Li Shuai, Wang Weiming, Liu Xianhong, et al. Image enhancement of adaptive fractional operator[J]. Opto-Electronic Engineering, 2019, 46(9): 180517. doi: 10.12086/oee.2019.180517
Citation: Li Shuai, Wang Weiming, Liu Xianhong, et al. Image enhancement of adaptive fractional operator[J]. Opto-Electronic Engineering, 2019, 46(9): 180517. doi: 10.12086/oee.2019.180517

Image enhancement of adaptive fractional operator

    Fund Project: Supported by National Natural Science Foundation of China (11372199) and Natural Science Foundation of Hebei (E2016210104)
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  • In order to highlight the texture details of the image while preserving the smooth region and saving the time to determine the fractional differential order, an improved adaptive fractional differential operator is proposed. Firstly, the classical Tiansi template is decomposed into four different directions, which are respectively convolved with the pixels to be processed to achieve the effect of enhancing the texture details of the image. Secondly, the current situation of the optimal differential order is determined by the experiment for the Tiansi operator. The local feature information of the image constructs a fractional order model with an adaptive ability, which can obtain more detailed information than the original image. The experimental results of multiple sets of different scene images show that the constructed adaptive fractional differential operators effectively enhance the texture details of the image. The subjective visual effects and objective evaluation indexes of the adaptive fractional differential operators are better than the original images. The average gradient, information entropy and contrast in the objective evaluation index are increased by 190.3%, 8.1%, and 18.3%, respectively. The average gradient and contrast are 45.0% and 9.6% higher than that of the Tiansi operator.
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  • [1] Svoboda T, Kybic J, Hlavac V. Image Processing, Analysis & and Machine Vision: A MATLAB Companion[M]. CL-Engineering, 2007: 712-717.

    Google Scholar

    [2] 周尚波, 王李平, 尹学辉.分数阶偏微分方程在图像处理中的应用[J].计算机应用, 2017, 37(2): 546-552.

    Google Scholar

    Zhou S B, Wang L P, Yin X H. Applications of fractional partial differential equations in image processing[J]. Journal of Computer Applications, 2017, 37(2): 546-552.

    Google Scholar

    [3] Gao R, Gu C, Li X. Image zooming model based on fractional-order partial differential equation[J]. Journal of Discrete Mathematical Sciences and Cryptography, 2017, 20(1): 55-63. doi: 10.1080/09720529.2016.1178901

    CrossRef Google Scholar

    [4] 黄果, 陈庆利, 许黎, 等.可变阶次分数阶微分实现图像自适应增强[J].沈阳工业大学学报, 2012, 34(4): 446-454.

    Google Scholar

    Huang G, Chen Q L, Xu L, et al. Realization of adaptive image enhancement with variable fractional order differentials[J]. Journal of Shenyang University of Technology, 2012, 34(4): 446-454.

    Google Scholar

    [5] 蒲亦非.将分数阶微分演算引入数字图像处理[J].四川大学学报(工程科学版), 2007, 39(3): 124-132. doi: 10.3969/j.issn.1009-3087.2007.03.023

    CrossRef Google Scholar

    Pu Y F. Application of fractional differential approach to digital image processing[J]. Journal of Sichuan University (Engineering Science Edition), 2007, 39(3): 124-132. doi: 10.3969/j.issn.1009-3087.2007.03.023

    CrossRef Google Scholar

    [6] Pu Y F, Siarry P, Chatterjee A, et al. A fractional-order variational framework for retinex: fractional-order partial differential equation-based formulation for multi-scale nonlocal contrast enhancement with texture preserving[J]. IEEE Transactions on Image Processing, 2018, 27(3): 1214-1229. doi: 10.1109/TIP.2017.2779601

    CrossRef Google Scholar

    [7] 张绍阳, 解源源, 张鑫, 等.基于分数阶微分的模糊交通视频图像增强[J].光学精密工程, 2014, 22(3): 779-786.

    Google Scholar

    Zhang S Y, Xie Y Y, Zhang X, et al. Enhancement of fuzzy traffic video images based on fractional differential[J]. Optics and Precision Engineering, 2014, 22(3): 779-786.

    Google Scholar

    [8] 汪成亮, 兰利彬, 周尚波.自适应分数阶微分在图像纹理增强中的应用[J].重庆大学学报, 2011, 34(2): 32-37.

    Google Scholar

    Wang C L, Lan L B, Zhou S B. Adaptive fractional differential and its application to image texture enhancement[J]. Journal of Chongqing University, 2011, 34(2): 32-37.

    Google Scholar

    [9] 杨柱中, 周激流, 晏祥玉, 等.基于分数阶微分的图像增强[J].计算机辅助设计与图形学学报, 2008, 20(3): 343-348.

    Google Scholar

    Yang Z Z, Zhou J L, Yu X Y, et al. Image enhancement based on fractional differentials[J]. Journal of Computer-Aided Design & Computer Graphics, 2008, 20(3): 343-348.

    Google Scholar

    [10] 黄果, 许黎, 蒲亦非.分数阶微积分在图像处理中的研究综述[J].计算机应用研究, 2012, 29(2): 414-420, 426. doi: 10.3969/j.issn.1001-3695.2012.02.003

    CrossRef Google Scholar

    Huang G, Xu L, Pu Y F. Summary of research on image processing using fractional calculus[J]. Journal of Computer Applications, 2012, 29(2): 414-420, 426. doi: 10.3969/j.issn.1001-3695.2012.02.003

    CrossRef Google Scholar

    [11] Ma Q T, Dong F F, Kong D X. A fractional differential fidelity-based PDE model for image denoising[J]. Machine Vision and Applications, 2017, 28(5-6): 635-647. doi: 10.1007/s00138-017-0857-z

    CrossRef Google Scholar

    [12] Pu Y F, Wang W X, Zhou J L, et al. Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation[J]. Science in China Series F: Information Sciences, 2008, 51(9): 1319-1339. doi: 10.1007/s11432-008-0098-x

    CrossRef Google Scholar

    [13] 余萍, 郝成成.基于分数阶微分和多尺度Retinex联合的雾霭图像增强算法[J].激光与光电子学进展, 2018, 55(1): 272-277.

    Google Scholar

    Yu P, Hao C C. Foggy image enhancement by combined fractional differential and multi-scale retinex[J]. Advances in Laser and Optoelectronics, 2018, 55(1): 272-277.

    Google Scholar

    [14] Pu Y F. Fractional-order euler-Lagrange equation for fractional-order variational method: A necessary condition for fractional-order fixed boundary optimization problems in signal processing and image processing[J]. IEEE Access, 2016, 4: 10110-10135. doi: 10.1109/ACCESS.2016.2636159

    CrossRef Google Scholar

    [15] 吴瑞芳, 宣士斌, 荆奇.基于局部特征的分数阶微分图像增强方法[J].计算机工程与应用, 2014, 50(3): 160-164. doi: 10.3778/j.issn.1002-8331.1203-0619

    CrossRef Google Scholar

    Wu R F, Xuan S B, Jing Q. Fractional differential image enhancement algorithm based on local feature[J]. Computer Engineering and Applications, 2014, 50(3): 160-164. doi: 10.3778/j.issn.1002-8331.1203-0619

    CrossRef Google Scholar

    [16] Wang Z, Bovik A C, Sheikh H R, et al. Image quality assessment: from error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612. doi: 10.1109/TIP.2003.819861

    CrossRef Google Scholar

  • Overview: Image processing technology has become increasingly prominent in the fields of intelligent transportation and video surveillance. Visibility is relatively low in foggy weather and nighttime scenes, and images collected by equipment often have severe degradation and distortion. Therefore, it is especially important to study how to improve the quality of video images in bad weather. In the image enhancement processing, in order to improve the visual effect of the image, it is desirable that the high-frequency component of the image can be enhanced to highlight the texture information of the image while further smoothing the low-frequency component of the image. The linear transformation of the image has the advantage of smoothing the low-frequency components of the image, but such a method retains too little high-frequency components to achieve the desired effect. When the image is averaged or integrated, blurring occurs. In order to make the edge contour extending in any direction in the image clearer, the image can be inversely operated, such as differential operation. The first-order differential gradient operator and the second-order differential Laplacian operator have the advantage of not only enhancing high-frequency components of the image and highlighting texture information in the image, but also increasing the image noise. The traditional image enhancement processing can not solve the contradiction of removing image noise while enhancing the texture details of the image.

    In recent years, fractional calculus has made breakthroughs in many fields. It has been found that fractional differential operators have the property of weak derivatives, and more and more people apply them to the field of image processing. In order to highlight the texture details of the image while preserving the smooth region and saving the time to determine the fractional differential order, an improved adaptive fractional differential operator is proposed. Firstly, the classical Tiansi template is decomposed into four different directions, which are respectively convolved with the pixels to be processed to achieve the effect of enhancing the texture details of the image. Secondly, the current situation of the optimal differential order is determined by the experiment for the Tiansi operator. The local feature information of the image constructs a fractional order model with an adaptive ability, which can obtain more detailed information than the original image. The experimental results of multiple sets of different scene images show that the constructed adaptive fractional differential operators effectively enhance the texture details of the image. The subjective visual effects and objective evaluation indexes of the adaptive fractional differential operators are better than the original images. The average gradient, information entropy and contrast in the objective evaluation index are increased by 190.3%, 8.1%, and 18.3%, respectively. The average gradient and contrast are 45.0% and 9.6% higher than that of the Tiansi operator.

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