Infrared Physics & Technology 89 (2018) 263–270
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Regular article
A novel ship CFAR detection algorithm based on adaptive parameter enhancement and wake-aided detection in SAR images Siqi Meng a, Kan Ren a,⇑, Dongming Lu a, Guohua Gu a, Qian Chen a, Guojun Lu b a b
Jiangsu Key Laboratory of Spectral Imaging and Intelligent Sense, Nanjing University of Science and Technology, Nanjing 210094, China North Information Control Research Academy Group Co., Ltd, No. 528, Jiangjun Avenue, Nanjing, China
h i g h l i g h t s The APT fusion result contains the intensity & spatial information is constructed. The screening criteria based on characteristics are used to eliminate false alarm. Wake aided detection in APT domain helps to verify the target.
a r t i c l e
i n f o
Article history: Received 24 November 2017 Revised 9 January 2018 Accepted 14 January 2018 Available online 20 February 2018 Keywords: Synthetic aperture radar (SAR) Constant false alarm rate (CFAR) Adaptive parameter transform (APT) domain Normalized Hough transform (NHT) Ship and ship wake
a b s t r a c t Synthetic aperture radar (SAR) is an indispensable and useful method for marine monitoring. With the increase of SAR sensors, high resolution images can be acquired and contain more target structure information, such as more spatial details etc. This paper presents a novel adaptive parameter transform (APT) domain constant false alarm rate (CFAR) to highlight targets. The whole method is based on the APT domain value. Firstly, the image is mapped to the new transform domain by the algorithm. Secondly, the false candidate target pixels are screened out by the CFAR detector to highlight the target ships. Thirdly, the ship pixels are replaced by the homogeneous sea pixels. And then, the enhanced image is processed by Niblack algorithm to obtain the wake binary image. Finally, normalized Hough transform (NHT) is used to detect wakes in the binary image, as a verification of the presence of the ships. Experiments on real SAR images validate that the proposed transform does enhance the target structure and improve the contrast of the image. The algorithm has a good performance in the ship and ship wake detection. Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction Synthetic aperture radar (SAR) images have been widely used for ship traffic monitoring and fishing vessel detection [1]. Among all those traditional and modern tools, such as land-based, ship borne and airborne detection means and visible light, infrared remote sensing band and so on, SAR has the advantage of all-day, all-weather, long distance and wide swaths capabilities in the collecting data. And because of its special imaging principle, SAR can provide high-resolution remote sensing images. Therefore, it is propitious to detect ocean ships and ship wake, and additional parameters can be extracted from the wake for the estimation of moving-ship condition, such as velocity and direction [2]. Ships usually appear as bright objects in SAR images because they are strong reflectors of the radar pulses emitted by the
⇑ Corresponding author. E-mail address:
[email protected] (K. Ren). https://doi.org/10.1016/j.infrared.2018.01.016 1350-4495/Ó 2018 Elsevier B.V. All rights reserved.
satellite. In images with finer resolution, it is possible to discern the structure of ships, making it possible to detect and even identify ship types. The more space information, the better detection of ships. And the most obvious characteristic of wake components are the linear features in a SAR image. Ship wakes appear as bright or dark lines that may keep for several kilometers behind the ships [3]. However, due to the effects of sea clutter and speckle noise, the target features are not obvious in SAR images, which greatly affects the detection of ships and wake. Many algorithms have been tried and achieved good performance in ship target detection. Constant false alarm rate (CFAR) detection is one of the most widely used methods for ship detection in SAR images, which is based on constant false alarm function and adaptive threshold. The commonly used CFAR algorithms mainly include: twoparameter CFAR (2p-CFAR), Cell-average CFAR (CA-CFAR) [4], smaller of CFAR (SO-CFAR) [5], greater of CFAR (GO-CFAR) [6]. They use only the intensity characteristics of the target to do the detection. In high resolution images, it is a waste of the target spatial
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structure information. Moreover, in [7,8], the use of spatial characteristics to improve the accuracy of detection is just an auxiliary means. The bilateral CFAR combines the intensity distribution and spatial distribution as the fusion distribution and has a good performance [9]. However, it still lacks constraints on the characteristics of the target itself. Motivated by the above problem, in this paper we focus on the enhancement of target itself and the suppression of background in SAR images. Moreover, combined with the characteristics of the target, we also propose false alarm exclusion criterion with CFAR detection. As a result, the whole algorithm incorporates the intensity and spatial characteristics to adjust the target context adaptively. Based on the exclusion criterion and wake aided detection, it can detect targets effectively. The remainder of this paper is organized as follows. Section 2 introduces the proposed algorithm flow and methodology in detail. Section 3 validates the method by testing on simulated images and real SAR images. Finally, Section 4 concludes this paper.
2. Detection method 2.1. Principle and algorithm flow In fact, SAR images are inevitably affected by sea clutter and speckle noise. Due to their presence, it is difficult to balance the detection and loss detection. If the larger detection threshold is taken, a small detection rate and a low false alarm will be obtained. If the smaller detection threshold is taken, a larger detection rate and a high false alarm will be possible. The proposed algorithm can effectively reduce the interference and improve the detection effect. Input the SAR image
APT domian Intensity similarity
Space ditance
Dynamic weights
APT transform CFAR False alarm exclusion
Wake detection
Kernel density estimation (KDE)
Niblack algorithm
Target region (TR)
Morphology operation
Aspect ratio (AR)
Normalized Hough transform (NHT)
Fusion Ship candidates
Ship wakes
Detection results Fig. 1. Flow diagram of the proposed algorithm.
In Fig. 1, the main processes of the algorithm are shown. In the APT domain, the adaptive parameter method, which combines intensity and spatial structure, is used to enhance the target. The APT method is applicable to ship and wake images. In the APT domain, the image is processed with two parameter CFAR, and the candidate ship target is detected with the discriminant criterion. Similarly, in the APT domain, the local threshold Niblack algorithm is used for the segmentation. Then, bright clutter spots are eliminated by morphology operation. NHT is used to mark the wake position and extract wake parameters. The fusion module, based on the detection of candidate ships and wake results, is used to confirm the target, and judge by humans in some special cases. Finally, the detection results are presented. 2.2. Adaptive parameter transform domain The pixels in an image don’t exist in isolation, and so do the SAR intensity images. The correlation between the intensity and distance is inseparable in SAR images. The closer the distance between pixels is, the stronger the gray similarity is. In SAR images, the detection ability of the algorithm is very limited by using only the statistical properties of intensity information. In high resolution images, the target usually has the more pronounced spatial structure and the relationship between pixels is closer. It is beneficial to distinguish the interference of clutter and speckle noise. Therefore, we transform the intensity value of the original images space to the new transform domain by combining the gray features and the position space relationship of the image pixels. In the new transform domain, the SAR image contrast is improved, and the targets are more prominent based on the following facts. First of all, we make full use of the intensity and spatial relations between adjacent pixels by using a local sliding window. At the current pixel position, the intensity and spatial structure information of the adjacent pixels are superimposed. Then, according to the intensity distribution relationship between the window pixel and the whole image, the weights are allocated dynamically to the window pixels. The central pixel intensity and adjacent window pixel effect are superimposed. The original pixel intensity value is mapped to a APT value. At the same time, the Euclidean distance is taken into account in the transformation relationship. Finally, in conjunction with the above-mentioned factors, we calculate a new APT value instead of the original intensity value. As a result, the target regions are more prominent in the APT domain, which is convenient for post-processing. (1) The difference level of intensity values The intensity values of adjacent pixels in the SAR image have a very high similarity. We quantify the gray scale features of the 256 levels in the SAR image into 16 levels. For example, the intensity value of 0–15 is level 1, the intensity value of 16–31 is level 2, . . ., the intensity value of 240–255 is level 16. The positions of two pixels in the image are ði; jÞ and ðm; nÞ, and their gray values correspond to f ði; jÞand f ðm; nÞ respectively. The similarity of two pixels is defined by the difference of their corresponding levels. The intensity difference (id) is defined as follows.
id ¼ jlev el½f ði; jÞ lev el½f ðm; nÞj
ð1Þ
We quantify the intensity difference between pixel by absolute values. (2) Effective range The effect that one pixel imposes to another pixel decreases with their increasing distance. Apparently, there exists a range L over which the effect can be neglected. The range should be neither
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too large to introduce useless computer loading nor too small to limit effects of space relations we want to take advantage of. L is determined by the size of ship targets and sea clutter. Experiments show that it should be bigger than the size of the sea clutter pattern and smaller than half of the minimum size of the ship width so that what is contained by the sliding window will be able to reflect their spatial difference correctly. While L varies in a large range usually, we give priority to the smallest L for two reasons. The first reason is that smaller L reduces more time consumption; the second one is that the spatial extraction of the edge of ship targets will be less affected by using smaller L. (3) Dynamic allocation of weights In order to measure the distribution of pixel intensity more easily, we consider the assumption that the background clutter conforms to the Gaussian distribution. The proportion of background area is larger in the image. The ship and wake regions are not only small in the image, but also darker (wake) or brighter (ship or wake) than background. Experiments show that the vast majority of target pixels are distributed at both ends of the histogram obviously. According to this rule, the dynamic distribution weights of different intensity values are given. Fig. 2 shows that histogram of the SAR image containing the ship and ship wake. According to the above analysis, we combine the ‘‘3r” criterion of Gaussian distribution. In case of avoiding loss detection, the discriminant function is
pixelship=wake ¼
true f ði; jÞ > l þ g^ ror f ði; jÞ < l g^ r flase else
ð2Þ
where f ði; jÞ is the original intensity value of SAR image, l is the image mean, r is the image standard deviation, and g^ is a design parameter. According to the analysis of experimental data, hundreds of image patches come from the TerraSAR-X dataset. They have verified the distribution model. In addition, considering the loss detection, g^ is set to 2.5–3 to guarantee the detection capability. When the intensity value satisfies the formula (2), the pixel can be considered as the ship or ship wake, but the speckle noise may not be excluded. Considering the Gaussian distribution, when the intensity value satisfies formula (2) and the neighborhood pixel is calculated for the weight, a L size square window is set around the pixel. Fig. 3 shows the process of calculating the pixel weight. The main
window is the process of transforming intensity images into APT domains. The sub-window is the process of calculating the weight of adjacent pixels. In the sub-window, the number of pixels satisfying the target domain condition is counted. The weighting formula is
n tk ¼ 1 þ 2 L
ð3Þ
where the n is the number of pixels that satisfy the condition in the sub-window and L is the size of the window. The t k is the weight of neighboring pixels. However, the central pixel is not calculated in the main window. In order to suppress the effects of background clutter and speckle noise, the sum of adjacent pixel weights is calculated in the main window. It is
sumweight ¼
X
tk :
ð4Þ
k2XðLÞ
And if the weight satisfies the following conditions, the formula is as follows:
f enh ði; jÞ ¼
trestrain f ði; jÞ sumweight < sumthreshold t k f ði; jÞ
:
ð5Þ
In the above formula, f ði; jÞ is the original intensity value, f enh ði; jÞ is the weighted new value, t restrain is the suppression parameter, tk is a weighted parameter of pixel intensity. sumweight is the sum of the weights of the main window pixels and sumthreshold is the partition threshold of weights. By this method, we can draw the conclusion that the more pixels that satisfy the condition, the greater probability that the pixel is the target pixel. And the pixel gets a bigger weight. It can be seen in Fig. 3(b). On the contrary, when the number of pixels satisfying the condition is small or not in the sub-window, the pixel may be speckle noise. It can be seen in Fig. 3(a). And the pixel gets a smaller weight. Through this adaptive weight selection, the image noise is relatively suppressed, and the contrast is enhanced. (4) Transform to APT domain According to the distribution of pixel intensity values, we use the intensity similarity between pixels to assign weights to the pixel intensity dynamically, and combine the spatial distance to calculate a new intensity value in the APT domain. The intensity values are similar and adjacent to the pixels, which will have a more significant effect on each other [10]. The mapping formula is
f APT ði; jÞ ¼ f ði; jÞ þ
X 16ii0 6L 16jj0 6L
Fig. 2. The histogram of SAR image.
else
0
0
t k f ði ; j Þ 0
0 2
Rði ; j Þ aid
ð6Þ
where f ði; jÞ is the value at ði; jÞ of the intensity image and f APT ði; jÞ is the new value in APT domain. t k is the adaptive weight value of dif0 0 ferent pixels. Rði ; j Þ is Euclidean distance between pixel ði; jÞ and 0 0 pixel ði ; j Þ. id is the intensity similarity. a is a constant that controls attenuation speed as intensity similarity tends to be less significant. a should be bigger than 1 to ensure the attenuation. Also, if a is too small, pixels with different intensity will cause nearly identical enhancement. If a is too large, the contribution of similar but not exactly equal intensity pixels will be very limited. This conclusion can be deduced from formula (6). Based on a large number of experimental data, a with value 1.5–1.8 is of good performance in SAR images. (5) Transform process of adaptive parameter intensity and space information Fig. 4 shows the intensity and spatial transform process of the adaptive parameters. The patch on SAR image is 3 3. First, the pixel intensities are enlarged, as shown on the upper part of
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sub-window
sub-window speckle noise
12
18
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21
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36
16
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target pixel
90
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main window
main window
(a)
(b) Fig. 3. Process of calculating the weight of adjacent pixels.
Intensty domain
Intensity value
Intensity level
Intensity difference
15
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1
2
2
2
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2
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0
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APT domain
1 1
1
3
id
Rescale to 0-255
weight t Euclidean distance 2
1
1 2
AP 8
2
1 1
2
46
Fig. 4. Example of the APT process.
Fig. 4. Different levels are calculated by the intensity values. In the statistical block, the difference between the neighborhood pixel and the central pixel is id. Second, as shown in the middle part of Fig. 4, according to the intensity distribution, the pixel weights tk around the center pixel is calculated in each statistical block. The total weight coefficients are calculated in conjunction with intensity difference (id). Third, the new transform domain value is calculated by combining the pixel intensity value and the Euclidean distance between neighboring pixels in combination with the above two steps. It can be observed that the adjacent pixels with the same intensity value have different contributions to the central pixels. Also, impacts from pixels with the same range to the center vary with each own intensity. Repeat this process to all image pixels. Those new AP pixels are normalized to 0–255. Finally, we can obtain a new adaptive parameter transform domain image, which combines the intensity and spatial structure information. Throughout the process, we particularly consider the following situations. First, the region of interest (ROI) contains bright or dark pixel intensity values. The intensity values of those pixels are greatly enhanced in the transform domain. Second, background and speckle pixels are slightly enhanced because the original intensity values are assigned smaller weights and the intensity similarity between those pixels is weaker.
2.3. CFAR detection in APT domain The CFAR is one of the adaptive threshold algorithms designed to search for pixel values that are usually bright compared with those in the surrounding sea. It requires a relatively high contrast of the target relative to the background, and the target detection is achieved by comparing each pixel intensity against a certain threshold. In the APT domain, the characteristics of the target area are greatly enhanced based on the intensity and spatial information of the pixels. On the contrary, low intensity and speckles greatly reduce superposition effect in clutter areas. Typically, PDF of clutter distribution in APT domain is close to Gaussian distribution. Furthermore, the enhanced contrast ratio increases tolerance for deviation of the chosen distribution model. According to the Gauss distribution model of background clutter, the threshold T can be calculated according to the probability of false alarm (PFA) formula
Z Pfa ¼ 1
Z
T
1
1
f pdf ðxÞdx ¼
f pdf ðxÞdx
ð7Þ
T
where f pdf ðxÞ is probability density function (PDF), the formula is as follows:
S. Meng et al. / Infrared Physics & Technology 89 (2018) 263–270
f pdf ðxÞ ¼
1 1 xAPT lb pffiffiffiffiffiffiffi exp 2 rb r b 2p
2 ! ð8Þ
where xAPT is the pixel value under test, lb is the background mean, rb is the background standard deviation, and t is the detector design parameter. The relationship between t and P fa satisfies the formula (9), which is expressed as follows:
Pfa ¼
1 1 t erf pffiffiffi : 2 2 2
ð9Þ
Error function (erf) is defined as
2 erf ðxÞ ¼ pffiffiffiffi
p
Z
x
2
et dt:
ð10Þ
0
Based on the above formulas, the threshold is
T¼
qffiffiffiffiffiffiffiffiffi 1 2r2b erf ð1 2P fa Þ:
ð11Þ
Finally, we achieve the target detection by the following formula
xAPT > T () targetship=wake :
267
ship wake detection can facilitate ship detection and ship motion parameters retrieval. In this paper, we use the Niblack algorithm to segment the enhanced wake image in the APT domain. The Niblack algorithm is a dynamic threshold algorithm that calculates thresholds based on neighborhood pixel intensity values. Then, the images are morphologically processed to suppress noise and sea clutter. Finally, normalized Hough transform is used to detect the wake line segment in the binary image [11,12]. The relationship is inseparable between the wake and the ship. The presence of wakes can verify the authenticity of the candidate ships. The fusion strategy is as follows. When targets are detected with wakes behind, the candidate is a ship with the very high confidence. When only ships or wakes are detected, we still believe that there is a target. The whole process is implemented by verifying whether there is another target (ship/wake) around the detected target (ship/wake). However, when the sea conditions are complex, SAR image is greatly affected by speckle noise and sea clutter, and the wake detection may be inaccurate. Therefore, they still need to be checked by humans.
ð12Þ 3. Experiments and results
2.4. False alarm exclusion of target
3.1. Ship enhancement and detection
On the premise of ensuring a higher detection rate, SAR image is processed by CFAR detector, which will inevitably lead to false alarm problem. In combination with the characteristics of the target, we use the following features as the screening criteria. (1) Kernel Density Estimation (KDE) The kernel density reflects the degree of gathering of the target, providing a good view of the internal structure feature [9]. Since false alarms usually appear as discrete spots or thin line segments, and ship targets display as aggregate pixel set, it is obvious in a comparison between them that targets (ship or ship wake) have a higher KDE value. The kernel density estimator is given by
f ðxÞ ¼
1 exp ðx xj Þ2 2 j2XðLÞ X
ð13Þ
where x1 , x2 , . . . , xj are the pixels of the same potential target. (2) Aspect Ratio (AR) Aspect ratio is referred to the ratio of length and width of a candidate target. The effect of AR is independent of the hull size, which is the characteristic of ship self on the sea. It can be used to identify ship targets and high bright spots on the sea. (3) Target Region (TR) The target region is the number of pixels of the potential target. The pixel number of the ship controls the target in terms of size. Pursuant to pixel spacing, we can set a minimum threshold for the target size. 2.5. Wake detection and the fusion of results The characteristics of ship wakes are very obvious compared with the ship itself on the sea, which usually appears as long line segments behind ships, stretching thousands of meters. In fact, range component of moving ship leads to azimuth offset in SAR images, which shows that ships deviate from their actual route. However, wakes indicate the true location of the ship. As a result,
(1) Simulated Data In order to verify the effect of the APT transformation, we use simulated images to test the performance of the proposed algorithm. Fig. 5(1.a) and (2.a) simulate the characteristics of bright and dark area respectively. They are created by posing a block of pixels with the same intensity value to a SAR image of sea clutters without any target. The background of the simulated image comes from TerraSAR-X with 3-m resolution. The block size pointed by the arrow is 5 ⁄ 10. Fig. 5(1.a) shows that although the region itself is of higher intensity, it is still interfered by sea clutter and speckle noise. It can be clearly stated in Fig. 5(1.c). In view of these conditions, we use the proposed algorithm to transform the image into the new APT domain. Fig. 5(1.b) shows the APT result. We can see that the bright area is much stronger, and the background is suppressed. The image contrast becomes larger, so the target is easier to detect. Alternatively, the block has a darker intensity value as shown in Fig. 5(2.a). Fig. 5(2.c) shows that the pixel block is completely submerged in the background. Considering the sea clutter model and the target intensity, the dark target is also enhanced greatly in the proposed algorithm. It can be seen in Fig. 5(2.b) and (2.d). (2) TerraSAR-X Data TerraSAR-X images is taken from Singapore sea area in Fig. 6. The resolution is 3 m in azimuth. The polarization mode and channel are single and HH respectively. As shown in Fig. 6, the top row shows the original intensity image, the enhanced image, and the corresponding detection images. The second row shows the worse sea condition images and the corresponding enhanced and detection results. In Fig. 6, We can observe that the target-clutter contrast ratio is relatively low, and the individual targets are less prominent. After the proposed algorithm, we can see that the background clutter is suppressed and the targets are more prominent as a result. In the enhanced image, the algorithm can detect the targets accurately, and it has less interference. In general, the APT-CFAR can improve image contrast effectively and detect ship targets more accurately based on the screening criteria.
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(1.a)
(2.a)
(1.b)
(2.b)
(1.c)
(1.d)
(2.c)
(2.d)
Fig. 5. Comparison of simulated image before and after transform. (1.a) Simulated bright target intensity image, (1.c) surf image of (1.a), (1.b) transformed image, (1.d) surf image of (1.b). (2.a)–(2.d) Corresponding images of simulated dark target.
(1.a)
(1.b)
(1.c)
(1.d)
(2.a)
(2.b)
(2.c)
(2.d)
Fig. 6. Enhancement effect evaluation using TerraSAR-X data (1.a) Intensity image. (1.b) Transformed image in APT domain. (1.c) Binary map of detection results in intensity image. (1.d) Binary map of detection results in APT domain. (2.a)–(2.d) Corresponding results in higher sea conditions.
3.2. Wake enhancement and detection Ship wakes appear dark or bright ones in SAR images, which are usually low contrast and difficult to detect. Fig. 7(1.a) shows the dark wakes accompanying the ships behind in the original image. Considering the brighter ship, if the ship is not masked, the ship and wake will be enhanced simultaneously and the wake is relatively suppressed. In order to enhance the wake contrast effectively and facilitate the detection of the wake, it is necessary to use the homogeneous sea pixels to replace the ship pixels. Fig. 7 (1.b) shows the enhanced wakes image in the APT domain, which is processed after the ship mask. Fig. 7(2.a) and (2.b) are
corresponding surf images respectively. It can be seen that the wakes are greatly enhanced, and the target-clutter contrast becomes larger. Furthermore, we learn that the combination of space and intensity become tighter based on the proposed algorithm in APT domain. Finally, we can observe that the wake enhancement is very evident. Fig. 8 shows the binary image and detection result of the wakes. For the enhanced image, we use the local threshold Niblack algorithm for image segmentation. In order to achieve detection results and parameter extraction further, we use normalized Hough transform to mark tracks. For the linear wake, it can mark the wake points effectively. However, for the non-linear wake, it may be
S. Meng et al. / Infrared Physics & Technology 89 (2018) 263–270
(1.a)
(1.b)
(2.a)
(2.b)
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Fig. 7. Comparison of wake in intensity domain and wake with masked ship in APT domain. (1.a) Original image, (1.b) enhanced wake image. (2.a) and (2.b) Corresponding surf images.
Fig. 8. (a) Binary image of the enhanced wake. (b) Detection results of the wakes.
necessary to take multiple extremes in the integration domain to get the complete track. 3.3. Comparison with other algorithms
where N fd is the number of false alarm targets and N groundtrue is the number of the ground truth targets. The ROC curve is shown below. As shown in Fig. 9, it is obvious that APT CFAR and bilateral CFAR are better than standard CFAR, just as the area under curve
In order to evaluate the performance of the algorithm, we compare it with standard CFAR and bilateral CFAR. Standard CFAR uses intensity as the criterion for the detection. Whereas bilateral CFAR uses fusion distribution for the detection, which is based on intensity and spatial information in different ways. In order to evaluate the performance of the algorithm in detail, we get the receive operating characteristic (ROC) curve through a large number of images from TerraSAR-X. At the same time, we define the target detection probability as
Pd ¼
Ntd Ntotaltarget
ð14Þ
where N td is the number of the detected targets and N totaltarget is the number of all targets. The estimation of the false alarm probability is defined as
Pfd ¼
N fd Ngroundtrue
ð15Þ Fig. 9. Comparison of performance curves for detection.
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(AUC) of the latter is smaller than others. This is because it considers only the intensity characteristics of the image. The trends of APT CFAR and bilateral CFAR are similar. However, when P f is less than about 104, Pd of the APT CFAR is higher than bilateral CFAR. It means that the detection accuracy of the former is higher in the more complicated sea condition and low contrast. And with the increase of Pf , the overall detection of APT CFAR is better than the latter. The main reason is that the process is based on the dynamic enhancement of the pixel weights, resulting in the improvement of target contrast. 4. Conclusions In the SAR images, according to the distribution relationship between the target and background, the model of the background clutter is considered as the Gaussian distribution. And the target pixels are distributed at both ends of the histogram obviously. Based on the distribution, The APT CFAR algorithm combining the intensity and spatial information is proposed to detect ships. In the APT domain, the characteristics of targets (ships or wakes) are more prominent. At the same time, it makes the model more tolerant. Moreover, in the high target contrast, it is more accurate for the detection, combining characteristics of the target self and the wake detection. Finally, simulated and real SAR images verify the robustness of the proposed algorithm. However, due to the variability of sea conditions and the complexity of different SAR image features, the distribution model of the background may be different. It is still a challenge for finding reliable detection algorithms. Conflict of interest The author declares that they have no conflict of interest concerning the content of this study. Acknowledgement This work was supported by the National Natural Science Foundation of China (61701233) and Open Foundation of State Key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2016-2-07).
Appendix A The dataset comes from the TerraSAR-X. It can be downloaded from http://www.intelligence-airbusds.com/en/6819-radar-dataset-sample-imagery-detail?product=37970. Its details are as follows. Location: Singapore File format: Geo Tiff Resolution: 3 m Acquisition mode: Strip Map Product type: MGD
Polarization mode: Single Polarization mode: HH Orbit: Ascending Angle of incidence: 23.93 Date: 05/17/2010
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