Algorithm of Removing Thin Cloud-fog Cover from Single Remote Sensing Image

Journal of Information & Computational Siene 11:3 (2014 817 824 February 10, 2014 Available at http://www.jois.om Algorithm of Removing Thin Cloud-fog Cover from Single Remote Sensing Image Yinqi Xiong, Hua Yan, Chao Yu Shool of Eletronis Information Engineering, Sihuan University, Chengdu 665, China Abstrat To remove thin loud-fog over from single remote sensing image effiiently, a new algorithm based on dark hannel prior is proposed. Firstly, the atmospheri veil is preliminarily estimated by the dark hannel period theory rather than defined as the minimal omponents of original image. And then, a Gaussian low-pass filter and a feedbak mehanism are applied to refine the preliminary estimated atmospheri veil, whih an eliminate the uneven fog-loud over effiiently. Subsequently, the atmospheri veil is further refined by the guided image filter under the guidane of the original image, whih an preserve the detail information. Finally, the experiment results show the proposed algorithm an remove the thin loud-fog over from single remote sensing image effetively and improve the image visibility greatly. Keywords: Remote Sensing Images; Thin Cloud-fog Cover; Dark Channel Prior; Atmospheri Veil 1 Introdution Remote sensing images are easily affeted by the loud-fog over, leading to redue visibility and ontrast, whih makes against further information extration and analysis. Therefore, removing loud-fog over is vitally important for the proessing of remote sensing images. Reent years, many sophistiated sholars have made deep researhes on removing the thin loud-fog over. And algorithms are mainly divided into two kinds. One is removing loud noises by using multiple images or additional information, suh as, multi-spetral images method [1], multi-soure images fusion method [2], and so on, whih has good results but needs meeting high requirements for the hardware or remote sensing data; the other is based on single image enhanement. And the most typial method is homomorphi filter based on the frequeny distribution of thin loud [3], whih has the property of simple implementation, but the bakground information is inevitable to be hanged when thin loud in the low frequeny is removed. Besides, another widely used method is wavelet transforms [4, 5], whih removes thin loud-fog over by dereasing the loud noise oeffiients of high levels and inreasing the detail oeffiients of low levels. Corresponding author. Email address: yanhua@su.edn.n (Hua Yan. 1548 7741 / Copyright 2014 Binary Information Press DOI: 10.12733/jis20102917

818 Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 However, the method has ideal results only when there are proper weight fators and wavelet levels. Reently, a simple but effiient defogging method based on dark hannel prior is proposed by HE [6, 7]. And the method has high quality results under the assumption of well-distributed fog, but it annot handle the remote sensing images with uneven loud-fog overs. To solve this problem, the global atmospheri light map based on Gaussian filter is proposed in [8]. But the method is in onflit with the derivative proess of the sattering model, in whih the global atmospheri light is a onstant vetor. Therefore, based on dark hannel prior, an improved algorithm is proposed by us. Firstly, the atmospheri veil is preliminary estimated by the dark hannel period theory rather than defined as the minimal omponents of original image without the theoretial support. And then, Gaussian low-pass filter with a feedbak mehanism and Guided image filter are introdued to refine the atmospheri veil, whih not only ould prevent the over-proess and under-proess problems, but also an keep more detail information. And quantities of omparison experiments show that the proposed algorithm is quite effiient to improve visibility for olor or gray remote sensing images even if there is no additional information. 2 Sattering Model Consider a remote sensing image taken under the foggy or hazy onditions by the satellite sensor. Imaging proess of the blurred image an be desribed by the sattering model based on Koshmieder s law: I(x, y = J(x, ye kd(x,y + A(1 e kd(x,y (1 where, (x, y is the image index, I is the blurred image, A is the global atmospheri light, and J is the sene radiane that we want to reover from the model. Besides, the exponential term e kd(x,y denotes the medium transmission of well-distributed fog, and d(x, y is the sene depth at the pixel (x, y, k is the sattering oeffiient of the medium. In Eq. (1, the former term J(x, ye kd(x,y is alled diret attenuation, whih desribes the sene radiane and its deay in the medium. The seond term is referred as the atmospheri veil and formed by the sattering of environmental illumination, whih is the main fator leading the remote sensing image to looking greyish white. Thus, the sattering model an be simplified as following: ( I(x, y = J(x, y 1 V (x, y + V (x, y (2 A where, t is the transmission map, and v is the atmospheri veil. Obviously, the number of parameters has been redued greatly. Aording to the modified model, the reovering model an be expressed as following: J(x, y = I(x, y V (x, y 1 V (x, y/a Thus, the lear image would be reovered when the atmospheri veil and the global atmospheri light are known. (3

Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 819 3 Proposed Method The proposed method to remove thin loud-fog over is based on dark prior hannel, and its realization mainly divides into three steps: (1 Estimating the global atmospheri based on dark hannel prior; (2 Estimating the atmospheri veil by using the Gaussian filter with a feedbak mehanism and guided image filter; (3 Reovering lear remote sensing images from the inverse modified model. The flowhart of proposed method is shown as following: The global atmospheri light Input image Dark hannel Parameter adjustment Reovering image Refining using gaussian filter Refining using guided image filter Fig. 1: The flowhart of proposed method 3.1 Estimating the Global Atmospheri Light After statistial analysis of massive lear images and hazy images, HE put forward the dark hannel prior theory; namely, the minimum intensity in loal window has a very low value in non-sky images. And the dark hannel an be got by I dark (x = min (I min (x, I min (x = min J (x (4 (x,y Ω (R,G,B where, I dark is the dark hannel of the original image I, and I min is minimal omponent of RGB hannels. Besides, the window size Ω is determined by the original image size and the dark hannel of a gray level image is the loal minimum of the image. In original method, the top 0.1% brightest pixels from the dark hannels of the input image are hosen as the most haze-opaque region. And then, atmospheri light A is estimated by the highest intensity pixel in the most haze-opaque region of the hazy image. The method ould void hoosing the brightest pixel in the original image as A, but it annot ensure that A is unaffeted by large white regions and noises. To solve the problem, pixels in the original image region orresponding to the most haze-opaque region, of whih the RGB omponent means are hosen as the global atmospheri light. Thus, the high saturation problem of the fog-free image an be avoided. 3.2 Estimating the Veil of Atmosphere 3.2.1 Preliminary Estimation The atmospheri veil would be onstant in a path when sene depth and sattering oeffiient β are loal invariable. Thus, the minimum filter among the loal path and the minimum filter

820 Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 among RGB hannel an be simultaneously operated on the modified model as following: { ( } min ( min I (x, y = min min J V (x, y (x, y 1 + V (x, y (5 (x,y Ω (R,G,B (x,y Ω (R,G,B A Aording to the dark hannel theory, min ( min (J (x, y approahes zero beause there (x,y Ω (R,G,B is no sky regions in the remote sensing images, so the preliminary estimated atmospheri veil an be given by V (x, y = min ( min I(x, y (6 (x,y Ω (R,G,B 3.2.2 Refining Using Gaussian Filter Unlike the outdoor images, most of loud-fog overs in remote sensing images are uneven distribution and have singularity. Therefore, the original algorithm will lead the regions where there is little fog or no fog to be over-enhaned, and the regions where there is heavy fog to be underenhaned. To solve the over-proessing and under-proessing problems, we put forward a simple but effetive method to refine the atmosphere veil. As we know, the loud-fog over is prinipally in low frequeny, while the sene of remote sensing image mainly distributes in high frequeny. And the image blurring aused by the sattering of partiles in the atmosphere is similar to the result aused by Gaussian multipliative noise. Therefore, Gaussian low-pass filter is applied after the intensity normalization proessing and Fourier transform are performed on original images. And then, the low frequeny oeffiient matrix t(x, y, whih reflets the distribution harateristis of the loud-fog over, an be got by transforming the filtering result into time domain. Thus, the refined atmospheri veil an be expressed as follow. Ṽ (x, y = (λ + t(x, y V (x, y (7 where, λ is the adjustment oeffiient and its range is from 0 to 1. The greater the value of λ is, the more loud-fog over an be eliminated, but it is easy to ause the strutural distortion problem. In order to determine λ of different images, a novel feedbak mehanism is introdued. In the mehanism, the mean strutural similarity Index Measure (MSSIM, whih reflets the loal strutural similarity degree between the original image I and the reovering image J, is Chosen as the feedbak signal. And it an be expressed as follow: MSSIM(I, J = 1 M l(i i, J i (I i, Js(I i, J i (8 M i=1 where, l(i i, J i is luminane omparison of the loal window, (I i, J i is ontrast omparison, s(i i, J i is struture omparison, and M is the total number of windows in the image. After determining the feedbak signal, the feedbak mehanism an be realized as following: Step 1 Inputting the original image, then, setting the initial values of step size λ, and adjustment oeffiient λ; Step 2 Reovering the lear image by proposed method; Step 3 Judging whether the urrent MSSIM is smaller than the one of previous iteration. If the ondition is satisfied, arry out λ; and the output image of previous iteration is the reovering image; otherwise, add λ to λ, and then, go to the Step 2.

821 Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 3.2.3 Refining Using Guided Image Filter 1.0 0.8 0.6 0.4 0.2 0 Y 0 (a Input image X Normalized intensity Normalized intensity Normalized intensity In order to smooth loud and fog noises and keep the detail information of the reovered image, the atmosphere veil should be further refined. However, the median filter easily ause halo effet as the poor performane in edges preserving. Therefore, the guided image filter based on the loal linear model is applied [9], and Fig. 2 illustrates the result of guided image filter. From whih, we an see the filter ould preserve as many details as possible under the ondition of minimizing the loal Mean Square Error (MSE. 0.9 0.8 0.7 0.6 0.5 0.4 Y 0 (b Guided image X 0. 0.45 0.40 0.35 0.30 0.25 Y 0 ( Filtering result X Fig. 2: The guided image filter result And the filtering proess an be shown as follows: V i = Wij (IV j (9 j where the filtering input V is the first refined atmospheri veil, and the filtering output V is the further refined atmospheri veil. Besides, the normalized filtering kernel W is a funtion of the guided image I, and it an be expressed by: ( 1 (Ii µk (Ij µk Wij = 1+ (10 σk2 + ε N 2 k:(i,j ωk where, µk and σk is the mean and variane of the guided image in the loal path ωk, N is the number of pixels in ωk, and ε is a small onstant regulating the global smoothness. On a separate note, the window radius of ωk should be proportional to input image size, otherwise, it will lead to details over-smoothness or the amplifiation of noise. Aording to the image restoration model, the intensity of reovered images might be negative if the atmospheri veil is too large. In order to improve the brightness of the reovering image, there is an important onstraint, namely, for the intensity in the loal path of the reovering image, the standard deviation should be lower than the mean. And it an be given by std(j mean(j Besides, the standard deviation and mean of the restoration model an be written as ( std(i (x, y I (x, y V (x, y = std(j = std 1 V (x, y/a 1 V (x, y/a mean(i (x, y V (x, y mean(j = 1 V (x, y/a (11 (12 (13

822 Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 Thus, the final value of atmospheri veils an be obtained by, ( I V (x, y = β min(v (x, y, min I std(i (R,G,B A (14 where the onstant parameter β is used to retain a small quantity of fog, so that the awareness of sene depth an be persevered. And Fig. 3 illustrates the results of estimating the atmospheri veil. From Fig. 3 (b, we an see the preliminary estimated atmospheri veil is a onstant, whih is not in agreement with the atual situation. After being refined by using Gaussian filter and guided image filter (see Fig. 3 (, the disontinuous edges are sharped and the blok effets are eliminated. (a Original image (b Preliminary result ( Refined result (d The reovering result Fig. 3: Estimating the atmospheri veil 3.3 Reovering the Sene Radiane After the global atmospheri light and the refined atmospheri veil are obtained, the restoration image an be got by: I (x, y V (x, y J (x, y = R (15 1 V (x, y/a where R is the olor reovery fator, and it an be expressed by: ( / R (x, y = log bi (x, y I (x, y (16 (r,g,b Besides, there would be slightly olor distortion if three reovered hannels are merged together diretly, beause the image proessing is applied respetively to the Red, Green, and Blue hannels. In order to redue the olor distortion, three reovered hannel should be merged by the proportion of RGB hannels in the original image. And the value of reovered pixels should range from 0 to 255 4 Experimental Results and Evaluation The proposed method is implemented by using matlab. In order to demonstrate the effetiveness of the proposed method, two olor remote sensing images aught by QuikBird, and one SPOT4 panhromati remote sensing image are proessed by our method and he s method. As Fig. 4 shown, the landsapes of original foggy remote images have low resolution and poor readability.

Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 823 The results by He s method an remove the over, but the regions with heavy fog are obviously under-enhaned. Compared with these, our method ould remove more fog and improve ontrast remarkably, espeially regions in the blak windows. (a (b ( λ = 0.80 (d (e (f λ = 0.80 (g (h (i λ = 0.40 Fig. 4: Experimental results. (a, (d and (g show original image; (b, (e and (h show results by He s method; (, (f and (i show results by our method Besides the subjetive visual evaluation, three objetive assessments ould also be used to evaluate the lear results, namely, entropy [10], MSSIM, and the geometri mean of the ratios of visibility level (R [11]. Entropy is applied to judge whether the information of the reovered image has been lost or not. MSSIM reflets whether the reovering proessing leads to the strutural distortion problem or not. And R refleting the average visibility and the ontrast of the reovering image is applied to judge whether the landsapes are lear or not. As shown in Table 1, our method is proved to be more effiieny. 5 Conlusions Based on the dark hannel prior theory, a new method to remove the fog-loud over from the remote sensing image has been introdued in this paper. Without additional requirements of remote sensing data, the proper global atmospheri light and the preliminary atmospheri veil are obtained by applying the dark hannel prior to single remote sensing images. And then, the smoothing atmospheri veil is estimated by using the Gaussian low-pass filter with a feedbak mehanism and guided image filter. Finally, the experimental results not only demonstrate our

824 Y. Xiong et al. / Journal of Information & Computational Siene 11:3 (2014 817 824 Table 1: Data of objetive evaluation Image Method Entropy MSSIM R Fig. (a Fig. (d Fig. (g Original image 7.08 He s result 7.31 0.9997 1.45 Our result 7.65 1.0000 2.18 Original image 6.35 He s result 6.68 0.9996 1.83 Our result 7.24 1.0000 2.82 Original image 6.92 He s result 7.71 0.9996 2.1068 Our result 7.78 0.9998 2.6184 method ould remove the uneven lod-fog over of the remote sensing image suessfully, but also show our method is more effetive for the remote sensing image than HE s method. Referenes [1] B. Wang, A. Ono, K. Muramatsu, N. Fujiwara, Automated detetion and removal of louds and their shadows from Landsat TM images, IEICE Transation on Information and System, 82(2, 1999, 453-460 [2] Li Lu, Yongtao Wang, Jinwen Tian, Cloud removal from Satellite Imagery based on SUSAN algorithm, Journal on Communiation, 27(8, 2006, 160-164 [3] Wenshui Shen, Xinzhi Zhou, Algorithm for removing thin loud from remote sensing digital images based on homomorphi filtering, High Power Laser and Partile Beams, 22(1, 2010, 45-48 [4] Xifang Zhu, Feng Wu, Yanbin Zhuang, An improved approah to remove loud and mist from remote sensing digital images based on mallat algorithm, Journal of Remote Sensing, 11(2, 2007, 241-246 [5] Weizhen Jiang, Xiaoli Liu, Weidong Jin, Image denoising algorithm base on urvelet transform and SVD, Journal of Information and Computational Siene, 9(16, 2012, 4889-4896 [6] K. He, J. Sun, X. Tang, Single image haze removal using dark hannel prior, IEEE Transations on Pattern Analysis and Mahine Intelligene, 33(12, 2011, 2341-1353 [7] Yinqi Xiong, Hua Yan, Chao Yu, Improved haze removal algorithm using dark hannel prior, Journal of Computational Information Systems, 9(14, 2013 [8] Liya Zhou, Zhiyuan Qin, Uneven loud and fog removing for satellite remote sensing image, 2011 Seond International Conferene on Mehani Automation and Control Engineering (MACE, 2011, 5485-5488 [9] K. He, J. Sun, X. Tang, Guided image filtering, European Conferene on Computer Vision (EC- CV 10, Hersonissos, Crete, Greee, 2010, 1-14 [10] Jingwen Zuo, Yuantao Chen, Jiaying Wu, Entropy based bi-region image segmentation, Journal of Information and Computational Siene, 8(14, 2011, 3123-3130 [11] N. Hautiere, J. P. Teral, D. Aubert, Blind ontrast enhanement assessment by gradient ratioing at visible edges, Image Analysis and Stereology Journal, 127(2, 2008, 87-95