# Towards Automatic Recognition of Wakes Generated by Dark Vessels in Sentinel-1 Images
## 2 Method  
Wake pattern recognition is used to support ship detection, as detailed in [33]. Firstly, the input image is analyzed by a scanning window (Step 1 of Figure 1). In details, at each position of scanning window, the wake presence in the window is analyzed by: (i) applying Radon Transform, (ii) detecting the peak and tough representative of narrow-V and turbulent wake, respectively, as bright and dark dots in the Radon domain within 4\({}^{\circ}\) of angular distance, and (iii) estimating merit indexes, which measure how distinguishable is the wake component appearance with respect to the background. Indeed, the wake is classified as distinguishable if it is composed by at least two components: a dark linear feature, representative of the turbulent wake, surrounded by a bright component, related to the narrow-V wake.  
Hence, at each step of the scanning window, the merit indexes of the bright (\(F_{v}\)) and dark (\(F_{I}\)) components are estimated as follows:  
\[F_{v}\ =\ \frac{CDF^{-1}(0.95)}{0.95 nT}-1 \tag{1}\]  
Figure 1: Main steps of the wake recognition in SAR images.  
\[F_{I}\ =\ \frac{\overline{I}_{t}}{\overline{I}}-1 \tag{2}\]  
where \(CDF(x_{i})\), the cumulative distribution function of the image intensity (\(x_{i}\)) along the identified half-line. In addition, \(n\) is the number of pixels of the wake component, and \(\overline{I}\) is the intensity mean value over the whole tile and \(\overline{I}_{t}\) is the intensity mean value over the turbulent wake.  
The outputs of the Step 1 are: confirmation or denial of wake presence at each position of scanning window, and if the wake is confirmed, the estimation of relative merit indexes and (\(\theta\),\(s\)) pair, representing the coordinates of peak and tough in the Radon domain, from which the wake direction in the image domain is obtained.  
Then, in Step 2 of Figure 1, a list of candidate wake positions are identified as the pixels satisfying Equation (3), in which \(\mu\) and \(\sigma\) are the mean value and the standard deviation of the \(F_{w}\) distribution, respectively, \(F_{v}\) and \(F_{I}\) are obtained by the previous step, \(k\) is assumed to be equal to 2 as in [33].  
\[F_{w}\ =\ F_{v}\cdot|F_{I}|>\mu+k\sigma \tag{3}\]  
From the knowledge of (\(\theta\),\(s\)) pair of each pixel satisfying Equation (3), it is possible to reconstruct the wake. In details, assuming a (\(x\),\(y\)) reference frame fixed in the center of the scanning window with \(x\)-axis oriented as ground range direction and \(y\)-axis oriented as the anti-azimuth direction, \(\theta\) defines the angle between the normal to the wake and the \(x\)-axis, whereas \(s\) defines the orthogonal distance between the wake and the center of the reference frame. From this information, it is possible to build the line representative of the wake, but it is not possible to set the wake vertex. To this end, the intensity distribution along the line is analyzed, and the darker half-line is selected as the turbulent wake component.  
Finally, since the turbulent component extends for kilometers, the same wake component is detected in neighbor pixels, i.e., in different positions of the scanning window (Step 3 in Figure 1) and pixels most likely affected by wakes are the ones crossed by the largest number of reconstructed wakes.