1. Introduction
Ship detection is of great significance in maritime traffic, immigration control, and fishing activity monitoring. Synthetic aperture radar (SAR) can work day and night with high resolution, even under cloudy conditions, and has been widely used in ship detection.
Constant false alarm rate (CFAR) detection is a classic method and has been used extensively and effectively in SAR images for ship target detection. The key to the CFAR method is the selection of a threshold, and the threshold depends on the probability density function (PDF) of the sea clutter (the backscatter of the sea surface). Many different probability density models have been proposed to simulate the sea clutter distribution, including the Log-normal, Weibull, Rayleigh, G
0, K, gamma, generalized Gamma, and generalized Gaussian Rayleigh distributions. Ni and Anfinsen [
1] discussed the advantages and disadvantages of using a statistical model to describe the sea clutter in the CFAR algorithm. Although CFAR detection has a better performance in a uniform background region, the results will be greatly affected in multitarget and clutter-edge environments. Ai et al. [
2] presented a new algorithm that utilizes the strong gray intensity correlation in the ship target and the 2-D joint Log-normal distribution in the clutter. Experiments demonstrated that the detection performance is much better. Qin et al. [
3] proposed a novel CFAR detection algorithm for high-resolution SAR images using the generalized Gamma distribution (GΓD), and the performance of the proposed algorithm is better than the Weibull distribution. However, with the higher resolution of the SAR image, the sea clutter becomes complex in the time and spatial domains, and then the existing models are not suitable, resulting in the severe degradation of the CFAR detection performance and many false alarms [
4]. Additionally, the parameter estimation is complex, and the threshold cannot be acquired easily [
5].
To overcome the drawbacks of the CFAR method, ship detection methods based on new features have been studied by researchers, and many results has been achieved [
6,
7,
8]. For example, based on Cloude decomposition, Wang et al. [
9] used the local uniformity of the third eigenvalue of a polarization coherence matrix (T) to detect ships. Sugimoto et al. [
10] combined Yamaguchi decomposition theory and the CFAR method to detect ships by analyzing the differences between the scattering mechanisms of the sea surface and ships. Shirvany et al. [
11] indicated the effectiveness of the degree of polarization (DoP) in ship detection. Then, this work was further studied by Touzi et al. [
12], who defined an extension of the DoP to enhance significant ship-sea contrasts. In contrast to using a single feature, Yin et al. [
13] investigated the capability of m-α and m-χ decompositions in coastal ship detection. Then, three features extracted from compact-polarimetric (CP) SAR were proven to have a good performance in ship detection in [
14]. Furthermore, Paes et al. [
15] provided a more detailed analysis of the detection capability and sensitivity of δ together with m, μ
c,|μ
xy|, and the entropy H
ω. Gui et al. [
16] extracted a new feature from the proposed power-entropy decomposition, called the high-entropy scattering amplitude (
HESA), to detect ships, and experiments verified that
HESA achieves good detection performance.
The polarization features used in ship detection are extracted from different SAR polarimetric modes. With the development of radar systems, SAR data acquisition modes have been extended from single-polarimetric, dual-polarimetric (DP) and full-polarimetric (FP) SAR to CP SAR [
16]. FP SAR can provide more target scattering information than single-polarimetric and DP SAR [
17]. Compared with FP SAR, CP SAR is a new type of sensor with a wider swath of coverage and smaller energy budget [
18]. According to the polarization state, three CP SAR modes exist, including π/4, dual circular polarization, and circular transmission and linear reception (CTLR) polarization [
19,
20,
21]. The CTLR mode is simpler, more stable and less sensitive to noise than the other two modes. Furthermore, the CTLR mode achieves a better performance in self-calibration and engineering [
22]. At present, RISA-1 in India, ALOS-2 in Japan, and even the future Canadian RADARSAT Constellation Mission (RCM) all support CP SAR. It can be predicted that there will be more polarization features for ship detection in the future.
Although much research has been done, there are still some drawbacks. (1) At present, there are dozens of polarization features, but most of the studies are based on just one or several features. The problem is how to choose suitable features from these features for marine vessel monitoring purposes. (2) Considering the difficulty of ship detection under complex sea states, how to develop new features to improve the ship detection rate, especially for the detection of weak and small ship targets in a high sea state, is another problem.
In this paper, we perform a comprehensive quantification and evaluation of the polarization features extracted from FP, CP and DP modes in C-band SAR data. Our motivation is to establish a reliable feature selection method for marine vessel monitoring purposes. CP SAR features [
23] are further studied owing to their advantages for ship detection. In order to develop new CP SAR features that are simple and suitable for complex sea states, we analyzed the scattering difference between the ships and the sea surface by introducing the sea surface roughness. On the basis, a new feature is proposed that is stable and simple for ship detection, especially in a high sea state. Finally, experiments are carried out to verify the better ship detection performance based on the new feature compared with the roundness, delta,
HESA and CFAR methods in low, medium and high sea states. The main parts are shown in
Figure 1.
Section 2 introduces DP, FP and CP SAR data and polarization features. In
Section 3, the feature selection method is analyzed by the Euclidean distance and mutual information. Three features are analyzed with the introduced sea surface roughness, and a feature is presented for ship detection in
Section 4. In
Section 5, the performances of different detectors are compared. Finally, conclusions are drawn in
Section 6.
4. A New Feature: Phase Factor
Section 3 concludes that the features in CP mode are more suitable than the DP and FP modes for ship target detection. Therefore, in this section, the features in CP mode are further studied. To analyze the theoretical ship detection performance of features, the relationship between the coherency matrix and the Stokes vector is established. Then, the X-Bragg scattering model is introduced to describe the Stokes vector. Finally, a new feature, which has a good ship detection performance, is proposed.
In CTLR mode, the radar antenna transmits a circular signal and simultaneously receives two orthogonal linear polarization signals. Consider a radar that transmits a right circular signal. The scattering vector [
37,
45] is
The coherency matrix T is defined by Huynen parameters [
46]:
where
, and
A0, B, B0, C, D, E, F, G, and
H are the Huynen parameters. Note that
A0, B0, and
F are rotation invariants.
Matrix T can be expressed by
SHH, SHV, and
SVV, but it is extremely complicated [
32]. In this case, a new idea is proposed by using the elements of the scattering vector:
Then, a new matrix Y is given by
Combined with matrix T and the Huynen parameters, matrix Y can be obtained:
In [
46], the Stokes vector of the scattered wave in CTLR mode is written as
Therefore, Y can be derived from Equations (23) and (24):
As a result, the Stokes vector is described by the coherency matrix:
Based on the theory mentioned above, the coherency matrix T is used to represent the Stokes vector through the constructed matrix Y. For a better description of the features, the X-Bragg scattering model is introduced below.
The X-Bragg scattering model was first introduced by Hajnsek to solve the case of nonzero cross-polarized backscattering and depolarization [
23]. By assuming a roughness disturbance-induced random surface slope
β, X-Bragg scattering is modeled as a reflection depolarizer by rotating the Bragg coherency matrix about an angle
β and performing configurational averaging over a given distribution
P(
β):
assuming that
P(
β) is a uniform distribution of approximately zero with width
β1 (β
1 < π/2). The width
β1 describes the roughness component of the sea surface. The coherency matrix for the rough surface becomes Equation (28) with
.
where
Substituting Equation (28) into Equation (26), the Stokes vector in CP SAR can be described by an X-Bragg scattering matrix
Note that and are rotation invariants because they are independent of , while and are related to the rotation angle . Hence, the features described by and are stable for separating ships from sea, even in a high sea state.
For a better explanation of the features with strong ship detection abilities, the roundness (
c11), delta (
c12) and the
HESA [
16] are listed as examples. Combined with the model derived from Equation (29), the polarization features are derived by the X-Bragg scattering matrix, which shows the scattering difference between ships and the sea surface. On this basis, a new feature, the phase factor, is presented.
4.1. Roundness
The formula of roundness is
According to Equations (29) and (30), roundness is given by
In Equation (31), the sign of the roundness is consistent with that of
. On the right side of Equation (31), the denominator is positive, so the sign of the roundness depends on the sign of the numerator. The numerator of Equation (31) can be derived as
As shown in Equation (32), the value of C
1–2C
3 is depends on
. When single scattering is dominant, the sign of
is positive, and when even scattering is dominant, the sign of
is negative [
47]. In fact, the sea surface is mainly characterized by single scattering, while ships are mainly characterized by even scattering. Consequently, the value of the sea surface should be positive, and the value of a ship should be negative. The areas shown in
Figure 6a–c represent the red box insets shown in
Figure 2a,b,e. The images are derived from RADARSAT-2 scenes 01, 02 and 05 respectively, which were each acquired at low sea state. The ships and the sea surface can be separated by a constant 0 in the feature roundness. Note that there exists a “ship” in the lower left corner of (a) without AIS information, so it is uncertain whether it is a ship or not.
Combined with Equations (29) and (31), the roundness is related to angle , which means that a higher sea state can lead to a decline of the roundness detector’s performance. What’s worse, small ships even cannot be distinguished from the sea clutter.
4.2. Delta
Then, delta is obtained by substituting Equation (29) into Equation (33):
In Equation (34), for single scattering, the sign of delta is negative; for even scattering, the sign of delta is positive [
47]. Due to the scattering differences, ships in the SAR image are mainly characterized by even scattering, while the sea is mainly characterized by single scattering. Therefore, the sign of delta for ships should be positive, and the sign of delta for the sea surface should be negative. The areas shown in
Figure 7a–c represent the red box insets shown in
Figure 2a,b,e. The images are derived from RADARSAT-2 scenes 01, 02 and 05 respectively, which were each acquired at low sea state. The constant 0 can be used to distinguish ships from the sea surface in the feature delta.
Note that the value of delta is related to angle in Equation (34), and the surface roughness increases with the increasing sea state. Therefore, the value of delta is unstably influenced by , making it difficult to use in distinguishing ships and the sea surface in a high sea state.
4.3. HESA
The formula of the
HESA is
where
The areas shown in
Figure 8a–c represent the red box insets shown in
Figure 2a,b,e. The images are derived from RADARSAT-2 scenes 01, 02 and 05 respectively, which were each acquired at low sea state. In Equation (35), the value of the
HESA is positive, as shown in
Figure 8, and the outlines of ships are clear. However, the
HESA is related not only to the dielectric constant and the incidence angle but also to the rotation angle
.
represents the sea surface roughness, and the
HESA may cause a severe decline when the sea state is high. The constant 1 can be selected to separate ships from the sea surface.
4.4. Phase Factor
Based on the analysis of the above features, a new feature
, called the phase factor, is presented in this paper. The formula of the phase factor is
Combined with Equation (29), the phase factor can be derived by
In Equation (38), the sign of the phase factor depends on the sign of
. For single scattering, the value of
is positive, so the value of the phase factor is negative; for even scattering, the value of the phase factor is positive [
47]. Considering that ships are mainly characterized by even scattering, while sea surfaces are mainly characterized by single scattering, the sign of ships is positive, and the sign of the sea surface is negative. In other words, the phase factor is able to distinguish single scattering and even scattering to determine the dominant scattering mechanism. When the phase factor is positive, the even scattering is stronger than the surface scattering; when the phase factor is negative, the surface scattering is stronger than the even scattering. The areas shown in
Figure 9a–c represent the red box insets shown in
Figure 2a,b,e. The images are derived from RADARSAT-2 scenes 01, 02 and 05 respectively, which were each acquired at low sea state. In
Figure 9, the sign of ships is positive, while the sign of the sea surface is negative, which means that the constant 0 can be used to distinguish ships and sea surface.
Furthermore, Equation (38) shows that the value of the phase factor is related only to the dielectric constant and incident angle and is independent of the random surface slope . This finding indicates that the phase factor is rotation invariant and stable to different sea states (especially the high sea state), which is of great benefit to ship detection. Therefore, the phase factor theoretically achieves a better detection performance than the other abovementioned polarization features.
5. Detection Results and Discussion
In this section, experiments were performed using CTLR mode emulated from C-band RADARSAT-2 FP SAR data to validate the superiority of the phase factor in ship detection. The phase factor is compared with the roundness, delta, HESA and CFAR detectors, respectively.
5.1. Comparisons Between Phase Factor and Roundness, Delta, HESA Detectors
In this section, comparisons are made among roundness, delta, HESA and phase factor detectors by analyzing the scattering difference between ships and the sea surface.
Two experiments comparing five detectors in ship detection are performed, as shown in
Figure 10 (#1) and
Figure 11 (#2).
Figure 10 shows the detection results in a medium sea state. The roundness, delta, the
HESA and the phase factor perform better than the amplitude in detection tasks because the detected ships in (b)–(f) all have clear outlines, and the ship pixels were very bright with respect to the surrounding sea clutter. The results indicate that the four features from CP decomposition can effectively distinguish ships from sea clutter. In (a), (d), (f) and (i), only one ship is detected by the amplitude and
HESA, while three ships are detected by the other three features. For the roundness, delta and phase factor, the signs of the ship and sea clutter data are opposites, which facilitate distinguishing ships from the sea clutter by means of a constant 0. For the
HESA, the signs of ships and sea clutter data are all positive, so it is hard to select a proper value to separate ships from sea surface. Note that the spans of the roundness, delta and the phase factor are dozens of times larger than that of the
HESA.
For the sake of fairness,
is used to evaluate the ship detection performance, where
and
correspond to the statistical average of the samples of ships and sea surface, respectively, and
f represents features. Note that
P ranges from 0 to 2, which can describe the scattering difference and can distinguish ships from the surrounding sea surface. This finding indicates that the higher the value
P, the better the detection performance is. The results are listed in
Table 5. Multiples represent the performance ratio of the roundness, delta,
HESA or phase factor to the amplitude.
The performances of five detectors are listed in descending order: phase factor, roundness, delta, HESA, and amplitude of RV polarization. Note that the performances of the phase factor, roundness, delta, and the HESA are 65, 54, 41 and 9 times the amplitude of RV polarization, respectively. Thus, according to the value and the scattering difference between the ships and the sea surface, the phase factor can detect ships better than the other four detectors. In another respect, the phase factor is irrelevant to the sea surface roughness, and thus it is sufficiently stable with an increasing sea state, as shown in (e) and (j). In contrast, the roundness, delta and HESA are related to the sea surface roughness. The sea surface is very rough in a high sea state, and sea spikes can cause false alarms and an increased difficulty in the detection.
Figure 11 is another comparison of the detectors in a high sea state (#2). Combined with the AIS, the image contains four small ships. All the ships can be detected with the five detectors. Influenced by strong winds, many false alarms appear in (b)–(d) and (g)–(i), resulting in the severe performance degradation of the roundness and
HESA detectors.
The performances of the five detectors are shown in
Table 5, which are consistent with results from #1. The performances of the phase factor, roundness, delta, and
HESA are 37, 27, 24 and 7 times that of the amplitude of the RV polarization, respectively. According to the performance ratio, although the detectors in a high sea state are smaller than those in a medium state, the phase factor is always the best among the five detectors. The results demonstrate that the phase factor is an effective detector with strong robustness, especially in a high sea state, which is useful in practical applications.
5.2. Comparisons Between Phase Factor and CFAR Detectors
Comparisons between phase factor and CFAR detectors were made to verify the superiority of the phase factor detector for ship detection in low, medium and high sea states. The CFAR detector is based on the Weibull, Log-normal, G0, K and generalized Gamma distribution (GГD) of the sea clutter, and the method of log-cumulants (MoLC) based on the Mellin transform is used for the parameter estimation of the sea clutter model.
Considering the false alarm rate and detection rate, the
FOM is used for the detection performance analysis [
48]
where
Ntt and
Nfa are the numbers of detected ships and false alarms, respectively.
Ngt is the number of ships that matched with AIS. It is indicated from (39) that the larger the
FOM, the better the detection performance.
The amplitude of RV (Radar transmit in right circular and receive in vertical) polarization emulated from the five RADARSAT-2 FP SAR images shown in
Figure 2 is used for ship detection. 19 regions of interest, including 97, 40 and 28 ships in low, medium and high sea states, respectively, are extracted, and each area is 400*400 pixels. The false alarm rate is set to 0.001, which is the best after multiple tests for CFAR ship detection. The phase factor detector uses a constant 0 to distinguish ships and the surrounding sea surface. In low, medium and high sea states,
Table 6 shows the detection results by the CFAR and phase factor detectors.
In low sea state, the FOMs of these detectors in descending order are phase factor, Log-normal-CFAR, Weibull-CFAR, GГD-CFAR, G0-CFAR and K-CFAR; in medium sea state, they are phase factor, Weibull-CFAR, Log-normal-CFAR, GГD-CFAR, G0-CFAR and K-CFAR; in high sea state, they are phase factor, GГD-CFAR, Weibull-CFAR, Log-normal-CFAR, G0-CFAR and K-CFAR. The results indicate that the phase factor detector has the best performance in low (FOM: 0.94), medium (FOM: 1) and high sea states (FOM: 0.86) for ship detection, followed by Weibull-CFAR, Log-normal-CFAR and GГD-CFAR, while G0-CFAR and K-CFAR are the worst, which is caused by high false alarms, low correct detection rates, or both. In contrast with the CFAR detector, the phase factor can discriminate ships and the sea easily by a constant 0 without complex calculation or false alarm rate setting. Moreover, the phase factor is independent of the sea surface roughness, and hence it can perform well in different sea states, even in high sea state.
Figure 12,
Figure 13 and
Figure 14 show three examples of detection results in low, medium and high sea states respectively. In
Figure 12,
Figure 13 and
Figure 14, (b)–(g) are the ship detection results of the Weibull-CFAR, Log-normal-CFAR, G
0-CFAR, K-CFAR, GГD-CFAR and phase factor detectors. The red boxes and red circles represent ships matched with AIS and false alarms respectively, and the red stars represent ships undetected. In
Figure 12 (low sea state), the Weibull-CFAR, K-CFAR and phase factor detectors are the best without false alarms or missing ships, while a ship is missing in Log-normal-CFAR and GГD-CFAR detection, what’s worse, two ships are missing in G
0-CFAR detection.
In
Figure 13 (medium sea state), the Log-normal-CFAR, GГD-CFAR and phase factor detectors perform better than the other detectors. Two and three false alarms exist in Weibull-CFAR and K-CFAR respectively, and a ship in G
0-CFAR is failed to be detected.
In
Figure 14 (high sea state), only the phase factor detector detects two ships without any false alarm. Weibull-CFAR, GГD-CFAR, Log-normal-CFAR and G
0-CFAR missing one or two ships, and K-CFAR detected all ships but with too many false alarms. The results indicate that the CFAR method is not stable in different conditions, easily causing false alarms and missing detection. In general, the phase factor performs better than the other detectors even in high sea state, while the detection performance of the Weibull-CFAR, Log-normal-CFAR, G
0-CFAR, K-CFAR and GГD-CFAR decrease with the increasing sea state. The results are in accordance with the theory presented in
Section 4.4.
6. Conclusions
In this paper, in order to establish a reliable feature selection method for marine vessel monitoring purposes, CP and DP SAR data were simulated by five FP RADARSAT-2 images, and forty features were extracted from the FP, CP and DP decomposition. We comprehensively quantified and evaluated these features for ship detection by using the Euclidean distance. The result indicated that features f7, f9, f11, c4, c5, c6, c11, c12, c15 and d5 perform better than the other features. For features selected by the Euclidean distance, the relevance between ships and features, along with the redundancy among different features, are further analyzed. The ship detection performance of f7, f9, f11, c4, c5, c6, c11, c12, c15 and d5 from the mutual information are consistent with those from the Euclidean distance. Furthermore, the mutual information among the features f7, f9, f11, c4, c5, c6, c11, c12, c15 and d5 are low. In conclusion, f11, c4, c6, c11 and c12 are used for ship detection, which indicates that the features’ performance in CP SAR mode is better than that in DP and FP SAR mode.
The features in CP SAR mode are further studied to present a new feature that is simple and suitable for use in complex sea states for ship detection. After a series of derivations and analyses by introducing the sea surface roughness, a new feature, named the phase factor, is proposed that can discriminate the ships and sea surface by a constant 0 and is simpler than the CFAR method without the need for false alarm setting and complex threshold calculations by using a segmentation algorithm. What’s more, it is independent of the sea surface roughness and can achieve good performance even in a high sea state.
Experiments demonstrate that the phase factor is stable and better than the roundness, delta, HESA and CFAR detectors in low, medium and high sea states. The performances of the phase factor, roundness, delta, and the HESA are 65, 54, 41 and 9 times that of the amplitude of RV polarization, respectively. In comparison with CFAR method, the phase factor detector is best in low (FOM: 0.94), medium (FOM: 1) and high sea states (FOM: 0.86) for ship detection, followed by Weibull-CFAR, Log-normal-CFAR and GГD-CFAR, while G0-CFAR and K-CFAR are the worst, which is caused by high false alarms, low correct detection rates, or both. Therefore, the phase factor can be used in complex sea states for ship detection, especially for the detection of weak and small ship targets in a high sea state.