# Large-Scale Automatic Vessel Monitoring Based on Dual-Polarization Sentinel-1 and AIS Data
## Materials and Methods
### Dual-Polarization Ship Detection Algorithm
In this study, we assumed that the variations of \(C_{VV-VH}^{un-norm}\) over the sea clutter remained constant for each image sub-swath. Therefore, a threshold value \(T\) was defined for each image sub-swath as a function of the \(C_{VV-VH}^{un-norm}\) first and second order statistics (i.e., mean and variance) over the sea clutter areas. Therefore, the dual polarization-based detector is defined as follows:  
\[\text{if}\quad C_{VV-VH}^{un-norm}(i_{swath},j_{swath})\geq T(\mu_{swath}^{ sea-clutter},\sigma_{swath}^{sea-clutter}),\quad\text{then detect target}, \tag{3}\]  
where \(i_{swath}\) and \(j_{swath}\) represent the pixel indexes for each image sub-swath, \(\mu_{swath}^{sea-clutter}\) and \(\sigma_{swath}^{sea-clutter}\) are the sea clutter mean and variance. As indicated previously, the objective of this work is to define an operational vessel detection algorithm, based on \(C_{VV-VH}^{un-norm}\), enabling the processing of large swath width SAR images in a timely manner. As detailed in Section 1, many research efforts have focused on adapting to the statistics of the SAR images intensity sea clutter to optimize vessel detection, considering for instance: Rayleigh or gamma pdfs, K-distribution pdf or generalized gamma pdf. In case of homogeneous areas, SAR image statistics are governed by the Gaussian pdf, and the variance of the data is fully explained by the multiplicative speckle noise model [55]. Nevertheless, in the presence of data texture or heterogeneous areas, as it may happen in sea surfaces [56], the multiplicative speckle noise model was unable to account for the increase in the data variability, especially in terms of longer pdf tails, so more complex statistical models need to be considered [57]. In addition to this consideration of more complex statistical models, in our case, we need to adapt to the statistics of \(C_{VV-VH}^{un-norm}\), and not to the intensity statistics. The statistics of the complex covariance matrix are difficult to obtain, even under the Gaussian scattering assumption [58; 59]. Consequently, to consider complex statistics in terms of the covariance matrix, and specifically in terms of \(C_{VV-VH}^{un-norm}\), would add a large computational burden which would be not acceptable when addressing an operational processing of large SAR images in a timely manner. Despite this complexity, we considered it necessary to adapt to this variability. Hence we proposed to define the threshold values of each sub-swath as follows:  
\[T(\mu_{swath}^{sea-clutter},\sigma_{swath}^{sea-clutter})=\mu_{swath}^{sea- clutter}+f\times\sigma_{swath}^{sea-clutter},\quad 6<f<12. \tag{4}\]  
In the case of Gaussian statistics, i.e., Rayleigh pdf for SAR images amplitude and Gamma pdf for the intensity, \(f\) is usually set to three to account for 99.7% of the sea clutter. However, we propose to increase this factor to a value comprised between 6 and 12 to account for the excess of variability not explained by the Gaussian scattering assumption. Larger values of \(f\) could be foreseen in cases with extreme sea state. The simplicity of the thresholding process makes it possible to process large SAR images in a timely manner. Figure 1 shows the difference in ship detection performance with or without adapting the threshold value to the local image swath. We can notice that if we applied a global threshold there are many false detections, especially in the near range part of the SAR image, as the values of the coherence for both vessels and sea clutter, vary with the range of the incidence angle. However, if we considered the proposed adaptive threshold, we can observe that the false detections were removed. Following the detection step, all the pixels that satisfy the thresholding condition are afterwards clustered into target-objects by considering the spatial resolution of the SAR images and the maximum and minimum possible sizes of a vessel.