and (d) by an EG. (b) and (e) The results produced using the distance measure in Eq. (6) with , respectively. (c) and (f) The results with . ![]() Motivated by the idea of quadtree mesh generation,25 we provide an initialization strategy with an EG instead of the RG to overcome this limitation. First, a RG is generated on the image according to the expected number of superpixels. Next, an automatic thresholding26 is applied on the extraction result of the DG-WMLE to get an edge map. Then, if the number of edge points in any block of the RG exceeds a preset threshold, the block is recursively subdivided into four smaller equal-sized parts. In this way, a multilayer grid adaptive to the edge information is generated, as displayed in Fig. 3(d). In Fig. 3, under the same value of and a similar amount of initial clusters, it is shown that EG-based initialization has a larger grid interval than RG. In addition, more initial centers are generated close to the real edges, which makes the spatial distance between pixels and cluster centers around the edges decrease a lot. In both cases, according to Eq. (6), the importance of spatial proximity will be weakened, i.e., the importance of edge information will be emphasized. Thus, the boundary adherence of superpixels around the real edges can be improved significantly, as shown in Figs. 3(e) and 3(f). In summary, the procedure of EDLC for superpixel generation is presented as follows:
An intuitive flowchart is shown in Fig. 4. 3.Experiments and Analyses3.1.DatasetsIn this section, we generate a simulated four-look SAR image based on the Monte Carlo procedure27 to objectively evaluate the performance of the proposed method. The size of the image is . The image contains five different regions, and the intensity of each region follows the gamma distribution, as shown in Fig. 5(a). The actual intensity values without the interference of noise in the five regions are set to 100, 400, 1600, 3600, and 8100, respectively. The corresponding ground truth of edges is given in Fig. 5(b). Fig. 5Simulated dataset. (a) A simulated SAR image with five regions following the gamma distribution. (b) The corresponding ground truth of edges. ![]() In addition, two TerraSAR-X StripMap images are used in our experiments, as shown in Figs. 6(a) and 6(c). The first one is extracted from Dessau, Germany, covering several crop areas. The second is from South Mississippi, USA, covering both water and vegetation areas. The size of each is . The pixel spacings are 3 m in both directions, and the number of looks is . The ground truth of edges from manual delineation is shown in Figs. 6(b) and 6(d). 3.2.Performance EvaluationTo evaluate the performance of the proposed method quantitatively, two commonly used metrics28 are applied in this section: boundary recall (BR) and under-segmentation error (USE). BR is defined as the fraction of the ground truth edges correctly recovered with the superpixel boundaries. In practice, BR measures the percentage of ground truth edges that fall within superpixel boundaries with a tolerance distance . USE compares superpixel segment areas to measure to what extent superpixels cover the ground truth segment border. If is a ground truth segment, is a superpixel, and indicates the size of the segment in pixels, USE is computed by Next, we compare the superpixel generation results of the EDLC with that of the other three methods, i.e., three different measures to represent the dissimilarity between a pixel and a cluster:
To make a fair comparison, we first replace the in Eq. (6) with the above three dissimilarities. Then, we perform the same local clustering and postprocessing procedures to get the final results. To obtain superpixels with a good balance between boundary adherence and regularity, the values of the weight are all set carefully for all the three methods according to Refs. 5, 11, and 12. The number of layers for EDLC is set as 3. The number of blocks in the top layer of EG in EDLC is also set suitably to get a number of the generated superpixels similar to that of the other three methods. The maximum number of iterations is set as 20. For the simulated data, the segmentation results of EDLC, LB-SLIC, PB-SLIC, and SLIC are shown in Fig. 7 from left to right. The expected number of superpixels in LB-SLIC, PB-SLIC, and SLIC is set as {100, 200, 300, 400, 500}, increasing from top to bottom. Additionally, in the same lines of the figures, the number of generated superpixels in EDLC is close to the other three methods. To provide superpixels with a better boundary adherence, is set as {0.5, 0.6, 1.0, 0.5} for the four methods, respectively. The numerical evaluation for the superpixels provided by these methods is shown in Fig. 8, using the aforementioned metrics BR and USE. Fig. 7Superpixels generated by the four methods on the simulated SAR image: (a) EDLC, (b) LB-SLIC, (c) PB-SLIC, and (d) SLIC. The number of superpixels is increasing from top to bottom (100 to 500). The weight is set as 0.5, 0.6, 1.0, and 0.5, respectively. ![]() Fig. 8Performance evaluation of EDLC, LB-SLIC, PB-SLIC, and SLIC on the simulated SAR image using (a) BR and (b) USE. In the legends, the numbers in brackets after the names of the methods are the values of . ![]() From Figs. 7 and 8, we notice that
For the two real images, the segmentation results of the four methods are shown in Figs. 9 and 10 from left to right. The expected number of superpixels in LB-SLIC, PB-SLIC, and SLIC is set as {200, 300, 400, 500, 600}, increasing from top to bottom. And the number of generated superpixels in EDLC is close to the other three methods in the same lines. is set as {0.5, 0.6, 1.0, 0.3} for the four methods, respectively. The numerical evaluation for the superpixels provided by these methods is shown in Figs. 11 and 12. From these figures, the proposed EDLC still provides better results than the other three methods, considering both BR and USE. Although with a low value of , LB-SLIC or PB-SLIC can obtain a good boundary adherence, which is close to or even a little bit better than EDLC, their performance of USE is worse. There are also many irregular superpixels generated both near the real boundaries and inside the homogenous areas. Furthermore, a lot of broken regions are produced during the local clustering, so the number of superpixels in the final results is much more than the preset value of . In general, the visual presentation of LB-SLIC and PB-SLIC is poorer because of these negative attributes. Fig. 9Superpixels generated by the four methods on the real image 1: (a) EDLC, (b) LB-SLIC, (c) PB-SLIC, and (d) SLIC. The number of superpixels isincreasing from top to bottom (200 to 600). The weight is set as 0.5, 0.6, 1.0, and 0.3, respectively. ![]() Fig. 10Superpixels generated by the four methods on the real image 2: (a) EDLC, (b) LB-SLIC, (c) PB-SLIC, and (d) SLIC. The number of superpixels is increasing from top to bottom (200 to 600). The weight is set as 0.5, 0.6, 1.0, and 0.3, respectively. ![]() 3.3.Parameter AnalysisAccording to Sec. 2.2, two parameters need to be determined before EDLC: the weight and the number of layers . As shown in Fig. 3, both and have a great influence on the superpixel segmentation results. To evaluate the impact of the two parameters, we set and ; then, we applied the EDLC to the simulated image. The performance on the condition of different parameters is shown in Fig. 13. From the figures, it is noticed that, with the increase of layers, the boundary adherence of EDLC is improved remarkably. In addition, the BR and USE curves under different values of become much closer to each other. This represents that, by the initialization of EG, the performance of EDLC is less sensitive to the change of than using RG. Thus, we used in all the experiments, and set in the range for EDLC. If the proposed method is applied for a larger dataset, more layers are recommended. However, the size of blocks in the bottom of EG is not suggested to be smaller than . 4.ConclusionsIn this paper, we propose an edge-dominated local clustering method to generate superpixels for SAR images. Edge information is introduced not only to define the dissimilarity of a pixel and a cluster but also to produce an adaptive grid for the initializations of cluster centers. Experiments on the simulated and real SAR images show that the proposed method provides an improved performance of boundary adherence and visual presentation, compared with the other methods using statistical model-based dissimilarities. In the future, we will extend the edge-dominated dissimilarity into multitemporal data and provide a segmentation result suitable for all the temporals. In this case, superpixels will become a basic element for multitemporal analysis. AcknowledgmentsThis work was supported by the State Key Program of the National Natural Science Foundation of China under Grant No. 61331015. The authors declare no conflict of interest. ReferencesC. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, Raleigh, North Carolina
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BiographyHao Hu received his MSc degree in electronics and communication engineering from Shanghai Jiao Tong University, Shanghai, China, in 2012, where he is currently working toward his PhD in information and communication engineering, Department of Electronic Engineering. His research interests are in the domain of synthetic aperture radar (SAR) image interpretation (segmentation, classification, and multitemporal analysis). Bin Liu received his PhD in signal and information processing from Shanghai Jiao Tong University in 2015. Currently, he is a research assistant professor in Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University. His main research interests include SAR/PolSAR image understanding and information mining, particularly spatial information analysis, segmentation and classification, multitemporal image analysis, target detection and recognition, and multisensor data joint interpretation. Zenghui Zhang received his PhD in information and communication engineering from the National University of Defense Technology (NUDT), Changsha, China, in 2008. From 2008 to 2012, he was a lecturer in the Department of Mathematics and System Science, NUDT. He is currently an associate professor in the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University. His main research interests include radar signal processing and compressed sensing theory and applications. Weiwei Guo received his PhD in information and communication engineering from the National University of Defense Technology in 2014. He was a joint PhD student at Queen Mary, University of London, London, United Kingom, from 2008 to 2010. Since 2015, he has been a postdoctorate researcher with Shanghai Jiao Tong University. His main research interests include areas of image and signal processing, computer vision, and pattern recognition. Wenxian Yu He received his PhD in communication and information system from the National University of Defense Technology (NUDT) in 1993. He is currently in the School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, where he is a Yangtze River scholar distinguished professor and the head of research and was the executive dean from 2009 to 2011. His current research interests include radar target recognition, remote sensing information processing, multisensor data fusion, and integrated navigation system. |