单幅图像利用暗通道先验去雾方法

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本文主要探讨了"Single Image Haze Removal Using Dark Channel Prior"这一主题，该研究由Kaiming He、Jian Sun 和 Xiaoou Tang（IEEE Fellow）提出。他们针对单一输入图像的雾气去除提出了一个简单而有效的图像先验——暗通道假设。暗通道假设是基于户外无雾场景图像的一个统计特性：大部分局部区域都包含至少有一个颜色通道中存在强度非常低的像素。这一观察基于户外图像中的自然现象，即大气中的悬浮颗粒和水滴导致的光散射和吸收，使图像的清晰度受到严重影响。论文的核心思想是利用暗通道先验与雾气成像模型相结合。通过检测图像中暗通道的强度分布，可以直接估计出雾气的厚度，进而恢复出高清晰度的无雾图像。这种方法的优势在于不需要复杂的多视图信息或特殊的硬件设备，只需要单张图像就能实现雾气去除。实验结果显示，这种方法在处理各种类型的模糊图像时展现出强大的效果，证明了暗通道先验的有效性。此外，作为雾气去除的副产品，高精度的深度地图也可以被获取。这不仅提高了图像的视觉质量，也为诸如3D重建、计算机视觉任务提供了额外的有用信息。因此，这项工作对于图像恢复、雾/霾消除以及相关的计算机视觉应用具有重要的理论和实际价值，尤其是在没有其他辅助数据的情况下进行单图像处理的场景中。关键词包括"Dehaze"（去雾）、"Defog"（去雾）、"Image Restoration"（图像恢复）以及"Depth Estimation"（深度估计），这些关键词突出了本文的主要研究内容和应用场景。这篇文章提供了一种实用且高效的图像处理技术，对于提高户外图像的质量和理解其深层次信息具有重要意义。

Based on this model, Tan’s method [11] focuses on

enhancing the visibility of the image. For a patch with

uniform transmission t, the visibility (sum of gradient) of

the input image is reduced by the haze since t<1:

krIðxÞk ¼ t

krJðxÞk <

krJðxÞk: ð4Þ

The transmission t in a local patch is estimated by

maximizing the visibility of the patch under a constraint

that the intensity of JðxÞ is less than the intensity of A.An

MRF model is used to further regularize the result. This

approach is able to greatly unveil details and structures

from hazy images. However, the output images usually

tend to have larger saturation values because this method

focuses solely on the enhancement of the visibility and does

not intend to physically recover the scene radiance. Besides,

the result may contain halo effects near the depth

discontinuities.

In [10], Fattal proposes an approach based on Indepen-

dent Component Analysis (ICA). First, the albedo of a local

patch is assumed to be a constant vector R. Thus, all vectors

JðxÞ in the patch have the same direction R, as shown in

Fig. 2b. Second, by assuming that the statistics of the surface

shading kJðxÞk and the transmission tðxÞ are independent

in the patch, the direction of R is estimated by ICA. Finally,

an MRF model guided by the input color image is applied

to extrapolate the solution to the whole image. This

approach is physics-based and can produce a natural

haze-free image together with a good depth map. But,

due to the statistical independence assumption, this

approach requires that the independent components vary

significantly. Any lack of variation or low signal-to-noise

ratio (often in dense haze region) will make the statistics

unreliable. Moreover, as the statistic is based on color

information, it is invalid for gray-scale images and it is

difficult to handle dense haze that is colorless.

In the next section, we present a new prior—dark

channel prior—to estimate the transmission directly from

an outdoor hazy image.

3DARK CHANNEL PRIOR

The dark channel prior is based on the following observa-

tion on outdoor haze-free images: In most of the nonsky

patches, at least one color channel has some pixels whose

intensity are very low and close to zero. Equivalently, the

minimum intensity in such a patch is close to zero.

To formally describe this observation, we first define the

concept of a dark channel. For an arbitrary image J, its dark

channel J

dark

is given by

dark

ðxÞ¼ min

y2ðxÞ



min

c2fr;g;bg

ðyÞ



; ð5Þ

where J

is a color channel of J and ðxÞ is a local patch

centered at x. A dark channel is the outcome of two

minimum operators: min

c2fr;g;bg

is performed on each pixel

(Fig. 3b), and min

y2ðxÞ

is a minimum filter (Fig. 3c). The

minimum operators are commutative.

Using the concept of a dark channel, our observation

says that if J is an outdoor haze-free image, except for the

sky region, the intensity of J’s dark channel is low and

tends to be zero:

dark

! 0: ð6Þ

We call this observation dark channel prior.

The low intensity in the dark channel is mainly due to

three factors: a) shadow s, e.g., the shad ows of cars,

buildings, and the inside of windows in cityscape images,

or the shadows of leaves, trees, and rocks in landscape

images; b) colorful objects or surfaces, e.g., any object with

low reflectance in any color channel (for example, green

grass/tree/plant, red or yellow flower/leaf, and blue

water surface) will result in low values in the dark

channel; c) dark objects or surfaces, e.g., dark tree trunks

and stones. As the natural outdoor images are usually

colorful and full of shadows, the dark channels of these

images are really dark!

To verify how good the dark channel prior is, we collect

an outdoor image set from Flickr.com and several other

image search engines using 150 most popular tags annotated

by the Flickr users. Since haze usually occurs in outdoor

landscape and cityscape scenes, we manually pick out the

haze-free landscape and cityscape ones from the data set.

Besides, we only focus on daytime images. Among them, we

randomly select 5,000 images and manually cut out the sky

regions. The images are resized so that the maximum of

width and height is 500 pixels and their dark channels are

computed using a patch size 15  15. Fig. 4 shows several

outdoor images and the corresponding dark channels.

HE ET AL.: SINGLE IMAGE HAZE REMOVAL USING DARK CHANNEL PRIOR 3

Fig. 3. Calculation of a dark channel. (a) An arbitrary image J. (b) For each pixel, we calculate the minimum of its (r, g, b) values. (c) A minimum filter

is performed on (b). This is the dark channel of J. The image size is 800  551, and the patch size of  is 15  15.

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