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发布时间: 2018-07-16
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DOI: 10.11834/jig.180009
2018 | Volume 23 | Number 7




    图像分析和识别    




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结构相似性的水下偏振图像复原
expand article info 范新南, 陈建跃, 张学武, 史朋飞, 张卓
河海大学物联网工程学院, 常州 213022

摘要

目的 针对水下偏振图像存在雾状模糊和场景细节不明显的问题,以水体透射率图与目标反射光图像存在的相互独立性为基础,提出一种基于结构相似性的水下偏振图像复原方法,旨在提高水下偏振图像的清晰度、对比度和色彩真实度。方法 首先,获取同一水下场景下具有正交偏振方向且分别具有最大和最小光强的两幅偏振图像;然后根据透射率图与目标反射光之间的统计无关性,使用结构相似性推导求解透射率的关系式,并通过偏振差分图像计算透射率的初始值,利用该关系式进行水体透射率的迭代求解;最后将透射率代入偏振成像模型得到目标反射光图像,进而进行颜色校正得到复原图像。结果 选取多组正交的水下偏振图像作为研究对象,采用本文提出的方法与另两种偏振复原算法对其进行复原处理,使用对比度、信息熵、灰度平均梯度、峰值信噪比、增强量以及时间等量化指标进行评估。对比实验结果表明,本文算法在对比度、信息熵、灰度平均梯度、增强量以及颜色恢复上都优于另两种偏振图像复原方法,并有较大幅度的提高;灰度平均梯度和对比度较YY算法提高了一倍左右;本文复原图像的色彩分布较均匀使得图像的信息含量大,信息熵高;而突出的EME也证明本文算法的结果纹理清晰、对比度高以及图像复原程度好;提出算法的复原效果有显著的改善,但算法运行时间较长,实时性有待提高。结论 本文基于水下偏振成像模型的分析以及透射率图与目标反射光图像之间的统计无关性,从水体透射率的估计出发进行图像复原,有效地解决了水下偏振图像细节模糊、对比度低的问题。通过对算法实验效果的主客观分析表明,本文算法能有效地复原水下偏振图像,得到对比度高、细节明显和色彩丰富的恢复图像。

关键词

水下偏振成像; 图像复原; 结构相似性; 透射率; 图像处理

Underwater polarized images restoration algorithm based on structural similarity
expand article info 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

0 引言

随着水下成像设备的发展,人们越来越重视水下清晰图像的获取。水下光线不足,通过单幅图像复原得到的结果会受到光线变化的影响,效果并不理想。偏振是光的基本特征,由于目标的反射光都表现为部分偏振光,近年来,基于多幅偏振图像的图像复原逐渐成为了研究热点。自Stokes参量、Mie散射和米勒矩阵等基础偏振理论提出以来,国内偏振技术研究已开展多年,安徽光机所、北京理工大学和西北工业大学等机构[1-7]在大气云层和复杂水体等散射介质中的应用、对偏振差分图像以及红外偏振成像等方面进行了深入的研究[8]。国外对偏振成像技术应用于图像处理上的研究[9-12]主要体现在应用线偏振和圆偏振技术减小介质中悬浮颗粒的后向散射影响,减小光学偏振成像的干扰因素;以及通过直接对偏振图像进行增强或融合,增强对目标的感知和识别能力。

针对偏振图像在存在的问题,研究人员提出了许多解决方法。曹念文等人[4]阐述了成像距离、水下成像清晰度与偏振成像的关系,并定量地说明偏振技术可以提高水下偏振图像的清晰度和成像距离。都安平等人[1]根据不同导电特性的表面对入射光偏振态的不同反射特性,提出了一种算法对偏振角、偏振度和Stokes图像进行基于能量特征的融合,实现对偏振图像的增强。Schechner等人[12]利用自主研发的Aqua-Polaricam水下偏振成像系统,对拍摄得到的水下偏振图像进行复原,显著提高了图像的对比度和色彩效果,但论文中存在许多不合理的假设。Huang等人[13]基于文献[12],考虑到目标反射光偏振特性,提出了基于目标偏振差分估计的图像恢复算法。该方法能有效地恢复出光照补偿下的水中人造物体的反射光,提高水下图像的质量。周明[14]根据偏振成像模型提出了一种分离目标偏振度与大气光偏振度的方法,得到传输图并有效地恢复天空有雾图像。目前,大部分偏振图像处理算法研究都集中于对图像偏振度的求取,再根据偏振度与成像模型复原图像。

本文基于对上述文献的综合分析与思考,提出了一种基于结构相似性的水下偏振图像复原方法。首先,获取两幅偏振化方向互相垂直的水下偏振图像;然后根据透射率图与目标反射光之间的统计无关性,由结构相似性推导出求解透射率的关系式,并使用偏振差分图像计算透射率的初始值,通过关系式得到透射率图;最后根据偏振成像模型得到目标反射光图像,并进行颜色校正后得到最终复原图像。实验结果表明,本文算法能够解决水下偏振图像细节模糊、颜色失真的问题,极大程度地提高了图像的对比度。

1 算法原理

1.1 水下偏振成像模型

根据相关文献[12]的描述,水下相机接收到的光可表示为

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

式中,${I_{\min }}\left( {x, y} \right)$${I_{\max }}\left( {x, y} \right)$是水下相机获取的两幅偏振方向互相垂直且分别具有最小和最大亮度的偏振图像。$B$为环境光被微粒散射后形成的背景光,$S$是目标信息光,其又由目标反射光的直接分量$D$与目标反射光的前向散射分量$F$构成。$D$可表示为目标反射光$J$与透射率$t$的乘积。水下偏振成像模型如图 1所示。

图 1 水下偏振成像模型
Fig. 1 Underwater polarization imaging model

在水下图像去模糊时,相较于背景光所产生的模糊效应,大量文献[12-13, 15-18]普遍认为$F$的作用可忽略不计。背景光来源于周围环境光的散射,背景光$B$可表示为

$ \begin{array}{l} B\left( {x, y} \right) = {B_\infty }\left( {1-t\left( {x, y} \right)} \right) = \\ \;\;\;\;{B_\infty }\left( {1-{{\rm{e}}^{-cd\left( {x, y} \right)}}} \right) \end{array} $ (2)

式中,${B_\infty }$为全局背景光,$c$是水体衰减系数,是水体内在参数,$d(x, y)$是景物与成像设备的距离,$t(x, y)$为水体透射率,是$c$$d(x, y)$的函数。可以看出背景光与目标的距离有关,目标距离越远,背景光越大。

若忽略前向散射的影响,则我们获取到的水下总光强图像${I_{{\rm{total}}}}\left( {x, y} \right)$可写成

$ \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)

水下复原的主要任务就是从偏振图像${I_{\max }}\left( {x, y} \right)$${I_{\min }}\left( {x, y} \right)$中恢复出目标反射光$J(x, y)$,即需要根据偏振图像估计全局背景光和水体透射率。

水下自然物体粗糙的表面导致其对自然光的解偏振度程度低;再者,由于随着景物距离的增加,水体的散射作用增强,导致水下相机捕获的图像目标反射光成份降低而背景光占比提高;所以,目标反射光中偏振光的含量很少,一般可以忽略目标反射光对偏振成像产生的影响[12],根据自然光的偏振规律,可认为两个偏振角度获取的目标反射光是无差别的,则相机获取的图像表示为

$ \left\{ \begin{array}{l} {I_{\min }} = \frac{S}{2} + {B_{\min }}\\ {I_{\max }} = \frac{S}{2} + {B_{\max }} \end{array} \right. $ (4)

式中,${B_{\min }}$${B_{\max }}$分别为两幅正交偏振图像中的背景光。

1.2 水体透射率估计

由于透射率$t(x, y)$只与场景深度$d(x, y)$、水体的衰减系数$c$相关,而目标反射光$J(x, y)$取决于目标物体的表面特性和入射光,结合文献[19-20],因此客观上可认为$t(x, y)$$J(x, y)$是统计无关的。文中使用结构相似性来表征两者的无关性。

结构相似性(SSIM)从亮度、对比度和结构来衡量两幅图像相似度,能够直观的描述两幅图像之间的相关性[21-22]。由于图像场景中的物体具有独立的结构和照度,通过分离照度对物体的影响可以获取图像中的结构信息。文中使用亮度和对比度来定义图像的结构信息,通过分别对场景中变化的亮度与对比度进行局部处理来得到更精确的结果。SSIM测量系统如图 2所示,系统由亮度、结构和对比度3个对比模块构成。亮度对比函数$l(t, J)$是两幅图像均值${\mu _t}$${\mu _J}$的函数,对比度对比函数$c(t, J)$是两幅图像标准差${\sigma _t}$${\sigma _J}$的函数,而结构对比函数$s(t, J)$与两幅图像的协方差${\sigma _{t, J}}$有关。将这3个函数组合,得到透射率与目标反射光的SSIM函数

图 2 结构相似性测量系统
Fig. 2 The measure system of SSIM

$ S\left( {t, J} \right) = l{\left( {t, J} \right)^\alpha }c{\left( {t, J} \right)^\beta }s{\left( {t, J} \right)^\gamma } $ (5)

式中,$t$表示$t(x, y)$$J$表示$J(x, y)$$\alpha, \beta, \gamma > 0$,用于对模块的权重进行调整。为了简化函数形式,一般令$\alpha = \beta = \gamma = 1$,则可得到函数形式为

$ S\left( {t, J} \right) = \frac{{\left( {2{\mu _t}{\mu _J} + {C_1}} \right)\left( {2{\sigma _{t, J}} + {C_2}} \right)}}{{\left( {\mu _t^2 + \mu _J^2 + {C_1}} \right)\left( {\sigma _t^2 + \sigma _J^2 + {C_2}} \right)}} $ (6)

式中,常数$C_1$是为了避免当$\mu _t^2 + \mu _J^2$趋近于0时造成系统不稳定。一般地,${C_1} = {\left( {{K_1}L} \right)^2}$$L$为图像灰度级数,对于一幅8位颜色深度的图像,$L$=256, 系数${K_1} \ll 1$,一般取0.01。常数${C_2} = {\left( {{K_2}L} \right)^2}$,且系数${K_2} \ll 1$,一般取0.03。根据透射率和目标反射光之间的不相关性,两者的结构相似性应为零,即

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

代入式(6)可得出$t$应满足

$ \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. $

由于对于一幅正常的彩色图像,其均值不会小于零,故式(8)不满足,所以$t$应满足

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

式中,协方差为

$ {\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)

将其代入式(10),并根据协方差计算公式与均值的性质可得透射率应满足

$ \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)

式中,全局背景光${B_\infty }$可由${I_{\max }}\left( {x, y} \right)$${I_{\min }}\left( {x, y} \right)$在同一位置的一个没有前景目标的背景区域内计算得到,具体做法为:分别在两幅偏振图像中选取无穷远处没有目标的同一背景区域Ω,然后在该区域内计算像素的亮度平均值,即

$ {B_\infty } = \mathop {{\rm{mean}}}\limits_\Omega \left( {I_{\max }^\Omega \left( {x, y} \right) + I_{\min }^\Omega \left( {x, y} \right)} \right) $ (15)

由于透射率$t(x, y)$与距离和光的波长相关,距离越大,透射率越小。而背景光会随着距离增加而增大,且两幅偏振图像中目标反射光部分是相同的,根据式(4),两幅偏振图像的差分$\Delta I\left( {x, y} \right) = {I_{\max }}\left( {x, y} \right)-{I_{\min }}\left( {x, y} \right)$即为背景光的差分,其还是距离的函数。故文中采用$\Delta I\left( {x, y} \right)$作为参考,将透射率的初始值表示为

$ {t_0}\left( {x, y} \right) = {{\rm{e}}^{-\varepsilon \Delta I\left( {x, y} \right)}} $ (16)

式中,$\varepsilon $为水体衰减系数的模拟值。在水中光的波长越长传输性能越差,考虑红绿蓝3种颜色光的波长分别为700 nm、546.1 nm、435.8 nm,取波长参数$\lambda $=(0.700, 0.546, 0.436),并令$\varepsilon = k \cdot \lambda $

对于调整参数$k$的选取,如图 3所示,其中横坐标表示$k$值变化,纵坐标为对应图像的信息熵;当$k$取0.25时,复原图像的信息熵$H$达到最大,所以在各颜色通道取$\varepsilon $=(0.36, 0.46, 0.57)时,可以得到较好的实验结果。然后将初始值代入式(14)进行迭代计算透射率。

图 3 最佳$k$值的选取
Fig. 3 Selection of the best $k$ value

由于图像的统计特征在空间中分布并不均匀以及在正常视距内,图像的模糊程度在空间中也是变化的,人眼视线的焦点通常只在图像的一个区域内,所以文中采用在局部计算SSIM指数,更符合人类视觉系统的特点,所有的处理过程都在一个个局部窗口内完成。文中首先定义一个宽度为$n \times n$的对称高斯加权函数$W = \left\{ {{\omega _i}|i = 1, 2, \cdots, N} \right\}$描述的加权窗口,用这个窗口逐像素地遍历整幅总图像。窗口内均值的计算为

$ \mu \left( {t\left( {\mathop x\limits_W, y} \right)} \right) = \sum\limits_{i = 1}^N {{\omega _i}{t_w}\left( i \right)} $ (17)

式中,$N$是窗口内像素个数,$\sum\limits_{i = 1}^N {{\omega _i} = 1} $。对于图像${I_{{\rm{total}}}}\left( {x, y} \right)$的每个像素点,用该公式在窗口内计算$\mu \left( {{t_0}\left( {x, y} \right)} \right), \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right)$,代入式(14)中验证,若等式(13)两边误差较小则取当前值为透射率$t(x, y)$在该像素点的值。由于$0 < t\left( {x, y} \right) < 1$,而局部窗口的$\mu \left( {{t_0}\left( {x, y} \right)} \right) \cdot \mu \left( {\frac{1}{{{t_0}\left( {x, y} \right)}}} \right)$${t_0}\left( {x, y} \right) \in \left( {0, 1} \right)$内是递减的,所以,若等式(13)左边较大,则将${t_0}$从当前值以步长0.01向上至1遍历;若等式(13)左边较小,则从当前值以步长0.01向下至0遍历;重新计算两个均值,代入等式比较,直到等式左右两边的误差小于0.05。若在(0, 1)范围内不存在令等式(14)近似成立的${t_0}\left( {x, y} \right)$,则令

$ \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)

即,取令上式最小的${t_0}\left( {x, y} \right)$为该点的透射率值。在遍历完整幅图像后,使用全局的SSIM指数进行验证,若对于全局的透射率,式(13)两边的误差小于0.05,则将$t(x, y)$作为输出结果,否则,令透射率的初值${t_0}\left( {x, y} \right) = t\left( {x, y} \right)$,重复上述步骤。

1.3 图像复原

在得到了精确的透射率图$t(x, y)$后,通过水下偏振成像模型得到目标反射光图像为

$ \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)

最后经过颜色校正得到最终复原结果。本文采用单点白平衡方法[12]对复原图像进行颜色校正,使算法结果更接近景物原有色彩。单点白平衡法的基本思想是:将图像中色彩信息保留较好的像素点作为参考,对全局像素归一化计算,实现整个图像的色彩校正。文中选取近景区域颜色失真较小的浅白色物体作为参考。整体算法如下:

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

为了验证本文复原算法的有效性,选择3组模糊的水下偏振图像进行复原实验,原图如图 4(a)(b)所示,原图来源于文献[10, 12]。实验结果如图 4所示。实验中,使用大小为11×11像素的高斯加权窗口计算SSIM,使用Matlab软件在配置有Windows 7系统、2.3 GHz Intel I3处理器的计算机上进行仿真。

图 4 实验结果对比
Fig. 4 Comparison of the experimental results
((a) ${I_{\max }}$; (b) ${I_{\min }}$; (c) YY; (d) Huang[13]; (e) ours)

图 4 (a)(b)的图像1—图像3分别为具有最大和最小亮度的偏振图像。各组图像中图 4(c)为YY算法[12]的复原结果,可以看出其在一定程度上去除了原图像的模糊,但在一些区域存在过饱和现象。图 4(d)为Huang算法[13]的复原结果,由于该算法目标反射光偏振度估计不精确导致图像总体偏暗。图 4(e)为本文算法的实验结果,可以看出本文算法能更好地对水下偏振图像进行去模糊和颜色校正,输出图像在对比度、清晰度和色彩恢复上都有较大的改善。

为了进一步说明复原效果,对实验结果进行客观评价,使用对比度$C$[12]、信息熵$H$、灰度平均梯度GMG、峰值信噪比PSNR、增强量EME[13]以及程序运行时间来评估3种复原算法的优劣。比较结果如表 1所示。从表 1中可以看出,本文算法在对比度、信息熵、灰度平均梯度以及增强量上都优于其他两种偏振图像复原方法,并有较大幅度的提高。灰度平均梯度和对比度较YY算法提高了一倍左右;本文复原图像的色彩分布较均匀使得图像的信息含量大,信息熵高;而突出的EME也证明本文算法的结果纹理清晰、对比度高以及图像复原程度好。由于Huang算法得到的图像在某些颜色通道上没有得到修复,色调单一,与原图都具有较低的数值,所以其均方误差小,峰值信噪比偏大。且PSNR并未考虑到人眼视觉系统的特性(人眼对亮度对比差异的敏感度高于色度、对低频的对比差异敏感度相对较高以及周围邻近区域会影响人眼对一个区域的感知结果等),故经常出现参数评价结果与人的主观评价不一致的情况。在算法的时间开销上,由于本文算法与Huang算法都涉及到参数遍历过程,算法运行时间较长。总体相比之下,本文算法的复原效果最优。

表 1 实验结果参数对比
Table 1 Comparison of experimental results

下载CSV
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。

本文算法从透射率图与目标反射光之间的不相关性出发,利用结构相似性合理地推导出计算水体透射率的公式,定量地估计透射率;文中不直接求取偏振度,而利用偏振差分图像来间接的计算透射率,避免了差分图像对偏振度的估计不准确导致复原失效的问题,减少处理过程中噪声。相比其他两种算法,得到的复原图像各项指标良好、对比度较高、色彩较均衡。但是算法对原图像的获取要求较高,否则在图像差分时容易产生噪声。且存在对参数迭代过程,运行时间有待改善。

3 结论

本文基于对水下偏振成像模型的分析,结合透射率图与目标反射光之间的统计无关性,使用偏振差分图像计算透射率初始值,通过迭代计算结构相似性推演的关系式得到水体透射率,然后反推偏振成像模型得到目标反射光图像,有效地解决了水下偏振图像细节模糊、对比度低的问题。算法最后对目标反射光进行颜色校正得到最终复原图像,去除了原图像的颜色失真。同时,因为算法不计算偏振度,可以有效地减少图像矩阵处理过程中产生的噪声。实验结果表明,相比于YY、Huang两种算法,本文算法能够更大程度地提高水下偏振图像的对比度、清晰度和色彩均衡性,为水下目标的识别和分析提供了重要的基础。

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