GUAN Jin-ge，ZHAO Yong，ZHENG Yong-qiu，MA Miao，SUN Peng，XUE Chen-yang

(1. School of Information and Communication Engineering, North University of China, Taiyuan 030051, China；2. Beijing Institute of Computer Application Technology, China North Industries Group Corporation Limited, Beijing 100089, China；3. Key Laboratory of Instrumentation Science and Dynamic Measurement(North University of China)，Ministry of Education, Taiyuan 030051, China；4. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China)

Abstract： For conventional optical polarization imaging of underwater target, the polarization degree of backscatter should be pre-measured by averaging the pixel intensities in the no target region of the polarization images, and the polarization property of the target is assumed to be completely depolarized. When the scattering background is unseen in the field of view or the target is polarized, conventional method is helpless in detecting the target. An improvement is to use lots of co-polarization and cross polarization detection components. We propose a polarization subtraction method to estimate depolarization property of the scattering noise and target signal. And experiment in a quartz cuvette container is performed to demonstrate the effectiveness of the proposed method. The results show that the proposed method can work without scattering background reference, and further recover the target along with smooth surface for polarization preserving response. This study promotes the development of optical polarization imaging systems in underwater environments.

Key words： polarization imaging; underwater optical scattering; optical information processing; target detection

0 Introduction

Light deviates from original path when propagating through scattering media. Therefore, optical imaging of objects in an scattering medium is characterized by the reduction of contrast and resolution[1-3]. In order to weaken the effect of light scattering on image quality, models dealing with light-media interactions are established, and physical properties including time-of-flight[4], polarization[5]and coherence[6]are employed to discriminate the target signal from the scattering noise. In this paper, we focus on target detection in the underwater scattering environment.

Polarization imaging through turbid media is promising because it is easy to operate with low cost, on which a variety of investigations have been implemented. Visibility in turbid water was enhanced by the reduction of backscatter with cross polarization detection[7-8]. Investigations further showed that when detecting depolarized targets, imaging performance using circular polarization is better than that using the linear polarization[9]. Alfano demonstrated that depolarization property of backscattered light was related to the relationship between the wavelength and the size of medium[10], and polarization memory effect could be used to detect polarized targets[11]. Since single polarization detection could not remove the backscatter completely, orthogonal polarization states were combined to enhance the performance of descattering. Tao et al calculated the difference between co- and cross polarizations to recognize the targets[12]. Walker subtracted a fraction of co-polarization from the cross polarization to further eliminate scattering effect theoretically[13]. Miller demonstrated the effectiveness of Walker’s method by experiment[14].

Inspired by image recovery in bad weathers using polarization information[15-16], underwater target recovery was also performed based on the two orthogonal polarizations[17]. Correlation technique was used as criterion to improve the detection performance of imaging polarimetry[18]. Hu further employed polarization-difference signal[19]and transmittance correction[20]to recover both depolarized and polarized targets. However, in the previous work on polarization recovery of targets in turbid water, depolarization property of the backscatter is estimated by measuring pixel intensities in the region without targets. When there exists no scattering region in the image, conventional method is invalid for target detection. To solve this problem, polarization subtraction method is proposed to calculate the value of polarization degree of backscatter. Also, depolarization of targets can be estimated by this method.

The remainder of this paper is organized as follows.Underwater optical imaging model, target recovery algorithm, and polarization subtraction method are contained in the theory in Section 1. Experimental setup is shown in Section 2. Experimental results and discussion are described in Section 3. Section 4 provides the conclusion.

1 Theory

1.1 Imaging model

For underwater active optical imaging, the interaction between light and medium can be described by Jaffe’s model[21]. With this model, light field received by the detector is composed of three categories. Backscattered light directly originates from the suspended particles, which contains no target information and degrades image contrast. The pathway along which light being reflected by the target is further classified into direct transmission and forward scattered component. The direct transmission is image-forming light without being scattered off the original path. The forward scattered light deviates from original path and is responsible for image blurring, which is often neglected in the process of image recovery[18]. Thus, the measured image is expressed as the sum of backscatter and direct transmission, namely

I(x,y)=IB(x,y)+ID(x,y),

(1)

where subscriptsBandDrepresent the underwater backscatter and direct transmission, respectively; and (x,y) indicates the pixel position in the image. The goal of image recovery is to separate the backscatter from the direct transmission.

1.2 Polarization recovery algorithm

Underwater active descattering and image recovery based on polarization information can be described as follows[18]. Under polarization illumination, two orthogonal polarization images are acquired: co-polarization and cross polarization, which are the detections in parallel and orthogonal states to the polarization illumination, respectively. Based on Eq.(1), the backscatter and the direct transmission are irrelevant to each other, and orthogonal polarization detections can be shown as

Ico(x,y)=Bco(x,y)+Dco(x,y),

(2)

and

Icross(x,y)=Bcross(x,y)+Dcross(x,y).

(3)

The polarization degree of both backscatter and direct transmission are defined as

(4)

and

(5)

According to polarization theory, light intensity is the sum of two arbitrary orthogonal polarization components. Thus, the backscatter and the direct transmission can be expressed as

IB(x,y)=Bco(x,y)+Bcross(x,y),

(6)

and

ID(x,y)=Dco(x,y)+Dcross(x,y).

(7)

Based on Eqs.(2)-(7), the direct transmission and the backscatter are estimated as

(8)

and

(9)

It can be observed from Eq.(8) that if the target wants to be recovered, the parameters ofpscatandpobjneed to be known except for recording the two orthogonal polarizations ofIcoandIcrossdirectly. For traditional methods, the value ofpscatis determined by measuring no target region, andpobjis assumed to be zero because it only makes a scale factor contribution to the signal reconstruction in the image. However, in some instances, it may become invalid. For example, when no scattering background in the field of view or the target in the medium is polarized, polarization recovery based on Eq.(8) is hard to be performed.

1.3 Polarization subtraction method

In this paper, polarization subtraction method is proposed to estimate the parameters of bothpscatandpobj. In fact, the subtraction method is an algorithm, and the corresponding polarization image is described as

Ips(x,y)=Icross(x,y)-γIco(x,y),

(10)

whereγis the subtraction factor.

In Eq.(10), backscattered light from the medium is not completely polarized under polarization illumination. Therefore, a part of the backscatter is still present in the cross polarization image. In order to further improve the image quality, a fraction of the co-polarization component is subtracted from the cross polarization component.

Based on Eqs.(2) and (3), Eq.(10) can be rewritten as

(11)

The principle of underwater active polarization imaging is based on the difference in polarization properties between the backscatter and the direct transmission. The polarization subtraction method employs depolarization information, defined as the process of changing polarized light into unpolarized light, for the purpose of target detection. Polarization subtraction algorithm based determination ofpscatandpobjcan be described by Fig.1.

Fig.1 Principle diagram of depolarization estimation

It can be observed from Fig.1 that the key for determination of parameterspscatandpobjis to obtain two special polarization images. One corresponds toγ1, in which the direct transmission is completely removed, and image has the worst performance. The other corresponds toγ2, in which the backscatter noise is completely eliminated, and image has the best performance.

With the aids of Eqs.(4) and (5), the estimations ofpobjandpscatcan be calculated as

(12)

and

(13)

According to the above analysis, we conclude that polarization subtraction method could assist with recovering underwater targets by using polarization information[22]. The parameter ofpobjcan be determined by Eq.(12), which illustrates the potential of recovery for polarized target. From Eq.(13), we can see that the parameter ofpscatcan be identified without scattering background reference. We further demonstrate the effectiveness of our work by experiments.

2 Experimental setup

Fig.2 shows the setup for underwater image recovery using polarization information.

Fig.2 Experimental setup for underwater polarization imaging

Light emitted from a semiconductor laser operating at the wavelength of 532 nm is used as the illumination source. A combination of polarization state generator (PSG) with beam expander (10×) provides polarization incidence with beam size of about 23 mm. Milk solution is contained in a 5 cm×5 cm×5 cm quartz cuvette to simulate the underwater environment[8,18]. The detailed description of targets used in the experiment is shown in Section.3.1. A micro-displacement (MDP) device is used to control the depth of targets in the medium. The polarization state analyzer(PSA)ensures two polarization detections: co-polarization and cross polarization. An 8-bit CCD camera is employed to record the images. An aperture (A) placed in front of the camera could modulate the amount of light entering the imaging system.

3 Results and discussion

3.1 Depolarization of targets

Three types of targets are used in the experiment of polarization subtraction method, as shown in the upper side of Fig.3. The optical disk (Fig.3(a)) and trademark (Fig.3(b)) are characterized by rough surfaces. The backside of coin of one yuan (Fig.3(c)) has smooth surface. Here, only depolarization feature is measured because polarization properties of the man-made targets are dominated by depolarization[23-24], as shown in the lower side of Fig.3. Illumination is linearly polarized light at 0° polarization with respect to the horizontal direction, and detected light is filtered out by the polarization analyzer, the axis of which ranges from 0° to 90° with intervals of 10°. Relative intensity of polarization is normalized by a division of the maximum value of detected light. From Figs.3(a) and 3(b), we can see that distributions of returned signals at any polarization direction are enough to illustrate the targets being depolarized. From Fig.3(c), we can see that illumination polarization is hardly changed into orthogonal polarization component, which makes the target be polarized.

Fig.3 Depolarization feature of targets

3.2 Polarization degree estimation of backscatter

In the experiment, the number of scattering mean free pathsN(N=μsL) is used to describe the underwater target depth, whereμsandLare the scattering coefficient and the geometric distance between the target plane and the wall of container, respectively. Fig.4 gives the images of the optical disk atN=3.773. The images are taken with modes of intensity, co-polarization, cross polarization, and conventional polarization recovery, respectively. For direct imaging, the performance is degraded because the backscatter is superimposed on the target signal, as shown in Fig.4(a). Since intensity distributions of polarized backscatter are concentrated in the co-polarization channel, the corresponding image (Fig.4(b)) shows poorer quality compared with direct imaging. In the cross polarization image (Fig.4(c)), most of the backscatter is suppressed by polarization filtering. Fig.4(d) presents the reconstruction of target based on Eq.(8), in which the backscatter is eliminated and numbers on the optical disk can be clearly observed.

Fig.4 Images of optical disk at N=3.773 with different methods

In Fig.4(d), polarization degree of the backscatter is obtained by measuring the average pixel intensities in the designated square region in Fig.4(a), which is 0.686. Fig.5 further shows the depolarization estimation of backscatter using polarization subtraction method, in which the interval of subtraction factor is 0.05. Figs.5(a)-5(c) give polarization subtraction images (Eq.(11)) corresponding to different factors and intensity profiles along the arrow crossing the horizontal line in the image. The image with subtraction factor of 0.15 has higher contrast than that with 0.60 and 0.90, which can be attributed to the polarized backscatter. When subtraction factor tends to one more, the target signal is more rejected due to its depolarization, as shown in Fig.5(c). Fig.5(d) shows image performance as a function of subtraction factor systematically, in which the factor ranges from 0 to 1 with intervals of 0.05. It can be observed from Fig.5(d) that when subtraction factor equals 0.20, the image has the best contrast of 0.849. Here, image contrast is calculated byImax-Imin)/(Imax+Imin), whereImaxandIminare the average values corresponding to peaks and valleys in the profiles, respectively. Based on Eq.(13), polarization degree of the backscatter is calculated as 0.667, which is very close to the value of 0.686 in traditional method.

Fig.5 Image quality obtained by polarization subtraction method

Table 1 shows the measured difference in polarization degree estimation of the backscatter between traditional and subtraction methods. This difference is evaluated by the error, which is calculated by |(ptrad-psubt)/ptrad|, where symbol |·| represents the absolute value in mathematics, andptradandpsubtare polarization degrees of the backscatter obtained by traditional and subtraction methods, respectively. In Table 1, Ⅰ, Ⅱ and Ⅲ indicate intervals with 0.1, 0.05 and 0.025 in polarization subtraction method, respectively. It can be observed that when the target depth increases from 3.230 to 3.773, the values ofpsubtwith intervals of both 0.1 and 0.05 are 0.667, and the corresponding errors are 0.029, 0.032 and 0.028, respectively. The value ofpsubtwith interval of 0.025 is 0.702, and the corresponding errors are 0.022, 0.019 and 0.023, respectively. When the depth of the target increases from 4.181 to 5.139, the values ofpsubtwith different intervals have the same value of 0.667, and the corresponding errors are 0.021, 0.013, and 0.003, respectively. By analyzing the above data, in the polarization subtraction method, the smaller the interval of subtraction factor is, the closer to that obtained by traditional method the estimation of polarization degree of backscatter.

Table 1 Depolarization of backscatter obtained by different methods

3.3 Polarization recovery without scattering background

The results in Fig.5 and Table 1 demonstrate the effectiveness of depolarization estimation of the backscatter using polarization subtraction method. Figs.6(a) and 6(b) represent the images obtained by direct imaging and polarization recovery without background reference, respectively. It can be observed from Fig.6(a) that image contrasts decrease from 0.204 to 0.000 when varying the depth of underwater target from 2.850 to 5.157. Here, the contrast is calculated by the difference between the average light intensity corresponding to the regions with and without words, respectively. Because backscatter is superimposed on the target signal, image performance degrades rapidly. From Fig.6(b), we can see that image contrasts decrease from 0.495 to 0.056 slightly with increasing the depth of underwater target. By comparing Figs.6(a) with Fig.6(b), it can be seen that polarization recovery shows a better image contrast than that obtained by direct imaging due to elimination of backscatter. WhenNequals 5.157, the words can still be observed while invisible in the direct imaging.

Fig.6 Comparison of image contrasts between direct imaging and polarization subtraction imaging

Recovery of polarizedtargets in turbid water is further performed. Direct imaging is presented in Fig.7(a). Compared with co-polarization image (Fig.7(b)), the patterns of the corn in the cross polarization image (Fig.7(c)) could not be observed because the target has smooth surface, the co-polarization component of which is hardly changed into the orthogonal one under polarization illumination. Fig.7(d) shows the result obtained by traditional polarization imaging method. The coin could not be observed since the polarization degree of backscatter is assumed to be zero in Eq.(8), while it is polarized.

Fig.7 Images of polarized target by different methods

We use polarization subtraction method to improve the performance, as shown in Fig.8. Figs.8(a) and 8(b) provide direct imaging and polarization recovery of the target, respectively. Here, the measure of enhancement (EME) is applied to evaluate the image quality[19,25], and it is calculated by

(14)

Fig.8 Comparison of image EME between direct imaging and polarization subtraction imaging

It can be observed from Fig.8 that the EME in Fig.8(a) is larger than that in Fig.8(b). This can be attributed to the superimposition of backscatter on the target signal in direct imaging. When the depth of target varies from 3.251 to 4.933, the EME of the former ranges from 1.832 to 1.260, and the EME of the latter decreases from 3.171 to 2.713. This is because when increasing the depth of underwater target, scattering effect is more serious to degrade image quality. The results shown in Figs. 7(d) and 8(b) demonstrate that polarization subtraction based image recovery rather than conventional method could detect polarized targets in turbid water.

4 Conclusion

In summary, for the purpose of underwater image recovery without scattering background reference, depolarization of the backscatter noise and the target signal is estimated based on polarization subtraction method. The experimental results demonstrate the effectiveness of the proposed method. However, only single type of target is investigated in this paper. More suitable image evaluation parameters need to be employed to assist the polarization subtraction method in detecting multiple targets in the same field of view, which is our next step of work.