（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：在惡略環境中獲取的數字圖像，很容易在它們將信息傳遞給讀者或計算機處理程序的能力方面退化。其中一個常見的原因就是霧或者霾。因此，一些圖像處理算法被提出來處理這些去霧問題，來恢復原本的場景信息。基於暗通道優先的方式，特別的，由於其令人滿意的性能和繼續提升的可能性與應用性，吸引了大量的相關研究。在本文中，對這種基於暗通道優先的幾種方式做了統一的回顧和評審。一種通過射線透射恢復模型的原理用於圖像去霧在此被檢驗，同時將通常採用的模型進行分類。實現圖像去霧算法的困難在此被提出並討論。一個關鍵問題的總結和一個未來發展趨勢的討論也被包含在本評論中
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. 介紹
有關於人類對室外場景色彩的感知並通過大氣來對比的能力的問題，在歷史上已經被提出過了。例如，達芬奇的繪畫經常包含背景場景的大氣透視[1]，這些繪畫被認爲在美學上令人愉悅。在引入了數字圖像後，由於這種技術廣泛的可用性，人們試圖恢復由於混濁的大氣介質而被污染退化的場景[2] [3] [4] [5]。這些要求的提出是由於這樣的事實：圖像的退化常常使人不能滿意一些戶外視覺的應用如監視，地形分類和許多其他基於視覺的計算機過程[6] [7] [8] [9]。在過去的十年裏，各種大氣退化圖像恢復算法，通常被稱爲去霧化，已經被開發用來從其降級退化的圖像中獲得高質量的圖像[10] [11] [12] [13] [14] [15] [16] [17]。 這個研究課題多年來吸引了越來越多的關注，fig1爲證據指出了10年來出版物的數量。 目前的方法一般可以分爲三類，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）多圖片方式
（3）單圖片方式，由於其方便，適應性和展示令人信服的結果更受歡迎。 最重要的是，在去除霧霾之後的圖像質量評估度量是可用的
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.
去霧方法的關係如表1所示，包括三個主要算法，相應的代表性文獻和缺點。 可以看出，已經對單圖像模糊去除進行了許多工作，並且需要進一步研究以克服現有的缺點。
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.
在暗通道先驗出現之前，已經詳細討論和討論了用於單圖像模糊去除的兩種算法。 一個是由Fattal [11]提出的，他假定透射和表面陰影是局部不相關的。 這種方法是基於物理的，並獲得良好的結果，然而，它將在稠密haze條件下失敗[36]。 另一個由Tan [13]提出，他通過模糊窗口的最大化局部窗口的對比度來恢復顏色和可見度。 雖然視覺效果令人信服，但這種方法可能會變得物理無效。
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，暗信道優先（DCP）被提出[12]，被認爲是最先進的。 基於DCP已經進行了許多研究，包括它的一些變體，改進和對於新應用的建議。 在本文中，報告了對DCP中發表的工作的回顧。 第二部分。我們從算法本身，假設和實際限制的描述開始。 在第三節中，包括對最近改進的討論以及未來研究的指示。 第四節得出結論。
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:
暗通道先驗是基於關鍵觀察:在室外無霧圖像上，至少一個顏色通道有一些像素的強度非常低並且接近於零，這意味着這塊區域中的最小強度接近零。 在計算機視覺和計算機圖形學中，以下模型[57] [58] [11] [13]廣泛的用於描述了衣服模糊圖像的構成，：
其中I是觀測強度，J是場景輻射，A是全球大氣光，t是介質透射用於描述未散射並且到達相機的光。 去霧的目標是由 I 恢復出J，A和t.
When the atmosphere is homogenous, the transmission t canbe expressed as
當大氣均勻時，透射率t可以表示爲
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是大氣的散射係數，d是場景深度，從（2）可以觀察到，一旦獲得透射率，深度可以恢復到某個未知的尺度，因此可以利用透射率t 以恢復場景輻射亮度J和深度d。
對於任意圖像J，暗通道Jdark由下式給出：
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的顏色通道，n（x）是中心在x的局部。 兩個最小運算符是可交換的。
基於在室外無霧圖像J中的非天空區域的關鍵觀察，J的暗通道強度低並接近零：
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.
這個觀察被稱爲暗通道先驗，是被衆所周知的暗物體減法技術[59]啓發得到的。 深度d和場景輻亮度J可通過以下步驟得到。
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].
從（6）可以看出，整個圖像最亮的像素可以比大氣光更亮，這不適合於精確的大氣光估計。因此，在暗通道最亮的0.1％亮的像素被選取[12]。 在這些像素中，輸入圖像I中最高亮度的像素被選中作爲大氣光A。該算法可以很好地工作，即使當在圖像中沒有處於無限遠處的像素，並且比由Tan提出[13]的“最亮像素”方法更魯棒。
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].