Underwater polarimetric imaging for visibility enhancement utilizing active unpolarized illumination

Accepted Manuscript Underwater polarimetric imaging for visibility enhancement utilizing active unpolarized illumination Liming Yang, Jian Liang, Wenfei Zhang, Haijuan Ju, Liyong Ren, Xiaopeng Shao

PII: DOI: Reference:

S0030-4018(18)31071-X https://doi.org/10.1016/j.optcom.2018.12.022 OPTICS 23690

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Optics Communications

Received date : 18 October 2018 Revised date : 30 November 2018 Accepted date : 4 December 2018 Please cite this article as: L. Yang, J. Liang, W. Zhang et al., Underwater polarimetric imaging for visibility enhancement utilizing active unpolarized illumination, Optics Communications (2018), https://doi.org/10.1016/j.optcom.2018.12.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Underwater polarimetric imaging for visibility enhancement utilizing active unpolarized illumination Liming Yanga, Jian Liangb, Wenfei Zhangb,c, Haijuan Jub, Liyong Renb,*, Xiaopeng Shaoa a

b c

School of Physics and Optoelectronic Engineering, Xidian University, Xi’an, Shaanxi 710071, China Research Department of Information Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, Shaanxi 710119, China School of Physics and Optoelectronic Engineering, Shandong University of Technology, Zibo, Shangdong 255000, China

Abstract:

Underwater imaging is attractive but challenging. Images could be severely degraded by the particles in turbid water because of backscatter generation and signal light attenuation. In this paper, we focus on the scheme of underwater imaging and study the methods of visibility enhancement of turbid underwater images based on polarimetric imaging utilizing active unpolarized illumination. Compared with traditional polarimetric imaging using linearly polarized illumination, using unpolarized illumination ensures the polarization effect of the signal light could be neglected, no matter the depolarization degree of the object is high or low, which expands the application range of underwater polarimrteic imaging and makes the underwater polarimetric imaging scheme more reliable and robust. Experimentally, the visibility and the contrast of underwater images are enhanced effectively. In addition, it is demonstrated that our method is applicable for objects of different materials and different imaging distances in turbid water. The contrast of underwater images could be promoted at least 100%, meaning that this kind of technique can be potentially used in many underwater environments.

Keywords: image enhancement, polarimetric imaging, imaging through turbid media. *Corresponding Author, E-mail: [email protected]

1. Introduction Nowadays, underwater imaging techniques become more and more significant for numbers of scientific researches and applications. However, the capacity of imaging is usually much limited due to the disturbance of the turbid media. Light passing through undergoes absorption and scattering by particles in the turbid water. Moreover, light that is scattered back from the medium along the light of sight veils the object. Both of these two effects lead to the image quality degradation [1, 2]. These images usually show poor visibility, low contrast, and sacrificial details of object that are submerged into the noise, which subsequently arouse problems in many underwater applications, such as exploration of marine resources, inspection of underwater pipelines, underwater archaeology, underwater search and rescue [3-5], etc. Previous studies have demonstrated some effective methods in mitigating such negative effects and enhancing the contrast of underwater images, such as time gating [6, 7], acoustic imaging [8], Super-Resolution fusion [9], etc. However, these methods are not suit for people in rescue or archaeological digs for complex equipment, at the same time some detailed information of objects may be lost during the treatment process. In contrast, polarimetric imaging is a more practical way benefiting from its simple structure and portability. Furthermore, polarimetric imaging technique has been proven very effective in recovering the detailed information of objects in scattering medium (including haze, fog and turbid water, etc) [10-16]. Previous underwater polarimetric imaging methods usually used linearly polarized illumination for backscatter removal. However, researchers found different behaviors of the SoP (state of the polarization) of the signal light when using linearly polarized light as the illumination. Some researchers assume that objects backreflect unpolarized light to the camera [17], while others believe this assumption could not be appropriate for all cases. In particular, in the case that the depolarization degree of the objects is low, the signal light could be significantly polarized [18-20], and then a method based on estimating the polarized-difference image of the signal light has been proposed [21]. However, the estimation process is complex and the computation is time consuming. Furthermore, it could sacrifice the image quality in regions of objects with low values of DoP. Therefore, a simpler imaging schemes and robuster descattering algorithm is still required. In this paper, we investigate the physical model of underwater imaging [22], and study the methods of visibility enhancement of underwater images based on polarimetric imaging utilizing active unpolarized illumination. There are two main differences compared with traditional polarimetric underwater imaging methods. The first one is that unpolarized light is used as the illumination in our method. According to Mie’s theory, the backscatter is partially polarized, while the signal light remains unpolarized. The distinction of their polarization states ensures our method can estimate the backscatter properly even if the surface of the object is specular (i.e. depolarization degree of the object is low). The second one is that the angle of polarization (AoP) is used in our algorithm as the initial parameter instead of the degree of polarization (DoP) for estimating the backscatter. It has been proven that the AoP is more accurate in inverting or estimating the backscatter information [14]. Therefore, we optimize the polarimetric dehazing algorithm [14] and first introduce it into turbid underwater imaging. Using proposed method, we carry out experiments with objects of different distances and different materials in water of different impurities and different turbidity. The results demonstrate that this method can effectively enhance the visibility and the contrast of turbid underwater imaging in different conditions.

2. Techniques The basic physical degradation model of underwater imaging is proposed in Ref. [23], in which the total irradiance received by the camera, I, can be expressed as (1) I  ID  IA , where ID, so-called the direct transmission or signal light, is the irradiance reflected from the object, which is attenuated due to the absorption and scattering by the particles in water. In this paper we assume that the DoP of the direct transmission can be neglected [14, 17, 23]. IA, so-called the veiling light or backscatter is the irradiance scattered towards the camera by the particles in water. Before detailing these components, note that backscatter is the major cause of contrast deterioration. ID and IA can be respectively expressed as I D  I L  t ( z ),

(2)

I A  I A [1  t ( z )],

(3)

where IL is the irradiance reflected from the object without being attenuated. IA is the veiling light from an infinite distance, and t(z) refers to the medium transmittance. For simplicity, the attenuation coefficient β(x, y) is usually considered to be spatially invariant [20-22], therefore t(z) can be expressed as t ( z )  e   z ,

(4)

where z is the distance between the object and the camera. Combining Eqs. (2) and (3), and eliminating t(z), the irradiance reflected from the object IL can be deduced as

IL 

I  IA . 1  I A I A

(5)

From Eq. (5), we can find that IA and IA are two key parameters for recovering IL. Our method of estimating these two key parameters are described as follows. First, four images with the linear polarizer oriented at 0°, 45°, 90° and 135° are snapped, and the intensities of four images are represented as I(0), I(45), I(90) and I(135), respectively. The linear Stokes parameters can be expressed as [24]

S0  I (0)  I (90) S1  I (0)  I (90)

(6)

S2  I (45)  I (135), where S0 represents the total intensity of the incident light, which is equal to I given by Eq. (1). S1 and S2 represent the linearly polarized components, in which, S1 represents the intensity difference between the horizontal and vertical linearly polarized components; S2 represents the intensity difference between the 45° and 135° linearly polarized components. Then, one can obtain the expression of the (DoP) p and the (AoP)  of the light as [24]

p

S12  S22

,

(7)

S2 . S1

(8)

S0

1 2

  aarctan

Then the DoP of o the veiling light (ddenoted as the pA) caan be estimated as thhe mean vaalues correspondingg to the pixels withouut object. Accordingg to Eq. (6), it is seenn that S0 coontains both the diirect transmission aand the veiling lighht, however S1 andd S2 are sccarcely affected by the direct transmisssion since we assuume that it is unpoolarized. Thherefore, comparedd with the DoP, the A AoP provides muchh more precise infoormation off the veiling light duue to its independennce of S0. As a resultt, it is beneficial to uuse AoP too estimate the intenssity of the veiling liight. In our algorithhm, we select AoP with w the hiighest appearance probability p as the AooP of the veiling ligght, which is denoteed as A. D Define the direction of 0° and 90° as x and y axes, respecctively. Thus, the poolarized irrradiance of the veilin ing light (IAp) in the x and y direction cann be expressed as I Apx  I Ap  cos 2  A ,

(9a)

I Apy  I Ap  sin 2  A .

(9b)

Meanwhile, IApxx and IApy can also be written as the totaal irradiance subtractting half off the unpolarized irraadiance. I Apx  I (0) 

S0 (1  p ) , 2

(10a)

S0 (1  p ) . 2

(10b)

I Apy  I (90) 

Combining Eqss. (9a) and (9b), Eqs. (10a) and (10b), IAAp can be derived as I Ap 

S1 I (0)  I (90)  , cos 2  A  sin 2  A cos 2 A

E ressults and discussions 3. Experimental A reeal-world underwat ater imaging scenarrio has been considdered as follows. F Fig. 1 show ws the schematic of the experimenntal setup. The illuumination source is an unpolarized LED lampp with the central waavelength of 510 nm m. The reason we chhoose D source is that, unnlike the laser sour urce, LED can outpput high power witthin a LED relattively smaller size of the device, whhich implies that thhis polarimetric im maging systtem can be convenieently transplanted innto the current undeerwater imaging sysstems. Onee linear polarizer is put p in front of the caamera as the analyzzer. The light outputt from the lamp reflects from m the object and trravels through a lin inear polarizer, andd then t tank (9000 mm × 450 mm × 450 imppinges on the CCD camera. We use a transparent mm m) filled with clean w water, and we makee the water turbid byy blending the waterr with diffe ferent impurities.

Fig. 1. Schematic of the expperimental setup for unnderwater imaging.

In the beginning, we validate the asssumption in sectioon 2 that the DoP of o the direct transmission cann be neglected, evven if the object yyields polarized speecular refleection (i.e. depolarizzation degree of the object is low). Therrefore, we choose a metal RM MB one-dollar coin made m of nickel platinng on steel as the obbject. The coin is stuuck on a plaastic plate and imm mersed in water. We make the water turbbid by blending the clean wateer with milk. By rottating the linear pollarizer, we obtain foour polarized imagess with the aangles of 0°, 45°, 990° and 135°, respectively, as shown inn Figs. 2(a)-(d). It ccan be seenn that the visibility of o these images is ppoor, and the detailss of the object can hhardly be sseen in such a turbidd water condition.

(11)

Thhen, IA can be estim mated by IA 

I Ap pA

,

(12)

Second, the othher key parameter IAA is estimated. Subbstituting Eqs. (2) annd (3) in Eqq. (1), we get the exxpression (13) I  I A  ( I L  I A )e    z . From Eq. (13), we can see that thee total intensity I (i.e., S0) equals to thee veiling ligght irradiance from m an infinite distancce IA either the distance d z is infinitee or the irrradiance reflected fr from the object IL eqquals to IA. Conside dering the fact that IL finally beecomes unpolarizedd light due to the multi-scattering m effecct and that IA is a partialpoolarization veiling liight with the DoP off pA. Therefore, I(0) can also be rewritteen as 1  pA I A 2 1  pA I I A )]e    z . [ L  ( I A p A cos 2  A  2 2 I (0)  I A p A cos 2  A 

(14)

Fig. 2. (a)-(d) The polariized images taken witth the angle of polari rizer 0°, 45°, 90° andd 135°, respeectively.

It is seen that iff z is infinite, the las ast term of Eq. (14) can be neglected ssince e-βz teends to 0, and then, th the expression of IA can be written as 2 I (0) (15) I A ( z   )  . 1  p A cos 2 A It should be noteed that although moost pixels in the imagge usually do not sat atisfy the coondition of z→.. At those pixels which satisfy thiss conditions there exist a reelationship I=IA∞. Therefore, to assist in finding thoose pixels in the image coorresponding to thee veiling light irraddiance from an infiinite distance, we ddefine a m matrix () of the sam me dimensions as thee image size

According to Eqs.. (7) and (8), DoP annd AoP images can be obtained, as shoown in Figss. 3(a) and 3(b), resppectively. It is seen that on the one hannd, the DoP of the ccoin is smaaller than that of the surroundings, meanning that the DoP off the direct transmisssion is low wer than that of the vveiling light; On thhe other hand, the ddistribution of AoP oof the whoole image is almost the same, meaningg that there is no diff fference between thee AoP of thhe coin and that off the surroundings. This means that th the direct transmission is eitheer with same polarrization direction aas the veiling light or it is unpolarizeed. To furthher identify this poiint, we conduct expperiments by changinng the position of oobject, the turbidity of water aand the azimuth off illumination. As a result, the similarr AoP distrribution is obtainedd. This verifies that the later explanatioon is reasonable, i.ee., the direct transmission is unpolarized. As a comparison, show wn in Fig. 4 is thee DoP distrribution of the samee object under the liinearly polarized illlumination. It is seeen that the D DoP of the direct traansmission is much higher than that of the t veiling light, meeaning that the polarization of tthe direct transmissiion can not be ignorred when illuminatiion by mpared with the polaarized a linnearly polarized lighht. Again, we emphhasize that, as com illum mination, under thee unpolarized illum mination the directt transmission is inndeed unpolarized, even if thhe depolarization ddegree of the objecct is low. Thus it really satissfies the assumptionn mentioned above.



I A ( z  ) . I

(16)

For simplicity, we w check the elemeents of (x0, y0) andd find the one whichh is very cllose to 1, where (x0, y0) can be regard ass the position of veilling light irradiance from an innfinite distance, andd this value of matriix IA(z→) at (x0, y0) can be regardedd as the esstimated IA. Finally, the recoovered image IL cann be obtained accordding to Eq. (5). It shhould be poointed out that this aalgorithm can estimaate both IA and IA precisely. p In particulaar, it can doo the descattering process without huuman-computer intteraction, and this method m might be very suitablle for real-time imagging.

Fiig. 3. (a) DoP distributioon of Fig2; (b) AoP dist stribution of Fig2.

Fig. 6. (a) The original imagge; (b) The recovered im mage processed by ourr method.

In the following, we use histogram m to show the contrrast improvement of o the imag age visualized. Figs. 7(a) and 7(b) shown wn the histograms off the original image iin Fig. 6(a)) and the recovered image in Fig. 6(b),, respectively. From m Fig. 7(a), it can bee seen that the distribution of tthe gray level is cenntralized in a narrow w range. It implies thhat the much broader than th that in detaailed information is submerged. In conntrast, Fig. 7(b) is m Fig. 7(a). As a result, m more details can be eaasily discerned, as shhown in Fig. 6(b).

Fiig. 4. DoP distribution under u polarized illuminnation.

Then we proceess these polarized images in Fig. 2 bby our algorithm. F For our M Matlab running on thhe computer with Inntel(R) Core(TM) i3-8100 i CPU @ 3.60GHZ prrocessor, and our alggorithm takes aboutt 1.06 s. The recoveered image is shownn in Fig. 5((a). Compared Fig. 5(a) with Fig. 2, it ccan be seen that the vvisibility of these im mages in Fiig. 2 is poor, and thhe details of the obbject can hardly bee seen in such turbiid water coondition. While thee visibility in Fig. 55(a) is significantlyy improved, and thee image quuality is greatly enhhanced. Besides, thee details of the coin in the scene becom me much cllearer. In particular, tthe number ‘2015’ aat the bottom of the coin becomes moree legible. It indicates that the m method can removee the veiling light efffectively. Furtherm more, we addditionally perform the image recoveryy based on a represenntative polarimetric method prroposed by Schechnner [10], as shown in i Fig. 5(b). It can bbe seen that the visib ibility of thhe recovered image bby our method is beetter than that by Schhechner’s method inn visual. Inn particular, comparring with Schechneer’s method, the deetailed performancee of the im mage recovered by oour method is muchh clearer. Furthermoore, we also investiigate the coomputation time off traditional underwaater polarimetric im maging method [21,, 25]. In R Ref. [21], just the iterrative algorithm takees about 70s for findding the optimal vallues and thhe entire process maay take more time. Similarly, in Ref. [[25], the iterative alg lgorithm taakes about 4s. In geeneral, our method m makes a good balan ance between the quuality of reecovered image andd the performance of computation tim me. The proposed method m might be much more convenient and reliiable in real-time unnderwater descatterinng.

Fiig. 5. (a) Recovered image by our methood; (b) Recovered imaage by traditional pollarimetric deehazing method.

In the followinng, to illustrate the universality of ourr algorithm for undderwater im mage recovery, we th then perform anotheer group of experime ment, in which the obbject is a m metal RMB fifty-cennt coin made of coppper plating on steel. The original imagee and the reecovered image by oour method are show wn in Figs. 6(a) andd 6(b), respectively. O One can seee that the recoveredd image shows goood contrast, and the iimage quality is bettter than thhe original image. Meanwhile, M the charracter on the plasticc plate also becomees much cllearer. It indicates thhat our algorithm is effective for targetts of different materrials and w water of different imppurities.

Fig. 7. (a) and (b) are the hiistograms of Figs. 6(a) aand (b), respectively.

Apart from milk, we also carry outt experiments in whhich we make the water turbbid by blending the clean c water with MggO powder. Similarrly, both RMB one--dollar coinn and RMB fifty-ceent coin were usedd, the original imagge and the correspon onding recoovered image processed by our methodd are given, as show wn in Figs. 8(a) andd 8(b), 8(c)) and 8(d) respectivvely. It can be seen that the detailed innformation of the coin c is harddly recognized in thee original image, whhile in the recoveredd image it becomes much cleaarer, and the image ccontrast is improvedd significantly. Besiddes, the rough contoour of the letter ‘O’ on the pplastic plate, which is marked by the bblue rectangle, is ffaintly visibble. It should be nooted that the black ddots in Fig. 8(a) andd 8(b) are bubbles oon the surfface of the tank, not tthe result of the algoorithm error.

Fig. 8. (a) and (c) are the original images; (b) aand (d) are the recoverred images processed bby our methhod.

It should be pointted out that, at preseent, there is not a coomprehensive evaluuation criteerion for image quuality, and subjectivve judgment is neeeded in most casess. But seveeral simple functionns can be used to evvaluate roughly the quality of the recoovered imag age. Here, we introdduce the contrast funnction proposed in [[10]. The contrast ccan be exprressed as C(I ) 

1 N





x, y

[ I ( x, y )  I ] ,



(17)

I



wheere N is the pixel number in the image, I is the mean intensity of o the imaage, and I(x, y) is the intensity of tthe pixel (x, y). U Using Eq. (17), wee can calcculate the contrasst of the recovered images obtainned in the above four

exxperiments, as shhown in Table 1. W We also calculatee the improvemennt ratio acccording to the vvalues of the conntrast. It can be seen that the conttrast of evvery recovered iimage is enhancced compared w with the corresponding orriginal image, andd meanwhile, the improvement rattios are all substanntial in diifferent experimeents. We regardd the experimennts above ordinaally as exxperiment 1, 2, 3 and 4, respectivvely. From Tablee 1, we can find, on the onne hand, experim ment 1, 2 and 4 is better than experiment e 3 in image im mprovement ratioo. The reason cann be analyzed as ffollows. The conttrast of thhe original imagees listed in Tablle 1 imply that the direct transm mission suuffers from moree scattering in eexperiment 1, 2 and 4 compared with exxperiment 3. Thuss, the depolarizatiion is more signifficant in experimeent 1, 2 annd 4. On the otheer hand, experimeent 1 is similar too experiment 2 inn image im mprovement ratioo. It indicates thatt our algorithm iss robust for imagees with siimilar contrast.

Fig. 9. The variation of thee contrast improvementt ratio with the distancee of the object in densee turbid wateer.

Table 1.

Im mage quality in diifferent experimennts. No.

C (Original)

C (Recovered)

IImprovement (%)

Exxperiment 1

0.2075

0.7685

270.4

Exxperiment 2

0.2479

0.8790

254.6

Exxperiment 1

0.3704

0.8080

118.1

Exxperiment 1

0.1284

0.4685

264.9

In the follow wing, we quantitattively evaluate thhe effect of distaance on mage contrast in dense turbid waater. The object is placed on a sstepper im m motor, which movees evenly within a distance betweeen 30 mm and 80 mm in stteps of 5 mm. Im mages at differentt distances are caaptured. The evaaluation reesults are shown iin Table 2. Table 2.

Im mage quality at diifferent distances.. Distance

C (Origginal)

C (Recovered)

Improovement (%)

330 mm

0.33333

0.7305

119.17

335 mm

0.32214

0.7468

132.36

440 mm

0.33340

0.7491

124.28

445 mm

0.29990

0.7344

145.62

550 mm

0.30055

0.8439

176.24

555 mm

0.26628

0.6490

146.95

660 mm

0.20038

0.5033

146.96

665 mm

0.18864

0.6081

226.23

770 mm

0.14452

0.4524

211.57

775 mm

0.11115

0.5221

368.25

880 mm

0.13324

0.5273

298.26

c According too Table 2, wee plot the variation of the contrast im mprovement ratio with the distancee of the object in dense turbid wateer with m milk, as shown in F Fig. 9. It is seen tthat the improvem ment ratio shows a rising trrend. The reason can be explainedd as follows. The contrast of the ooriginal mage is high whenn the object is cloose to the camera. Thus the improvvement im raatio is not high, w which means the image recovery effect is not obvviously; w while the object is getting farther froom the camera, thhe contrast of origginal is addversely affectedd, which highlighhts the effectivenness of the descaattering allgorithm. Therefoore, the improvem ment ratio is increeased, which meaans the im mage recovery efffect is more signiificant. If the distaance between thee object annd the camera keeps increasinng, the direct ttransmission is almost suubmerged in the veiling light annd eventually the image recoveryy effect reeaches its limit annd after that, the iimprovement ratioo begins to declinne. Fig. 100 gives three grroups of results processed by ouur method at diifferent diistances. The lefft row representts the original iimages snapped at the diistance of 30 mm m, 45 mm, and 75 mm, respectivelyy, and those in thhe right roow represents thhe correspondingg recovered imaages processed bby the m method we propossed. By comparisson, it is seen thaat both the contraast and thhe detailed inform mation of recovereed images are enhhanced.

Fig. 10. Three groups of rresults are processed bby our method. The lefft row represents the ooriginal imagges snapped at a distannce of 30 mm, 45 mm,, and 75 mm, respectivvely; the right row reprresents the ccorresponding recovereed images processed byy the method we propossed.

In the end, to furtther verify our methhod is suitable for th the object with bothh high depoolarization degree and low depolarizzation degree in loong range detectionn. We condduct another experiiments, in which thhe object is a subm marine model consiists of smoooth metal surface and dull polished plastic window. Th The depolarization oof the objeect depends on the su surface feature and thhe material of the obbject. Generally speeaking, the plastic usually leadds to high depolarizzation [26] while th the smooth metal oon the opposite. The submarinne model is placedd away from the cam mera about 800mm m. We addeed different amount nts of MgO powderr to generate the turrbid media with meedium denssity and high densityy. The original imagges and the recovereed images by our method m are shown in Figs. 11(aa) and 11(b), Figs 11(c) and 11(d), resspectively. It can bee seen that the visual effect is much better. Furtheermore, the details oof the object (markked by t green rectangle)) that are not visiblle in the original im mages the red rectangle and the becoome visible in the rrecovered images, aand the veiling lightt is almost removedd. The mosst important thing iss that the quality of th the recovered imagee enhanced effectiveely, no matttter the depolarizatiion degree of the object region is loow (marked by thhe red rectaangle) or the objectt region is high (mar arked by the green reectangle), and theree is no abnoormal dark region (mentioned in Reff.[21]) in the recovvered images. Thuus, the meth thod proposed in thiis paper is of great vvalue for underwateer rescue and underrwater archhaeology in dense tuurbid river, sea etc.

Fig. 11. (a) and (c) are thhe original images of tthe scene captured in turbid water withe diifferent mages processed by ourr method. denssities of MgO; (b) and ((d) are the recovered im

3. Conclusion In this paper, we propose a method of visibility enhancement of underwater images based on polarimetric imaging utilizing active unpolarized illumination. Using unpolarized illumination ensures the polarization effect of the signal light could be neglected, no matter the depolarization degree of the object is high or low, which is of benefit to enlarge the application range and enhance the estimation precision of the veiling light. In addition, our descattering scheme is fast and simple. The effectiveness of the method is demonstrated by real-world experiments. The experimental results show that both the visibility and the contrast of the underwater images can be improved effectively, and the visibility can be promoted at least 100%. In addition, more details get visible after the recovering process. In particular, the experimental results show that our method is suitable for enhancing contrast of objects of different materials and different imaging distances in turbid water. Besides, the method proposed in this paper does not need human-computer interaction. Acknowledgment This work is supported by National Natural Science Foundation of China (61505246, 61535015), the West Light Foundation of Chinese Academy of Sciences (XAB2017B20). References [1] J. S. Jaffe Computer modeling and the design of optimal underwater imaging system, IEEE J. Ocean. Eng. 15 (1990) 101-111. [2] S. F. Li, G. H. Chen, R. B. Wang, Z. X. Luo, Q. X. Peng, Monte Carlo based angular distribution estimation method of multiply scattered photons for underwater imaging, Opt. Commun. 381 (2016) 43-47. [3] A. Ortiz, M. Simo, G. Oliver A vision system for an underwater cable tracker Mach, Vis. Appl. 13 (2002) 129-140. [4] D. F. Coleman, J. B. Newman, R. D. 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F Figures list

Fiig. 1. Schematic of thhe experimental setuup for underwater im maging.

Fiig. 2. (a)-(d) The polarizzed images taken with the angle of polarizer 00°, 45°, 90° and 135°, reespectively.

Fiig. 3. (a) DoP distributioon of Fig2; (b) AoP dist stribution of Fig2.

Fiig. 4. .DoP distribution under polarized illuminnation.

Fiig. 5. (a) Recovered ima mage by our method; (b)) Recovered image by traditional t polarimetric dehazing method.

Fiig. 6. The original imagge; (b) The recovered im mage processed by our method.

Fiig. 7. (a) and (b) are thee histograms of Figs. 6(aa) and (b), respectively. y.

Fiig. 8. (a) and (c) are the original images; (b) annd (d) are the recoveredd images processed by our o method.

Fiig. 9. The variation of thhe contrast improvemeent ratio with the distancce of the object in densee turbid

Fiig. 10. Three groups oof results are processedd by our method. Thee left row represents thhe original images snaapped at a distance of 30 mm, 45 mm, and 75 mm, respectively; the right row represennts the coorresponding recoveredd images processed by tthe method we proposeed.

Fiig. 11. (a) and (c) are the he original images of thee scene captured in turbbid water withe differennt densities of MgO; (b)) and (d) are the recoveered images processed by our method.