# A Systematic Review of Ship Wake Detection Methods in Satellite Imagery
## 3 Results
### Overview of Traditional Methods of Wake Detection
#### 3.2.1 Methods Based on the Extraction of Linear Features  
As stated, the most common traditional approaches for ship wake detection are based on exploiting their linear structure. The most common methods used in this context to detect straight lines [6] in images are RT [26], the Hough transform [27; 28], and the scan curve [29]. These methods are applied to images, turning a line detection problem into a simpler task closer to the detection of dark or bright spots. Of the three, the RT is the most commonly used for wake detection [3; 30; 31; 32; 33; 34; 35; 36; 37; 38]. The RT is an invertible transform that was first published by [PERSON] in 1986 [26]. A form of the RT for a 2D image f(x,y) is given by Equation (2):  
\[ \begin{array}{c}\iint_{x,y}f(x,y)\delta(x\cos\theta+y\sin\theta)\,dx\,dy,\\ -\infty<x<\infty,\\ -\infty<y<\infty,\\ 0\leq\theta<\pi.\end{array}  \tag{2}\]  
where (x \(\cos\theta+y\) sin\(\theta\)) is the range \(\rho\) in the Radon-transformed space. The RT was not originally intended for line detection, but it fits the task for images of the sea. This is because ship wakes are either very bright or very dark, while the sea returns are generally average. When all the pixels of a given line are bright, and the others are closer to dim, in the Radon-transformed space the particular \(\rho\) and \(\theta\) of the line are highlighted [7]. A threshold can then be used to extract these peaks and isolate straight wake structures. Figure 3 shows an example of RT usage for ship wake detection. It is necessary to note that, while ship wakes are characterized by linear features, they do not appear as ideal lines with uniform brightness in satellite imagery, due to noise, clutter, and other atmospheric or sea surface phenomena. Thus, ship wake detection using traditional methods may lead to poor accuracy. Enhancing the linear features of wakes from  
Figure 3: (**a**) Original Sentinel-1 image, where the red rectangle indicates a mask used to cover the ship and propeller wake returns; (**b**) detected wake features in the Radon domain. Two red sinusoidal curves define the restricted Radon domain. The blue diamond is the turbulent wake, the green squares are the narrow-V wakes, and the yellow dots are the Kelvin arms. Reprinted with permission from Ref. [39]. 2017, [PERSON] et al. space [3; 31; 32; 33; 34; 32; 34; 3] is insufficient to reduce false detections due to other linear phenomena, for example, those that might be generated by waves. Some applications used other forms of processing to further enhance the wakes in imagery before or after using RT or other line-based transforms [8]:  
* Wavelet transform was used to sharpen wake edges using the frequency difference between sea clutter and wake stripes [37]. [PERSON] et al. [44] proposed a wake detection method for SAR imagery using wavelet filters together with the RT. * Recent studies have used the idea of compressed sensing to separate wake signals from sea clutter. A so-called low-rank plus sparse decomposition (LRSD) algorithm was used to suppress sea clutter and extract wake components [32; 38]. * Sparse regularization was used to enhance linear features of the RT [31; 45]. The scanning-based method was first described in [29]. It starts by computing the mean picture brightness in all directions surrounding the object ship to create a scanning curve. From this curve, one can infer the likely wake direction. By using pre-processing to improve the wake signal, [PERSON] et al. [46] and [PERSON] [47] increased algorithm performance. A Kelvin arm's alternating light and dark streaks were found by [PERSON] et al. [48] using a periodic function as the scanning curve. Recognizing that Kelvin wakes exhibit distinct periodic patterns due to the interference of divergent and transverse waves forming at specific angles relative to the ship's heading, they modeled the Kelvin arms as sinusoidal periodic surfaces through nonlinear fitting of the wave elevation data.