发布时间: 2018-07-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180009 2018 | Volume 23 | Number 7 图像分析和识别

 收稿日期: 2018-01-08; 修回日期: 2018-02-27 基金项目: 国家自然科学基金项目（61573128，61671202）；国家重点研发计划基金项目（2016YFC0401606）；江苏省自然科学基金项目（BK20170305） 第一作者简介: 范新南, 1965年生, 男, 教授, 1987年于河海大学获自动化专业博士学位, 主要研究方向为水下探测与成像、智能感知与信息处理、物联网技术与应用。E-mail:fanxn519@163.com;张学武, 男, 教授, 研究方向为水下探测与成像。E-mail:Lab_112@126.com;史朋飞, 男, 讲师, 研究方向为水下探测与成像。E-mail:shipf@hhu.edu.cn;张卓, 女, 讲师, 研究方向为信息采集与处理。E-mail:zhangz@hhuc.edu.cn. 中图法分类号: TP751.1 文献标识码: A 文章编号: 1006-8961(2018)07-1033-09

# 关键词

Underwater polarized images restoration algorithm based on structural similarity
Fan Xinnan, Chen Jianyue, Zhang Xuewu, Shi Pengfei, Zhang Zhuo
College of Internet of Things Engineering, Hohai University, Changzhou 213022, China
Supported by: National Natural Science Foundation of China (61573128, 61671202)

# Abstract

Objective Numerous restoration algorithms for single images exist. They are remarkable in the defogging of sky images, but most of them cannot be applied directly to the restoration of underwater images. Image restoration aims to process degenerated images to recover the original image (before degeneration). Underwater illumination is insufficient and unevenly distributed, and these light variations affect the results obtained by restoration methods of single images. In general, the results are unsatisfactory. Polarization is the basic feature of light, and the reflected light of underwater objects are mostly partially polarized. Therefore, polarized underwater images have special polarization characteristics, and underwater image restoration based on multiple polarized images has gradually become popular in recent years. Focusing on the mistiness and unobvious details of underwater polarized images, a restoration method for underwater polarized images based on structural similarity is proposed. This method is expected to improve the clarity, contrast, and color fidelity of images. Method First, images taken through a polarizer at orthogonal orientations are obtained. The images have the best and worst backscatters. The water transmittance is only related to the depth of field and the attenuation coefficient of the water body; the object radiance depends on the incident light and the surface characteristics of the object. Therefore, we can assume that they are mutually independent. The structural similarity can measure the similarity of two images from brightness, contrast, and structure and can directly describe the correlation between the two images. Second, on the basis of the irrelevance relationship between the transmittance and the object radiance, the solution formula of water transmittance is derived by the structural similarity. The difference of the two polarized images is also the difference of the background lights in these images. This difference is also the function of depth of field. Thus, the polarized-difference image is used for calculating the initial value of transmittance during the iterative solution. An accurate transmittance is necessary for the good restoration of images. Finally, object radiance is obtained by inversing the underwater polarization imaging model, and color is corrected to produce the restored image. The color correction is based on a single point and chooses the point that has well-kept color information as the reference pixel. Then, the global pixels are normalized by the reference pixel to realize the color correction of the entire image. Result In the experiment, the proposed algorithm is compared with two other polarized restoration algorithms to test its effectiveness, and several groups of underwater polarized images are selected as research objects. The images used in this study were obtained from relevant studies. Quantitative indicators, such as contrast, information entropy, gray mean grads (GMG), peak signal-to-noise ratio (PSNR), measure of enhancement (EME), and runtime, are used for evaluating the effect. Results show that the contrast, information entropy, and GMG of our method are better than those of the two other algorithms. Moreover, a great restoration improvement effect is achieved. The YY algorithm removes the blur of the original images to a certain extent, but certain object areas of the recovered images are supersaturated. The images restored by the Huang algorithm are generally too dark to enable the identification of the scene details due to the inaccurate estimation of the degree of polarization of the object radiance. A comparison of the evaluation parameters shows that the contrast and GMG of our method are twice as high as those of the YY algorithm. Furthermore, the color distribution of the images recovered by our method are more homogeneous than those by YY, thus resulting in sufficient image information and the highest information entropy. The prominent EME also shows that our result has clear texture, high contrast, and good restoration. Certain color channels of the images obtained by the Huang algorithm are not recovered; thus, they have single color tones and the values of several color channels are as low as those of the raw images, thereby resulting in a small mean square error and an extremely high PSNR. In terms of time cost, our method and the Huang algorithm run relatively longer than YY because of the traversal process of the parameters. Conclusion On the basis of the analysis of the underwater polarization imaging model and the statistical independence relationship between the object radiance and water transmittance, image restoration is conducted successfully after the estimation of transmittance. The problems of blurred details and low contrast in polarized underwater images are effectively solved. The results of the subjective and objective analyses show that the proposed algorithm can recover polarized underwater images effectively and obtain restored images with high contrast, obvious details, and rich color. Compared to other algorithms, the proposed algorithm can improve the contrast, clarity, and color balance of polarized underwater images significantly, thus providing an important foundation of underwater target recognition and analysis.

# Key words

underwater polarization imaging; image restoration; structural similarity; transmittance; image processing

# 1.1 水下偏振成像模型

 ${I_{\max }} + {I_{\min }} = S + B = J \cdot t + F + B$ (1)

 $\begin{array}{l} {I_{{\rm{total}}}}\left( {x, y} \right) = {I_{\max }}\left( {x, y} \right) + {I_{\min }}\left( {x, y} \right) = \\ \;\;J\left( {x, y} \right)t\left( {x, y} \right) + {B_\infty }\left( {1-t\left( {x, y} \right)} \right) \end{array}$ (3)

# 1.2 水体透射率估计

 $S\left( {t, J} \right) = 0$ (7)

 $\left\{ \begin{array}{l} 2{\mu _t}{\mu _J} + {C_1} = 0\;\;\;\;\;或\;\;\;\;\;\;\;\;\;\;\left( 8 \right)\\ 2{\sigma _{t, J}} + {C_2} = 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( 9 \right) \end{array} \right.$

 ${\sigma _{t, J}} =-\frac{{{C_2}}}{2}$ (10)

 ${\sigma _{t, J}} = \mu \left( {t \cdot J} \right)-\mu \left( t \right) \cdot \mu \left( J \right)$ (11)

$\mu \left( \cdot \right)$表示均值。根据式(2)(3)，透射率和目标反射光可分别表示为

 $t\left( {x, y} \right) = 1-\frac{{B\left( {x, y} \right)}}{{{B_\infty }}}$ (12)

 $J\left( {x, y} \right) = \frac{{{I_{{\rm{total}}}}\left( {x, y} \right)-{B_\infty }}}{{t\left( {x, y} \right)}} + {B_\infty }$ (13)

 $\begin{array}{l} \mu \left( {t\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{t\left( {x, y} \right)}}} \right) = \\ 1- \frac{1}{2}{C_2}{\left[{{B_\infty }-{I_{{\rm{total}}}}\left( {x, y} \right)} \right]^{ -1}} \end{array}$ (14)

 $\begin{array}{l} t\left( {x, y} \right) = \\ \mathop {\arg \min }\limits_{0 \le {t_0}\left( {x, y} \right) \le 1} \left( \begin{array}{l} \left| {\mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right) + } \right.\\ \left. {\frac{1}{2}{C_2}{{\left( {{B_\infty }-{I_{{\rm{total}}}}\left( {x, y} \right)} \right)}^{-1}}} \right| \end{array} \right) \end{array}$ (18)

# 1.3 图像复原

 $\begin{array}{l} J\left( {x, y} \right) = \\ \frac{{\left( {{I_{\max }}\left( {x, y} \right) + {I_{\min }}\left( {x, y} \right)} \right)-{B_\infty }}}{{t\left( {x, y} \right)}} + {B_\infty } \end{array}$ (19)

1) 根据两幅偏振图像的差分$\Delta I$计算透射率图的初始值${t_0}\left( {x, y} \right)$

2) 估计透射率。对于在总光强图像${I_{{\rm{total}}}}$的每个像素点：

(1) 在高斯加权窗口内计算透射率图初始值对应像素的均值$\mu \left( {{t_0}\left( {x, y} \right)} \right)$$\mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right) (2) 将两均值代入关系式(13)进行验证： \left| \begin{array}{l} \mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right)-\\ {\left( {1-\frac{1}{2}{C_2}\left( {{B_\infty }-{I_{{\rm{total}}}}\left( {x, y} \right)} \right.} \right)^{ - 1}} \end{array} \right| \le 0.05，则令t\left( {x, y} \right) = {t_0}\left( {x, y} \right)，窗口滑至下一像素；否则，若  \begin{array}{l} \mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right) > \\ 1-\frac{1}{2}{C_2}{\left( {{B_\infty }-{I_{{\rm{total}}}}\left( {x, y} \right)} \right)^{-1}} \end{array} 则以步长0.01遍历{t_0}\left( {x, y} \right) \to 1, 重复第(1)歩；否则，若  \begin{array}{l} \mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right) < \\ 1-\frac{1}{2}{C_2}{\left( {_\infty ^B-{I_{{\rm{total}}}}\left( {x, y} \right)} \right)^{-1}} \end{array} 则以步长0.01遍历{t_0}\left( {x, y} \right) \to 0, 重复第(1)歩；否则，令  t\left( {x, y} \right) = \mathop {\arg \;\min }\limits_{0 \le {t_0}\left( {x, y} \right) \le 1} \left| {\begin{array}{*{20}{l}} {\mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right) + }\\ {\frac{1}{2}{C_2}{{\left( {{B_\infty }-{I_{{\rm{total}}}}\left( {x, y} \right)} \right)}^{-1}}-1} \end{array}} \right| 即当{t_0}\left( {x, y} \right) \ge 1$${t_0}\left( {x, y} \right) \le 0$，取令上式最小的${t_0}\left( {x, y} \right)$为输出。窗口滑至下一像素。

3) 利用估计出的水体透射率计算全局SSIM验证式(14)，若偏差大于0.05，则令${t_0}\left( {x, y} \right) = t\left( {x, y} \right)$，重复第2)步。

4) 根据式(19)计算目标反射光。

5) 颜色校正得到复原图像。

# 2 实验结果分析

Table 1 Comparison of experimental results

 图像 算法 参数 C H GMG PSNR/dB EME 时间/s 图像1 YY 0.13 6.87 0.012 28.90 1.95 2.97 Huang 0.14 6.84 0.016 39.52 2.40 314.84 本文 0.32 7.45 0.031 28.33 6.51 6.20 图像2 YY 0.18 7.44 0.010 25.29 1.87 2.45 Huang 0.17 7.25 0.025 28.48 3.61 186.43 本文 0.27 7.66 0.028 25.75 3.98 5.66 图像3 YY 0.20 15.11 0.010 6.61 1.92 3.35 Huang 0.27 13.09 0.014 18.87 2.79 629.18 本文 0.32 15.44 0.025 10.64 5.40 8.87 注：加粗字体为最优结果。

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