## 2 Morphological Reconstruction and Multi-feature Analysis for TIR Ship Images
### Gray-Level Morphological Reconstruction for Sea Clutter Suppression and Saliency Detection
#### 2.2.2 Pre-Processing and Intensity Foreground Saliency Detection
Meanwhile, the CGMR can also be used to roughly estimate the background of infrared dark ship image, and then the IFSM for dark ship image is derived as:  
\[IFSM_{d}(x,y)=\|f(x,y)-CGMR_{f}[h](x,y)\|^{2}. \tag{13}\]  
Figure 4 shows the illustration of pre-processing results of a synthetic TIR ship image based on opening or closing GMR. Their corresponding 3-D mesh plots are shown in the second row. The bright ship targets are labeled in boxes and the dark ship targets are labeled in circles. Figure 4a is the original synthetic TIR image including three bright ship targets and three dark ship targets, which are polluted by heavy white Gaussian noise at the standard deviation of 10. Figure 4b is the pre-processing result for bright ship target image filtered by CGMR, and Figure 4c is the pre-processing result for dark ship target image filtered by OGMR. The average pixel intensity of the background in Figure 4a-c is 165, 176, and 158, respectively. It can be seen from Figure 4b,c that after the simulated TIR ship target image filtered by CGMR (OGMR), the dark (bright) components, and heavy noise clutter are totally removed  
Figure 4: The illustration of pre-processing results of synthetic TIR ship image based on gray-level morphological reconstruction (GMR). **(a)** Original synthetic TIR image that contains three bright ship targets and three dark ship targets submerged in heavy white Gaussian noise at the standard deviation of 10. **(b)** The pre-processing result for bright ship target image filtered by closing-based gray-level morphological reconstruction (CGMR). **(c)** The pre-processing result for dark ship target image filtered by opening based gray-level morphological reconstruction (OGMR). and the bright (dark) ship targets are completely restored with almost no loss of important signals. Therefore, because the synthetic TIR image contains various types of ship targets and heavy noise, the simulation results show that the OGMR- or CGMR-based pre-processing not only is robust to ship targets with different quantities, sizes, and shapes contaminated by heavy noise clutter, but also has fine intensity, shape, and contour-preserving capability. To further illustrate the efficiency and robustness of the proposed method, we conducted experiments on the three selected representative TIR ship images with complex sea scene clutter. Figure 5 shows their corresponding pre-processing results for sea clutter removal based on GMR. Figure 5d,f shows the pre-processing results of Figure 5a,c based on CGMR, respectively. Figure 5e shows the pre-processing result of Figure 5b based on OGMR. By comparing Figure 5a-c with Figure 5d-f, the sea clutter can be effectively removed and the detailed information of ship targets can be completely retained by the GMR-based pre-processing. This benefits largely from the fact that opening or closing marker-controlled GMR is a robust and flexible approach for removing local maxima or minima regions of sea clutter with closed contours, where their boundaries are depicted as ridges. Meanwhile, the opening or closing marker is used to reconstruct the original TIR image, so each object including bright or dark ship targets on the desired ridges can be automatically separated to preserve their boundaries. Figure 5: The pre-processing results for removing sea clutter based on gray-level morphological reconstruction. (**a**–**c**) are selected three representative TIR ship images with complex sea background clutter, (**d**) the pre-processing result of (**a**) filtered by CGMR, (**e**) the pre-processing result of (**b**) filtered by OGMR, (**f**) the pre-processing result of (**c**) filtered by CGMR. Figure 6 shows the processed results of TIR ship images by IFSM. The estimated backgrounds of original TIR ship images by OGMR or CGMR are shown in the first row of Figure 6. Figure 6d,f are the results of Figure 5a,c processed by proposed IFSM for bright ship image, and Figure 6e is the result of Figure 5b processed by IFSM for dark ship image.