# Large-Scale Automatic Vessel Monitoring Based on Dual-Polarization Sentinel-1 and AIS Data
## Materials and Methods
### Dual-Polarization Ship Detection Algorithm  
In order to benefit from the dual-polarization characteristics we propose to merge the complex co- and cross-polarization channels for an improved vessel detection from SAR imagery. The availability of complex dual-polarization data allows us to extract different polarimetric features (e.g., coherence, eigenvalue decompositions, etc.) based on the elements of covariance matrix. For the dual-polarization basis (VV-VH), the 2 \(\times\) 2 Hermitian covariance matrix is defined as follows:  
\[C_{2}= \begin{bmatrix}<|S_{VV}|^{2}>&<S_{VV}S_{VH}^{*}>\\ <S_{VH}S_{VV}^{*}>&<|S_{VH}|^{2}>\end{bmatrix} , \tag{1}\]where \(<\cdot>\) represents the ensemble average function and \({}^{*}\) the complex conjugate. \(S_{VV}\) and \(S_{VH}\) denote the dual-polarization complex SAR images. The ensemble average is usually estimated over a sliding window (average kernel) of a size equal to \(k\times k\) pixels. The complex off-diagonal element, denoted in this study as the non-normalized coherence, is defined as the channel correlation among the co- and cross-polarization images given in Equation (2) [52]. This study makes use of the coherence magnitude as indicated in Equation (2). \[C_{VV-VH}^{un-norm}=\left|<S_{VV}S_{VH}^{*}>\right|=\left|<S_{VH}S_{VV}^{*}> \right|. \tag{2}\]  
As demonstrated in [41], \(C_{VV-VH}^{un-norm}\) allows to measure the reflection symmetry of the SAR scene. Under the hypothesis that the sea clutter is a natural distributed target, i.e., reflection symmetric target, the expected values of \(C_{VV-VH}^{un-norm}\) for this class are very low. On the contrary, for man-made structures such as vessels, the assumption of reflection symmetry is no longer valid and this results in values of \(C_{VV-VH}^{un-norm}\) significantly higher to those of the sea clutter. Under these circumstances, the \(C_{VV-VH}^{un-norm}\) presents a high target-to-clutter ratio with respect to the individual intensity channels, and is consequently suited for the detection of vessels as denoted in [34; 41] for the reflection symmetry approach. As demonstrated in the scientific literature, the dual-polarization coherence presents high values of the ratio between the targets and the sea clutter making a thresholding operation in this domain suitable for detecting the vessels. Based on these considerations, in this study, we propose to extend the dual-polarization coherence thresholding technique in order to reduce its dependency on the incidence angle and to make it suitable for large swath width SAR images. To this end, we propose to apply an adaptive threshold to \(C_{VV-VH}^{un-norm}\) by considering the variability of the incidence angle. In practice, SAR SLC images are constituted of 2D arrays of a size superior to 10,000 pixels in both dimensions, i.e., azimuth and range. For such large scenes, the values of \(C_{VV-VH}^{un-norm}\) change gradually in the range direction as a consequence of the incidence angle characteristics, as observed in Figure 1. The SAR backscattering exhibits variations depending on the near to far range of incidence angle and normalization operations considering the incidence angle values are necessary for different applications, including also oceanographic ones [53; 54]. In this study, we detected the vessels by thresholding the values of \(C_{VV-VH}^{un-norm}\). In order to consider the variations of \(C_{VV-VH}^{un-norm}\) we proposed to apply an adaptive thresholding approach that defines the threshold values at a local level depending on the range values of the incidence angle. The ScanSAR mode, which is widely used for maritime surveillance due to its capabilities of covering large areas (from 100 km up to 500 km), is characterized by narrow incidence angle ranges for each image sub-swath. The Sentinel-1 terrain observation with progressive scans SAR (TOPSAR) acquisition mode captures three image sub-swath for IW images and five image sub-swath for extra wide swath (EW) images with variations of up to \(5^{\circ}\) of the incidence angle per swath.