## 2 Morphological Reconstruction and Multi-feature Analysis for TIR Ship Images
### Saliency Map Fusion Based on Gray-Level Morphological Reconstruction  
The previous part has discussed in detail the computation process of the intensity foreground saliency detection and brightness contrast saliency detection based on gray-level morphological reconstruction, respectively. From the above mentioned, the IFSM depicts the distinctive gray intensity features between TIR ship targets and sea background clutter. The BCSM describes the spatial properties of TIR ship targets against background clutter, including brightness uniformity and local region contrast features. The purpose of saliency map fusion is to improve the ship targets' reliability in an infrared image and reduce false alarms by utilizing the information of all feature saliency maps. However, because the above two saliency maps have different magnitudes, we should normalize all the saliency maps to the same range [0, 1] by maximum and minimum values of each map. Given a saliency map \(S\), its normalization operation can be expressed as:  
\[\mathbf{N}[S](x,y)=\frac{S(x,y)-S_{\text{min}}}{S_{\text{max}}-S_{\text{min}}}, \tag{16}\]  
where \(S_{\text{max}}\) and \(S_{\text{min}}\) are the maximum and minimum values of saliency map \(S\). \(\mathbf{N}[S](x,y)\) denotes the normalized result of \(S\) at location \((x,y)\). Accordingly, the normalized result of IFSM can be written as \(\mathbf{N}[\textit{IFSM}]\), and the normalized result of BCSM can be written as \(\mathbf{N}[\textit{BCSM}]\). Therefore, the proposed final saliency map is generated by a pixel-wise multiplication fusion manner:  
\[SM_{b}(x,y) =\mathbf{N}[\textit{IFSM}_{b}](x,y)\times\mathbf{N}[\textit{BCSM} _{b}](x,y), \tag{17}\] \[SM_{d}(x,y) =\mathbf{N}[\textit{IFSM}_{d}](x,y)\times\mathbf{N}[\textit{BCSM} _{d}](x,y), \tag{18}\]  
here, \(SM_{b}\) and \(SM_{d}\) represent the final saliency maps of infrared bright and dark ship images, respectively. Then, the candidate ship targets can be separated and extracted from the final saliency map \(SM\) by an adaptive threshold [4; 24], and the adaptive threshold is determined as:  
\[\tau=\overline{SM}+\varepsilon\times\sigma(SM), \tag{19}\]  
where \(\overline{SM}\) and \(\sigma(SM)\) are the mean value and standard deviation of the final saliency map \(SM\), respectively. \(\varepsilon\) is an experimentally selected constant and it can be chosen from the interval [10; 15] for most scenarios. Finally, the binary segmentation result \(BSM\) of the final saliency map is acquired:  
\[BSM(x,y)=\begin{cases}1,&SM(x,y)\geq\tau\\ 0,&\textit{otherwise}\end{cases}, \tag{20}\]  
Figure 8 gives the final results of saliency map fusion. The first row is the results of saliency map fusion of Figure 5a-c, their corresponding 3-D mesh plots are shown in the second row, and the third row is the binary segmentation result \(BSM\) of their final saliency maps. The red boxes have enlarged point ship targets, and the purple boxes have enlarged small-size false targets. As shown in Figure 8a,c, the proposed saliency map can be directly used for detecting TIR ship targets with different sizes and quantities submerged in complex backgrounds with sea-sky line/coastline or long ribbon-like sea clutter. Figure 8b demonstrates that for low-contrast ship targets buried in intricate backgrounds with strongly rolling sun-glint clutter, the proposed saliency map can make ship targets stand out but fail to distinguish real ship targets from chaotic sea clutter, because some strong clutter also has non-negligible saliency even in the final saliency map. To cope with this problem, a two-step ship verification strategy is introduced in the following Section 2.4 part based on contour feature description and shape feature constraint.