Foggy image enhancement based on adaptive Riesz fractional differential

doi:10.11772/j.issn.1001-9081.2017102480

Abstract

Abstract: In order to improve clarity of foggy images and solve the problem of unicity of fractional order, a new adaptive fractional differential image enhancement method was proposed. Based on an approximate formula of Riesz fractional differential with six order accuracy, a new high precision fractional differential mask:RH operator (Riesz Higher order operator) was constructed, and the IRH operator (Improved Riesz Higher order operator) was proposed by improving RH operator. A fractional differential function was established based on image local features, and a selection criterion of fractional differential order was proposed, and then the adaptive selection method of order point by point was implemented. Combining with IRH operator, an adaptive fractional differential image enhancement algorithm was formed. For color images, due to low independence among components in RGB space, color distortion may occur after enhancement of each channel. Therefore, the image was converted from the RGB space to the HSV space and only the luminance channel was enhanced. A group of foggy images was selected compared with Tiansi operator, the segmentation-based adaptive fractional differential image enhancement algorithm and the adaptive fractional-differential compound bilateral filtering algorithm. The results show that the proposed method has obvious enhancement effect by calculating the information entropy and average gradient in comparison with methods in the reference, which further demonstrates the effectiveness of the proposed algorithm.

Key words: Riesz fractional differential, image enhancement, adaptive fractional order differential, Hue, Saturation, Value (HSV) space, foggy image

摘要： 为了提高雾天图像的清晰度，解决分数阶微分阶数取值的单一性问题，提出了一种新的自适应分数阶微分的图像增强方法。基于具有六阶精度的Riesz分数阶微分的近似计算公式，构造了一种新的高精度分数阶微分掩模——RH算子，并对其进行改进，形成了IRH算子。针对图像局部特征建立了分数阶微分函数，提出了一种分数阶微分选取准则，实现了阶数逐点自适应选取的方法。结合IRH算子，形成了自适应IRH图像增强算法。对于彩色图像，由于RGB空间各通道之间独立性低，对各通道增强后再叠加可能会出现颜色失真，因此将图像由RGB空间转化到HSV空间且只对亮度通道进行增强处理。选择一组雾天图像进行了实验，并与Tiansi算子，基于分割的自适应分数阶微分图像增强算法以及自适应分数阶微分的复合双边滤波算法进行了比较，实验结果表明所提算法具有明显的增强效果，并且通过计算信息熵和平均梯度进一步表明了该算法的有效性。

关键词: Riesz分数阶微分, 图像增强, 自适应分数阶微分, HSV空间, 雾天图像

CLC Number:

TP751.1

LEI Sijia, ZHAO Fengqun. Foggy image enhancement based on adaptive Riesz fractional differential[J]. Journal of Computer Applications, 2018, 38(5): 1427-1431.

雷思佳, 赵凤群. 基于自适应Riesz分数阶微分的雾天图像增强[J]. 计算机应用, 2018, 38(5): 1427-1431.

References

[1] PU Y F, ZHOU J L, YUAN X. Fractional differential mask:a fractional differential based approach for multi-scale texture enhancement[J]. IEEE Transactions on Image Processing, 2010, 19(2):491-511
[2] 陈庆利,黄果,张秀琼,等.数字图像的Caputo分数阶微分增强[J].计算机辅助设计与图形学学报, 2013, 25(4):519-525.(CHEN Q L, HUANG G, ZHANG X Q, et al. A Caputo fractional differential approach to image enhancement[J]. Journal of Computer-Aided Design and Computer Graphics, 2013, 25(4):519-525.)
[3] SAADIA A, RASHDI A. Echocardiography image enhancement using adaptive fractional order derivatives[C]//Proceedings of the 2016 IEEE International Conference on Signal and Image Processing. Piscataway, NJ:IEEE, 2017:166-169.
[4] HEMALATHA S, ANOUNCIA S M. G-L fractional differential operator modified using auto-correlation function:texture enhancement in images[EB/OL].[2017-12-06]. https://doi.org/10.1016/j.asej.2016.12.003.
[5] 姒绍辉,胡伏原,付保川,等.自适应非整数步长的分数阶微分掩模的图像纹理增强算法[J].计算机辅助设计与图形学学报,2014,26(9):1438-1449.(SI S H, HU F Y, FU B C, et al. An algorithm for texture enhancement based on fractional differential mask using adaptive non-integer step[J]. Journal of Computer-Aided Design and Computer Graphics, 2014, 26(9):1438-1449.)
[6] SAADIA A, RASHDI A. Fractional order integration and fuzzy logic based filter for denoising of echocardiographic image[J]. Computer Methods and Programs in Biomedicine, 2016, 137:65-75.
[7] WANG Z, SU J, ZHANG P. Image edge detection algorithm based on wavelet fractional differential theory[C]//Proceedings of the 201635th Chinese Control Conference. Piscataway, NJ:IEEE, 2016:10407-10411.
[8] KHANNA S, CHANDRASEKARAN V. Fractional derivative filter for image contrast enhancement with order prediction[C]//Proceedings of the 2012 IET Conference on Image Processing. Piscataway, NJ:IEEE, 2012:1-6.
[9] SUMAN S, JHA R K. A new technique for image enhancement using digital fractional-order Savitzky-Golay differentiator[J]. Multidimensional Systems and Signal Processing, 2017, 28(2):709-733.
[10] HU F Y, SI S H, WONG H S, et al. An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order[J]. Neurocomputing, 2015, 158(C):295-306.
[11] LI B, XIE W. Adaptive fractional differential approach and its application to medical image enhancement[J]. Computers and Electrical Engineering, 2015, 45(C):324-335.
[12] DING H F, LI C P, CHEN Y Q. High-order algorithms for Riesz derivative and their applications (Ⅱ)[J]. Journal of Computational Physics, 2015, 293(C):218-237.
[13] HACINI M, HACINI A, AKDAG H, et al. A 2D-fractional derivative mask for image feature edge detection[C]//Proceedings of the 2017 International Conference on Advanced Technologies for Signal and Image Processing. Piscataway, NJ:IEEE, 2017:1-6.
[14] CHE J, GUAN Q, WANG X Y. Image denoising based on adaptive fractional partial differential equations[C]//Proceedings of the 20136th International Congress on Image and Signal Processing. Piscataway, NJ:IEEE, 2014:288-292.
[15] SHOURYA S, KUMAR S, JHA R K. Adaptive fractional differential approach to enhance underwater images[C]//Proceedings of the 20166th International Symposium on Embedded Computing and System Design. Piscataway, NJ:IEEE, 2017:56-60.
[16] LI B, XIE W. Image denoising and enhancement based on adaptive fractional calculus of small probability strategy[J]. Neurocomputing, 2016, 175:704-714.
[17] 胡伏原,姒绍辉,张艳宁,等.自适应分数阶微分的复合双边滤波算法[J]. 中国图象图形学报, 2013, 18(10):1237-1246.(HU F Y, SI S H, ZHANG Y N, et al. Multi-bilateral filtering algorithm based on adaptive fractional order differentiation[J]. Journal of Image and Graphics, 2013, 18(10):1237-1246.)