翻译 Dark Channel Prior based Image De-hazing: A Review

      （Abstract-Digital images captured under poor environments are vulnerably degraded in their capacities to convey adequate amount of information to the viewer or computer-based processes.One of the common causes affecting the quality of outdoor images can be traced to that coming from atmospheric condensations such as fog or haze. Image processing algorithms, hence, had been developed to address the de-hazing problem in order to recover the scene information. Approaches based on the dark channel prior, in particular, had initiated a large number of research activities because of its satisfactory performance and possibilities for further improvements and applications. In this paper, a review on methods based on the dark channel prior is presented. The principle of restoration by a ray transmission model applied in image de-hazing is examined together with a classification of the models commonly employed. The difficulties encountered in the implementation of de-hazing algorithms are addressed and discussed. A summary of critical issues and a discussion of future trends are also included in this review.）

      摘要：在恶略环境中获取的数字图像，很容易在它们将信息传递给读者或计算机处理程序的能力方面退化。其中一个常见的原因就是雾或者霾。因此，一些图像处理算法被提出来处理这些去雾问题，来恢复原本的场景信息。基于暗通道优先的方式，特别的，由于其令人满意的性能和继续提升的可能性与应用性，吸引了大量的相关研究。在本文中，对这种基于暗通道优先的几种方式做了统一的回顾和评审。一种通过射线透射恢复模型的原理用于图像去雾在此被检验，同时将通常采用的模型进行分类。实现图像去雾算法的困难在此被提出并讨论。一个关键问题的总结和一个未来发展趋势的讨论也被包含在本评论中

I. INT RODUCT ION

      （The question of human perception of outdoor scene color and contrast through the atmosphere had been asked through history. For instance, Leonardo da Vinci's paintings often contain atmospheric perspective of the background scene [1],which was argued to be aesthetically pleasing to humans. After the introduction of digital imagery and because of its wide availability, attempts had been made to restore scene appearances despite degradations caused by the turbid atmospheric medium [2][3][4][5]. These demands aroused due to the fact that degradations in images often hinder satisfactory performance in outdoor vision applications such as surveillance, terrain classification and many other vision-based computer processes [6][7][8][9]. In the past decade, variousalgorithms for atmospheric degraded image restoration, commonly called de-hazing, had been developed in order toobtain high quality images from their degraded counterparts [10][11][12][13][14][15][16][17]. This research topic is attracting more attention over the years which is evident from Fig. 1, indicating the number of publications in recent 10 years. The current methods can be generally classified into three categories including:)

I. 介绍

     有关于人类对室外场景色彩的感知并通过大气来对比的能力的问题，在历史上已经被提出过了。例如，达芬奇的绘画经常包含背景场景的大气透视[1]，这些绘画被认为在美学上令人愉悦。在引入了数字图像后，由于这种技术广泛的可用性，人们试图恢复由于混浊的大气介质而被污染退化的场景[2] [3] [4] [5]。这些要求的提出是由于这样的事实：图像的退化常常使人不能满意一些户外视觉的应用如监视，地形分类和许多其他基于视觉的计算机过程[6] [7] [8] [9]。在过去的十年里，各种大气退化图像恢复算法，通常被称为去雾化，已经被开发用来从其降级退化的图像中获得高质量的图像[10] [11] [12] [13] [14] [15] [16] [17]。 这个研究课题多年来吸引了越来越多的关注，fig1为证据指出了10年来出版物的数量。 目前的方法一般可以分为三类，包括：

     ( (1) Additional information approaches [18][19][20], in which information such as the scene depth, geometrical model of the captured scene should be available. Since this requirement cannot be practically satisfied, they are not suitable for real-world applications in many cases.

      (2) Multiple image methods [2][21][22][23], are generallyapplicable; however, they suffer from additional cost and attract less research interests.）

      (3)Single image approaches [24][25][11][12][26][13][14][27] [28][29] [30] [31] [32] [33] [34][ 17] [35], are more popular due to their convenience, adaptability, and exhibit compelling results. Most importantly, an image quality assessment metric after haze removal is available [23].）

     （1）附加信息方式

     （2）多图片方式

     （3）单图片方式，由于其方便，适应性和展示令人信服的结果更受欢迎。 最重要的是，在去除雾霾之后的图像质量评估度量是可用的

     The relationship of de-hazing methods is shown in Table I,including the three main algorithms, corresponding representative literatures and shortcomings. It can be seen that lots of work has been done on single image haze removal and further research is needed to overcome existing shortcomings.

       去雾方法的关系如表1所示，包括三个主要算法，相应的代表性文献和缺点。 可以看出，已经对单图像模糊去除进行了许多工作，并且需要进一步研究以克服现有的缺点。

     

     Before dark channel prior appears, two algorithms for single image haze removal have been referred and discussed in details. One is proposed by Fattal [11], who assumed that the transmission and the surface shading are locally uncorrelated. This approach is physics-based and achieves good result, however, it will fail in the dense haze condition [36]. The other one is presented by Tan [13], who recovered the color and visibility by maximizing the contrast in local window of hazy image. Although the visual result is compelling, this method may become physics-invalid.

    在暗通道先验出现之前，已经详细讨论和讨论了用于单图像模糊去除的两种算法。 一个是由Fattal [11]提出的，他假定透射和表面阴影是局部不相关的。 这种方法是基于物理的，并获得良好的结果，然而，它将在稠密haze条件下失败[36]。 另一个由Tan [13]提出，他通过模糊窗口的最大化局部窗口的对比度来恢复颜色和可见度。 虽然视觉效果令人信服，但这种方法可能会变得物理无效。

     In 2009, the Dark Channel Prior (DCP) was proposed[12], which has been regarded as the state-of-the-art. Lots of researches have been conducted based on DCP including its variations, improvements, and proposals for new applications. In this paper, a review of published work in DCP is reported. We begin with a description of the algorithm, itsassumptions and practical limitations in Section II. In SectionIII, a discussion on recent refinements is included togetherwith indications for future research. A conclusion is drawn inSection IV.

    2009年，暗信道优先（DCP）被提出[12]，被认为是最先进的。 基于DCP已经进行了许多研究，包括它的一些变体，改进和对于新应用的建议。 在本文中，报告了对DCP中发表的工作的回顾。 第二部分。我们从算法本身，假设和实际限制的描述开始。 在第三节中，包括对最近改进的讨论以及未来研究的指示。 第四节得出结论。

    II. DARK CH ANNEL PRIOR

    The dark channel prior is based on the key observationon outdoor haze-free images that at least one color channel has some pixels whose intensities are very low and close tozero, which means that the minimum intensity in such a patchis close to zero. The model [57][58][11][13] widely used todescribe the formation of a hazy image in computer visionand computer graphics is:

      暗通道先验是基于关键观察:在室外无雾图像上，至少一个颜色通道有一些像素的强度非常低并且接近于零，这意味着这块区域中的最小强度接近零。 在计算机视觉和计算机图形学中，以下模型[57] [58] [11] [13]广泛的用于描述了衣服模糊图像的构成，：

   

    where I is the observed intensity, J is the scene radiance, A isthe global atmospheric light, and t is the medium transmissiondescribing the portion of the light that is not scattered andreaches the camera. The goal of haze removal is to recover J,A and t from I.

    其中I是观测强度，J是场景辐射，A是全球大气光，t是介质透射用于描述未散射并且到达相机的光。 去雾的目标是由 I 恢复出J，A和t.

    When the atmosphere is homogenous, the transmission t canbe expressed as

    当大气均匀时，透射率t可以表示为

    

      where (3 is the scattering coefficient of the atmosphere and d is the scene depth. From (2), it can be observed that the depth could be recovered up to an unknown scale once the transmission is obtained, hence the transmission t can be utilized to recover both of the scene radiance J and the depth d.

      For an arbitrary image J, the dark channel Jdark is given by：

      其中（3是大气的散射系数，d是场景深度，从（2）可以观察到，一旦获得透射率，深度可以恢复到某个未知的尺度，因此可以利用透射率t 以恢复场景辐射亮度J和深度d。
      对于任意图像J，暗通道Jdark由下式给出：

      where Jdark(X) is a color channel of J and n(x) is a local patch centered at x. The two minimum operators are commutative.

      Based on the key observation on non-sky regions in an outdoor haze-free image J, the dark channel intensity of J is low and close to zero

      

      其中Jdark（X）是J的颜色通道，n（x）是中心在x的局部。 两个最小运算符是可交换的。

      基于在室外无雾图像J中的非天空区域的关键观察，J的暗通道强度低并接近零：

      This observation is called dark channel prior, which is inspired by the well-known dark-object subtraction technique [59]. The depth d and the scene radiance J can be obtained according to the following steps.

      这个观察被称为暗通道先验，是被众所周知的暗物体减法技术[59]启发得到的。 深度d和场景辐亮度J可通过以下步骤得到。

A. Estimate the atmospheric light

      The scene radiance of each color channel considering the sunlight is given by

      

      where R <= 1 is the reflectance of the scene and S is the sun light. Then, the haze imaging model could be written as

      

      From (6), it can be seen that the brightest pixel of the whole image can be brighter than the atmospheric light, which is not appropriate for accurate atmospheric light estimation.Consequently, the top 0.1 percent brightest pixels in the dark channel were picked [12]. Among these pixels, the pixels with highest intensity in the input image I are selected as the atmospheric light A. This algorithm can work well even when there are no pixels at infinite distance in the image and functions more robustly than the "brightest pixel" method proposed by Tan [13].

      从（6）可以看出，整个图像最亮的像素可以比大气光更亮，这不适合于精确的大气光估计。因此，在暗通道最亮的0.1％亮的像素被选取[12]。 在这些像素中，输入图像I中最高亮度的像素被选中作为大气光A。该算法可以很好地工作，即使当在图像中没有处于无限远处的像素，并且比由Tan提出[13]的“最亮像素”方法更鲁棒。

B. Estimate the transmission

      According to (1 )(3)(4), a rough estimation of the atmospheric light is obtained by

     Particularly, in the sky regions, we have. 

    

     since the color of the sky in a hazy image I is usually verysimilar to the atmospheric light A. From (7), it can be seen thatt(x) --+ O. Since the sky is infinitely far away, its transmissionis indeed close to zero according to (2); hence, this methodcould effectively deal with both sky and non-sky regions.Moreover, a constant parameter w (0 < w <1) is added to(7) to make sure the haze is not removed thoroughly,

since the presence of haze is a fundamental cue for human toperceive depth [60][61], which is called aerial perspective [1].After the refinement, the transmission t is obtained.

C. Recover the scene radiance

     After the atmospheric light A and the transmission map tare obtained, the scene radiance could be recovered accordingto (1). The final scene radiance J(x ) is recovered by

     

     where to, a lower bound, whose typical value is 0.1, isintroduced to make this algorithm more robust to noise.

     Dark channel prior is very efficient in obtaining a satisfactoryresult, the reason of which is specifically analyzedby Gibson [62], using principal component analysis, andminimum volume ellipsoid approximations. Moreover, theeffective performance of dark channel prior could also beobserved in the work of Fang [63], which discussed about theimage quality assessment on image haze removal. Althoughdark channel prior has been employed as the most efficientalgorithm for haze removal, there are still some practicallimitations:

      1) The dark channel prior method will underestimate thetransmission of objects when the scene objects are inherentlysimilar to the atmospheric light and no shadowis cast on them [12].

     2) This algorithm will fail when the haze imaging model in(1) is physically invalid. For example, when the sunlightis very influential, the constant-airtight assumption willbe violated [12].

     3) The color distortion phenomenon will occur when thetransmission is different among three color channels[12].

     4) The soft matting algorithm used by He is time consuming,thus, not suitable for real-time implementation [40].