# A Systematic Review of Ship Wake Detection Methods in Satellite Imagery
## 3 Results
### DL-Based Applications for SAR Imagery
It is important to note that the SAR images in the application in question are used as gray-scale images, as polarization and multi-channel image information are deemed less critical. Similarly to in previously described applications, the linear features of the wake are exploited to enhance the capabilities of the model. In particular, horizontal BBs are used in conjunction with the wake line (considered as the turbulent wake), which is aligned with the diagonal of the corresponding BB. To do this, intersection over union (IoU) is insufficient, and an angle-IoU loss function is proposed to achieve high angular correlation. This angle-IoU is defined as the normalized angular distance coefficient between actual and predicted wakes, as shown in Equation (4):  
\[RAIoU=\frac{|\theta^{p}-\theta^{s}|}{\theta^{c}}, \tag{4}\]  
where the superscripts p, g, and c denote the prediction box, the ground truth, and the smallest enclosing box covering two boxes, respectively. This angular consideration was further improved by adding a distance loss between the diagonal of the predicted BBs and the actual wake line. Finally, [PERSON] et al. [8] developed a loss function which takes into consideration integrity, coincidence degree, and directionality, which they identified as the critical elements for a wake BB. Figure 5: Subset of a TerraSAR-X product in VV polarization (azimuth–slant range coordinates). (**a**) Reference image. (**b**) Segmentation results of the model based on Cascade Mask-RCNN. Adapted with permission from Ref. [61]. 2021, [PERSON] et al. As with previous applications, [PERSON] et al. also collected a dataset for their training and testing activities. Their dataset contained 862 pairs of ships and wake SAR images from Gaofen-3, containing different scales of ship and wake images in various sea conditions and imaging modes, including spotlight, stripmap, and scan, to ensure diversity. [PERSON] et al. [62] used YOLOv5 for their application, which focused on detecting non-linear ship wakes and weak wakes in SAR images. The authors made large use of simulated data to augment their dataset of SEASAT SAR and TerraSAR-X imagery, using a semi-deterministic facet scattering model (SDFSM) to simulate the electromagnetic scattering distribution of the sea surface and Kelvin ship wakes. The modeling process involved generating a composite scene of the sea surface and ship wake, simulating various conditions such as different sea states, ship speeds, and headings. Then, key parameters like the radar incident frequency, radar incident angle, ship dimensions, and sea surface wind speed were used to generate realistic SAR image simulations. The authors then employed several models to simulated various facets of the scene:  
* The sea surface was simulated utilizing the Elfouhaily wave spectrum and Mitsuyasu directional function to simulate the sea surface's randomness and anisotropic characteristics. * A Kelvin wake mathematical model was used to simulate the wake's wave height, considering ship speed and direction. * An SAR image simulation was obtained combining the facet scattering distribution and the SAR imaging mechanism to produce SAR images of the composite sea surface and wake scenes under various conditions. The authors compared the performance of YOLOv5 with traditional RT-based methods. According to their analysis, the DL-based solution successfully detected the non-linear wakes, while methods based on linear feature extraction were obviously unable to succeed. Finally, in early 2024, [PERSON] and [PERSON] [65] addressed the scarcity of publicly available SAR ship wake datasets by introducing OpenSARWake, a large-scale dataset annotated with oriented bounding boxes, as cited in Table 1. To effectively detect ship wakes, they also developed SAR Wake Net (SWNet), a two-stage detection algorithm tailored for SAR imagery.