Journal of Information & Computational Science 11:16 (2014) 5855–5862 Available at http://www.joics.com November 1, 2014 Image Defogging Approach Based on Dark Channel Prior with Feedback Mechanism ⋆ Jianlong Xu ∗, Xinfu Chen, Yaming Wang School of Informatics, Zhejiang Sci-Tech University, Hangzhou 310018, China Abstract Aimed at degradation of image gotten in misty weather, an image defogging algorithm based on dark channel prior with feedback mechanism is proposed. This algorithm can not only retain excellent treatment effect of the dark channel prior defogging algorithm on the image of non bright areas but also restore scene perfectly from the image with bright areas. Experimental results show that the algorithm can efficiently alleviate the color distortion caused in process of defogging the image with bright areas using dark channel prior algorithm, and make the image defogged smoother and more natural. Keywords: Dark Channel Prior; Defog; Color Coefficient of Variation 1 Introduction In most cases, the outdoor computer vision system works effectively under normal circumstance in which system can obtain the image feature clearly and accurately. However, computer vision system is sensitive to weather, light, and many other factors. An effective image defogging algorithm plays a very important role in improving system’s robustness and reliability in extreme weather of fog. Recently defogging methods for fog-degraded images are of two main types: image enhancement and image restoration. Image enhancement method is to improve the visual effect of image by enhancing the contrast and highlighting the details, such as histogram equalization algorithm [1] and Retinex theory [2] method, but the processing results with these methods were disappointing. Another kind of method, image restoration is based on the atmospheric physical model which analyzes light’s scattering and attenuation during the physical process of transmission. This atmospheric model can more accurately express the influence from fog, dust, mist and so on. Fattal [3] proposed a refined image formation model to account for the surface shading and the scene transmission, he assumed that the transmission and shading are locally uncorrelated and broke the image into regions of constant albedo, from which the scene can be inferred. However, this approach may be failed in the cases that the assumption is broken. Tan [4] found that the ⋆ ∗ Project supported by the National Nature Science Foundation of China (No. 61272311). Corresponding author. Email address: [email protected] (Jianlong Xu). 1548–7741 / Copyright © 2014 Binary Information Press DOI: 10.12733/jics20104891 5856 J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 clear-day images have higher contrast compared with fog-degraded images, and he removed the haze by maximizing the local contrast of the restored image. Though it produced a remarkable effect, may be not physically sound. Based on a great deal of statistics data He [5] proposed dark channel prior, that is in a image most local regions have very low intensity in at least one color channel. He used the statistical regularity to effectively estimate the transmission, then refined the transmission with soft matting and finally got the output image.This algorithm is simple and efficient. However, when it is used to handle the image with bright areas, dark channel prior is no longer valid and the restored image often suffers from color distortion. To solve this problem, the causes of distortion in color are analyzed, and then an improved algorithm with feedback mechanism is proposed. 2 2.1 Defogging Using Dark Channel Prior Physical Model for Light’s Scattering and Attenuation [6] In computer vision and image processing, light’s scattering and attenuation during the physical process of transmission can be expressed as a physical model which is widely used to explain the formation of a fogged image: I(x) = J(x)e−rd(x) + A(1 − e−rd(x) ) (1) where d(x) is the scene depth, r is the medium extinction coefficient. Eq. (1) can be converted into Eq. (2) by replacing exponential attenuation e−rd(x) with transmission t(x): I(x) = t(x)J(x) + A(1 − t(x)) (2) where I(x) is the input image, t(x) is transmission function, vector A is the global atmospheric light which has nothing to do with image coordinates and usually can be treated as a constant value, J(x) is the scene need to be restored. So the key to recover the scene J(x) is how to solve the transmission t(x). 2.2 Defogging with Dark Channel Prior The dark channel prior is a kind of statistics of the haze-free outdoor images. It is based on a key observation that most local patches in haze-free outdoor images contain some pixels which have very low intensities in at least one color channel. For an image J(x), its dark color channel can be defined as following: J dark (x) = min ( min J c (y)) (3) y∈Ω(x) c∈{r,g,b} where J(c) is a color channel of an image, Ω(x) is the patch with the center x, in He’s paper he did statistical analysis of quite a large number of pictures and arrived at the conclusion that the dark color channel of an image tends to be zero: J dark → 0. Further assuming that the transmission in a local patch Ω(x), is constant, then taking the min operation among three color channels on Eq. (2), Eq. (4) can be obtained: ( ( J c (y) ) I c (y) ) = t(x) min min + 1 − t(x) (4) min min c c y∈Ω(x) y∈Ω(x) Ac Ac J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 5857 As mentioned before, J dark (x) = min ( min J c (y)) = 0. According to Eq. (3) and Eq. (4), a y∈Ω(x) c∈{r,g,b} rough estimate of transmission map can be gotten as Eq. (5). t(x) = 1 − min y∈Ω(x) ( min c I c (y) ) Ac (5) In this paper, guided filter [7] instead of soft matting is used to refine the transmission map efficiently. Then, the final scene J(x) is recovered by: J(x) = I(x) − A +A t(x) (6) where A consists of 3 equivalent components, the component equals the mean value of the top 0.1% maximum gray value of pixels in the dark channel. 2.3 Defect of Defogging with Dark Channel Prior Fig. 1 shows two groups of defogging results. Fig. 2 shows histograms of intensities of pixels in dark channels. As Fig. 2 shows that majority of pixel intensities are of very small value. This statistic gives very strong support to dark channel prior and He’s method produces impressive visual results without distortion in color. (a) (b) (c) (d) Fig. 1: Defogging results using dark channel prior. (a) Input images; (b) Defogged images; (c) Transmission maps; (d) Dark channels Dark channel prior is a powerful prior based on the statistics of quite a lot of images, most of which are non-sky or non bright area images. When the scene objects are inherently similar to the atmospheric light such as sky regions, the dark channel prior is invalid. Recovered result by dark channel prior from the image with sky regions suffers from color distortion as shown in Fig. 3. It can be seen according to Fig. 3 (d) that intensities are distributed randomly and a portion of the pixel values of intensity are even higher than 200. This is because that intensities of the bright region pixels in three channels are high. Dark channel prior theory is no longer suitable for handling bright regions. Jiang et al. [8] did a lot of experiments and his experiments show that non-bright region is restored quite well with dark channel prior algorithm, but fatal noise and color distortion are prone to be caused while this algorithm is used to process the bright regions 5858 J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 6000 8000 7000 6000 5000 4000 3000 2000 1000 0 5000 4000 3000 2000 1000 0 0 50 100 150 200 250 0 50 (a) 100 150 200 250 (b) Fig. 2: Statistics of the dark channels. (a) Histogram of the intensity of the pixels in image of woods; (b) Histogram of the intensity of the pixels in image of ducks (a) (b) 12000 10000 8000 6000 4000 2000 0 0 (c) 50 100 150 (d) 200 250 Fig. 3: Color distortion caused by defogging. (a) Input image; (b) The defogged image; (c) Dark channel; (d) Histogram of the intensity of the pixels in dark channel such as sky region, large white object and water. This is because that the actual transmission in bright regions is greater than the transmission estimated by dark channel prior, moreover, the higher the brightness, the greater is the transmission deviation. 3 Image Defogging Approach Based on Dark Channel Prior with Feedback Mechanism On the basis of above discussion, an improved algorithm with feedback mechanism is proposed. The algorithm process is described as follows: Step 1. Defog the input image with dark channel prior and get the estimated transmission map. Step 2. Compare the two images before and after defogging, segment the distorted area by color J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 5859 difference. Step 3. Adjust the transmission in color distortion area segmented. Step 4. Refine the transmission with guided filter. Step 5. Recover the scene with the final refined transmission. 3.1 Color Difference between Images before and after Defogged Color is an important feature of an image, it contains the essential information of an image. The coefficient of variation is used to measure the variation of a large number of independent data. It is calculated from the average and standard deviation as follows: cv = S tandard Deviation Average (7) Since pixel intensities of three channels in bright regions are close to each other, color coefficient of variation Ccv is defined as following to describe color difference of three channels: N ∑ (I R + I G + I B ) i=1 µ= 3N √ N 1 ∑ [(I R − µ)2 + (I G − µ)2 + (I B − µ)2 ] 3N i=1 ccv = µ (8) where N is the number of pixels within a patch. According to the definition, a bright white patch’s Ccv tends to be zero while a colorful patch’s Ccv tends to be much larger. c is defined as follows to describe the color difference between images before and after defogged with dark channel prior. Where Ccv1 is the color coefficient of variation of input image, Ccv2 is the color coefficient of variation of the image defogged. c= |Ccv1 − Ccv2 | Ccv1 + Ccv2 (9) It can be seen from Eq. (9) that the larger the difference between color coefficients of variation, the larger the value of c is. When the value of c exceeds the threshold, the patch in an image defogged is identified as color distortion. Fig. 4 (a) shows the color difference map between input image and defogged image, where the brighter the region, the more severe the distortion is. The color difference map is converted to binary one as Fig. 4 (b) shown by suitable threshold. The white regions of Fig. 4 (b) corresponding to the regions where color distortion are severe, are the areas in which transmissions need to be adjusted. 5860 J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 (a) (b) Fig. 4: Color difference map and color distortion region segmented. (a) Color difference map; (b) Color distortion regions 3.2 Adjusting the Transmissions in Color Distortion Regions The actual transmission can be calculated by Eq. (10): ( ( c )) 1 − min min I A(y) c c y∈Ω(x) ( tactual = ( c )) 1 − min min J A(y) c c (10) y∈Ω(x) 1400 1200 1000 800 600 400 200 0 0 he rs ot -0 .1 09 -0 . 09 0. 08 0. 08 -0 . 07 0. 0. 06 -0 .0 7 06 5 -0 . 05 0. 0. 04 -0 .0 04 -0 . 03 0. -0 .0 02 02 -0 . 0. 01 0. 00. 3 Patch numbers 01 Distribution of Ccv The dark channel prior is invalid and the denominator cannot be approximately equal to 1 for the white areas. As a result, actual transmission tactual is larger than the estimated t(x). As introduction above, the brighter the local region, the more severe the distortion, the less the Ccv is. The values of Ccv corresponding to all distorted patches in lots of image defogged with dark channel prior are collected and the statistics show that most values of Ccv have a range of 0 to 0.1. For example, the distribution of Ccv for Fig. 3 (a) is illustrated in Fig. 5. Fig. 5: Distribution histogram of Ccv Because the transmission adjusted should share the same range with original transmission which is less than or equal to 1 (see Eq. (5)), gamma function is used to adjust the transmission in this paper. e t(x) = t(x)min(10Ccv1 ,1) (11) According to the above transformation, the brighter the region, the less the Ccv , the larger the transmission is increased. The adjusted transmission map is illustrated in Fig. 6 (b). 4 Experiment and Analysis The images with bright region selected from baidu are used to make contrast tests for He’s algorithm and our algorithm. For the image of grasslands, the patch size is set to 8 × 8 and the 5861 J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 (a) (b) Fig. 6: Contrast of transmission before and after adjusted. (a) He’s transmission map; (b) Adjusted transmission map (a) (b) (c) Fig. 7: Comparison with He’s work. (a) Input images; (b) He’s results; (c) Our results ×104 2.5 ×104 2.5 ×104 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0 0 50 100 150 200 250 ×104 0 0 50 100 150 200 250 ×104 0 0 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0 0 50 100 150 (a) 200 250 0 0 50 100 50 100 150 200 250 150 200 250 ×104 50 100 150 (b) 200 250 0 0 (c) Fig. 8: Color histograms (a) Histograms of input; (b) He’s histograms; (c) Our histograms threshold is set to 0.65, 100% of Ccv corresponding to distorted areas have a range of 0 to 0.1. For the image of mountains, the patch size is set to 10 × 10 and the threshold is set to 0.6, about 91.04% of Ccv corresponding to distorted areas have a range of 0 to 0.1. During guided filtering, guidance image is the grayscale image of input, local window radius r is set to 30, regularization parameter ε is set to 10−6 . In Fig. 7, we compare our approach with He’s work. 5862 J. Xu et al. / Journal of Information & Computational Science 11:16 (2014) 5855–5862 The contrast tests show that the bright sky regions restored look smoother and more natural in our work than He’s. The reason is that this algorithm relieves the color distortion in bright sky regions by adjusting the transmission with gamma function. A good defogging approach should restore the image clearly and recover maximal information of the original image. Image histograms before and after defogged should maintain a high degree of similarity [9]. Fig. 8 shows color histograms of three channels, the top 3 charts are histograms of grassland and the bottom 3 charts are histograms of mountains. Fig. 8 indicates that our histograms can maintain a higher degree of similarity to the histograms of input images than He’s histograms especially in bright regions such as sky where the three channels intensities are high. 5 Conclusion An improved approach with feedback mechanism is proposed to solve the color distortion caused in process of defogging images with bright areas by dark channel prior. By means of comparing images before and after defogged with dark channel prior, color distortion regions are segmented by color difference, then the transmissions corresponding to distortion regions are adjusted using gamma function, and finally the scene is restored with adjusted transmission. Experimental results show that the algorithm can efficiently alleviate the color distortion caused in process of defogging on the image with bright areas using dark channel prior algorithm, and make the image defogged smoother and more natural. References [1] Yishu Zhai, Xiaoming Liu, Yayuan Tu, Yaning Chen, An improved fog-degraded image clearness algorithm [J], Journal of Dalian Maritime University, 33(3), 2007, 55-58 [2] Daniel J. Jobson, Zia-ur Rahman, Properties and performance of a center/surround retinex [J], IEEE Transactions on Image Processing, 6(3), 1997, 451-454 [3] R. Fattal, Single image dehazing [J], SIGGRAPH, ACM Press, 2008, 1-9 [4] R. Tan, Visibility in bad weather from a single image [C], IEEE Conference on Computer Vision and Pattern Recognition, 2008, 1-8 [5] Kaiming He, Jian Sun, Xiaoou Tang, Single image haze removal using dark channel prior [C], Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2009, 1956-1963 [6] E. J. 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