## 2 Morphological Reconstruction and Multi-feature Analysis for TIR Ship Images
### Ship Target Verification Based on Contour Description and Shape Constraint
#### 2.4.2 Shape Constraint for TIR Ship Identification Based on Statistical Knowledge  
After the above GMR induced operation steps, the binarized candidate ship targets are successfully extracted from backgrounds, and their simple geometric shape parameters, such as _Perimeter_ and _Area_, are retained and rapidly obtained. The geometric shape feature not only can efficiently distinguish the true ship targets from the non-ship targets, such as ocean waves, tail waves, sea-sky line/ coastline, and islands but also is less sensitive to the change of viewing angle and ship target size. As some previous studies [23; 41] mentioned that the ship target usually appears as a long narrow body, and the main body of the ship target has a regular shape feature. Hence, three widely used shape descriptors are adopted in this paper:  
\[Ratio_{mami}=\frac{L_{majoraxes}}{L_{minaxes}}, \tag{24}\]  
\[Compactness=\frac{(Perimeter)^{2}}{Area}, \tag{25}\]  
Figure 10: The final detection results according to STAEM calculation. (**a–c**) are the STAEM maps of Figure 5. (**d–f**) display the binarized saliency map fusion and STAEM maps simultaneously, and the STAEM values of true ship targets and some representative false alarms are marked, (**g–i**) the final detection results after the threshold division of STAEM values. \[Rectangularity=\frac{Area}{Rectangle}, \tag{26}\]  
where \(L_{majoraxes}\) and \(L_{minoraxes}\) are the lengths of the major axes and minor axes, respectively. _Rectangle_ indicates the circumscribed rectangle of the candidate region. The ratio of major to minor axes \(Ratio_{mani}\) can be used to describe its best fit ellipse because ship targets are usually long and thin. The _Compactness_ depicts the degree of circular similarity by fully considering the influence of object boundary changes on the average radius. The _Rectangularity_ represents the degree of rectangular similarity by assuming the values in the range of [0, 1], and 1 indicates the perfect rectangular region. Shape feature constraint methods are widely used to identify a ship target in the field of infrared ship target detection [14; 23], and those methods roughly set a large constraint range of shape parameters according to the statistics of ship shape parameters in their own datasets to output the final detected ship targets. However, because small ship targets are captured by long-distance TIR imaging sensors, the dynamic range of their shape parameters is relatively small and specific. By analyzing the TIR imaging characteristics of small ships and the statistics and observation of small ships in our datasets, it was found that the main distribution range of their shape parameters is similar to that of most TIR ships in VAIS database [31]. The VAIS database contains 1242 sliced TIR ship images, which are composed of 264 different types of ships captured during daytime and nighttime with variable view-angles and diverse distances. Therefore, in order to further identify true ship targets according to shape features, we randomly select 700 TIR ship targets from VAIS database to compute and count their shape parameters. Through the statistics and observation of the shape parameters of selected TIR ship targets, the statistical shape knowledge is reliably obtained and can be effectively utilized to further distinguish true ship targets from non-ship targets. Figure 11 shows some representative TIR ship targets selected from VAIS database and their corresponding binary images (manually labeled). Table 2 shows the statistical measurements of three shape descriptors on 700 TIR ship targets selected from VAIS database. Additionally, according to the statistical knowledge in Table 2, in order to further accurately identify small ship targets with shape feature, the ranges of \(Ratio_{mani}\), _Compactness_ and _Rectangularity_ in our paper are also empirically set to 1.1002-8.7857, 11.2813-118.6254, and 0.3826-0.8769, respectively.