图像增强中分数阶阶次自适应模型的构造
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摘要
为了解决分数阶微分算子在图像增强中需要人工寻找最佳阶次,缺乏阶次自适应的问题,构造了分数阶微分阶次自适应数学模型。该模型以反正切函数为原型,以图像的梯度信息、局部信息熵、亮度和对比度为自变量,建立了微分阶次与图像局部信息之间的关系,从而可以根据图像的局部信息特征自动计算图像中各个像素点的最佳阶次,并将该模型应用在分数阶微分Tiansi算子的图像增强中。为了验证该模型的有效性,选用标准图像库中的多幅纹理图像进行实验,对实验结果进行了定性和定量分析,在定量分析中采用图像信息熵、平均梯度、清晰度和对比度四个评价指标衡量图像增强的效果,并与二阶微分Laplacian算子、Tiansi算子进行比较。理论分析和实验结果均表明建立该模型的有效性,对灰度图像可以得到连续变化的增强效果,接近于最佳分数阶微分增强效果,符合人们的视觉感受。
It is very ambitious to search the optimal degree of fractional order differential operator manually, lack of order adaptive in image enhancement. In order to tackle this problem, a mathematical model of adaptive degree for fractional order differential operator is presented, which takes the arctangent function as prototype and adopts local image information as independent variables, such as the image gradient information, local information entropy, brightness and contrast.Therefore, the relationship between the optimal degree and local image information can be built up, and the optimal degree at every pixel location can be calculated automatically according to the characteristics of image. And then, the model provided is applied to fractional order differential Tiansi operator in image enhancement. Images from standard library with texture are selected as the object for the experiment to verify the validity of the mode. The experimental results are analyzed qualitatively and quantitatively. In quantitative analysis, image information entropy, image average gradient, image definition and image contrast are selected to evaluate the enhancement effect and comparison results to Laplacian and Tiansi operator are also provided. Theoretical analysis and experimental results have shown that the model presented is effective and the gray image can be enhanced continuously to the optimal level of fractional order differential enhancement effect, satisfying people's visual perception.
It is very ambitious to search the optimal degree of fractional order differential operator manually, lack of order adaptive in image enhancement. In order to tackle this problem, a mathematical model of adaptive degree for fractional order differential operator is presented, which takes the arctangent function as prototype and adopts local image information as independent variables, such as the image gradient information, local information entropy, brightness and contrast.Therefore, the relationship between the optimal degree and local image information can be built up, and the optimal degree at every pixel location can be calculated automatically according to the characteristics of image. And then, the model provided is applied to fractional order differential Tiansi operator in image enhancement. Images from standard library with texture are selected as the object for the experiment to verify the validity of the mode. The experimental results are analyzed qualitatively and quantitatively. In quantitative analysis, image information entropy, image average gradient, image definition and image contrast are selected to evaluate the enhancement effect and comparison results to Laplacian and Tiansi operator are also provided. Theoretical analysis and experimental results have shown that the model presented is effective and the gray image can be enhanced continuously to the optimal level of fractional order differential enhancement effect, satisfying people's visual perception.
引文
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[3]Guillon S,Baylou P,Najim M,et al.Adaptive nonlinear filters for 2D and 3D image enhancement[J].Sjgnal Proeessing,1998,67(3):237-254.
[4]邢世,杨晓东,姜璐,等.薄雾条件下退化图像的直方图均衡模型[J].计算机工程与应用,2016,52(3):211-214.
[5]云海姣,吴志勇,王冠军,等.结合直方图均衡和模糊集理论的红外图像增强[J].计算机辅助设计与图形学学报,2015,27(8):1498-1505.
[6]Gonzalez R C,Woods R E,Eddins S L.数字图像处理[M].阮秋琦,译.3版.北京:电子工业出版社,2011.
[7]黄果,许黎,蒲亦菲.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.
[8]Pu Y F,Zhou J L,Yuan X.Fractional differential mask a fractional differential based approach for multiscale texture enhancement[J].IEEE Transactions on Image Processing,2010,19(2):491-511.
[9]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.
[10]晏祥玉,周激流.分数阶微积分在医学图像处理中的应用[J].成都信息工程学院学报,2008,23(1):39-41.
[11]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像学报,2008,20(3):333-348.
[12]张涌,蒲亦非,周激流.基于分数阶微分的图像增强模板[J].计算机应用研究,2012,29(8):3195-3197.
[13]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.
[14]黄果,陈庆利,许黎,等.可变阶次分数阶微分实验图像自适应增强[J].沈阳工业大学学报,2012,34(4):446-453.
[15]Candan C,Kutay M A,Ozaktas H M.The discrete fractional Fourier transform[J].IEEE Transactions on Signal Processing,2000,48(5):1329-1337.
[16]闫日亮,张会林,黄金钰.基于信息熵和Harris算法的人脸图像质量评价[J].计算机安全,2011(9):11-12.
[17]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.
[18]Yang Z,Lang F,Yu X,et al.The construction of fractional differential gradient operator[J].Journal of Computational Infomation Systems,2011,7(12).
[19]赵青,何建华,温鹏.基于平均梯度和方向对比度的图像融合方法[J].计算机工程与应用,2012,48(24):165-168.