# Analysis of Ship Detection Performance with Full-, Compact- and Dual-Polarimetric SAR

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## Abstract

**:**

## 1. Introduction

^{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].

_{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.

## 2. Data and Polarization Features

#### 2.1. Data

#### 2.2. Extraction of Features from FP, CP and DP Data

#### 2.2.1. Features from FP Data

_{HV}= S

_{VH}, each pixel of an image can be represented by a linear scattering vector as follows:

_{HH}, S

_{HV}, and S

_{VV}are elements of the scattering matrix. The Pauli scattering vector enhances the scattering mechanism and is given by:

#### 2.2.2. Features from CP and DP Data

_{RH}and S

_{RV}represent the scattering coefficients.

_{RH}and S

_{RV}. c3 and c4 are the polarimetric coherence and phase difference between S

_{RH}and S

_{RV}, which we calculated using the same formulas as (3) and (4). Features c5 and c6 are the entropy and the alpha angle, respectively, extracted from the reconstructed coherency matrix proposed by Nord [36]. The formulas are

#### 2.3. Sample Selection

## 3. Comprehensive Quantification and Evaluation of Features for Ship Detection

#### 3.1. Evaluation of Different Features by Euclidean Distance

#### 3.2. Mutual Information Analysis

_{i}) are the prior probabilities for all values of X and P(x

_{i}|y

_{j}) are the posterior probabilities of X given the values of Y.

## 4. A New Feature: Phase Factor

_{0}, B, B

_{0}, C, D, E, F, G, and H are the Huynen parameters. Note that A

_{0}, B

_{0}, and F are rotation invariants.

_{HH}, S

_{HV}, and S

_{VV}, but it is extremely complicated [32]. In this case, a new idea is proposed by using the elements of the scattering vector:

_{1}(β

_{1}< π/2). The width β

_{1}describes the roughness component of the sea surface. The coherency matrix for the rough surface becomes Equation (28) with $\mathrm{sin}c(x)=\mathrm{sin}(x)/x$.

#### 4.1. Roundness

_{1}–2C

_{3}is depends on $\mathrm{Re}({S}_{HH}{S}_{VV}^{\ast})$. When single scattering is dominant, the sign of $\mathrm{Re}({S}_{HH}{S}_{VV}^{\ast})$ is positive, and when even scattering is dominant, the sign of $\mathrm{Re}({S}_{HH}{S}_{VV}^{\ast})$ 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.

#### 4.2. Delta

#### 4.3. HESA

#### 4.4. Phase Factor

## 5. Detection Results and Discussion

#### 5.1. Comparisons Between Phase Factor and Roundness, Delta, HESA Detectors

#### 5.2. Comparisons Between Phase Factor and CFAR Detectors

^{0}, 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.

_{tt}and N

_{fa}are the numbers of detected ships and false alarms, respectively. N

_{gt}is the number of ships that matched with AIS. It is indicated from (39) that the larger the FOM, the better the detection performance.

^{0}-CFAR and K-CFAR; in medium sea state, they are phase factor, Weibull-CFAR, Log-normal-CFAR, GГD-CFAR, G

^{0}-CFAR and K-CFAR; in high sea state, they are phase factor, GГD-CFAR, Weibull-CFAR, Log-normal-CFAR, G

^{0}-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 G

^{0}-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.

^{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.

^{0}-CFAR is failed to be detected.

^{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

^{0}-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.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The RGB images of Scenes 01–05 after geometric correction. R = HH, G = HV, B = VH. (

**a**) Scene 01: areas of the West Lamma Channel in Hong Kong; (

**b**) scene 02: areas of the Yangtze Estuary; (

**c**) scene 03: areas of the Yellow River Estuary; (

**d**) scene 04: areas of Lianyungang; (

**e**) scene 05: areas of Singapore.

**Figure 5.**Normalized mutual information among different features, and samples are from scene 01 (

**a**) and scene 03 (

**b**).

**Figure 6.**Three examples of the values of ships and the sea surface in the roundness. (

**a**) Area in the red box from scene 01. (

**b**) Area in the red box from scene 02. (

**c**) Area in the red box from scene 05.

**Figure 7.**Three examples of the values of ships and the sea surface in the delta. (

**a**) Area in the red box from scene 01. (

**b**) Area in the red box from scene 02. (

**c**) Area in the red box from scene 05.

**Figure 8.**Three examples of the values of ships and the sea surface in the HESA. (

**a**) Area in the red box from scene 01. (

**b**) Area in the red box from scene 02. (

**c**) Area in the red box from scene 05.

**Figure 9.**Three examples of the values of ships and the sea surface in the phase factor. (

**a**) Area in the red box from scene 01. (

**b**) Area in the red box from scene 02. (

**c**) Area in the red box from scene 05.

**Figure 10.**Comparison of the five detectors in a medium sea state. (

**a**) Amplitude of RV polarization. (

**b**) Roundness. (

**c**) Delta. (

**d**) HESA. (

**e**) Phase factor. (

**f**) 3-D display of amplitude. (

**g**) 3-D display of roundness. (

**h**) 3-D display of delta. (

**i**) 3-D display of HESA. (

**j**) 3-D display of phase factor.

**Figure 11.**Comparison of the five detectors in a high sea state. (

**a**) Amplitude of RV polarization; (

**b**) Roundness; (

**c**) Delta; (

**d**) HESA; (

**e**) Phase factor; (

**f**) 3-D display of the amplitude; (

**g**) 3-D display of roundness; (

**h**) 3-D display of delta; (

**i**) 3-D display of HESA; (

**j**) 3-D display of phase factor.

**Figure 12.**Detection performance comparison of CFAR and phase factor detectors in a low sea state. (

**a**) Amplitude of RV polarization; (

**b**) Weibull-CFAR; (

**c**) Log-normal-CFAR; (

**d**) G

^{0}-CFAR; (

**e**) K-CFAR; (

**f**) GГD-CFAR; (

**g**) phase factor detector.

**Figure 13.**Detection performance comparison of CFAR and phase factor detectors in a medium sea state. (

**a**) Amplitude of RV polarization; (

**b**) Weibull-CFAR; (

**c**) Log-normal-CFAR; (

**d**) G

^{0}-CFAR; (

**e**) K-CFAR; (

**f**) GГD-CFAR; (

**g**) phase factor detector.

**Figure 14.**Detection performance comparison of CFAR and phase factor detectors in a high sea state. (

**a**) Amplitude of RV polarization; (

**b**) Weibull-CFAR; (

**c**) Log-normal-CFAR; (

**d**) G

^{0}-CFAR; (

**e**) K-CFAR; (

**f**) GГD-CFAR; (

**g**) phase factor detector.

Scene ID | Imaging Time | Polarization Mode | Incident Angle | Resolution |
---|---|---|---|---|

01 | 16 December, 2008 | HH/HV/VH/VV | 28° | 8/m |

02 | 22 January, 2014 | HH/HV/VH/VV | 44° | 8/m |

03 | 25 September, 2014 | HH/HV/VH/VV | 40° | 8/m |

04 | 29 March, 2015 | HH/HV/VH/VV | 27° | 8/m |

05 | 21 November, 2015 | HH/HV/VH/VV | 20° | 8/m |

Scene ID | 01 | 02 | 03 | 04 | 05 |
---|---|---|---|---|---|

Average wind speed (m/s) | 3.8 | 2.6 | 9.1 | 10.9 | 4.7 |

Sea state | 3 | 2 | 5 | 6 | 3 |

FP SAR | CP SAR | DP SAR |
---|---|---|

Amplitudes: f1: |HH| f2: |HV| f3: |VV| f4: |HH-VV| f5: |HH+VV| | c1: |RH| c2: |RV| | d1: |HH| d2: |HV| |

Polarimetric coherences: f6: HH/HV f7: HH/VV | c3: RH/RV | d3: HH/HV |

Polarimetric phase differences: | ||

f8: HH/HV f9: HH/VV | c4: RH/RV | d4: HH/HV |

Eigenvalue parameters: f10: Entropy f11: Alpha f12: Anisotropy | c5: Entropy c6: Alpha | d5: Entropy d6: Alpha |

Freeman decomposition: f13: Surface f14: Double f15: Volume Yamaguchi decomposition: f16: Surface f17: Double f18: Volume f19: Helix | Cloude decomposition: c7: Surface c8: Double c9: Random Raney decomposition: c10: DoP c11: Roundness c12: Delta c13: Surface c14: Double c15: Random |

Feature | f7 | f9 | f11 | c4 | c5 | c6 | c11 | c12 | c15 | d5 |
---|---|---|---|---|---|---|---|---|---|---|

I(x|y) | 0.383 | 0.522 | 0.603 | 0.610 | 0.519 | 0.625 | 0.658 | 0.631 | 0.315 | 0.359 |

Feature | Experiment no. | Amplitude | Roundness | Delta | HESA | Phase Factor |
---|---|---|---|---|---|---|

P | #1 | 0.02 | 1.07 | 0.82 | 0.18 | 1.29 |

#2 | 0.05 | 1.37 | 1.19 | 0.32 | 1.83 | |

Multiples | #1 | 1 | 54 | 41 | 9 | 65 |

#2 | 1 | 27 | 24 | 7 | 37 |

Model | Sea State | False Alarms | Correct Detections | FOM |
---|---|---|---|---|

Weibull-CFAR | Low | 22 | 89 | 0.75 |

medium | 4 | 40 | 0.9 | |

high | 16 | 28 | 0.64 | |

Log-normal-CFAR | Low | 1 | 83 | 0.85 |

medium | 1 | 36 | 0.88 | |

high | 0 | 16 | 0.57 | |

G^{0}-CFAR | Low | 0 | 58 | 0.59 |

medium | 2 | 32 | 0.76 | |

high | 0 | 12 | 0.43 | |

K-CFAR | Low | 74 | 94 | 0.55 |

medium | 14 | 40 | 0.74 | |

high | 40 | 28 | 0.41 | |

GFD-CFAR | Low | 6 | 74 | 0.72 |

medium | 1 | 36 | 0.88 | |

high | 8 | 28 | 0.78 | |

Phase factor | Low | 5 | 96 | 0.94 |

medium | 0 | 40 | 1 | |

high | 0 | 24 | 0.86 |

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## Share and Cite

**MDPI and ACS Style**

Cao, C.; Zhang, J.; Meng, J.; Zhang, X.; Mao, X.
Analysis of Ship Detection Performance with Full-, Compact- and Dual-Polarimetric SAR. *Remote Sens.* **2019**, *11*, 2160.
https://doi.org/10.3390/rs11182160

**AMA Style**

Cao C, Zhang J, Meng J, Zhang X, Mao X.
Analysis of Ship Detection Performance with Full-, Compact- and Dual-Polarimetric SAR. *Remote Sensing*. 2019; 11(18):2160.
https://doi.org/10.3390/rs11182160

**Chicago/Turabian Style**

Cao, Chenghui, Jie Zhang, Junmin Meng, Xi Zhang, and Xingpeng Mao.
2019. "Analysis of Ship Detection Performance with Full-, Compact- and Dual-Polarimetric SAR" *Remote Sensing* 11, no. 18: 2160.
https://doi.org/10.3390/rs11182160