# Preliminary Results of Ship Detection Technique by Wake Pattern Recognition in SAR Images
## 3 Results  
The proposed approach has been applied on a StripMap image (Figure 3) gathered by TerraSAR-X over the Gulf of Naples, whose parameters are listed in Table 1. The VV polarization monostatic product only is used, whose geometric resolutions (1.2 m-slantrange, 6.6 m-azimuth) coincide with those of the standard TerraSAR-X dual-polarization, Stripmap product. The image is characterized by calm sea conditions with low wind speed (i.e., 4-6 m/s) and with a local incidence angle of about 28\({}^{\circ}\). As detailed in [36], wind speed has been estimated by using XMOD [37] with the local incidence angle. The image has been selected since it shows wakes very similar to the one generated by go-fast boats,  
Figure 2: Score logic approach. The lines are representative of the turbulent components built on the pixels satisfying Equation (4). i.e., (a) no bright returns from the ship, (b) at least one dark and one bright component, and (c) no classical Kelvin pattern appearance. It is worth noting that a portion of sea without wakes is included in the image allowing the test of the false detection performance of the technique, i.e., detected wakes when they are not imaged. The candidate wake identification is hereinafter detailed for the pixel shown as a yellow dot in Figure 3. It has been chosen as an interesting test case since the tile (see Figure 5a), on which the wake detection analysis is carried out, includes portions of all the three wakes. The main steps of the wake reconstruction around the pixel are summarized in Figure 4. Only the detection of the turbulent and one narrow-V components are included in the procedure, whose details can be found in [24]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Acquisition Epoch** & **June 9 th, 2011-16:49 UTC** \\ \hline Mode & StripMap–Dual polarization \\ Level & L1B \\ Polarization & VV and VH (only VV used) \\ Range Resolution & 2.5 m \\ Azimuth Resolution & 6.5 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main SAR image Parameters. Figure 3: SLC image gathered by TerraSAR-X over the Gulf of Naples on 9 th June 2011. The yellow dot is the center of the tile shown in Figure 5. Tile size: \(10.7\times 5.5\) km. The tile of \(2000\times 2000\) pixels is set (Figure 5a). It includes portions of three wakes: only wake \(a\) crosses the pixel under analysis corresponding to the tile center, whereas wake \(b\) is very prominent and wake \(c\) is weaker. This implies a stronger couple peak/trough relative to wake \(b\) in the Radon domain than the couple of wake \(c\) (Figure 5b). The peaks/troughs are only searched where they are expected to be, opportunely limiting the search area in terms of (\(\theta\),s). In details, the trough/peak pair corresponding to the turbulent wake and one narrow-V wake must be within a 4\({}^{\circ}\) of angular distance. To this end, the Radon domain is restricted to search only the wake crossing the tile center [24], and the trough/peak pair is selected as the one which maximizes their intensity difference. The results of the previous detection phase are two points in the Radon domain, each one identified by the coordinates (\(\theta\),s) and representing a candidate component of the typical wake appearance. The estimation of merit indexes is performed in the input domain (intensity image), thus the inverse Radon Transform is applied. However, the 180\({}^{\circ}\)-ambiguity in the ship heading must be solved, i.e., the inverse Radon Transform returns lines and not-half-lines. To this end, the lines of the wake components are intersected with the constant-range line passing through the tile center. Then, the turbulent wake is identified as the half line with lower mean intensity. The narrow-V half-line is identified as the ones within 90\({}^{\circ}\) from the unambiguous turbulent wake half line. Results (Figure 5c) show that the wake \(a\) is correctly detected, whereas the wakes \(b\) and \(c\) are discarded, since they do not cross the tile center.