## 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  
References [36; 37] indicated that gray-level morphological reconstruction (GMR) can be used to extract objects, which are connected components with the same intensity value and larger (smaller) than the intensity value of the external boundary pixels, while keeping their intensity, shape, and contour detail information and suppressing trivial background clutter and noise. Motivated by this vision, as analyzed in above Section 2.1 part, since the ship target is also a small uniform region with higher (lower) contrast compared with its surrounding backgrounds in TIR remote sensing image, we adopt morphological reconstruction [38] on gray-level infrared images in a dual method to highlight ship targets and remove sea clutter simultaneously. Concisely, we let the result of the opening operation \(g=f\circ B\) as the marker image, original TIR image \(f\) as the mask image, hence the opening-based gray-level morphological reconstruction (OGMR) of \(f\) from \(g\), denoted by \(OGMR_{f}[g]\), is computed by iterating elementary geodesic dilations of \(g\) under \(f\) until stability is reached:  
\[OGMR_{f}[g](x,y)=\underset{i\geq 1}{\cup}gd^{(i)}(x,y), \tag{8}\]  
where \(gd^{(i)}(x,y)\) is the \(i\)-th iterating elementary geodesic dilation and the geodesic dilation is defined as follows:  
\[gd^{(i)}(x,y)=[g\oplus B]\cap f(x,y)=\min[g\oplus B(x,y),f(x,y)], \tag{9}\]  
where intersection operation \(\cap\) stands for pixel-wise minimum and union operation \(\cup\) stands for pixel-wise maximum. OGMR attempts to automatically restore the original image \(f\) from the result image of the opening operation \(g\) by using an iterative process, and then the connected regions brighter than the surrounding backgrounds in \(f\) will be fully removed, while the dark connected regions will be restored completely with a fine shape-preserving capability, as illustrated in Figure 4c. Therefore, considering the good performances of OGMR, the OGMR operation is used for pre-processing TIR dark ship image in this paper to enhance ship targets and suppress heavy sea clutter and noise. In addition, because ship target and sea clutter have different thermal radiation characteristics, the OGMR can also be used to roughly estimate the background of infrared bright ship image, and then the proposed intensity foreground saliency map (IFSM) for infrared bright ship image is defined as follows:  
\[IFSM_{b}(x,y)=\left\|f(x,y)-OGMR_{f}[g](x,y)\right\|^{2}, \tag{10}\]  
Figure 3: The processing results of classical THF/BHF filters on three representative TIR ship images with complex sea background clutter. (**a–c**) Original TIR images, (**d**) the result of (**a**) filtered by classical THF. (**e**) The result of (**b**) filtered by BHF. (**f**) The result of (**c**) filtered by THF. where \(||\cdot||\) represents \(\ell_{2}\)-norm. Similarly, let \(h=f\bullet B\), the closing-based gray-level morphological reconstruction (CGMR) of \(f\) from \(h\), denoted as \(CGMR_{f}[h]\), is computed by iterating elementary geodesic erosions \(h\) above \(f\) until stability is achieved:  
\[CGMR_{f}[h](x,y)=\underset{i\geq 1}{\cap}ge^{(i)}(x,y), \tag{11}\]  
where \(ge^{(i)}(x,y)\) is the \(i\)-th iterating elementary geodesic erosion, defined as:  
\[ge^{(i)}(x,y)=[h\Theta B]\cup f(x,y)=\max[h\Theta B(x,y),f(x,y)], \tag{12}\]  
CGMR tries to automatically restore the original image \(f\) from the result image of closing operation \(h\) by using an iterative process, and then the connected regions darker than the surrounding backgrounds in \(f\) will be fully removed, while the bright connected regions will be restored completely with a fine shape-preserving capability, as Figure 4b demonstrates. Accordingly, CGMR operation can be used for pre-processing infrared bright ship image to enhance a ship target and suppress sea clutter.