Gray-Scale Image Dehazing Guided by Scene Depth Information

Research ArticleGray-Scale Image Dehazing Guided by Scene Depth Information

Bo Jiang1 Wanxu Zhang1 Jian Zhao1 Yi Ru1 Min Liu2 Xiaolei Ma3

Xiaoxuan Chen1 and Hongqi Meng1

1School of Information Science and Technology Northwest University Xirsquoan 710127 China2Key Laboratory of Space Active Opto-Electronics Technology Shanghai Institute of Technical Physics ofthe Chinese Academy of Sciences Shanghai 200083 China3Department of Physics Emory University Atlanta GA 30322 USA

Correspondence should be addressed to Hongqi Meng mhqstumailnwueducn

Received 18 February 2016 Revised 14 September 2016 Accepted 26 September 2016

Academic Editor Ruben Specogna

Copyright copy 2016 Bo Jiang et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Combined with two different types of image dehazing strategies based on image enhancement and atmospheric physical modelrespectively a novel method for gray-scale image dehazing is proposed in this paper For image-enhancement-based strategy thecharacteristics of its simplicity effectiveness and no color distortion are preserved and the common guided image filter is modifiedto match the application of image enhancement Through wavelet decomposition the high frequency boundary of original imageis preserved in advance Moreover the process of image dehazing can be guided by the image of scene depth proportion directlyestimated from the original gray-scale image Our method has the advantages of brightness consistency and no distortion over thestate-of-the-art methods based on atmospheric physical model Particularly our method overcomes the essential shortcoming ofthe abovementionedmethods that are mainly working for color image Meanwhile an image of scene depth proportion is acquiredas a byproduct of image dehazing

1 Introduction

Image dehazing is a basal methodology to restore image withhazy or foggy scenes which has been drawing increasingattention in recent years due to its crucial role played innumerous fields like aerial photography To date a con-siderable number of methods for image dehazing haveemerged which can be categorized into two types of strategieswith one based on images enhancement and the otherone on atmospheric physical model Nevertheless both ofthe aforementioned methods suffer from some drawbackswhich inhibit their further widespread applications Morespecifically in the former strategy the limited resolution ofhuman vision is primarily considered however ignoring thephysical origin of image degradation The haze-free imagewill be recovered by adjusting the local and global contrastsand color coefficients in the corresponding algorithms Resul-tantly the ultimate dehazing effect of images with differentscenes differs a lot because the detail information may beenhanced excessively for complex scene images though this

kind of method is characterized by low complexity widerange of application and satisfactory validity for both hazeand haze-free images

In comparison the physical origin of image degradationis taken into account in the latter strategy wherein thedegradation model of haze image is built to more accuratelycompensate the lost information in the process of imagingin foggy weather Even though this kind of strategy becomesthe leading tendency with abovementioned advantages itsuffers fromhigh computational complexity because the priorinformation for example scene depth and contrast statisticsof haze image should be obtained in advance What is moreonce the transcendental hypothesis fails the model cannot bemathematically solved

The independent component analysis for estimating thescene reflection intensity is proposed by Fattal [1] assum-ing that the reflection intensity of a local region in hazeimage is constant and there is no relevance between thetransmission and the surface color of objects Howeverthis assumption is not considered to be solid because the

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 7809214 10 pageshttpdxdoiorg10115520167809214

2 Mathematical Problems in Engineering

(a) (b) (c)

Figure 1 Gray-scale image dehazing using proposedmethod (a) Gray-scale image (b) Haze-free image (c) Image of scene depth proportion

statistical characteristics will be ineffective due to the lack ofsufficient color information for dehazing thick haze imagesOn the other hand the assumption of dark channel prioris proposed by He et al [2] based on the statistics of largenumbers of haze-free images in outdoor scenes Followed byHe et alrsquos seminal work the corresponding fast algorithm isproposed in [3] and the halo effect is remarkably reducedby template segmentation in the dark channel calculation in[4] Nevertheless this proposal drastically suffers from highcomputational complexity and it yet fails to work for imageswith thick haze or large sky region due to the occurrence ofserious color distortion Therefore it is urgent to propose amethod to tackle the difficulty regarding images with thickhaze or large sky region which is one aim of this paper

In addition there have been other emerging importantmethods regarding image dehazing in recent years Forexample Ancuti firstly demonstrates the utility and effective-ness of a fusion-based technique for dehazing based on asingle degraded image [5] Chen proposes a novel visibilityrestoration approach based on Bi-Histogram modificationwhich can integrate a haze density estimation module anda haze formation removal module for accurate estimation ofhaze density in the transmission map [6] One of the seminalrepresentatives of nighttime dehazing method is reported byLi et al [7] where a framework is proposed in order to reducethe effect of glow in the original nighttime image leadingthe original image to consist of direct transmission andairlight only Huang in [8] presents a novel Laplacian-basedvisibility restoration approach to effectively solve inadequatehaze thickness estimation and alleviate color cast problemsMeng benefits much from an exploration on the inherentboundary constraint that is combined with a weighted 1198711-norm based contextual regularization and it is modeled intoan optimization problem to estimate the unknown scenetransmission in [9]

Huang et al employ the combinations of three majormodules namely a depth estimation module a color analysismodule and a visibility restoration module for visibilityrestoration [10] and also present an effective haze removalapproach to remedy problems caused by localized lightsources and color shifts which thereby achieves superiorrestoration results for single hazy images [11] Zhu proposesa simple but powerful color attenuation prior by creating alinear model for modeling the scene depth of the hazy image

under this novel prior and learning the parameters of themodel with a supervised learning method [12]

In terms of gray-scale image dehazing the abovemen-tioned methods based on atmospheric physical model arerather restricted because they solely work for color imagesComparably Hersquosmethod still works while very strict restric-tions are made on the gray-scale images [2] In brief a colorimage generally contains much more information than agray-scale image so it makes the dehazing model solvedmore easily In contrast there is no confirmed solution togray-scale image by the abovementioned methods owing toless information contained in the gray-scale image As anindispensable part of image processing the resolution ofgray-scale image is almost four times more than that of colorimage with the same image size leading to the increasingsignificance of gray-scale image dehazing owing to its crucialrole in the field of high resolution observation for exampleaerospace industry which makes up the other aim of thispaper

In this paper we present a novel method for gray-scaleimage dehazing which takes into account the advantagesof two aforementioned categorized dehazing strategies Theperformance of our proposed method is shown in Figure 1in which Figure 1(a) is the original gray-scale image withthick haze and large sky region and Figures 1(b) and 1(c)illustrate the haze-free image and the image of scene depthproportion respectively More specifically the image of scenedepth proportion is estimated according to the originalgray-scale image directly Scene depth is the straightforwardreflection of enhancement demands for various regions inthe original image so the processing of enhancement canbe automatically layered guided by the image of scene depthproportion With this differential compensation the invalid-ity of atmospheric physical model for the image with thickhaze or large sky region can be reasonably solved Meanwhilethe phenomenon of excessive enhancement is avoided in theenhanced image and the brightness consistency can also beguaranteed simultaneously

The framework of this paper is organized as follows InSection 2 the problems in existing methods and correspond-ing solutions are stated In Section 3 the proposed methodis introduced and the experimental results are shown inSection 4 to demonstrate the effectiveness of the proposedmethod The paper is ultimately concluded in Section 5

Mathematical Problems in Engineering 3

(a) (b) (c)

(d) (e) (f)

Figure 2 Contrast results between common and modified guided image filters (a) and (d) Hazy images (b) and (e) Extracted detail imagesusing common guide image filter (c) and (f) Extracted detail images using modified guided image filter

2 Issues in Existing Methods andCorresponding Solutions

21 Guided Image Filter and Modified Guided Image FilterNowadays image enhancement can be effectively realizedby guided image filter [13] which is widely prevalent in thefield of computer vision Assuming that the original image isexpressed by119901 and the output image 119902 is linearly related to theguide image 119868 in a local window 120596119896 then the output image 119902in this window with radius 119903 centered at the pixel 119896 can bewritten as

119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (1)

where (119886119896 119887119896) is the constant coefficient in window 120596119896 andthe pixel 119894 is involved in all overlapping windows that cover 119894collectively

Hence the values of 119902119894 in (1) are not equalwhen computingin different windows and then the average value strategy isadopted as stated in [13] Meanwhile due to the symmetry ofthe box window the filtering output 119902119894 is computed by

119902119894 = 119886119894119868119894 + 119887119894 (2)

where 119886119894 = (1|120596|)sum119896isin120596119894 119886119896 and 119887119894 = (1|120596|)sum119896isin120596119894 119887119896 are theaverage coefficients of all windows overlapping 119894

Based on the definition above the filtering output 119902 canbe obtained and the difference value (119868 minus 119902) is regarded asboundary information Here the image noise is neglectedtemporarily because it is the secondary high frequency infor-mation compared to the primary image boundaryUltimatelythe image boundary is amplified several times and added to119902 and the enhanced image 119868119890 can be expressed as

119868119890 = 119902 + 120576 (119868 minus 119902) (3)

where 120576 is the enhancement coefficient Since boundarypreserving is the most prominent characteristic for guidedimage filter all the boundary in original image 119901 can be the-oretically preserved in filtering output image 119902 Realisticallysome of the boundaries will be removed by filtering operationowing to the solution of filtering output being an approximatevalue In brief the characteristics of boundary preserving areat any rate favorable to image filtering but it is adverse to theimage enhancement

Since the boundary information can also be preservedin the filtering output image 119902 it may lead to incompleteextraction of boundary which is also the major disadvantageof haze image degradation In order to tackle this problema modified guided image filter is built by mean filtering forguide image 119868119894 only in (2) to reduce the ability of boundarypreserving for image enhancement

We compare the performance of common and modifiedguided image filtering and the results are illustrated inFigure 2 To improve the fairness the parameters of bothcommon and modified guided image filters in Figure 2 areall set to the same values Figure 2(a) shows the original hazeimage and the extracted boundary images using commonand modified guided image filters are illustrated in Figures2(b) and 2(c) respectively Here all the pixel values of Figures2(b) and 2(c) are uniformly amplified 5 times for facilitatingdisplay Note that the test images in this paper are taken fromthe Internet

It is observed that the image contrast of extracted bound-ary is obviously increased by proposedmethod especially forthe boundary with low brightness (ie dark pixels) in Figures2(b) and 2(c) Figure 2(d) shows another haze image withthicker haze layer and the extracted boundary images usingcommon guided image filter andmodified guided image filterare showed in Figures 2(e) and 2(f) respectively which are


also amplified 5 times uniformly for display As can also beeasily seen the modified guided image filter is advantageousover the common one because more details are preserved inFigure 2(f)

22 Dark Channel Prior and Image of Scene Depth ProportionMcCartney atmospheric physical model is widely adopted inthe second dehazing category and it is defined as

119868 (119909) = 119869 (119909) 119905 (119909) + 119860 (1 minus 119905 (119909)) (4)

where 119868(119909) is the original hazy image 119869(119909) is the haze-freeimage 119860 is the atmospheric light value 119905(119909) is the mediumtransmission and 119909 is the corresponding pixel The processof image dehazing is to estimate 119860 and 119905(119909) from 119868(119909) andthen recover the ultimate haze-free image 119869(119909)

Dark channel prior [2] is considered to be the mosteffective method to solve the atmospheric physical model in(1) and is described by

119871dark (119909) = min119910isinΩ(119909)( min119888isin119903119892119887119871119862 (119910)) (5)

where 119871119862 is a channel of image 119871 and Ω(119909) is a templatecentered at 119909 He et al [2] reported that the intensity ofdark channel in nonsky region 119871dark rarr 0 and thenthe complicated multiplicative term 119869(119909)119905(119909) in (4) can beeliminated to estimate the transmission image 119905(119909) andultimately the approximate solution of haze-free image 119869(119909)in (4) can be obtained Note that the solution procedure is inallusion to the color image because it contains much moreinformation conducive to solving the atmospheric physicalmodel

The softmatting adopted in [2] can be replaced by guidedimage filter [13] to improve the processing speed Howeverboth the softmatting and guided image filtering are all stayingat the stage of optimizing transmission image 119905(119909) Differentlyfrom the color image there is no confirmed solution of119905(119909) for the gray-scale image due to too little informationcontained in the gray-scale image to solve the atmosphericphysical model As a result the haze-free image 119869(119909) cannotbe recovered accordingly In order to overcome this difficultythe scene depth information will be adequately used in thispaper which is estimated directly from original gray-scaleimage and its reverse can be regarded as the approximateestimation of transmission image The detailed process ofacquiring the image of scene depth proportion is as follows

First of all atmospheric light value 119860 is estimated whichis the furthest pixel rather than the brightest one in theoriginal haze image 119868(119909) according to [14] On a foggy daythere is a large quantity of fog droplets suspending in theatmosphere In this case the scattering intensity of lightwithin the visible spectrum is almost the same on the wholeresulting in the sky region with the bright white color Thefurthest pixel generally belongs to the sky region but it isnot always the brightest one because the pixels in the nearbyscenesmay bewith the bright color (eg artificial light sourceand bright white object) which might be brighter than thefurthest pixel value 119860 in 119868(119909) Therefore it is incorrect for

the gray-scale image to take the brightest pixel in 119868(119909) as theestimation of 119860

To exclude the abovementioned nearby pixels first thelocalminimumfiltering is adopted for the gray-scale image inthis paper With this operation differently from the far scenepixels the brightness of nearby pixel can bemarkedly reducedafter thisminimumfiltering especially in the case of adoptinglarge filtering template because there are always some pixelswith low brightness around the bright pixels in the nearbyscenes As a result the remaining bright pixels afterminimumfiltering are limited to the sky region and the position of thebrightest pixel in the sky region is exactly the furthest pixelin 119868(119909) so its intensity value can then be regarded as theaccurate approximate of 119860 Figures 3(a) 3(b) and 3(c) showthe atmospheric light value 119860 found by proposed methodHere the position of 119860 is marked with black and the area ofblack pixel is expanded for facilitating display as indicated bythe arrow

Based on the analysis above the image of scene depthproportion 119863 can be obtained by calculating the differencevalues between119860 and other pixels inminimum filtered image119871dark min so the concrete expression of 119863 is given by

119863 = 1 minus (119860 minus 119871dark min) (6)

Figures 3(d) 3(e) and 3(f) illustrate the corresponding119863images of Figures 3(a) 3(b) and 3(c) respectively As can beseen under normal conditions the further the pixel is thehigher its 119863 value will be

The abovementioned algorithm for estimating 119860 is inallusion to haze image 119868(119909) and this algorithm can alsobe directly applied to the haze-free image 119869(119909) to acquireits atmospheric light value 1198601015840 Since the haze layer mainlyreflects the natural light with balanced RGB values the wholebrightness of 119869(119909) is lower than that of 119868(119909) Therefore thevalue of 1198601015840 in the haze-free image 119869(119909) is larger than 119860 inthe haze image 119868(119909) As can be seen from the process ofestimating 1198601015840 its value is at or near the brightest pixel valuein 119869(119909) so 1198601015840 is larger than the pixel value in 119869(119909) as a wholeBased on (4) we have

119868 (119909) = 119869 (119909) 119905 (119909) + 119860 (1 minus 119905 (119909))gt 119869 (119909) 119905 (119909) + 1198601015840 (1 minus 119905 (119909))gt 119869 (119909) 119905 (119909) + 119869 (119909) (1 minus 119905 (119909)) = 119869 (119909)

(7)

One can see from (7) that the brightness of haze-freeimage 119869(119909) is lower than that of haze image 119868(119909) as a wholeMathematically it is out of the question to estimate the image119869(119909) according to (4) However the visual effect of haze-freeimage is inconsistent with the haze image Comparing thebrightness of images before and after dehazing it is thoughtthat they are under the inconsistency illumination for humanvision In Section 4 the contrast experiments will be furthercarried out on the issue of brightness consistency

3 Proposed Method

The low frequency layer and the three high frequency layers(in horizontal vertical and diagonal directions) are produced


(a) (b) (c)

(d) (e) (f)

Figure 3 Image of scene depth proportion (a) (b) and (c) Gray-scale hazy images (d) (e) and (f) Corresponding images of scene depthproportion of (a) (b) and (c) respectively

by wavelet decomposition of the original image Since thedifferent features of the original image are preserved inthe low and high frequency layers respectively differentdehazing strategies are adopted for different frequency layersResultantly the low frequency layer after wavelet decomposi-tion has the smoother boundary and contains less noise thanthe original image which makes up the foundation of detailenhancement for image dehazing The three high frequencylayers contain almost the whole boundary information oforiginal image which plays a key role in the ultimate effectof image enhancement In a word the boundary informationof original image can be extracted and preserved in the highfrequency layers by simple wavelet decomposition for thesake of avoiding damaging the boundary in the subsequentoperating for example image filtering In practice theboundary information is significant for human vision tounderstand and recognize the image scenes as a whole Thiscrucial information in the haze image has different levels ofdegradation by the haze layer so the simple and effectivemethod for image dehazing is to enhance the boundaryinformation accordingly

The scheme sketch of proposed method is illustrated inFigure 4 Based on the modified guided image filtering pro-posed in this paper the difference value between the originalimage and filtering output image is called detail layer Afterbeing amplified by a certain coefficient the amplified detaillayer is added to the filtering output image to achieve theimage enhancement This enhancement method is applied tothe three high frequency layers after wavelet decompositionrespectively Due to the simple feature of high frequencylayer this straightforward enhancement can be regarded asthe effective scheme However for the low frequency layerthe complex feature may lead to excessive enhancementin the region with the obvious boundary and insufficientenhancement in the region with the fuzzy boundary

There is a direct relationship between the brightness ofboundary pixel and its scene depth Since the light reachingthe camera from the far scene is easy to be scatted by thehaze layer the value of boundary pixel is low at large Tothe contrary the light from the nearby scene is less affectedby the haze layer so the value of boundary pixel is generallyhigh Hence it is reasonable to enhance the haze image with


Computing the proportion

of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer

High frequencylayer in horizontal

direction

High frequencylayer in vertical

direction

High frequencylayer in diagonal

direction

Hierarchical enhancing using

modified guide image filtering

Enhancing using modified

guide image filtering





Enhanced lowfrequency layer

Enhanced highfrequency layer in

horizontal direction

Enhanced highfrequency layer invertical direction

Enhanced highfrequency layer indiagonal direction

Waveletreconstruction

Haze-free image

Figure 4 Scheme sketch of proposed method

(a)

(b) (d) (f)

(c) (e) (g)

Figure 5 The process of gray-scale image dehazing by proposed method (a) Original gray-scale hazy image (b) Low frequency layer (c)Enhanced image of (b) (d) High frequency layer in horizontal direction (e) Enhanced image of (d) (f) Dehazing result with the image ofscene depth proportion (g) Dehazing result using modified guided image filtering directly

the help of the image of scene depth proportion so theenhancement coefficient is set to the higher value in theregion of far scene and the lower one in the region of nearbyscene Resultantly this enhancement method guided by thescene depth information is applied to the fundamental lowfrequency layer

The process of gray-scale image dehazing by proposedmethod is illustrated in Figure 5 Figure 5(a) is the originalgray-scale image and Figures 5(b) and 5(d) are the lowfrequency layer and high frequency layer in horizontal

direction respectively Note that only the enhancement pro-cess of high frequency layer in horizontal direction is shownhere and the process of other high frequency layers is basedon the same way The enhancement effect of low frequencylayer using the modified guided image filtering by 4 timesenhancement is illustrated in Figure 5(c) which is guided bythe image of scene depth proportion and Figure 5(e) showsthe enhancement effect of high frequency layer in horizontaldirection using the modified image guided filtering by 2times enhancement directly Here all the pixel values of


(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 6 Experiment on image with thin haze and small sky region (a) Color hazy image (b) Result by method of Fattal [1] (c) Result bymethod of He et al [2] (d) Result by method of Meng et al (119860 is acquired manually) [9] (e) Result by method of Li et al [7] (f) Gray-scalehazy image (g) Gray-scale result by proposed method (h) Color result by proposed method

Figures 5(d) and 5(e) are amplified 5 times for facilitatingdisplay

Figure 5(f) illustrates the ultimate dehazing result ofgray-scale image by wavelet reconstruction of enhanced lowfrequency layer and three high frequency layers As can beseen from Figure 5(f) it has the remarkable effect comparedto the original image in Figure 5(a) Since the enhancementprocess is guided by the image of scene depth proportionthe dehazing effect of far scenes can be guaranteed and thephenomenonof excessive enhancementmeanwhile does notappear in the nearby scenes To verify how useful the imageof scene depth proportion is the modified guided imagefiltering is directly applied to enhance the original haze imagewith the same enhancement coefficient 4 for the sake of com-paring it with our method and the dehazing effect of nearbyscenes shows the obvious excessive enhancement as showninFigure 5(g) Scene depth information is the straightforwardreflection of enhancement demands for various regions in theoriginal image so that the processing of image enhancementcan be automatically layered and the original method withthe uniform enhancement becomes an efficient hierarchicalmethod

4 Experimental Results

The comparison between the image-enhancement-basedmethod and our method has been illustrated in Figure 5and the classic and effective methods based on atmosphericphysical model for example Fattal [1] He et al [2] Menget al [9] and Li et al [7] will be further compared withour method in this section In order to fully demonstratethe power of proposed method the major parameters in theabovementioned methods are set to the appropriate valuesto get the satisfactory results in this section Moreover theguided image filtering [13] is applied to the method ofHe et al [2] further to improve its dehazing effect Theexperiment is performed using the software Matlab2010bwhich is installed on a personal computer with an Intel Corei7-4510U processor

The experiment is composed of two main parts and thetest image with thin haze and small sky region is processedprimarily which is easier to deal with under normal cir-cumstances The experimental results are shown in Figure 6The original haze image is illustrated in Figure 6(a) Figures6(b) 6(c) 6(d) and 6(e) are the dehazing results by the


(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 7 Experiment I on image with thick haze and large sky region (a) Color hazy image (b) Result by method of Fattal [1] (c) Result bymethod of He et al [2] (d) Result by method of Meng et al (119860 is acquired manually) [9] (e) Result by method of Li et al [7] (f) Gray-scalehazy image (g) Gray-scale result by proposed method (h) Color result by proposed method

method of Fattal [1] He et al [2] Meng et al [9] andLi et al [7] respectively One can see that both of themexhibit outstanding dehazing effect for this type of imageHowever the inconsistency of brightness is obvious whencompared with the original image in Figure 6(a) To testthe dehazing effect for gray-scale image we transform theoriginal color image (Figure 6(a)) into the correspondinggray-scale one (Figure 6(f)) Figure 6(e) shows the gray-scaledehazing result by proposedmethod and it is easily observedthat the dehazing effect for gray-scale image is remarkable

Applying our proposed method directly to each RGBchannel of a color image will acquire the dehazing result ofthe color image in Figure 6(h) It is observed that the dehazingeffect of proposed method for color image is comparableto that of other methods but has the better brightnessconsistency between the original image and haze-free imageThese two images are easier for human vision to considerthat the imaging process is on the condition of the sameillumination

To verify the performance of proposed method theimages with thick haze and large sky region are selectedas the test images and the results are shown in Figure 7

Figures 7(a) and 7(f) are the original color haze image andits corresponding gray-scale one respectively The resultsby the methods of Fattal [1] He et al [2] Meng et al [9]and Li et al [7] are illustrated in Figures 7(b) 7(c) 7(d)and 7(e) respectively It can be obviously seen that seriouscolor distortion appears in Figures 7(b) 7(c) 7(d) and 7(e)especially in the large sky region Figure 7(g) shows the resultof gray-scale image dehazing by our method and Figure 7(h)illustrates the result of corresponding color result by ourmethod in order to make a comparison with other methods

One can see from Figures 7(g) and 7(h) that the obviousdehazing effects of our method for both gray-scale andcolor images with thick haze and large sky region areexperimentally demonstrated and the distortion is avoidedeffectively without changing the visual brightness Besidesthe appropriate haze layer will be automatically preserved inthe region of distant sky in this paper because there are fewboundaries there and the presence of appropriate haze is infavor of human vision to perceive scene depth [2]

To further verify the advantages of our method for theimage with thick haze and large sky region the gray-scaleimage of Figure 1(a) and its corresponding color image are


(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 8 Experiment II on image with thick haze and large sky region (a) Color hazy image (b) Result by method of Fattal [1] (c) Result bymethod of He et al [2] (d) Result by method of Meng et al (119860 is acquired manually) [9] (e) Result by method of Li et al [7] (f) Gray-scalehazy image (g) Gray-scale result by proposed method (h) Color result by proposed method

used to make a contrast experiment as illustrated in Figure 8Figure 8(a) shows the color haze image and Figures 8(b)8(c) 8(d) and 8(e) are the dehazing results by the methodsof Fattal [1] He et al [2] Meng et al [9] and Li et al[7] respectively The gray-scale hazy image is shown inFigure 8(f) and Figures 8(g) and 8(h) illustrate the dehazingresults of gray-scale image and corresponding color imageby our method respectively One can easily conclude fromFigure 8 that there is no obvious distortion when our methodis applied to either the gray-scale or color image and itsvisual luminance is also consistent with the original imageTherefore our proposedmethod has beendemonstrated to besatisfactorily effective in dehazing both color and gray-scaleimages and advantageous over the state-of-the-art dehazingmethods

5 Conclusion

In this paper we report a novel and efficient method forgray-scale image dehazing in which the advantages of thedehazing strategies based on the image enhancement and

atmospheric physical model are taken into account simul-taneously For the image-enhancement-based strategy thecharacteristics of its simplicity effectiveness and no colordistortion are preserved in the proposed method Mean-while the shortcomings of its excessive detail enhancementreckoning without image degradation model are overcomeCompared with the dehazing strategy based on the atmo-spheric physical model our method also exhibits superiorityWhen dealing with the image with the thin haze or thelarge sky region the proposed method effectively avoidsthe color distortion and the inconsistency of visual bright-ness Besides our method shows the higher performancewhen dealing with the image with thick haze and large skyregion

It is particularly important for the proposed method toovercome the essential shortcoming of the abovementionedmethods which are mainly working for color image Theguided image filter used for boundary preserving is alsomod-ified to improve the dehazing effect in this paper Moreover ahigh-quality image of scene depth proportion can be obtaineddirectly in the process of image dehazing as a byproduct


Additional Points

Limitations It should be addressed that the effectiveness ofour method also has two limitations The imaging degrada-tion under hazy weather conditions is inversely proportionalto the imaging distance of scene This means that the objectsthat are close to camera are less degraded by haze comparedto those that are far away Unfortunately owing to the lackof obvious boundary structures in the thick haze region faraway our method may fail to recover the true scenes thereMoreover image degradation by the suspended haze in theatmosphere is divided into two processes in essence (1)direct attenuationwhich describes the percentage of the sceneradiance reaching the camera and (2) additive airlight whichrepresents nonscene light participates in imaging processleading to the shift of scene colors General enhancementmethods suffer from a common problem that is althoughproblem (1) is relatively easy to deal with problem (2) cannotbe effectively solved And we leave these problems for futureresearch

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by Foundation of Key Laboratoryof Space Active Opto-Electronics Technology of ChineseAcademy of Sciences (no AOE-2016-A02) National NaturalScience Foundation of China (nos 61379010 and 41601353)Natural Science Basic Research Plan in Shaanxi Province ofChina (no 2015JM6293) and Scientific Research ProgramFunded by Shaanxi Provincial Education Department (no16JK1765)

References

[1] R Fattal ldquoSingle image dehazingrdquoACMTransactions on Graph-ics vol 27 no 3 article 72 pp 1ndash9 2008

[2] K He J Sun and X Tang ldquoSingle image haze removal usingdark channel priorrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 33 no 12 pp 2341ndash2353 2011

[3] F-C Cheng C-H Lin and J-L Lin ldquoConstant timeO(1) imagefog removal using lowest level channelrdquo Electronics Letters vol48 no 22 pp 1404ndash1406 2012

[4] T M Bui H N Tran W Kim and S Kim ldquoSegmenting darkchannel prior in single image dehazingrdquo Electronics Letters vol50 no 7 pp 516ndash518 2014

[5] C O Ancuti and C Ancuti ldquoSingle image dehazing by multi-scale fusionrdquo IEEE Transactions on Image Processing vol 22 no8 pp 3271ndash3282 2013

[6] B-H Chen S-C Huang and J H Ye ldquoHazy image restorationby bi-histogrammodificationrdquo ACM Transactions on IntelligentSystems and Technology vol 6 no 4 article 50 2015

[7] Y Li R T Tan and M S Brown ldquoNighttime haze removalwith glow and multiple light colorsrdquo in Proceedings of the IEEEInternational Conference on Computer Vision (ICCV rsquo15) pp226ndash234 Santiago Chile December 2015

[8] S-C Huang J-H Ye and B-H Chen ldquoAn advanced single-image visibility restoration algorithm for real-world hazyscenesrdquo IEEE Transactions on Industrial Electronics vol 62 no5 pp 2962ndash2972 2015

[9] G Meng Y Wang J Duan S Xiang and C Pan ldquoEffi-cient image dehazing with boundary constraint and contextualregularizationrdquo in Proceedings of the 14th IEEE InternationalConference on Computer Vision (ICCV rsquo13) pp 617ndash624 IEEESydney Australia December 2013

[10] S-C Huang B-H Chen and W-J Wang ldquoVisibility restora-tion of single hazy images captured in real-world weatherconditionsrdquo IEEETransactions on Circuits and Systems for VideoTechnology vol 24 no 10 pp 1814ndash1824 2014

[11] S-CHuang B-H Chen andY-J Cheng ldquoAn efficient visibilityenhancement algorithm for road scenes captured by intelligenttransportation systemsrdquo IEEE Transactions on Intelligent Trans-portation Systems vol 15 no 5 pp 2321ndash2332 2014

[12] Q Zhu J Mai and L Shao ldquoA fast single image haze removalalgorithm using color attenuation priorrdquo IEEE Transactions onImage Processing vol 24 no 11 pp 3522ndash3533 2015

[13] K He J Sun and X Tang ldquoGuided image filteringrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol35 no 6 pp 1397ndash1409 2013

[14] B Jiang W Zhang H Meng Y Ru Y Zhang and X MaldquoSingle image haze removal on complex imaging backgroundrdquoin Proceedings of the 6th IEEE International Conference onSoftware Engineering and Service Science (ICSESS rsquo15) pp 280ndash283 IEEE Beijing China September 2015

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(a) (b) (c)

Figure 1 Gray-scale image dehazing using proposedmethod (a) Gray-scale image (b) Haze-free image (c) Image of scene depth proportion

statistical characteristics will be ineffective due to the lack ofsufficient color information for dehazing thick haze imagesOn the other hand the assumption of dark channel prioris proposed by He et al [2] based on the statistics of largenumbers of haze-free images in outdoor scenes Followed byHe et alrsquos seminal work the corresponding fast algorithm isproposed in [3] and the halo effect is remarkably reducedby template segmentation in the dark channel calculation in[4] Nevertheless this proposal drastically suffers from highcomputational complexity and it yet fails to work for imageswith thick haze or large sky region due to the occurrence ofserious color distortion Therefore it is urgent to propose amethod to tackle the difficulty regarding images with thickhaze or large sky region which is one aim of this paper

In addition there have been other emerging importantmethods regarding image dehazing in recent years Forexample Ancuti firstly demonstrates the utility and effective-ness of a fusion-based technique for dehazing based on asingle degraded image [5] Chen proposes a novel visibilityrestoration approach based on Bi-Histogram modificationwhich can integrate a haze density estimation module anda haze formation removal module for accurate estimation ofhaze density in the transmission map [6] One of the seminalrepresentatives of nighttime dehazing method is reported byLi et al [7] where a framework is proposed in order to reducethe effect of glow in the original nighttime image leadingthe original image to consist of direct transmission andairlight only Huang in [8] presents a novel Laplacian-basedvisibility restoration approach to effectively solve inadequatehaze thickness estimation and alleviate color cast problemsMeng benefits much from an exploration on the inherentboundary constraint that is combined with a weighted 1198711-norm based contextual regularization and it is modeled intoan optimization problem to estimate the unknown scenetransmission in [9]

Huang et al employ the combinations of three majormodules namely a depth estimation module a color analysismodule and a visibility restoration module for visibilityrestoration [10] and also present an effective haze removalapproach to remedy problems caused by localized lightsources and color shifts which thereby achieves superiorrestoration results for single hazy images [11] Zhu proposesa simple but powerful color attenuation prior by creating alinear model for modeling the scene depth of the hazy image

under this novel prior and learning the parameters of themodel with a supervised learning method [12]

In terms of gray-scale image dehazing the abovemen-tioned methods based on atmospheric physical model arerather restricted because they solely work for color imagesComparably Hersquosmethod still works while very strict restric-tions are made on the gray-scale images [2] In brief a colorimage generally contains much more information than agray-scale image so it makes the dehazing model solvedmore easily In contrast there is no confirmed solution togray-scale image by the abovementioned methods owing toless information contained in the gray-scale image As anindispensable part of image processing the resolution ofgray-scale image is almost four times more than that of colorimage with the same image size leading to the increasingsignificance of gray-scale image dehazing owing to its crucialrole in the field of high resolution observation for exampleaerospace industry which makes up the other aim of thispaper

In this paper we present a novel method for gray-scaleimage dehazing which takes into account the advantagesof two aforementioned categorized dehazing strategies Theperformance of our proposed method is shown in Figure 1in which Figure 1(a) is the original gray-scale image withthick haze and large sky region and Figures 1(b) and 1(c)illustrate the haze-free image and the image of scene depthproportion respectively More specifically the image of scenedepth proportion is estimated according to the originalgray-scale image directly Scene depth is the straightforwardreflection of enhancement demands for various regions inthe original image so the processing of enhancement canbe automatically layered guided by the image of scene depthproportion With this differential compensation the invalid-ity of atmospheric physical model for the image with thickhaze or large sky region can be reasonably solved Meanwhilethe phenomenon of excessive enhancement is avoided in theenhanced image and the brightness consistency can also beguaranteed simultaneously

The framework of this paper is organized as follows InSection 2 the problems in existing methods and correspond-ing solutions are stated In Section 3 the proposed methodis introduced and the experimental results are shown inSection 4 to demonstrate the effectiveness of the proposedmethod The paper is ultimately concluded in Section 5


(a) (b) (c)

(d) (e) (f)




119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (1)



119902119894 = 119886119894119868119894 + 119887119894 (2)



119868119890 = 119902 + 120576 (119868 minus 119902) (3)








119868 (119909) = 119869 (119909) 119905 (119909) + 119860 (1 minus 119905 (119909)) (4)














(7)


3 Proposed Method



(a) (b) (c)

(d) (e) (f)







of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer


direction


direction


direction















Haze-free image


(a)

(b) (d) (f)

(c) (e) (g)






(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)

(d) (e) (f)




119902119894 = 119886119896119868119894 + 119887119896 forall119894 isin 120596119896 (1)



119902119894 = 119886119894119868119894 + 119887119894 (2)



119868119890 = 119902 + 120576 (119868 minus 119902) (3)








119868 (119909) = 119869 (119909) 119905 (119909) + 119860 (1 minus 119905 (119909)) (4)














(7)


3 Proposed Method



(a) (b) (c)

(d) (e) (f)







of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer


direction


direction


direction















Haze-free image


(a)

(b) (d) (f)

(c) (e) (g)






(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119868 (119909) = 119869 (119909) 119905 (119909) + 119860 (1 minus 119905 (119909)) (4)














(7)


3 Proposed Method



(a) (b) (c)

(d) (e) (f)







of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer


direction


direction


direction















Haze-free image


(a)

(b) (d) (f)

(c) (e) (g)






(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)

(d) (e) (f)







of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer


direction


direction


direction















Haze-free image


(a)

(b) (d) (f)

(c) (e) (g)






(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra











of scene depth

Wavelet

decomposition

Original hazy image

Image of scenedepth

proportion

Low frequencylayer


direction


direction


direction















Haze-free image


(a)

(b) (d) (f)

(c) (e) (g)






(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)

(d) (e) (f)

(g) (h)








(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)

(d) (e) (f)

(g) (h)









(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b) (c)

(d) (e) (f)

(g) (h)



5 Conclusion





Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Additional Points


Competing Interests


Acknowledgments


References






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Gray-Scale Image Dehazing Guided by Scene Depth Information

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Transcript of Gray-Scale Image Dehazing Guided by Scene Depth Information