## 2 ROI Extraction
### The Proposed Saliency Map Detection Method  
Aiming at these addressed problems, a novel saliency map detection method is proposed based on the improved PQFT algorithm, called the modified PQFT (MPQFT). The method improves the PQFT in two aspects: one regards how the quaternion is constructed for the panchromatic remote sensing image to obtain uniform and complete target areas; the other regards how the saliency map is generated to ensure that differently sized targets can be detected at the same time. As shown in Figure 2, the proposed algorithm in the process of the MPQFT mainly consists of four steps: constructing the quaternion using different feature maps, carrying out hyper-complex Fourier transform to the quaternion, calculating multi-scale saliency maps, and generating the best saliency map. The process of the MPQFT is shown in Figure 2.  
Figure 2: Procedure for the modified phase spectrum quaternary Fourier transform (MPQFT) algorithm. For the ship target itself, it usually has a large change in intensity and obvious boundaries compared with clouds, fog, islands, and other scenes. In addition, texture and spatial similarity of ships are also conducive information in the complex background. Combining the two aspects would benefit the extraction process. Therefore, in the process of constructing the quaternion, we adopted the contrast map, the Gabor filtering map, and the fusion feature map that is established through combining spatial correlation with texture feature. The construction process of these feature maps is shown in detail below. Firstly, the contrast value of one pixel is measured by the Euclidean distance of regions R1 and R2, and the calculation formula is as follows:  
\[\mathrm{c(i,j)}=D[\frac{1}{\mathrm{N1}}\sum_{\mathrm{k=1}}^{\mathrm{N1}}\mathrm{ p}_{\mathrm{k}1},\frac{1}{\mathrm{N2}}\sum_{\mathrm{k=1}}^{\mathrm{N2}} \mathrm{p}_{\mathrm{k2}}] \tag{11}\]  
where \(\mathrm{p}_{\mathrm{k1}}\) and \(\mathrm{p}_{\mathrm{k2}}\) are gray values of pixels in R1 and R2, respectively. \(D[. ]\) indicates the Euclidean distance. R1 and R2 are the square regions centered on the same pixel \((\mathrm{i,j})\). i and j are the position of the row and column in the image. N1 and N2 are the number of pixels in R1 and R2, respectively. The size of regions R1 and R2 are \(5\times 5\) and \(41\times 41\) pixels, respectively. Both of them are empirical parameters. We c obtain the contrast map of the whole image by Equation (11). Secondly, the Gabor filtering map that is sensitive to the scale and direction of the images is introduced [24; 25]. The Gabor kernel function is multiplied by a Gaussian and sine function as follows:  
\[\mathrm{g(x,y,\lambda,\theta,\sigma,\varphi,\gamma)}=\exp(-\frac{x^{\prime 2}+ \gamma^{2}y^{\prime 2}}{2\sigma^{2}})\exp(i(2\pi x^{\prime}/\lambda+\varphi)) \tag{12}\]  
where \(x^{\prime}=x\cos\theta+y\sin\theta\), \(y^{\prime}=-x\sin\theta+y\cos\theta\). \(\lambda\) is expressed in pixels when participating in the calculation. In general, it is less than one-fifth of the size of the input image and greater than or equal to 2. \(\theta\) represents the direction of Gabor filter fringes, and ranges from \(0^{\circ}\) to \(360^{\circ}\). \(\varphi\) is the phase offset that ranges from \(-180^{\circ}\) to \(180^{\circ}\). \(\gamma\) is used to adjust the elliptic aspect ratio after the Gabor transform and when \(\gamma\) equals 1, and the shape is approximately circular. \(\sigma\) is the standard deviation of the Gaussian function in the Gabor function. We selected the following parameters: \(\lambda=2\), \(\theta=0^{\circ}\), \(\gamma=0.5\), \(\varphi=0^{\circ}\), and \(\sigma=0.5\). As shown in Figure 3, one example with different parameters is given. Next, a fusion feature map is established through combining spatial correlation with texture to enhance the quaternion. The lower the spatial correlation, the more likely a candidate it is.