Ship detection from PolSAR imagery using the ambiguity removal polarimetric notch filter

ISPRS Journal of Photogrammetry and Remote Sensing 157 (2019) 41–58

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Ship detection from PolSAR imagery using the ambiguity removal polarimetric notch filter

T

Tao Zhanga, Linfeng Jianga, Deliang Xiangb, Yifang Banc, Ling Peia, Huilin Xionga,

⁎

a

Shanghai Key Lab. of Intelligent Sensing and Recognition, Shanghai Jiao Tong University, Shanghai, China National Innovation Institute of Technology, Beijing, China c Division of Geoinformatics, KTH Royal Institute of Technology, Stockholm, Sweden b

ARTICLE INFO

ABSTRACT

Keywords: PolSAR Ship detection Azimuth ambiguity removal GP-PNF PSH Depolarized energy ratio of targets

Ship detection from Polarimetric Synthetic Aperture Radar (PolSAR) imagery has attracted a lot of attention in recent years. Some studies highlight that azimuth ambiguity caused by the Doppler phase aliasing is one of the primary factors degrading the performance of ship detection. To address this problem, a new algorithm is proposed in this paper, which is based on improving the geometrical perturbation-polarimetric notch filter (GPPNF). Specifically, we first give the explanation of the polarimetric feature pedestal ship height (PSH) and theoretically verify that it can reflect the depolarized energy ratio of targets. Subsequently, the backscattering differences between ship and rough sea surface are analyzed using the Yamaguchi four-component decomposition. Based on these analyses, a new feature vector aimed at removing azimuth ambiguity and detecting ships is finally constructed to improve GP-PNF. In order to demonstrate the effectiveness of proposed algorithm, we carry out five experiments using real PolSAR datasets acquired by the UAVSAR L-Band and AIRSAR C-Band sensors. A sufficient comparison with five other state-of-the-art methods shows that the proposed algorithm is characterized by a better capability to remove azimuth ambiguities and detect ships simultaneously. Last but not least, we also theoretically deduce that the depolarization-only methods are unable to detect ships when sea surface is rough enough.

1. Introduction Synthetic Aperture Radar (SAR) system can operate both during day and night, as well as in almost all weather conditions (Atteia and Collins, 2013), and it has been widely used for ocean monitoring. In particular for maritime surveillance track, the ship location is useful for many applications, e.g., maritime traffic safety, fisheries monitoring, and oil spill detection. The backscattering, denoting the scattering characteristics of objects, is usually used to detect ships. Nonetheless, ship detection is still a challenging task since the misinterpretation of the backscattering caused by ocean surface can produce a large number of false alarms. Fortunately, ships often have more complicated scattering mechanisms than sea surface. For example, few dihedral backscattering takes place over the sea surface, yet they are plentiful on most ships. Following these rationales, much effort has been devoted to developing approaches for ship detection in recent years. Iervolino et al. (2015) adopted the generalized likelihood ratio test (GLRT) method to detect

ships. In Crisp (2004), the constant false alarm rate (CFAR) algorithms using different statistical distributions of background clutter were proposed to detect ships. Liu and Lampropoulos (2006) also demonstrated that the multi-CFAR detector was effective in ship detection. However, the methods associated with statistical models are likely to be useless when the statistical difference that describes the scattering intensity distribution difference between ship pixels and sea clutter pixels is not obvious. Alternatively, the intensity information collected by single-polarization model is applied to ship detection. For instance, the intensity of the cross-polarization channel HV was adopted to detect ships in Marino et al. (2013b). However, the single-polarization-based methods are also sensitive to the scattering mechanisms of background clutter (Nunziata et al., 2012). Clutter pixel with higher intensity may be detected as ship pixel, which is a major limitation for the use of this kind of algorithms. In contrast to single-polarization models, multi-polarization models can provide more polarimetric scattering information to reveal the differences between ship and sea clutter. Primitively, the polarimetric

Corresponding author. E-mail addresses: [email protected] (T. Zhang), [email protected] (L. Jiang), [email protected] (Y. Ban), [email protected] (L. Pei), [email protected] (H. Xiong). ⁎

https://doi.org/10.1016/j.isprsjprs.2019.08.009 Received 9 January 2019; Received in revised form 4 August 2019; Accepted 8 August 2019 Available online 05 September 2019 0924-2716/ © 2019 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

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power detector (SPAN), polarimetric whitening filter (PWF) detector, and power maximization synthesis (PMS) detector (Chaney et al., 1990; Novak et al., 1993), just fusing multi-channel polarimetric information, were constructed to discriminate ships from sea clutter. Even though these detectors are able to detect ships, they may still lose some low backscattering vessels (Gao et al., 2013). In Nunziata et al. (2012), Nunziata et al. exploited different reflection symmetry (RS) to characterize man-made metallic targets and sea clutter. Then, a filter was developed to detect ships. Experimental results showed that RS can be effective for ship detection. Similarly, Xiang et al. (2016) used the reflection asymmetry of man-made targets to extract small man-made targets. By decomposing polarimetric targets, Cloude and Pottier (1996) utilized polarimetric parameters, such as entropy, eigenvalues, and scattering angle to detect ships, whereas they were also easily influenced by sea state. With the aim of finding a more robust approach, Yang et al. (2001) introduced a new parameter to reflect the similarity degree between two scattering matrices. For ship detection, the crucial point is to extract useful polarimetric features, e.g., the degree of polarization (DoP) which represents the distance of a normalized Stokes vector’s last three components from the origin on the Poincare sphere (Shirvany et al., 2012). Touzi et al. (2015) took advantage of the quad-polarization datasets to demonstrate that an optimization over the all possible DoPs was able to detect ships. Based on the dual-pol SAR data and different polarimetric scattering models, Shirvany et al. (2012) verified the effectiveness of the degree of depolarization (DoD) in detecting man-made objects over the sea surface. In Praks et al. (2009), Praks et al. constructed a depolarization metric (Dep) to indicate how far one matrix from a set of Muller matrices of nondepolarizing targets. In practice, the performance of the depolarization-only methods is also related to oceanic condition. They may be noneffective for the non-Bragg scattering sea surface. Apart from the mentioned methods, Marino et al. (2012), Marino (2013) and Marino and Hajnsek (2015) proposed a new detector derived from the polarimetric target complex space to detect targets at sea, which was named geometrical perturbation-polarimetric notch filter (GP-PNF). A series of experiments on different PolSAR datasets verified its ability to detect ships. In spite of this, GP-PNF is unable to effectively remove azimuth ambiguities since the characteristics of azimuth ambiguities are also included in the feature vector of GP-PNF. As far as we know, few studies have been done to cure this deficiency. Therefore, it is meaningful to develop a new feature vector for further improving the detection performance of GP-PNF. The range and azimuth ambiguities can constantly cause false alarms and seriously decrease ship detection accuracy if they are not screened out. This is because such targets usually have similar scattering intensities as their corresponding real ships. By decomposing the coherency matrix [T], Liao et al. (2009) and Wang et al. (2012a) found that the third eigenvalue 3 was useful for discarding azimuth ambiguities and detecting ships. However, this method may not obtain the complete structures of ships and still produces missing detections. Wei et al. (2016) used the cross-correlation between volume scattering and helix scattering to remove azimuth ambiguities for improving the accuracy of ship detection. Although experimental results showed that this method is useful for the removal of azimuth ambiguities, it may still miss the detection of small ships when the sea surface is rough. Velotto et al. (2013) found that HV and VH channels were approximately equal in phase for ships, whereas the phase difference was close to for azimuth ambiguities. Then, a detector HVfree was developed to remove azimuth ambiguities. However, HVfree asked us to have independent HV and VH channels firstly. Since only a few sensors (e.g., TerraSAR-X) can obtain different HV and VH channels simultaneously, this method cannot be widely used in practical applications. In the early work (Zhang et al., 2017), we proposed a ship detection scheme by combining the scattering intensity and the polarimetric feature pedestal ship height (PSH) which are both derived from polarimetric covariance difference matrix [CPCDM ] together (here, we name it BPCDM). Despite

that the experiments verified the effectiveness of BPCDM on azimuth ambiguities removal, the structures of detected ships are incomplete. Besides, the scattering characteristic of PSH was also not clarified in Zhang et al. (2017) where we just experimentally found that PSH was able to remove azimuth ambiguities. As a fact, PSH plays an important role in the new method developed in this paper. Thus, we will theoretically explain its scattering meaning in the following sections. Overall, inspired by the above-mentioned methods, this paper presents a new azimuth ambiguity removal method, i.e., the ambiguity removal polarimetric noth filter for ship detection by improving the original feature vector of GP-PNF (for simplicity, we here call the new method “AR-PNF”). The main contributions of this paper are highlighted below: (1) Aiming at the lack of the theoretical interpretation on PSH, we first analyze the scattering meaning of PSH in both cases of sea surface and ship, and then theoretically verify its capability to reflect the depolarized ratio of targets and remove azimuth ambiguities. (2) The X-Bragg scattering model [TX ] is adopted to analyze the polarimetric scattering differences between ship and rough sea surface. Through comparing the surface scattering model [Ts ] (i.e., the Bragg scattering model) and [TX ], we theoretically verify that the depolarization-only methods may lose their effectiveness on ship detection when the sea surface is rough enough. (3) We construct a new feature vector t via combining the features PSH, “T11 + T22 ”, T23, and T33 together. Then, by replacing the original feature vector of GP-PNF with t , a new ship detection algorithm AR-PNF is developed for overcoming the deficiency of GPPNF in dealing with azimuth ambiguity removal. The experiments carried out on five different PolSAR datasets show that the new algorithm holds a better capability to detect ships than five other state-of-the-art methods. The remainder of this paper is organized as follows: Section 2 describes the theoretical background. Section 3 presents the proposed scheme of ship detection in details. In Section 4, experimental results on five real PolSAR datasets are shown, and the results of other detection methods are also compared. Conclusions and perspectives are given in Section 5. 2. Theoretical background 2.1. Azimuth ambiguities Azimuth ambiguities, usually called “false ships” or “ghost ships”, are caused by the sampling of the Doppler spectrum at finite intervals of the pulse repetition frequency (PRF) (Velotto et al., 2013; Liu and Gierull, 2007). When Doppler frequencies are higher than PRF, they are folded into the central part of the azimuth spectrum leading to producing aliased signals. Different from traditional “noises” in the SAR image, ambiguities are spatially distributed in azimuth ( xAZ ) and range( xRA ) directions as follows (Li et al., 1983),

xAZ xRA

nfP v fDR n fP fDR

,

(fDC +

(1)

nfP 2

),

(2)

where n is the number of ambiguities (n = 1,2,3…), fP is the PRF, v denotes the velocity of a platform, is the radar wavelength, fDR and fDC are the Doppler rate of the azimuth reference function and the Doppler centroid frequency, respectively (Wang et al., 2012a). Obviously, analyzing Eq. (1), we can find that there is no difference between the C-Band image and its corresponding L-Band image in the azimuth direction when the other parameters are fixed, since Eq. (1) is unrelated to the wavelength. However, analyzing Eq. (2), one can see 42

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T. Zhang, et al.

that the range distance between real targets and their corresponding ambiguities becomes closer when a radar system has a shorter wavelength with other unchanged parameters. Namely, in the range direction, there is less a problem in ambiguity for a radar system of long wavelength in comparison with that of short wavelength because the ambiguity is far away from the corresponding target or it can be outside of the area of interest (Wei et al., 2014). Consequently, ambiguities will appear severely in the C-Band SAR image, whereas almost no ambiguities can be found in the corresponding locations of L-Band SAR image (Wang et al., 2012a; Wei et al., 2014). Thus, like many similar studies, we here also focus on the removal of azimuth ambiguities in the C-Band PolSAR imagery. Moreover, from a viewpoint of scattering mechanism, the single- and double-bounce scatterings of ships mainly yield their corresponding azimuth ambiguities that look like relatively double- or single-bounce scattering, and the last eigenvalue (i.e., the third eigenvalue) of azimuth ambiguity is low (Wang et al., 2010; Freeman, 1993).

vector k. The superscript (·)T denotes matrix transpose and “∗” means complex conjugate. Then, the partial target to be detected is renewedly named t T . A pseudo target t P is further obtained by perturbing t T slightly, in other words, all the components of t T are modified slightly. After a series of mathematical manipulations, the expression of the GP-PNF detector is finally given by Marino et al. (2012),

In this section, we theoretically deduce the scattering meaning of the polarimetric feature pedestal ship height (PSH). Then the scattering differences between ship and sea surface are analyzed based on the Yamaguchi four-component decomposition (Yamaguchi et al., 2006). At last, a new ship detector AR-PNF is proposed by combining a redesigned feature vector and the frame of GP-PNF together. 3.1. Analysis for ocean surface psh polarimetric signature It is well known that sea polarimetric behavior changes as the incidence angle, currents, wind velocity, etc., changes. Reflection symmetry (RS) is an important symmetry property to characterize the ocean background, which can lead to the like- and cross-polarized scattering amplitudes uncorrelated (Nghiem et al., 1992; Nghiem et al., 1993; Yueh et al., 1994). In other words, sea surface without man-made artifacts such as oil rigs or ships, satisfying reflection symmetry, calls for a negligible correlation between the like- and cross-polarized channels (Nunziata et al., 2012), i.e.,

(3)

where the superscript means conjugate transpose, · indicates spatial averaging. And, k is a 3-D Pauli scattering vector derived from the Sinclair scattering matrix [S] in the case of monostatic sensor and reciprocity,

(·) H

[SHH + SVV , SHH

(4)

Then, when the scattering belongs to the Bragg scattering, the eigenvalues in Eq. (5) can be simplified in terms of the scattering amplitudes as follows (Buono et al., 2016; Jin, 2010),

where SHH , SVV , and SHV are the elements of [S]. ki (i = 1,2,3) mean the abbreviations of scattering elements in the scattering vector, and the superscript (·)T denotes matrix transpose. Based on the eigenvalue–eigenvector decomposition, we can obtain three corresponding eigenvalues of [T] at each pixel in PolSAR imagery (Cloude and Pottier, 1997),

1

3

[T ] =

i [Ti ], i=1

1

= 2 ( |SHH |2 + |SVV |2 ) 1 | SHH |2 | SVV |2 2 | SHH |2 + | SVV |2

2

=

3

= 4 |SHV |2 ,

(1

2,

), (9)

where the configuration parameter

(5)

=

here, real eigenvalues 1, 2 , and 3 ( 1 2 3 ) represent the weights for each independent rank-1 target [Ti ], respectively.

SHH SVV SVV SHH |SHH |2 + |SVV |2

(10)

varies from 0 of totally random media to 1 of ordered media, i.e., norandom case (Jin, 2010). Since the window sizes of SHH SVV and SVV SHH are the same, is a real number. From Eq. (9), we can find that 1 and 2 depend on the co-polarized channels while 3 merely depends on the cross-polarized one. Therefore, the constructed feature PSH can be redefined as,

2.3. Geometrical Perturbation-Polarimetric Notch Filter (GP-PNF) GP-PNF is developed by Marino et al. (2012) and can effectively detect objects over sea surface by isolating and rejecting the sea returns in the polarimetric space of the scattering matrix. Here, we briefly introduce this method. More details of the mathematical and physical justifications of GP-PNF can be found in Marino et al. (2012), Marino et al. (2010) and Marino et al. (2013a). In GP-PNF, a 6-D feature scattering vector t is first defined to describe partial target (Marino et al., 2012), i.e.,

t = Trace([T ] 6) = [t1, t2, t3, t4, t5, t6]T = [ |k1 |2 , |k2 |2 , |k3 |2 , k1 k2 , k1 k3 , k 2 k3 ]T ,

(8)

SHH SHV = SHV SVV = 0.

SVV , 2SHV ]T

= [k1, k2, k3],

(7)

3. The proposed method

[T ] = k· k H

1 2

,

where RedR is a parameter named reduction ratio, PT means the power of target pixel. If the partial target has a stronger component on the target of interest, PT will be higher, which results in being closer to 1.

In order to interpret the polarimetric scattering information contained in PolSAR imagery, it is necessary to analyze and use the secondorder-statistics matrices consisting of the covariance matrix [C] and the coherency matrix [T] (Cloude and Pottier, 1996; Cloude et al., 2001). Here, we adopt the coherency matrix [T] to construct our method.

k=

1

1 + RedR P

T

2.2. Coherency matrix and eigenvalue decomposition

T11 T12 T13 = T21 T22 T23 , T31 T32 T33

1

=

3

PSH = 1

+

(11a)

2

=8×

|SHV |2 . |SHH |2 + |SVV |2

(11b)

In Eq. (11b), PSH obviously represents the ratio between the crossand co-polarizations. Different from the formula in Zhang et al. (2017), the absolute value signs are not adopted in Eq. (11a), because the eigenvalues derived from [T] are all positive. Furthermore, Eq. (11b) is equal to the formula of the depolarization ratio (DR) (Maghsoudi,

(6)

where 6 is a complete set of 6 × 6 basis matrix under a Hermitian inner product and ki (i = 1,2,3) are the elements of the 3-D Pauli scattering 43

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T. Zhang, et al.

Fig. 1. The distribution curves of depolarized energy ratio calculated from five different purple transects. (a) The purple transect in the dataset A; (b) The purple transect in the dataset B; (c) The purple transect in the dataset C; (d) The purple transect in the dataset D; (e) The purple transect in the dataset E. Note that, we here use four different formulas to calculate the depolarized energy ratio.

2011), dividing by the constant “8”,

DR =

=

1 × 8

ships are reflection asymmetry with a considerable SHH SHV term. Naturally, the formula of PSH is different from that of DR in this case, and Eqs. (11) and (12) will not be established. According to Holm-Barnes decomposition theorem (Holm and Barnes, 1988), [T] can be separated into polarized and unpolarized terms,

|2

|SHV |SHH |2 + |SVV |2 3 1

+

. 2

(12a) (12b)

T11 T12 T13 [T ] = U3 T21 T22 T23 U3 1 T31 T32 T33

It means that PSH can not only be computed from eigenvalues but also from the intensities of three different scattering channels. Consequently, PSH is another expression of DR which can reflect the depolarized energy ratio of targets.

= U3

3.2. Analysis for ship PSH polarimetric signature Compared to sea surface, a different backscattering behavior can be expected in ship. Due to the complicated structures, ship backscatters are often various, including single-bounce returns, double-bounce returns, multiple-bounce returns and so on Velotto et al. (2013). Thus,

p1

+ U3

44

p3 0 0

(13a)

0 p2

0 p3 0 U3 1 0 0

p3 0 0 0 p3 0 U3 1, 0 0 p3

(13b)

(13c)

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T. Zhang, et al.

where U3 is the eigenvectors of [T], pi (i = 1, 2, 3) are the eigenvalues that are normalized using SPAN which is defined as the total backscattering power of [T] (Ainsworth et al., 2000), i.e.,

Table 2 The results of Pd and FoM. Scene

(14)

SPAN = T11 + T22 + T33.

The term of Eq. (13c) is completely independent of the transmitted and received polarizations. It is related to the depolarized energy ratio of the radar returns. The whole depolarized energy ratio is mathematically equal to 3 p3 that is proportional to p3 (Ainsworth et al., 2000). In order to study the relationship between PSH and the depolarized energy ratio, here, we first find the relationship between PSH and p3 . Due to the fact that p1 + p2 + p3 = 1, p1 p2 p3 0 (if 1 p2 = p3 = 0, p1 > 0 ), we can achieve 0 p3 . Recalling Eq. (11a), 3 we redefine it in terms of p3 ,

PSH =

p3 p1 + p2

=

p3 1

p3

.

Under the condition of 0 further calculated as:

PSH =

(15)

p3

1 , 3

Method

Ngt

Nfa

Ndt

Pd (%)

FoM

A

PSH-only RS HV BPCDM GP-PNF AR-PNF

70 70 70 70 70 70

1 0 0 0 0 0

68 70 70 70 70 70

97.1 100 100 100 100 100

0.958 1 1 1 1 1

B

PSH-only RS HV BPCDM GP-PNF AR-PNF

10 10 10 10 10 10

>20 1 1 1 1 0

5 7 8 8 7 9

50 70 80 80 70 90

0 0.64 0.73 0.73 0.64 0.90

C

PSH-only RS HV BPCDM GP-PNF AR-PNF

12 12 12 12 12 12

>100 2 0 1 5 0

0 10 9 12 10 12

0 83.3 75 100 83.3 100

0 0.714 0.75 0.923 0.588 1

D

PSH-only RS HV BPCDM GP-PNF AR-PNF

15 15 15 15 15 15

>50 3 1 0 4 1

0 12 15 15 14 15

0 80 100 100 93.3 100

0 0.667 0.938 1 0.737 0.938

E

PSH-only RS HV BPCDM GP-PNF AR-PNF

9 9 9 9 9 9

>100 2 2 1 3 0

0 6 8 9 4 9

0 66.7 88.9 100 44.4 100

0 0.545 0.73 0.90 0.333 1

Average

PSH-only RS HV BPCDM GP-PNF AR-PNF

… … … … … …

… … … … … …

… … … … … …

29.4 80 88.8 96 78.2 98

0.19 0.713 0.829 0.911 0.66 0.968

the derivative of PSH can be

PSH 1 = > 0. p3 (1 p3 )2

(16)

Observing Eq. (16), we clearly find that PSH is a monotonic function. This means that a positive correlation relationship exists in PSH and p3 . Therefore, the characteristic of PSH is similar as p3 to some extent. That is to say, when p3 is able to depict the depolarized energy ratio of targets, PSH can also reflect the depolarized energy ratio. Different from some traditional depolarized parameters, such as DoD, the range of PSH is [0, 0.5]. To summarize, the analyses of the above two subsections demonstrate that PSH can reflect the depolarized level of targets. The target is totally polarized for PSH = 0, totally depolarized for PSH = 0.5. When dealing with most natural scenarios, depolarized scattering mechanism is generally applied. Ocean surface usually has negligible unpolarized energy. Nevertheless, when a rough sea surface takes place, the depolarized energy ratio of sea surface will be higher and cannot be ignored. In such situation, only using the depolarization characteristic for ship detection may be useless. To verify this speculation, here, we analyze the depolarization distribution curves of five different transects that are respectively chosen from the experimental datasets A, B, C, D, and E (i.e., the five 1 × 400 purple lines in the SPAN subgraphs of Fig. 4). Four different formulas of depolarized energy ratio, i.e., DoD, Dep, PSH, and p3 are also adopted for comparison. Note that, the detailed descriptions of these five datasets can be found in Section 4. Observing Fig. 1, we can find that the depolarized energy ratio differences between ship pixels and clutter pixels are more obvious in the purple transect of A than those of B, C, D, and E. Namely, the depolarization-only methods will be insufficient to detect ships over rough sea surfaces (i.e., the datasets B, C, D, and E). More theoretical reasons will be presented in the following subsection. On the other hand, these curves also indirectly reflect that different expressions of the depolarized energy ratio are related to each other. To some extent, they all have a similar variation when the normalized eigenvalue p3 changes. Next, we focus on the performance comparison between PSH and p3 . Note that, the lines of these two features have been normalized in Fig. 2

for a fair comparison. From Fig. 2, it can be seen that the values of PSH are lower than p3 . This means that PSH can more easily suppress the depolarized energy ratio of targets (including ships, sea clutter, and azimuth ambiguities) than p3 . The TCR values shown in Fig. 8, Tables 3–6 can also verify this point, where each value of PSH is lower than p3 . In spite of this, observing Tables 3–6, we can also find that the T difference between PSH and p3 is respectively 0.29 dB, 0.02 dB, 0.19 dB, and 0.19 dB. This directly implies that the depolarized energy ratio of azimuth ambiguities can be suppressed more seriously by PSH than p3 . Therefore, in this paper, we adopt PSH rather than p3 to distinguish ships from azimuth ambiguities. Considering that ship breaks the reflection symmetry, here, we still use Eq. (11a) to calculate PSH. 3.3. The scattering differences between ship and rough sea surface It is well known that the scattering mechanisms of sea surface and

Table 1 Parameters of these five SAR data sets. Sensor

Location

Scene ID.

Date

Resolution (m) Slant Range × Azimuth

Band

Range Looks

Azimuth Looks

Polarization

UAVSAR AIRSAR AIRSAR AIRSAR AIRSAR

Barataria Bay San Francisco Bay Kojima-wan Bay Tokyo Bay Hiroshima Bay

A B C D E

2010/06/23 1994/07/15 2000/10/04 2000/10/02 2000/10/04

7.2 × 5.0 6.7 × 9.3 4.6 × 3.3 4.6 × 3.3 4.6 × 3.3

L C C C C

8 1 1 1 1

12 18 9 9 9

Full Full Full Full Full

45

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Fig. 2. The normalized distribution curves of depolarized energy ratio calculated from PSH and p3 . (a) The purple transect in the dataset A; (b) The purple transect in the dataset B; (c) The purple transect in the dataset C; (d) The purple transect in the dataset D; (e) The purple transect in the dataset E. Table 3 The TCR values of the chosen area in B (dB).

Table 4 The TCR values of the chosen area in C (dB).

Method

Method

Target

p3

PSH-only

RS

HV

BPCDM

GP-PNF

AR-PNF

Target

p3

PSH-only

RS

HV

BPCDM

GP-PNF

AR-PNF

S1 S2 S3 T3 T4 T5 T6 T7 T8 T9 A4 T

4.87 3.75 2.93 −3.51 2.92 5.28 −5.47 4.01 2.66 1.92 −9.59 4.12

5.04 3.87 3.01 −3.55 3.04 5.58 −5.53 4.17 2.80 1.99 −9.67 4.41

10.35 7.43 3.19 38.77 34.12 27.95 40.97 29.93 28.41 23.45 20.90 −17.71

11.13 6.13 6.77 29.39 27.43 26.53 31.84 25.02 25.96 19.21 8.73 −2.60

5.91 5.53 3.73 −2.85 2.90 5.77 −3.53 4.87 2.48 3.12 −10.81 6.28

10.78 12.60 12.56 33.36 28.16 30.83 30.04 28.90 33.58 27.58 22.34 −11.56

22.82 17.29 15.87 35.36 34.38 36.25 30.94 32.63 34.23 27.67 13.03 2.84

T11 T12 S5 A11 A12 T

−3.95 −13.55 −5.52 −15.64 −26.70 2.09

−4.38 −14.49 −6.26 −16.60 −27.68 2.11

22.80 20.99 10.10 10.40 22.45 −11.35

19.08 10.84 7.32 −0.59 7.51 −0.19

0.11 −9.80 −0.88 −17.51 −16.91 8.71

26.49 28.80 16.19 19.11 25.99 −9.8

19.96 14.72 12.37 5.41 0.92 6.96

T: The difference between the lowest ship TCR and the highest azimuth ambiguity TCR.

ships are different. Analyzing their intrinsic scattering differences is an important way for ship detection. In Yamaguchi et al. (2006), Yamaguchi et al. used four scattering coherency matrices to describe the coherency matrix [T],

T: The difference between the lowest ship TCR and the highest azimuth ambiguity TCR. 46

ISPRS Journal of Photogrammetry and Remote Sensing 157 (2019) 41–58

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when the backscattering over the sea surface belongs to the non-Bragg scattering. Here, we use the X-Bragg scattering model as a means to describe the non-Bragg scattering (Hajnsek et al., 2003; Yin et al., 2015),

Table 5 The TCR values of the chosen area in D (dB). Method Target

p3

PSH-only

RS

HV

BPCDM

GP-PNF

AR-PNF

S6 S7 T22 T23 T24 A22 T

−1.57 −2.41 −6.26 −3.97 −5.19 −17.09 10.83

−1.85 −2.79 −6.90 −4.47 −5.78 −17.92 11.02

13.57 12.44 23.99 30.48 35.40 22.07 −9.63

6.84 6.33 15.58 23.74 24.11 4.93 1.40

1.88 1.41 −2.45 1.78 −1.34 −18.24 15.79

17.55 17.72 26.09 29.10 29.15 23.42 −5.87

11.95 12.13 19.53 24.22 24.90 7.74 4.21

[TX ] C1 C2sinc (2 1) = C2sinc (2 1) C3 (1 + sinc (4 1)) 0 0 C3 (1

C1 = |SHH + SVV |2 /2, C2 = (SHH + SVV )(SHH C3 = |SHH SVV |2 /4,

Method Target

p3

PSH-only

RS

HV

BPCDM

GP-PNF

AR-PNF

T31 T32 T33 S10 S11 S12 S13 S14 S15 A31 A32 A33 T

−4.66 −5.16 −8.13 −6.75 −2.41 −8.02 −3.35 −3.06 −5.96 −8.22 −15.50 −8.62 0.09

−5.46 −5.89 −8.94 −7.74 −2.97 −8.98 −4.04 −3.71 −6.90 −9.26 −16.64 −9.69 0.28

27.09 24.17 29.18 11.27 12.94 12.82 15.47 13.20 16.91 0.63 13. 08 2.02 −1.81

19.37 15.49 13.52 3.73 7.86 1.58 6.65 4.86 6.64 −1.73 0.88 −1.96 0.7

0.91 −0.19 −7.63 −1.63 3.44 −7.38 1.20 0.39 −0.74 −8.58 −14.92 −8.93 0.95

27.99 25.54 31.26 14.94 13.29 17.53 14.43 12.81 17.16 13.48 22.02 15.13 −9.21

19.08 16.83 13.04 10.05 12.06 8.76 11.25 9.46 12.70 5.70 8.06 5.74 0.7

LLRR

[T ] = fs [Ts] + fd [Td] + fv [Tv ] + fc [Tc ] 1

fv 4

(17)

are the expansion coefficients to be dewhere fs , fd , fv , fc , and termined. [Ts ] , [Td] , [Tv ] , and [Tc ] correspond to surface, doublebounce, volume, and helix scattering mechanisms, respectively. is related to the reflection coefficients ( < 1). Usually, man-made objects can be characterized by these four scattering models. However, the scattering mechanisms of sea surface are different and predominated by the Bragg scattering, which can be described using the Bragg scattering model, i.e., the surface scattering model Xi et al. (2017),

1 [Ts] =

0 | |2 0 . 0 0 0

(20)

T22 T33 = sinc (4 1). T22 + T33

(21)

With the increasing of the roughness 1, the HV backscattering power will increase (Hajnsek et al., 2003). When 1 = 0, the HV power is zero, the coherence matrix will be equal to the “pure” Bragg matrix, i.e., Eq. (18) (Hajnsek et al., 2003). Seeing Eq. (19), we can find that the (3,3) term TX 33 of [TX ] is not zero, leading to the cross-polarized scattering HV. Fortunately, due to the complicated reflections of ship structure, ship often has much stronger HV intensity than sea surface. Thus, the cross-polarized scattering HV is still capable of detecting ships and we cannot neglect it. Though several studies have demonstrated why HV-VH has less ambiguity (e.g., (Liu and Gierull, 2007)), further work should be carried out on identifying why HV alone appears to have less ambiguities. In this paper, we still add the cross-polarized intensity T33 as a key polarimetric feature into the new feature vector. Moreover, due to the existence of HV, using Eq. (12a) we can obtain an non-zero DR value, which means that the depolarization energy is not zero in this case. If the depolarization energy is strong enough, only using PSH (i.e., the PSH-only method) for ship detection is impossible because the depolarization difference between ship and sea surface is not obvious as shown in Fig. 1(b)-(d). However, as mentioned before, the depolarized scattering of azimuth ambiguities is lower than their corresponding ships (Wang et al., 2010). Hence, we choose PSH as another important feature for removing azimuth ambiguities in the new feature vector. In Eq. (17), the Yamaguchi decomposition also gives the helix scattering model. It is clear that the (2,3) term of [Ts ] or [TX ] is zero, which theoretically reflects that the helix scattering cannot exist over sea surface. In practice, the helix scattering is produced by the combination of two or more coherent scatterers (e.g., diplanes), and often exists in man-made objects (Wang et al., 2012b). Thus, the helix scattering can be directly used to detect ships via thresholding. As another fact, the scattering mechanisms of azimuth ambiguity mainly consist of the single-bounce scattering and double-bounce scattering (Wang et al., 2012a). Although no work has theoretically verified the effectiveness of helix scattering on the removal of azimuth ambiguities, some experimental results have indirectly reflected that the helix scattering is able to distinguish ships from azimuth ambiguities. For instance, in Wei et al. (2016), Wei et al. empirically found that the helix scattering of azimuth ambiguities is much smaller than ships. Therefore, we here adopt T23 which includes the helix scattering component into the new feature vector.

T: The difference between the lowest ship TCR and the highest azimuth ambiguity TCR.

+

SVV ) /2,

here 1 is the surface roughness parameter, lying in the interval of [0, 90°] (Buono et al., 2016; Hajnsek et al., 2003). It can be calculated from Eq. (23) in Hajnsek et al. (2003), that is,

Table 6 The TCR values of the chosen area in E (dB).

0 | |2 0 | |2 0 + fd 1 0 0 0 0 0 0 0 0 0 0 2 0 0 f 0 1 0 + 2c 0 1 ±j , 0 0 1 0 ±j 1

(19)

where

T: The difference between the lowest ship TCR and the highest azimuth ambiguity TCR.

= fs

0 0 , sinc (4 1))

(18)

From Eq. (18), one can find that the sea surface backscattering is mainly related to Ts11 with three small scattering elements (i.e., Ts12, Ts21, and Ts22 ). It is worth noting that the cross-polarized scattering Ts33 is zero here, which directly results in that only two eigenvalues can be calculated from [Ts ] and the third eigenvalue 3 is zero. Therefore, we can deduce that the corresponding PSH value is theoretical zero using Eq. (11a). It suggests that the depolarization-only methods can be used to detect ships in the case of the Bragg scattering sea surface (see Fig. 1(a)). In fact, these methods will loss the efficacy of ship detection

3.4. The ambiguity removal GP-PNF (AR-PNF) In practical, the mentioned features may be difficult to detect ships 47

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with low backscattering from azimuth ambiguities over rough sea surface. For example, a small ship with simple structure may have similar depolarization or HV intensity to azimuth ambiguity. Thus, we should expect complementary information provided by other polarimetric features to further improve the detection accuracy. To achieve this goal, we adopt another intensity feature here. Different from the way applied in the original feature vector of GP-PNF, we take the sum of the intensities of single- and double-bounce scatterings as one polarimetric feature in the proposed vector. This modification can contribute to detecting small ships because of the enhanced intensity. At the same time, it can also reduce the dimension of the new vector compared to the original GP-PNF one. Therefore, the new polarimetric feature vector is finally designed as,

t

= PSH × [(T11 + T22), T23, T33]T = [PSH × (T11 + T22), PSH × T23, PSH × T33]T = [t1 , t 2, t3].

(22)

The purpose of using the multiple operation in Eq. (22) is to further avoid the detection of azimuth ambiguity. For example, azimuth ambiguity often has strong single- and double-bounce scattering, so “T11 + T22 ” may lose the ability to remove the azimuth ambiguity with high scattering intensity. Then, a variation needs to be performed on “T11 + T22 ”. An easy way to solve this problem is by multiplying an extra feature that can effectively suppress azimuth ambiguity. Hence, we choose PSH as one key multiplier in t1 . In summary, compared to Eq. (6), the redesigned vector t is focused on the more useful features that can separate ships from azimuth ambiguities and sea clutter. In Eq. (6), only the ordinary six elements of the covariance matrix [C] are used for ship detection, that the characteristics of azimuth ambiguity are contained simultaneously. Thus, GPPNF cannot remove azimuth ambiguity effectively. On the contrary, the information of azimuth ambiguity is separated well in Eq. (22). We then replace the original feature vector t with t in the GP-PNF frame, and construct a new ambiguity removal polarimetric notch filter, i.e., the AR-PNF method as follows: new

=

1 1 + RedR

1 t

T

t

Fig. 3. The flowchart of the proposed method.

C, D, and E) are obtained by the NASA/JPL AIRSAR C-Band PolSAR sensor. In detail, B was obtained from San Francisco Bay on July.15, 1994, which Pauli and SPAN images are respectively presented in Fig. 4(b) and (e). D was acquired on Oct.4, 2000 that covered Kojimawan Bay in Japan (see Fig. 4(c) and (f)). C was achieved from Tokyo Bay on Oct.2, 2000 (see Fig. 4(g) and (i)). E was obtained from Hiroshima Bay on Oct.4, 2000 (see Fig. 4(h) and (j)). More details on these datasets can be found in Table 1. Note that, in this study, all the datasets are filtered by a 5 × 5 boxcar filter.

M,

| t t sea |

4.2. Estimations of the ground truth data

(23)

Due to the lack of the ground truth data, we here determine the ship locations via visual inspection. About the sea surface roughness, we mainly assess it by analyzing the scattering mechanisms over the sea surface. Besides, 1 is also used to quantitatively reflect the sea surface roughness of the adopted dataset. In detail, we randomly select a transect (1 × 400) from each dataset as the basis of analysis. The five transects are drawn using cyan lines in Fig. 4(d), (e), (f), (i), and (j). Then, the diagonal elements, i.e., T11, T22 , and T33 , are extracted from the coherence matrices of these transects and the corresponding distribution curves are respectively shown in Fig. 5(a)-(d). From Fig. 5(a), we can see that the distributions of A are in accordance with the Bragg scattering model [Ts ]. T11 is the largest departure from zero and T33 is close to zero. So, the sea surface scattering in A is deemed to be composed of the Bragg scattering. Conversely, the distributions of T22 and T33 are both near zero in Fig. 5(b), which means that [Ts ] cannot be adopted to characterize B. The distributions of C also break the surface scattering model, because T33 is much higher than zero and T22 is also occasionally higher than T11 (see Fig. 4(b)). It implies that the scattering in C belongs to the complicated X-Bragg scattering. Hence, the model [TX ] in Eq. (19) can be used to describe it. Similarly, we deduce that the X-Bragg scattering exists in D and E. In addition, the corresponding 1 distributions of the five transects are also shown in Fig. 6, where the 1 values of A are around 3.68°. It means that A has the calmest sea surface among these five datasets. B has a moderate sea surface, since its 1 values are around 10.95°. Similarly, we can also deduce that C has a rougher sea surface than B

where t sea is the normalized version of tsea (i.e., the partial vector of sea clutter). M is a threshold, which is most often calculated by Tello et al. (2005)

M=µ+c ,

(24)

where µ stands for the mean of the image, whereas is its standard deviation and c is an empirically adjusted parameter. The whole flowchart is also shown in Fig. 3. 4. Experiments and discussions In this section, the ship detection performance of AR-PNF is carried out on real PolSAR datasets. Five algorithms, namely, the PSH-only method, the HV method (Sugimoto et al., 2013), the Reflection Symmetry (RS) method (Nunziata et al., 2012), the Geometrical Perturbation-Polarimetric Notch Filter (GP-PNF) (Marino et al., 2012), and the BPCDM method (Zhang et al., 2017), are further adopted to compare the performance. 4.1. datasets Five PolSAR datasets acquired by two platforms and with different sea surface roughness are investigated to evaluate the performance of the proposed method. Specifically, the first dataset A was a NASA/JPL UAVSAR L-Band PolSAR dataset acquired on Jun.23, 2010, which covered Barataria Bay in the USA. Fig. 4(a) show its Pauli RGB image and Fig. 4(d) presents its SPAN image. The other four datasets (i.e., B, 48

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Fig. 4. Datasets A, B, C, D, and E. (a), (b), (c), (g), and (h) are their Pauli RGB images (Red: |SHH SVV |, Blue: |SHH + SVV |, Green: 2|SHV |). (d), (e), (f), (i), and (j) are their corresponding SPAN images. Yellow rectangles mean the real ships and orange dashed circles denote the azimuth ambiguities. The purple lines represent the chosen transects for calculating the depolarized energy ratio. The cyan lines are the chosen transects for analyzing the roughness of sea surfaces. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

because of its higher 1 values (around 11.60°). The 1 values of D are mainly around 11.93°, so the sea surface of D is rougher than the former three datasets. E has the roughest sea surface among the five datasets, since most of its 1 values are around 12.10°.

Pd =

Pf =

4.3. Evaluation criteria

Ndt , Ngt

Nfa Ncp

FoM =

In order to quantitatively evaluate the ship detection performance of these methods, we choose three metrics here, i.e., the receiver operating characteristic (ROC) curve which is a plot describing the probability of detection Pd against the probability of false alarms Pf while the threshold changes (Zhang et al., 2016), the figure of merit FoM (Zhang et al., 2017), and the target-to-clutter ratio TCR, which are respectively defined as

(25)

,

(26)

Ndt , Ngt + Nfa

TCR = 10log10

IT (dB), IC

(27) (28)

where Ndt denotes the number of detected targets, Ngt is the number of ground truth targets, Nfa means the number of false alarms, Ncp represents the number of sea clutter pixels, IT and IC denote the values of the adopted detector for target and clutter, respectively. Smaller values of Pd and FoM indicate lower detection performance. When all targets 49

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Fig. 5. (a), (b), (c), (d), and (e) respectively show the diagonal element distribution curves of the cyan transects in A, B, C, D, and E.

are detected without false alarms, Pd and FoM will be both equal to 1. In this paper, the threshold for each detector is selected manually to obtain the best detection mask. Note that, the parameters in GP-PNF and AR-PNF are both set to same values for a fair comparison, i.e., WinTest = 3, WinTrain = 45. Here, WinTest is the area where we check for presence of a target. It is usually a smaller window. WinTrain is the window used to evaluate the clutter, which is larger and surrounding the WinTest. More details can be found in Marino et al. (2010) and Marino et al. (2013a). 4.4. Experiment on the UAVSAR L-Band dataset

Fig. 6. The

1

The dataset A is a UAVSAR L-Band PolSAR image whose size is 1110 × 1650. Its corresponding SPAN image is shown in Fig. 4(d), where 70 ships are totally presented and none azimuth ambiguities exist. Fig. 7 shows the experimental results of these six methods. Although each method can detect all the 70 ships except for PSH-only, it is still necessary to briefly state the reasons behind these results. In Fig. 7(a),

distribution curves of the five cyan transects in A, B, C, D, and E.

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Fig. 7. The experimental results of A. (a) PSH-only; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the green dashed circles are the undetected ships, and the brown dashed circle denotes the false alarm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

most of the ships are detected by PSH-only, whereas one false alarm F1 (marked by a brown dashed circle) is still detected. This is reasonable because ships often have higher depolarized energy than ocean surface, using PSH can directly help us detect them as deduced in Section 3. Here, F1 is mainly caused by the ship wakes of W1 that have complicated scattering mechanisms. The reason for the result of RS (see Fig. 7(b)) is due to the fact that ships are reflection asymmetry, yet sea surface is reflection symmetry. Since the HV intensity of sea clutter is often lower than that of ship, using the HV detector can obtain a satisfying result (see Fig. 7(c)). Considering the efficiency and the fact that none azimuth ambiguities exist in A, we just adopt the first part of the BPCDM method here, i.e., the power of [CPCDM ] (Zhang et al., 2016), to detect ships. Obviously, BPCDM detects all the ships in Fig. 7(d) because of their enhanced powers. Owing to using the features derived from the complex space, in Fig. 7(e), GP-PNF also detects all the ships without one false alarm. Similarly, all the ships are detected by AR-PNF in Fig. 7(f). This is because the useful information for ship detection is still retained in the new feature vector of AR-PNF, though its dimension decreases from 6 to 3. Fig. 9 further shows the ROC curves of these different methods, where we can see that AR-PNF outperforms most detectors. When Pf is small enough, GP-PNF outperforms AR-PNF. Moreover, we also list the Pd and FoM values of these methods in Table 2, from which one can see that PSH-only has the lowest values on this dataset. However, the values of other five methods are the same to each other. In such situation, just using Pd and FoM cannot help us further evaluate the detection performance of these six detectors. Therefore, we further compare their corresponding TCR values. Fig. 9 shows the TCR values of these 70 ships, where AR-PNF holds the highest average TCR value which surpasses other five methods from 0.53 dB (GP-PNF) to 27.47 dB (PSH-only). This directly demonstrates that all the chosen features in the redesigned feature vector include sufficient information for distinguishing ships from sea clutter. From Fig. 9, it can also be seen that PSH-only has the lowest average TCR value among these six methods, which witnesses that PSH-only may

lose its ability to detect ships when the ocean surface becomes rougher. Furthermore, we also draw the TCR values calculated from p3 in Fig. 9. Obviously, the PSH-only average is a little higher than the p3 average, which verifies that PSH can enhance ships’ TCR more effectively than p3 . To sum up, the traditional methods can detect ships effectively when none azimuth ambiguities exists, and the proposed algorithm ARPNF may not have a significant advantage in this case, as shown in Fig. 8. 4.5. Experiments on the AIRSAR C-Band datasets The second dataset B is an AIRSAR C-Band PolSAR image with the size of 495 × 470. The corresponding SPAN image is shown in Fig. 4(e), where we can find one azimuth ambiguity A4 (marked by a brown

Fig. 8. The ROC curves of different methods on A. 51

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Fig. 9. Different TCR values of the 70 ships in A.

dashed circle). Please note, here, the complete BPCDM method is adopted for ship detection due to the existence of azimuth ambiguity. The results of these six detectors on B are exhibited in Fig. 10. Although PSH-only detects some ships, many false alarms are still detected simultaneously in Fig. 10(a). This is because the sea surface has high depolarized energy ratio. RS and GP-PNF have similar results, which both lose the detection of three small ships, and detect A4 in Fig. 10(b) and (e). In Fig. 10(c), HV detects A4 and misses two small ships. BPCDM removes A4 successfully in Fig. 10(d), while two small ships are missed and one false alarm F2 is also detected. Besides, the structures of some detected ships (e.g., T8) are not complete. This is because, when ship pixels have similar scattering mechanisms with their surrounding clutter pixels, the polarimetric covariance difference matrix [P] used in BPCDM cannot effectively reflect the scattering difference information of ships. Therefore, the scattering intensity calculated by [P] is near zero in this case, which directly leads to that some ship pixels cannot be detected by thresholding. The result of AR-PNF is shown in Fig. 10(f), where the azimuth ambiguity A4 is removed well. This directly verifies that the new feature vector of AR-PNF is effective

Fig. 11. The ROC curves of different methods on B.

on the removal of azimuth ambiguities. Nevertheless, the small ship S3 is missed by AR-PNF, which may be caused by its simple structure. It is noted that, compared to the detected ships in Fig. 10(d), the detected ships in Fig. 10(f) are much completer, such as T8, which also means that more ship pixels can be detected by AR-PNF. Hence, the detection performance of AR-PNF is better than BPCDM. Both the quantitative results listed in Table 2 and the ROC curves shown in Fig. 11 can also demonstrate this point. In addition, we list the TCR values of these targets in Table 3, where the T denotes the TCR difference between the lowest ship TCR value and the highest azimuth ambiguity TCR value. Thus, the negative T values of RS, HV, and GP-PNF imply that all of these three methods must detect A4 as long as we want to detect small ships. The positive T values of PSH-only, p3 , and BPCDM verify the effectiveness of the depolarized energy ratio on the removal of azimuth ambiguities. Fig. 10. The experimental results of B. (a) PSHonly; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the green dashed circles mean the undetected ships. The brown dashed circles represent the detected false alarms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 12. The experimental results of C. (a) PSHonly; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the green dashed circles mean the undetected ships. The brown dashed circles represent the detected false alarms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Moreover, the T value of PSH-only is 0.29 dB higher than p3 , which further demonstrates that PSH is better than p3 for removing azimuth ambiguities. Comparing AR-PNF and GP-PNF, we can find that the T value of the former is 14.4 dB higher than the latter. This means that the new feature vector t is useful for the azimuth ambiguities removal. The dataset C is another AIRSAR C-Band PolSAR image with size 1099 × 955. Fig. 4(f) shows its SPAN image, where we can easily find the azimuth ambiguities, e.g., A11. Fig. 12 shows different experimental results. Based on the visualized observation, we can find that AR-PNF has the best detection result among these methods. In detail, Fig. 12(a) presents the result of PSH-only, in which none ships except many false alarms are detected. The reason is that the sea surface has high unpolarized energy ratio caused by its nondeterministic X-Bragg scattering. In Fig. 12(b), the small ships S4 and S5 are both missed by RS because their scattering mechanisms are similar to the sea surface. The same reason also applies to Fig. 12(e) where S4 and T14 are missed by GP-PNF. Moreover, observing Fig. 12(b) and (e), we can also find that both methods detect some azimuth ambiguities, which reflects their unavailability of removing azimuth ambiguities. As to the result of HV, all the azimuth ambiguities are removed well in Fig. 12(c). Nevertheless, the HV detector still misses the real ships S4, S5, and T17, since their HV intensities are lower than those existed in azimuth ambiguities. In Fig. 12(d), none azimuth ambiguities are detected by BPCDM, which owes to the fact that the PSH values of ships computed from [CPCDM ] are much higher than those of azimuth ambiguities. Despite of this, the detected ship T12 is not complete, and one false alarm F3 is still detected (marked by a brown dashed circle). As can be seen in Fig. 12(f), AR-PNF detects all the 12 ships, and meanwhile, all the azimuth ambiguities are also removed. Moreover, none false alarms, comparing with Fig. 12(d), are detected in Fig. 12(f). Fig. 13 further presents the ROC curves of these methods, where we can see that ARPNF outperforms other five detectors. The values of Pd and FoM listed in Table 2 also show that AR-PNF holds the best detection result among the six algorithms.

Fig. 13. The ROC curves of different methods on C.

To further compare the performance of these different methods, one subarea highlighted by a red dashed rectangle in Fig. 4(f) is investigated, in which A11 and A12 are the azimuth ambiguities corresponding to the real ships T11 and T12. Fig. 14 presents the power images of these methods regarding this sample area. It is important to note that the power values of the adopted detector is normalized into the interval of [0,1] for a fair comparison. From Fig. 14(a), one can see that rough sea surface holds higher PSH values than ships. Therefore, all the TCR values of these three ships calculated by PSH-only are negative, as shown in Table 4. Hence, only using PSH to distinguish ships from sea clutter is impossible under this condition, which is consistent with our deduction in Section 3. However, the T value is positive, i.e., 2.11 dB, which directly verifies that PSH has an ability to separate ships from azimuth ambiguities. By analyzing Fig. 14(d), we can further demonstrate this point. Since the 53

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Analogously, even though HV is useful for removing azimuth ambiguities, false alarms are still detected around T20 in Fig. 15(c). BPCDM detects all the ships without one azimuth ambiguity in Fig. 15(d). Nevertheless, the structures of some detected ships are not complete, such as T20 and T26. The result of GP-PNF is shown in Fig. 15(e), where one small ship S6 is missed and two azimuth ambiguities are detected simultaneously. Although GP-PNF detects few false alarms surrounding T20, another two false alarms F4 and F5 (marked by brown dashed circles) caused by sidelobes are detected. This further gives the evidence that the feature vector of GP-PNF is not optimistic for detecting ships from azimuth ambiguities. The result in Fig. 15(f) shows that ARPNF can effectively remove azimuth ambiguities. However, some false alarms caused by ship wakes are still detected around T20. The reason is that the features adopted in t cannot reflect the scattering differences between ships and their corresponding wakes. Ship wakes often have complicated scattering mechanisms which may consist of low surface scattering power and high polarization entropy (Zhou et al., 2018), therefore the feature vector t is unable to remove them effectively. The values of Pd and FoM on this dataset are also correspondingly listed in Table 2. For calculating conveniently, we consider those false alarm pixels surrounding T20 as one false alarm here. Analyzing Table 2, it can be seen that BPCDM outperforms AR-PNF, whose FoM value is 0.062 higher than AR-PNF in Table 2. The main reason is that BPCDM detects all the ships without the detection of ship wakes. On the contrary, AR-PNF detects the ship wakes surrounding T23. In spite of this, analyzing the ROC curves in Fig. 16, we can find that AR-PNF is able to detect more ship pixels than BPCDM. Besides, in Fig. 16, when Pf is set high, HV can also outperform AR-PNF. This is reasonable because HV has the ability to remove azimuth ambiguities. In order to further compare the performance of these methods, we here also select one subarea marked by a red dashed rectangle in Fig. 4(i) as our probing area. Fig. 17 shows the corresponding power images of the six approaches. In Fig. 17(a), the sea surface obviously has higher PSH values than ships and azimuth ambiguities. It means that only using PSH to detect ships from sea clutter is impossible because of the negative TCR values which are shown in Table 5. Observing Fig. 17(b), it can be seen that the power of A22 is higher than ships. However, in Fig. 17(c) and (d), HV and BPCDM can easily distinguish ships from A22. Compared to Fig. 17(e), the power image of AR-PNF is also much clearer in Fig. 17(f). Once again, it verifies the effectiveness of t on azimuth ambiguities removal. Analyzing Table 5, we can see that the T values of BPCDM and PSH-only are in the first two places, i.e., 15.79 dB and 11.02 dB. It implies that the depolarization feature PSH dose have an ability to remove azimuth ambiguities. Following that, AR-PNF yields the highest T value, i.e., 4.21 dB which is 10.08 dB higher than GP-PNF. Therefore, it further confirms the effectiveness of AR-PNF on the removal of azimuth ambiguities. Meanwhile, in Table 5, we can also find that PSH-only is 0.19 dB higher than p3 . So, PSH has a better ability to remove azimuth ambiguities than p3 . The last experiment also concerns an AIRSAR C-Band scene with rough sea surface. The SPAN image of the dataset E in size of 653 × 481 is shown in Fig. 4(j), where ships and azimuth ambiguities are visible. The result of PSH-only in Fig. 18(a) is in agreement with what was experienced previously. None ships but lots of false alarms are detected by PSH-only. Although RS removes azimuth ambiguities successfully, five small ships are still missed in Fig. 18(b). Besides, the impact of side lobes are not eliminated well, as indicated by brown dashed circles (i.e., F6 and F7). From Fig. 18(c), we can see that HV detects misses one small ship S12 and detects two false alarms (i.e., F8, and F9). The result presented in Fig. 18(d) verifies the effectiveness of BPCDM, though one false alarm F10 is detected. In Fig. 18(e), GP-PNF only detects four ships. At the same time, the azimuth ambiguity A32 and two false alarms (i.e., F11 and F12) are also detected. Indirectly, this reflects that the feature vector of GP-PNF is useless for detecting ships from azimuth ambiguities. On the contrast, AR-PNF detects all the ships without one false alarm in Fig. 18(f). The validity of the new feature vector is

Fig. 14. The corresponding power images regarding the sample area in Fig. 4(f). (a) PSH-only; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Note that, we here normalize the power values of the adopted detector into the interval of [0,1].

PSH values are derived from [CPCDM ] in BPCDM, ships have much higher TCR values than azimuth ambiguities, which corresponding T value is positive as well (i.e., 8.71 dB). Once again, it demonstrates the ability of PSH to remove azimuth ambiguities. In Fig. 14(b), (c), and (e), the power of azimuth ambiguities is higher than S5. Therefore, RS, HV, and GP-PNF cannot effectively remove azimuth ambiguities on this dataset. From Table 4, it can also be seen that all the T values of RS, HV, and GP-PNF are negative. It further verifies that, the azimuth ambiguities must be detected as long as the small ship S5 is detected. Obviously, the power of azimuth ambiguities is much lower than S5 in Fig. 14(f), which directly verifies that AR-PNF can effectively remove azimuth ambiguities. Interestingly, compared to GP-PNF, although all the TCR values calculated by AR-PNF decrease in Table 4, the corresponding T value (i.e., 6.96 dB) is much higher than that of GP-PNF (-9.8 dB). The reason lies in the fact that AR-PNF can make the TCR values of A11 and A12 decrease much severely than those of S5, T11, and T12. Therefore, it proves that the feature vector of AR-PNF is more suitable for suppressing azimuth ambiguities than the one of GP-PNF. Besides, in Table 4, we can also see that PSH-only has a higher T value than p3 . It further verifies that PSH has a better capable of suppressing azimuth ambiguities than p3 . The third AIRSAR C-Band dataset D has a size of 1013 × 1013 and is composed of 15 real ships, which SPAN image is shown in Fig. 4(i). In this scene, azimuth ambiguities can also be easily found, such as A20 and A22. Fig. 15 presents the results of different methods. Observing Fig. 15(a), we can see that PSH-only detects none ships except for a lot of false alarms. Fig. 15(b) shows the result of RS where three small ships (S6, S7, and S9) are missed. Besides, azimuth ambiguities are also detected. The reason is that the reflection asymmetry characteristic lies in azimuth ambiguity. Aside from this point, some false alarms surrounding the ship T20 are detected as well, which may result from the ship wakes with complicated scattering mechanisms. 54

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Fig. 15. The experimental results of D. (a) PSHonly; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the green dashed circles mean the undetected ships and the brown dashed circles are the false alarms. The yellow rectangles denotes the real ships. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 16. The ROC curves of different methods on D.

verified again. Besides, observing Fig. 19, it is also obvious that the Pd values of AR-PNF are much higher than those of other five methods. Thus, AR-PNF has the best detection performance among these detectors. The corresponding Pd and FoM values listed in Table 2 can also demonstrate this point. Similarly, we present different power images of this scene in Fig. 20. The TCR values corresponded to each detector are listed in Table 6. It can be seen that the T values of PSH-only and BPCDM are both positive. The former is 0.28 dB and the latter is 0.95 dB. This means that PSH has the ability to remove azimuth ambiguities. In Table 6, the T value of GP-PNF is negative, i.e., −9.21 dB. Once more, it reflects the unavailability of the feature vector of GP-PNF on removing azimuth ambiguities. Contrarily, the T value of AR-PNF is 0.7 dB which is 9.21 dB higher than GP-PNF. Therefore, the effectiveness of the proposed feature vector is verified again.

Fig. 17. The corresponding power images of the sample area in Fig. 4(i). (a) PSH-only; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the power values of the adopted detector have been normalized into the in.terval of [0,1].

In general, AR-PNF holds the best detection performance among the six methods by comparing the average FoM value (bold font in Table 2), which outperforms GP-PNF 0.308. However, AR-PNF takes more time 55

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Fig. 18. The experimental results of E. (a) PSHonly; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Here, the green dashed circles mean the undetected ships and the brown dashed circles are the detected false alarm targets. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 19. The ROC curves of different methods on E.

than other four methods except for BPCDM. Table 7 lists the time consumptions (in seconds) of these six detectors. Obviously, on average, AR-PNF is ten times slower than GP-PNF, since it needs to calculate the eigenvalues. Note that, all the experiments are carried on a personal computer with an Intel(R) Core(TM) i7-6700HQ processor at 2.60 GHz and 12.00 GB RAM. The time consumption of each method was tested and averaged by 10 times.

Fig. 20. The corresponding power images regarding E. (a) PSH-only; (b) RS; (c) HV; (d) BPCDM; (e) GP-PNF; (f) AR-PNF. Note that, the power values of the adopted detector have been normalized into the interval of [0,1] here.

5. Conclusions In this paper, we interpreted the polarimetric feature pedestal ship height (PSH) and theoretically deduced that it was another expression of the depolarization energy ratio of target and had an ability to remove azimuth ambiguities. Generally speaking, by analyzing the scattering differences between ships and sea surface, PSH together with other

three polarimetric features were chosen as the key signatures for detecting ships. Subsequently, a new ship detection algorithm was developed by designing a three-dimensional polarimetric feature vector, which replaced the original one in the geometrical perturbation56

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Table 7 Time consumptions of different methods in seconds.

Info Sciences Lab. Freeman, A., 1993. The effects of noise on Polarimetric SAR data. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 799–802. https://doi.org/10.1109/ IGARSS.1993.322215. Gao, G., Shi, G., Zhou, S., 2013. Ship detection in high-resolution dual-polarization SAR amplitude images. Int. J. Antennas Propagat. 3, 188–192. https://doi.org/10.1155/ 2013/519296. Hajnsek, I., Pottier, E., Cloude, S.R., 2003. Inversion of surface parameters from polarimetric SAR. IEEE Trans. Geosci. Remote Sens. 41 (4), 727–744. https://doi.org/10. 1109/IGARSS.2000.858033. Holm, W., Barnes, R., 1988. On radar polarization mixed state decomposition theorems. In: USA Natinal Radar Conference, https://doi.org/10.1109/NRC.1988.10967. Iervolino, P., Guida, R., Whittaker, P., 2015. A new GLRT-based ship detection technique in SAR images. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 3131–3134. https://doi.org/10.1109/IGARSS.2015.7326480. Jin, Y.Q., 2010. Polarimetric scattering modeling and information retrieval from SAR remote sensing: A review of FDU work. Progress Electromagnet. Res. 104, 333–384. https://doi.org/10.3969/j.issn.1004-0323.2005.01.002. Li, F.K., Johnson, W.T.K., 1983. Ambiguities in spacebornene synthetic aperture radar systems. IEEE Trans. Aerosp. Electron. Syst. AES-19 (3), 389–397. https://doi.org/10. 1109/TAES.1983.309319. Liao, M.S., Wang, C.C., Wang, Y., Song, X.G., 2009. Ship detection from polarimetric SAR images. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. IV987–990. https://doi.org/10.1109/IGARSS.2009.5417545. Liu, C., Gierull, C.H., 2007. A new application for PolSAR imagery in the field of moving target indication/ship detection. IEEE Trans. Geosci. Remote Sens. 45 (11), 3426–3436. https://doi.org/10.1109/TGRS.2007.907192. Liu, T., Lampropoulos, G., 2006. A new polarimetric CFAR ship detection system. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 137–140. https://doi.org/ 10.1109/IGARSS.2006.40. Maghsoudi, Y., 2011. Analysis of Radarsat-2 full polarimetric data for forest mapping. Degree of PhD, Department of Geomatics Engineering, University of Calgary. Marino, A., 2013. A notch filter for ship detection with polarimetric SAR data. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 6 (3), 1219–1232. https://doi.org/10.1109/ JSTARS.2013.2247741. Marino, A., Hajnsek, I., 2015. Statistical tests for a ship detector based on the polarimetric notch filter. IEEE Trans. Geosci. Remote Sens. 53 (8), 4578–4595. https://doi.org/10. 1109/tgrs.2015.2402312. Marino, A., Cloude, S.R., Woodhouse, I.H., 2010. A polarimetric target detector using the huynen fork. IEEE Trans. Geosci. Remote Sens. 48 (5), 2357–2366. https://doi.org/ 10.1109/tgrs.2009.2038592. Marino, A., Cloude, S.R., Woodhouse, I.H., 2012. Detecting depolarized targets using a new geometrical perturbation filter. IEEE Trans. Geosci. Remote Sens. 50 (10), 3787–3799. https://doi.org/10.1109/tgrs.2012.2185703. Marino, A., Cloude, S.R., Lopez-Sanchez, J.M., 2013a. A new polarimetric change detector in radar imagery. IEEE Trans. Geosci. Remote Sens. 51 (5), 2986–3000. https://doi.org/10.1109/tgrs.2012.2211883. Marino, A., Sugimoto, M., Nunziata, F., Hajnsek, I., Migliaccio, M., Ouchi, K., 2013b. Comparison of ship detectors using polarimetric Alos data: Tokyo Bay. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 2345–2348. https://doi.org/10.1109/ IGARSS.2013.6723289. Nghiem, S.V., Yueh, S.H., Kwok, R., Li, F.K., 1992. Symmetry properties in polarimetric remote sensing. Radio Sci. 27 (5), 693–711. https://doi.org/10.1029/92RS01230. Nghiem, S.V., Yueh, S.H., Kwok, R., Nguyen, D.T., 1993. Polarimetric remote sensing of geophysical medium structures. Radio Sci. 28 (6), 1111–1130. https://doi.org/10. 1029/93RS01376. Novak, L.M., Burl, M.C., Irving, W.W., 1993. Optimal polarimetric processing for enhanced target detection. IEEE Trans. Aerosp. Electron. Syst. 29 (1), 234–244. https:// doi.org/10.1109/7.249129. Nunziata, F., Migliaccio, M., Brown, C.E., 2012. Reflection symmetry for polarimetric observation of man-made metallic targets at sea. IEEE J. Oceanic Eng. 37 (3), 384–394. https://doi.org/10.1109/JOE.2012.2198931. Praks, J., Koeniguer, E.C., Hallikainen, M.T., 2009. Alternatives to target entropy and alpha angle in SAR polarimetry. IEEE Trans. Geosci. Remote Sens. 47 (7), 2262–2274. https://doi.org/10.1109/TGRS.2009.2013459. Shirvany, R., Chabert, M., Tourneret, J.Y., 2012. Ship and oil-spill detection using the degree of polarization in linear and hybrid/compact dual-pol SAR. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 5 (3), 885–892. https://doi.org/10.1109/JSTARS. 2012.2182760. Sugimoto, M., Ouchi, K., Nakamura, Y., 2013. On the novel use of model-based decomposition in SAR polarimetry for target detection on the sea. Remote Sens. Lett. 4 (9), 843–852. https://doi.org/10.1080/2150704X.2013.804220. Tello, M., López-Martínez, C., Mallorqui, J.J., 2005. A novel algorithm for ship detection in SAR imagery based on the wavelet transform. IEEE Geosci. Remote Sens. Lett. 2 (2), 201–205. https://doi.org/10.1109/lgrs.2005.845033. Touzi, R., Hurley, J., Vachon, P.W., 2015. Optimization of the degree of polarization for enhanced ship detection using polarimetric Radarsat-2. IEEE Trans. Geosci. Remote Sens. 53 (10), 5403–5424. https://doi.org/10.1109/TGRS.2015.2422134. Velotto, D., Soccorsi, M., Lehner, S., 2013. Azimuth ambiguities removal for ship detection using full polarimetric X-Band SAR data. IEEE Trans. Geosci. Remote Sens. 52 (1), 76–88. https://doi.org/10.1109/TGRS.2012.2236337. Wang, C., Wang, Y., Liao, M., 2010. Polarimetric characteristics analysis of ship target and its azimuth ambiguities based on PolSAR images, in: Multimedia Technology. In: (2010 International Conference on ICMT). IEEE, pp. 1–4. https://doi.org/10.1109/ ICMULT.2010.5631342. Wang, C., Wang, Y., Liao, M., 2012a. Removal of azimuth ambiguities and detection of a

Method Scene

PSH-only

RS

HV

BPCDM

GP-PNF

AR-PNF

A B C D E Average

56.54 7.61 27.61 25.80 9.11 25.33

1.37 1.69 0.99 0.58 0.87 1.10

1.27 1.63 2.08 0.97 0.91 1.37

39.27 12.65 45.17 42.47 14.61 30.83

4.04 2.29 2.45 2.60 1.81 2.64

57.38 7.69 28.22 26.69 10.38 26.07

polarimetric notch filter (GP-PNF). Experiments on five PolSAR datasets with different sea surfaces demonstrated that the proposed algorithm can effectively remove azimuth ambiguities and have a better ship detection performance compared with other methods. Last but not least, we adopted the X-Bragg scattering model to characterize the nonBragg scattering over sea surface, and verified that the depolarization cannot be directly used for ship detection when the X-Bragg scattering existed. Although the proposed algorithm was effective in distinguishing ships from azimuth ambiguities, it still had some disadvantages. For example, it cannot effectively remove ship wakes due to their complicated scattering mechanisms. In the future work, we will focus on the analysis of ship wakes in order to minimize their impacts for ship detection. More different polarimetric features need to be considered for replacing the merely combinational feature (i.e., “T11 + T22 ”). Besides, it is also necessary to analyze the differences between different formulas of depolarized energy ratio in detail. More datasets acquired from other sensors should also be adopted to demonstrate the robustness of the proposed algorithm. Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant 61331015, 61866016, 41801236, and 61490693, and the Shanghai Science and Technology Committee under Grant 17DZ1100803, and the gsponsorsimpleGS3ESA/NRCSS Dragon-4 program under the project 32235. The authors are also grateful for ESA and Alaska Satellite Facility for providing experimental datasets. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.isprsjprs.2019.08.009. References Ainsworth, T.L., Lee, J.S., Schuler, D.L., 2000. Multi-frequency Polarimetric SAR data analysis of ocean surface features. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 1113–1115. https://doi.org/10.1109/IGARSS.2000.858039. Atteia, G.E., Collins, M.J., 2013. On the use of compact polarimetry SAR for ship detection. ISPRS J. Photogramm. Remote Sens. 80 (6), 1–9. https://doi.org/10.1016/j. isprsjprs.2013.01.009. Buono, A., Nunziata, F., Migliaccio, M., Li, X., 2016. Polarimetric analysis of compactpolarimetry SAR architectures for sea oil slick observation. IEEE Trans. Geosci. Remote Sens. 54 (10), 5862–5874. https://doi.org/10.1109/TGRS.2016.2574561. Chaney, R.D., Bud, M.C., Novak, L.M., 1990. On the performance of polarimetric target detection algorithms. IEEE Aerosp. Electron. Syst. Mag. 5 (11), 10–15. https://doi. org/10.1109/62.63157. Cloude, S.R., Pottier, E., 1996. A review of target decomposition theorems in radar polarimetry. IEEE Trans. Geosci. Remote Sens. 34 (2), 498–518. https://doi.org/10. 1109/36.485127. Cloude, S.R., Pottier, E., 1997. An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geosci. Remote Sens. 35 (1), 68–78. https:// doi.org/10.1109/36.551935. Cloude, S.R., Papathanassiou, K.P., Pottier, E., 2001. Radar polarimetry and polarimetric interferometry. IEICE Trans. Electron. 84 (12), 1814–1822. Crisp, D.J., 2004. The state-of-the-art in ship detection in synthetic aperture radar imagery. Tech. rep., Defence Science And Technology Organisation Salisbury (Australia)

57

ISPRS Journal of Photogrammetry and Remote Sensing 157 (2019) 41–58

T. Zhang, et al. ship: Using polarimetric airborne C-Band SAR images. Int. J. Remote Sens. 33 (10), 3197–3210. https://doi.org/10.1080/01431161.2011.633123. Wang, N., Shi, G., Liu, L., Zhao, L., Kuang, G., 2012b. Polarimetric SAR target detection using the reflection symmetry. IEEE Geosci. Remote Sens. Lett. 9 (6), 1104–1108. https://doi.org/10.1109/lgrs.2012.2189548. Wei, J., Li, P., Yang, J., Zhang, J., Lang, F., 2014. A new automatic ship detection method using L-Band polarimetric SAR imagery. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 7 (4), 1383–1393. https://doi.org/10.1109/JSTARS.2013.2269996. Wei, J., Zhang, J., Huang, G., Zhao, Z., 2016. On the use of cross-correlation between volume scattering and helix scattering from polarimetric SAR data for the improvement of ship detection. Remote Sens. 8 (1), 74–89. https://doi.org/10.3390/ rs8010074. Xiang, D., Tang, T., Ban, Y., Su, Y., 2016. Man-made target detection from polarimetric SAR data via nonstationarity and asymmetry. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 9 (4), 1459–1469. https://doi.org/10.1109/JSTARS.2016.2520518. Xi, Y., Lang, H., Tao, Y., Huang, L., Pei, Z., 2017. Four-component model-based decomposition for ship targets using PolSAR data. Remote Sens. 9 (6), 238–621. https://doi. org/10.3390/rs9060621. Yamaguchi, Y., Yajima, Y., Yamada, H., 2006. A four-component decomposition of PolSAR images based on the coherency matrix. IEEE Geosci. Remote Sens. Lett. 3 (3),

292–296. https://doi.org/10.1109/LGRS.2006.869986. Yang, J., Peng, Y.N., Lin, S.M., 2001. Similarity between two scattering matrices. Electron. Lett. 37 (3), 193–194. https://doi.org/10.1049/el:20010104. Yin, J., Yang, J., Zhou, Z.S., Song, J., 2015. The extended Bragg scattering model-based method for ship and oil-spill observation using compact polarimetric SAR. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 8 (8), 3760–3772. https://doi.org/10.1109/ JSTARS.2014.2359141. Yueh, S.H., Kwok, R., Nghiem, S.V., 1994. Polarimetric scattering and emission properties of targets with reflection symmetry. Radio Sci. 29 (6), 1409–1420. https://doi.org/ 10.1029/94RS02228. Zhang, T., Yang, Z., Xiong, H., Yu, W., 2016. Ship detection based on the power of the Radarsat-2 polarimetric data. In: Geoscience and Remote Sensing Symposium (IGARSS), pp. 1254–1257. https://doi.org/10.1109/IGARSS.2016.7729318. Zhang, T., Yang, Z., Xiong, H., 2017. PolSAR ship detection based on the polarimetric covariance difference matrix. IEEE J. Sel. Top. Appl. Earth Obser. Remote Sens. 10 (7), 3348–3359. https://doi.org/10.1109/JSTARS.2017.2671904. Zhou, X., Bo, T., Cheng, S., 2018. Faint ship wake detection in PolSAR images. IEEE Geosci. Remote Sens. Lett. PP (99), 1–5. https://doi.org/10.1109/LGRS.2018. 2823007.

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