# Nighttime Image Dehazing Based on Point Light Sources
## 2 Related Work
The local maximum intensity of each color channel in the image is mainly provided by artificial light source, so it is inaccurate to use global atmospheric light values to preserve the color characteristic of nighttime images. Therefore, we can reduce the attention on ambient light and directly estimate the ambient illumination and transmittance to recover foggy images. Most of the light radiated by point-like artificial sources varies smoothly in space, except for some sudden changes between bright and dark areas due to shading. In the estimation of ambient illumination, it is necessary to use light intensity normalization and maintain the color component of the artificial light source. Many researchers have analyzed the night scenes and reworked the atmospheric imaging model, as shown in the Table 1. [PERSON] et al. [32] splits the atmospheric light value \(A\) in Equation (1) into \(I_{x}\eta_{x}\), which is mathematically represented as:  
\[I_{x}=J_{x}t_{x}\eta_{x}+L_{x}\eta_{x}(1-t_{x}) \tag{5}\]  
where \(L_{x}\) represents the ambient illumination, and \(\eta_{x}\) represents the environmental color coefficient. Although the improved model is effective in the nighttime defogging task, it still can not remove the halo effect from the nighttime images. For removing the above halo effect, [PERSON] et al. [25] suggested adding a nighttime halo term to the original equation:  
\[I_{x}=J_{x}t_{x}+A(1-t_{x})+A_{x}*APSF \tag{6}\]  
The atmospheric point spread function is expressed as a halo term in the proposed model, and it decays with increasing depth of field. The halo term can represent the halo characteristics of the image, and the new proposed model can estimate the atmospheric light pixel by pixel, so that the halo can be removed from the image more accurately. Nevertheless, it should be noted that some noise in the recovered image is amplified and some color artifacts are generated around the light source. [PERSON] et al. [32] observed that each color channel of fog-free images contains some high-intensity pixels. For nighttime images, the high-intensity pixels of their color channels are all contributed by artificial ambient lighting. Based on these observed phenomena, the authors put forward the maximum reflection prior (MRP) to estimate the atmospheric light map. Due to the influence of the color of the artificial light source, the maximum reflectance map of the nighttime image is mathematically expressed as:  
\[ \begin{split} M^{\text{c}}_{\Omega(x)}=\underset{x\in\Omega(y)}{ max}& I^{c}_{x}=\underset{x\in\Omega(y)}{max}R^{\text{c}}_{x}(L_{\Omega(y)}\eta^{c}_{ \Omega(y)}t_{\Omega(y)})\\ &+L_{\Omega(y)}\eta^{c}_{\Omega(y)}(1-t_{\Omega(y)})\end{split}  \tag{7}\]  
Under the action of light, the maximum reflectance is approximated as \(1\):  
\[\underset{x\in\Omega(y)}{max}R^{\text{c}}_{x}\approx 1 \tag{8}\]  
\[M^{\text{c}}_{\Omega(x)}=L_{\Omega(y)}\eta^{c}_{\Omega(y)}\rightarrow\eta^{c} _{\Omega(y)}=\frac{M^{\text{c}}_{\Omega(x)}}{L_{\Omega(y)}} \tag{9}\]  
\[L_{\Omega(y)}=\underset{c\in\{\tau,g,b\}}{max}(\underset{x\in\Omega(y)}{max} \widetilde{I}^{c}_{x}) \tag{10}\]  
In nighttime images, the color channel of the glow part of the light source has a high-intensity value, and MRP can be used to improve the halo around the light source to some extent. The prior models, however, are built based on clear daytime image characteristics, which in some cases are different from the nighttime image characteristics. The fog-free image output with MRP alone will be distorted. On the basis of MRP, [PERSON] et al. [35] proposed the Optimal Scale-Based Maximum Reflectance Prior algorithm (OSFD), which considers the maximum reflectance as the probability of a pixel block that completely reflects the incident light in all frequency ranges. Moreover, color correction and defogging are separated and solved sequentially. In addition, the extinction Laplace matrix in the MRP method is replaced by the maximum value of the light intensity in all channels as a way to facilitate the calculation of the light intensity normalization.