Ship target detection and segmentation method based on multi‐fractal analysis

The Journal of EngineeringVolume 2019, Issue 21 p. 7876-7879 IET International Radar Conference (IRC 2018)Open Access Ship target detection and segmentation method based on multi-fractal analysis Liyang Zhu, Liyang Zhu Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this authorGang Xiong, Corresponding Author Gang Xiong gxiong@sjtu.edu.cn Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this authorDongmei Guo, Dongmei Guo Shanghai Radio Equipment Research Institute, Shanghai, People's Republic of ChinaSearch for more papers by this authorWenxian Yu, Wenxian Yu Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this author Liyang Zhu, Liyang Zhu Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this authorGang Xiong, Corresponding Author Gang Xiong gxiong@sjtu.edu.cn Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this authorDongmei Guo, Dongmei Guo Shanghai Radio Equipment Research Institute, Shanghai, People's Republic of ChinaSearch for more papers by this authorWenxian Yu, Wenxian Yu Shanghai Key Laboratory of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, People's Republic of China School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of ChinaSearch for more papers by this author First published: 02 October 2019 https://doi.org/10.1049/joe.2019.0764Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract A novel automatic ship target detection and segmentation approach based on modified multi-fractal method in synthetic aperture radar (SAR) image is proposed in this study. Firstly, singular power spectrum (SPS) is developed to two-dimensional SPS (2D-SPS), and applied to feature extraction and SAR target detection. Secondly, 2D Holder exponent and 2D multi-fractal spectrum are jointly used to ship target segmentation in SAR image. The algorithm steps and detection flow is here conceptually assessed, analytically derived, numerically verified, and also tested on actual SAR images. Results indicate that the proposed method has significant advantages in ship target detection and segmentation in SAR image. 1 Introduction Synthetic aperture radar (SAR) target detection is a topic of increasing interest as a result of rapid developments in remote sensing systems. The traditional radar target detection methods are mostly based on matched filtering and maximum output-signal-to-noise ratio (SNR) criterion. However, in the condition of low SNR, complex background, non-cooperation and small or hidden targets, it is hard to obtain ideal detection probability for traditional detection methods. The introduction of fractal theory provides a new idea for target detection. Lo et al. [1] first applied the fractal dimension to target detection in sea clutter and showed good performances. In [2], a fractal detector is designed based on the Gaussian distribution of the fractal dimension. Based on detrended fluctuation analysis, Xu [3] proposed a method to detect the weak targets in sea clutter based on the joint fractal characteristics, and further enriched the application of the single fractal feature in target detection. However, fractal dimension cannot fully describe complex objects and some significant characteristics have been ignored. In [4], a sea clutter modeling method based on multi-fractal spectrum was put forward. Gan and Shouhong [5] studied the multi-fractal characteristics of sea clutter and proposed a fuzzy detection method. Some other detection methods related to multi-fractal spectrum are introduced in [6-10]. While the generality of above studies on multi-fractal spectrum (MFS) are based on spatial differentiability characteristics, they failed to provide the power distribution of fractal signal along with the singularity exponent [11]. In this case, singular power spectrum was proposed in [12]. In this paper, we proposed a novel automatic detection approach for SAR target based on multi-fractal analysis. Specifically, two-dimensional singular power spectrum was extended and applied to the target detection in the first stage. Then, Holder exponents and multi-fractal spectrum are well combined to segment the specific targets in the sea clutter. The proposed methods take great advantage of multi-fractal characteristics, and to some extent, theoretically overcome the influence of low SNR. The outline of this paper is as follows. In Section 2, improved 2D-SPS method and related algorithm steps are introduced. In Section 3, we simulate and analyse the detection performance, compared with other methods. Finally, conclusion is made in Section 4. 2 Methodology In recent years, fractal theory has been gradually developed from fractal dimension and MFS to time-singularity 2D-MFS and singular power spectrum (SPS) [11]. In this paper, SPS is well extended to two-dimensional singular power spectrum (2D-SPS). Also, Holder exponents [6], 2D-MFS [6] and improved 2D-SPS are well combined for SAR target detection and segmentation. Fig. 1 shows the flowchart of the entire experiment in this paper. First, SAR images with and without target are simulated and analysed by 2D-SPS/MFS. Several statistics parameters are extracted and applied to SAR image detection. Result of the receiver operating characteristic curve (ROC) and the area under the curve (AUC) are given. Next, Holder exponents and 2D-MFS are well combined for SAR target segmentation. Fig. 1Open in figure viewerPowerPoint SAR target detection and segmentation 2.1 Two-dimensional singular power spectrum The SPS reflects the fractal energy in the per unit singularity exponent internal, and the fractal power distributes with the variation of singularity exponent [12]. More theory and details about SPS can be found in [13-15]. Here, we mainly extend the SPS to 2D-SPS and apply it to SAR target detection. The algorithm steps are as follows. Step 1 : Calculate the local Holder exponent for the given SAR image at each point [6]. All values of are derived, where represents the total point set of the image. Step 2 : Define: , Then divide into N sections, where represents the ith singular value. Step 3 : Two-dimensional SPS is defined as (1) Finally, the singular power spectrum is determined. 2.2 SAR target detection In this section, the SAR target detection based on 2D-SPS method is proposed. As shown in Fig. 1, training samples are used to train the detection processing, including detection threshold, feature selection and optimiastion. By feature extraction based on 2D-SPS method and ROC detection statistics, the best threshold parameters can be obtained. The process of the proposed method includes three steps. Step 1 : Calculate the 2D-SPS, of each image using the proposed method in Section 2.1. Step 2 : Construct detection parameters based on 2D-SPS: Step 3 : Calculate , , for all the images with targets and without targets. Then we can get the false alarm rate , and the detection rate . The AUC shows the detection performances. Also the best threshold will be given. 2.3 SAR target segmentation Here, Holder exponents and 2D-MFS are considered. Since Holder exponents describe the local characteristics of the image, 2D-MFS are well combined to determine whether certain points are on the edge. If the value of the multi-fractal spectrum corresponding to the Holder exponent of a point is close to 1, the point is considered to fall on the edge [16]. The specific algorithm steps are as follows. Step 1 : Considering one SAR image, calculate its Holder exponents [6]. represents the total point set of the image. Then ' -SAR image' is obtained. Step 2 : Calculate the MFS of the image, referring to Section 2.2. Then is obtained. Step 3 : Calculate , of 2D-MFS that satisfy equation , i.e. . Step 4 : Binarise the SAR image. If the value of the point in ' -SAR image' is between [, ], set it to 0. Otherwise it is set to 1. Then we finally get the segmentation result – binary image 3 Simulation analysis and results In our experiments, we used a TerraSAR-X image acquired on June 19, 2011, located at port of Yokohama. The azimuth resolution is 3.04 m and the ground range resolution is 3.01 m. Our dataset, which have 36 small images of pixels, are cut from the large origin image. Of these images, 17 have no targets and the remaining 19 contained targets. 3.1 SAR target detection Fig. 2 shows four slice images cut from the large origin image. Multi-fractal spectrum and singular power spectrum are simulated in Fig. 3. In Fig. 3 a, the maximum multi-fractal spectrum values of them are 2, but the width of the spectrum are different. In Fig. 3 b, we can see that SAR images containing targets show greater values of SPS than those containing no targets. This shows different singular power for them. Thus, the detection parameters mentioned above, like , , can be used in SAR image target detection. Fig. 2Open in figure viewerPowerPoint TerraSAR image slices with and without ship targets (a) Pure sea surface (i1), (b) Sea surface with false goals (i2), (c) Sea surface with ship target (i3), (d) Sea surface with small target (i4) Fig. 3Open in figure viewerPowerPoint Multi-fractal analysis of SAR image (a) Multi-fractal spectrum of different slice types, (b) Singular power spectrum of different slice types In our SAR target detection experiments, 36 images are prepared. Each of the size is 256 × 256. Around 17 images of them contain no targets and 19 images contain targets. Fig. 4 shows the four detection parameters , , , of SAR images and the best threshold value are given. Except for the , the other three detection parameters show significant differences between SAR images containing targets and no targets. The results are also in agreement with the analysis of the SPS in Fig. 3. Fig. 4Open in figure viewerPowerPoint Detection parameters simulation ( , , , ); the first 17 SAR index contain no targets and the remaining 19 contain targets; the green lines show the best thresholds Fig. 5 shows the ROC of four detection statistics – , , , . The target detection results based on , , show better performance than . We can see that is close to 1 based on , , and the AUC of them is 1. This indicates that the proposed four detection statistics based on 2D-SPS analysis can be a promising detection method. Compared with other SAR target methods in [17, 18], the detection rate of our algorithm detector (, , ) can reach almost 1.0 when . Results are shown in Table 1. Fig. 5Open in figure viewerPowerPoint Receiver operating characteristic curve (ROC) of the four detection parameters – , , , ; the AUCs of them are given Table 1. Comparison of detection results with other methods Algorithm/Pd Detection probability bilateral CFAR [17] 0.95 0.94 0.75 modified CFAR [18] 0.90 0.90 0.90 our method 0.99 0.97 0.97 3.2 SAR target segmentation Fig. 6 shows the Holder exponents and 2D-MFS of the given SAR images. Holder exponents show the local characteristics of the image, and 2D-MFS shows statistical characteristics of edges at different scales. Fig. 7 shows the segmentation results of different algorithms on the given SAR images. In Fig. 7, compared with the other three algorithms, the 2D-MFS better shows the details, especially the edge of the ships than other three algorithms. In Fig. 8, segmentation result of 2D-MFS basically reflects the ship's profile. However, there exists some noises. This is due to the excessive display of details in the multi-fractal spectrum. In general, we can see that segmentation results based on 2D-MFS perform better than Roberts, Sobel and Prewitt operators. Fig. 6Open in figure viewerPowerPoint ' -SAR' images analysis (a) Origin SAR image of ship1 with size of 256 × 256, (b) ' -SAR' image of ship1, (c) Origin SAR image2 of ship2, (d) ' -SAR' image of ship2 Fig. 7Open in figure viewerPowerPoint Comparison with segmentation results of traditional methods for ship1 (a) Roberts operator, (b) Sobel operator, (c) Premitt operator, (d) Our methods Fig. 8Open in figure viewerPowerPoint Comparison with segmentation results of traditional methods for ship2 (a) Roberts operator, (b) Sobel operator, (c) Premitt operator, (d) Our methods 4 Conclusion In this paper, we proposed a novel SAR target detection approach based on multi-fractal analysis. The whole detection process can be divided into two phases. One is for target detection and another is for target segmentation. In the first stage, 2D-SPS is extended and applied to the SAR target detection. Results based on , , parameters perform better than . Also the corresponding ROCs and AUCs are also given. Then Holder exponents and 2D-MFS are combined to segment the SAR ships. Compared with traditional methods, our methods show good advantages in complex natural background. Due to the limitation of data volume, we will further work with neural networks. More efforts will be focused on target classification, not just detection. 5 Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC. 61571294 and 61171168) and Chinese Equipment pre-research area fund project (6140413020116JW03001). We are grateful to the anonymous reviewers for valuable comments and suggestions. 6 References 1Lo T., Leung H., Litva J. et al.: 'Fractal characterisation of sea-scattered signals and detection of sea-surface targets', IEE Proc. 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