# Nighttime Image Dehazing Based on Point Light Sources
## 2 Related Work  
The light will come into contact with suspended particles in the atmosphere during its propagation process, and some of the light will be scattered by the particles, so the light received by the imaging device will be weaker [29]. In 1976, [PERSON] et al. [13] proposed that transmission light of the target would be attenuated by scattering, and the transmission device will receive not only the reflected light from the target but also a layer of atmospheric scattered light. [PERSON] et al. [30] constructed a method to recover scenes for foggy days with low visibility by visual performance under different weather conditions. [PERSON] [13] developed an atmospheric scattering model based on the Mie scattering theory, and the expression of the pixel value received by the device is expressed by the following equation:  
\[I_{x}=J_{x}t_{x}+A(1-t_{x}) \tag{1}\]  
where \(x\) represents the position of the pixel in the image, \(I_{x}\) represents the foggy image, \(J_{x}\) represents the fog-free image, \(t_{x}\) represents the transmission at the position of \(x\) in the image, and \(A\) represents the atmospheric light value of the image. This model divides the light received by the device into two parts. The first part represents the target reflected light, which means that the reflected light is directly transmitted to the device through the absorption and scattering of airborne particles, also known as the direct attenuation term of incident light; the other part is that the ambient light (mainly including direct sunlight, atmospheric diffuse light, and ground reflected light), which will also be attenuated by the action of the medium in the air. Many daytime physical model dehazing methods and some nighttime dehazing methods have been designed based on this model. The most typical one is the dark channel dehazing algorithm (DCP), which takes into account the global uniformity of atmospheric light in the daytime environment and can recover satisfactory images of the scene. He et al. [14] studied many fog-free images and found that at least one channel of the non-sky color block of the fog-free image contains very low-intensity pixels, and this color channel is called the dark channel. Ideally, the dark channel of a clear image is approximately zero and is mathematically represented as follows:  
\[J_{x}^{dark}=\underset{y\in\Omega(x)}{min}(\underset{c\in\{r,g,b\}}{min})\int_{x }^{c})\approx 0 \tag{2}\]  
However, in foggy images, air light causes the intensity of the color block pixels in these dark channels to increase. Therefore, during the process of recovery, it is necessary to adjust the light transmittance and the atmospheric light value to make the image clear. The author in [14] takes the average value of the first 0.1% pixels of illumination in the dark channel as the atmospheric light value, which is expressed by \(A^{c},c\in\{r,g,b\}\). The transmittance is estimated from the atmospheric light value, which is mathematically expressed as:  
\[t_{y}=1-\omega\underset{y\in\Omega(x)}{min}(\underset{c\in\{r,g,b\}}{min}) \frac{I_{y}^{c}}{A^{c}}) \tag{3}\]  
Among them, \(\omega\) is the introduction parameter which represents the concentration of fog. \(t_{y}\) is the transmission at the position of \(y\) in the image, where the position \(y\) is a point belonging to the set of light sources \(\Omega(x)\). \(A^{c}\) means atmospheric light values in the channel \(c\). \(I_{y}^{c}\) means pixel value at the position of \(y\) in the channel \(c\). The image obtained in this way will have a block effect. To solve the above problem, [PERSON] et al. [14] proposed a soft-matting algorithm to correct the initial transmission map. Finally, the atmospheric light value and transmission map are brought into Equation (1) to obtain the final restored image:  
\[J_{x}=\frac{I_{x}-A}{t}+A \tag{4}\]  
However, in night scenes, the atmospheric ambient light is susceptible to nighttime lighting [31].