Visibility in Bad Weather from a Single Image (Tan)

引入了一种只需要一个输入图像的自动方法，作者基于两点：

1.      增强之后的图像也就是清晰的图像比有雾的图像对比度高。

2.      Airlight的变化主要依赖于物体与观察者的距离d，所以airlight趋于平滑。

基于该两点建立马科夫模型的代价方程，通过各种技术（如图形切割或信念传播）进行有效优化。 该方法不需要输入图像的几何信息，并且适用于彩色和灰色图像。

目标：增强对比度以此来提高visibility。

摘要

背景：Bad weather, such as fog and haze, can significantly degrade the visibility of a scene. Optically, this is due to the substantial presence of particles in the atmosphere that absorb and scatter light. In computer vision, the absorption and scattering processes are commonly modeled by a linear combination of the direct attenuation and the airlight.

现存方法：Based on this model, a few methods have been proposed, and most of them require multiple input images of a scene, which have either different degrees of polarization or different atmospheric conditions. This requirement is the main drawback of these methods, since in many situations, it is difficult to be fulfilled.

提出的方法：To resolve the problem, we introduce an automated method that only requires a single input image. This method is based on two basic observations: first, images with enhanced visibility (or clearday images) have more contrast than images plagued by bad weather; second, airlight whose variation mainly depends on the distance of objects to the viewer, tends to be smooth. Relying on these two observations, we develop a cost function in the framework of Markov random fields, which can be efficiently optimized by various techniques, such as graph-cuts or belief propagation. The method does not require the geometrical information of the input image, and is applicable for both color and gray images.

Optical Model

1、  首先构建该雾天图像的光学模型，即Optical Model

ρ：物体的反射率； 大气衰减系数（假设不同波长的衰减系数是常量）；d(x)物体和观察者之间的距离；

Chromaticity（色度） 

• light chromaticity （α）： 假设物体无限远，则物体的色度只依赖 atmospheric light（）；

• object chromaticity：假设不受到散射粒子的影响，即没有大气光影响，则物体的色度只依赖于direct attenuation。

则结合式（3）（4）可将式（1）重写为：

方法的主要任务：求得，估计。

这里：

使用单个图像的解决方案

（1）clue1-->最大化对比度：定义图像边缘的个数和对比度有相关联系；

损失函数： 

 （2）clue2-->大气光平滑约束

 

方法步骤

1、  首先估计输入图像的atmospheric light也就是A 。

寻找图像I中具有最大intensity的小点。

2、  然后从atmospheric light中获取light chromaticity，也就是光的色度 。

通过公式（3）从L∞ 计算ight chromaticity,值α ，为了更加精确 ，也可以用已经存在的color constancy method (e.g. [3]).

3、  依据获取的光的色度，将原图像中illumination color去除 。

用公式（8）去除图像I的illumination color ,形成I′.获取去除light color图像的方法就是在有雾图像的每个通道上除以αc，也就是除以每个颜色通道的色度，这样就可以获取 。

4、  然后从图像截取的小块的中计算每个像素的data cost。

计算图像I′的每个像素的数据损失

5、  然后从两个相邻像素的标签的差异或距离（其中标签与大气光值相同）中计算每个像素的smoothness cost.

6、  现在可以构建马科夫模型包括datacost和smoothness cost，最优化该代价方程之后就可以得到airlight A。

7、  基于估计的A，最后我们计算直接衰减，代表具有增强可见性的场景。