## 3 Methodology
One can find a detailed description of the HSBA algorithm in [33]. The purple box displays the histogram of backscattering values for the complete scene, in which the bimodality is less noticeable, making it difficult to identify T and BG. The red box presents the backscattering value histogram for the areas selected by HSBA, where oil slick is present, clearly highlighting a bimodal behavior. The green box is a histogram of the sea’s backscattering value. We can assign the threshold (THS) to the average value of the \(PDF_{T}\), which represents pixels that have a high likelihood of belonging to T. To choose THSRG, many thresholds are evaluated. The selection is made by minimizing the root-mean-squared error between the \(PDF_{T}\) and the histogram produced by the region growth process. The two thresholds are automatically determined within the regions specified by HSBA, and subsequently applied to the full image to obtain the ultimate classification. The algorithm is applied separately to detect the four different targets, T1-T4, which reflect the oil-slick/look-alike class in the different input images. Satellite images must be preprocessed before being used as input for the proposed algorithm, including the determinations of NRCS (from Sentinel-1/ICEYE), average RGB oil index (from Sentinel-2/Landsat-8), and T865 variable (from Sentinel-3). These inputs are normalized and converted into dB with the mean value of each scene in order to remove anomalies and possible changes in the acquisition conditions, i.e., incidence angle and wind speed/direction for SAR data, as well as sun glint for optical images. For instance, the NRCS decreases with increasing incidence angles and reduced wind speed. Likewise, strong surface winds may significantly affect the homogeneity of oil films, which can produce a large difference in NRCS intensity of oil pixels, as shown in Figure 2a. (2) In complex scenarios where oil objects and look-alikes have similar input values, HSBA may struggle to distinguish between them. To differentiate between oil slicks and their look-alikes, we have considered the variation in backscattering coefficients or surface reflectance near the boundaries of the oil as a crucial parameter for distinguishing them. Therefore, to enhance the HSBA-based oil-slick detection, we applied the determination of oil contours [11; 45; 46] as an additional technique to distinguish oil slicks from look-alikes. To this end, first, we utilized the two non-linear filters, i.e., mean filter [47] and standard deviation filter [48], to input data (NRCS, oil index, and T865 variable). The mean filter is defined as follows:  
\[G(x,y)=\left\{\left[\prod_{i,j\in S}S(i,j)\right]^{\frac{1}{m}}\right\} \tag{3}\]  
\(G(x,y)\) is the output image, \(S(x,y)\) is the original image, and the filter mask is \(m\) by \(n\) pixels. This technique [47] helps to reduce the noise, which enhances the differences between dark/bright areas and the sea background. The mean filter is essential for object contour determination, and is based on the standard deviation filter [11; 45; 46] generally defined as follows:  
\[K(x,y)=\left\{\sqrt{\frac{1}{N}\sum_{i,j\in S}^{N}\left(G(i,j)-\overline{G} \right)^{2}},W(p,q)\right\} \tag{4}\]  
\(G(x,y)\) and \(K(x,y)\) are the input and output images of the standard deviation filter in Equation (4), respectively. \(N\) is the pixel number of the image/sub-image, and \(W(p,q)\) is the window size of the filter. The selection of the parameters of the mean and standard deviation filters (i.e., window size and moving step) [47; 48] is crucial to obtain satisfactory results. Although increasing the window size and moving step gives us images with reduced noise, there is a risk of removing some of the oil pixels. Therefore, the selection of the filter parameters should depend on the extents of the oil slicks. (3) We use the adaptive thresholding approach [49] to identify oil contours in the T1-T4 classes identified by HSBA on the filtered images.