## 2 Morphological Reconstruction and Multi-feature Analysis for TIR Ship Images  
### Characters of Small Ship Targets and Sea Clutter in TIR Image  
TIR images and visible (VIS) or near-infrared (NIR) images are both numerical representations of electromagnetic radiation in a specific wavelength region, so they have many common grounds. The VIS spectra are the visible part of the electromagnetic spectrum with a wavelength of 0.38\(\sim\)0.75 \(\upmu\)m. The infrared spectra can be roughly divided into: Near-infrared (NIR, wavelength 0.75-3 \(\upmu\)m) and thermal infrared (TIR, 3-15 \(\upmu\)m). Radiation emitted by an object spans a series of wavelengths, but because a specific sensor usually only collects radiation within a specific bandwidth, it is only interested in a limited range of the spectrum. According to Wien's displacement law [32; 33], the peak emission wavelength \(\lambda_{\text{max}}\) of the radiation is inversely proportional to the absolute temperature \(T\) of the object, and can be simply written as:  
\[\lambda_{\text{max}}T=2898.8\ \upmu\text{m K} \tag{1}\]  
According to this law, we can compute the temperature of blackbody radiation at each wavelength, and the temperatures of blackbody of VIS, NIR, and TIR are listed in Table 1. As can be seen from Table 1, the temperatures of blackbody of VIS and NIR spectra are very high, so they have little or no thermal imaging characteristics in natural conditions. In fact, the VIS is visible to the human eye with color perception. NIR is different from thermal imaging, and it is more like the extension of the grayscale of VIS imaging, so NIR is sometimes called \"reflected infrared\". Since the temperature range of blackbody of TIR is \(-\)79.9-693.12 \({}^{\circ}\)C, it is often used as thermography in natural conditions. Therefore, TIR imaging also has different physical characteristics from VIS light and NIR imaging. There are several special characteristics of small ship targets and sea clutter in TIR images. Firstly, the pixel intensity value in TIR image has a different physical significance with the pixel value in VIS or NIR images. The pixel intensity represents the thermal intensity (\"heat\") of objects. In TIR images, because different materials have different thermal radiation, the hotter object appears \"white\" while the cooler object appears \"black\". Due to this characteristic, the small ship targets as a manmade object in sea clutter can naturally form bright or dark objects in the TIR image despite the ship camouflage colors and the illumination condition in VIS or NIR images. Secondly, owing to the limited manufacturing level of sensors, the TIR images are usually less informative than the images captured by VIS or NIR optical sensors. In other words, the TIR images are relatively lower in resolution, contrast, and clarity, resulting in the lack of textural and structural information about objects. Thirdly, because thermal infrared radiation determines the temperature of objects, the infrared thermography can be used to remotely detect the ship targets. To conclude, because of the long imaging distance for TIR images, the signal intensity of a small ship target is usually very weak without sufficient texture and structure information. Furthermore, in TIR images, the natural scene background has strong local self-similarity even for sea clutter, but the small ship target as a manmade object will destroy these characteristics of background. Therefore, the ship targets can be viewed as local bright or dark uniform abnormal regions under the sea background clutter in TIR images due to long imaging distance, as illustrated in Figure 2.  
TIR small ship imaging results are complex and comprehensive processes, which are easily affected by non-stationary inputs, such as atmospheric radiation, solar refraction and engine temperatures. Therefore, detection is very important when the ship target is small and embedded in sea clutter.