## 3 Method
### Denoising Caused by the Airplane  
SLAR images show noise zones caused by the absence of a radar signal. These noise zones are a consequence of three circumstances: a hidden area under the aircraft fuselage without a radar signal, and changes in location and aircraft turns that take place during an emergency mission and during which the radar signal is lost (Figure 2). The noise zones lead to significant measurement errors which are subsequently registered as erroneous values in the pixels obtained by the digitalized process. It is, therefore, important to be able to automatically detect the pixels caused by noise zones for their subsequent labeling so that they will not be considered in the oil spill detection process. Those pixels that represent noise could cause false positives in the detection process. It is assumed that the hidden area is always unique for each input image, that its location in the image is unknown and that both the number of noise zones and their locations in the image owing to changes and turns are also unknown. The methodology for noise zone detection is implemented as a three-step algorithm. First, the input images I(\(x\),\(y\)) are filtered using Gabor filters [34]; H. Gabor filters use directional masks to detect abrupt changes of intensity in different directions. Second, the Hough transform [35] is applied to the filtered image in order to obtain the straight lines which delimit the abrupt changes as the border of the noise zone. Third, the input image is cropped to eliminate the pixel regions in which the noise zones were detected. A new SLAR image, which is smaller than original image, is consequently built from the input image to be used later in the detection process. Examples of the first and second steps of our algorithm are shown in Figure 4. The detection process carried out using the output of this first phase is described in the following section. The Gabor filter, H, is a low-pass filter that passes signals with a frequency that is lower than a reference frequency, f. Gabor makes it possible to eliminate texture pattern by detecting the pixels (\(x\),\(y\)) with intensity values which have a specific level of repetitiveness, i.e., that are homogeneous areas in the image. The Gabor filter is defined as follows:  
\[H(x,y,\lambda,\ \theta,\psi,\sigma,\gamma)=e^{(\frac{(x\cos\theta+y\sin\theta)^{2 }+\gamma^{2}-(x\sin\theta+y\cos\theta)^{2}}{2\sigma^{2}})}.e^{i(2\pi\frac{x \cos\theta+y\sin\theta}{\lambda}+\psi)}, \tag{1}\]  
where \(\lambda\) defines the wavelength of the sinusoidal factor, \(\theta\) is the orientation of the normal to the parallel stripes of a Gabor filter, \(\psi\) is the phase offset, \(\sigma\) is the standard deviation of the Gaussian envelope and \(\gamma\) is the spatial aspect ratio. Nevertheless, the output of Terma SLAR sensor is an image digitalized from a time sequence of scanning and H can, therefore, be represented as a discrete filter as follows:  
\[H(x,y,\ \theta,f,\sigma)=e^{(\frac{x^{2}+y^{2}}{2\sigma^{2}})}.e^{i(2\pi f \tau)} \tag{2}\]  
where \(f\) represents the frequency that determines the type of texture pattern and \(\theta\) is its orientation direction. The neighbors considered are controlled with the parameter of the Gaussian standard deviation \(\sigma\). In our experimentation, we have used \(\theta=92^{\circ}\) and \(\sigma=5\) to obtain good results with our dataset of SLAR images. Note that each turn area is a noisy region between two horizontal imaginary lines whose orientation is close to \(0^{\circ}\). Besides, hidden area is another noisy area between two vertical parallel lines whose orientation is close to \(90^{\circ}\) (Figure 4a). For this reason, we tested values close to\(0^{\circ}\) and \(90^{\circ}\) for the texture patterns in a range of \(\pm 10^{\circ}\). We got the best results with \(0^{\circ}\) and \(92^{\circ}\). Later, we apply a Gaussian filter \(G_{\sigma=5}\) and size \(3\times 3\) to remove noise due to the response of Gabor filters.