分数阶微积分在图像处理中的应用  

Application of Fractional Calculus to Image Processing

作　　者：周昌雄[1] 颜廷秦[1] 

机构地区：[1]苏州市职业大学电子信息工程学院,江苏苏州215104

出　　处：《苏州市职业大学学报》2014年第1期12-16,共5页Journal of Suzhou Vocational University

基　　金：国家自然科学基金资助项目(60970058);江苏省自然科学基金资助项目(BK2009131);苏州市职业大学创新团队建设项目(3100125);江苏省青蓝工程资助项目

摘　　要：为了增强图像边缘和纹理以及去除图像噪声,讨论分数阶微积分算子频域特性,提出新型的分数阶微积分算子模板和算法.考虑边缘和纹理具有方向性、空间邻域内像素的关联性以及相邻像素灰度值的相近性,利用3×3模板,在分数阶微分增强时,取中心点4个方向最大值为增强值;在分数阶积分去噪时,将图像分别在8个方向卷积,按照在8个方向卷积结果总和中所占的比例大小进行线性加权,从而得到去噪后的图像.实验结果表明,提出的分数阶微积分算子能明显地增强图像的边缘和纹理信息以及去除图像噪声,并且视觉效果明显.In order to improve the ability of image enhancement and denoising,the frequent domain characteristics of fractional calculus are discussed,and some new improved fractional calculus masks and methods are proposed. The edge and texture of images have direction,and there is spatial correlation between the neighbored pixels,so there is the adjacent gray value. When the image is enhanced using 3×3 template of fractional differential operator,the enhancing value,which is maximum value of the four direction values, can be gained. Taking the arithmetic mean of the weighting sum value in 3×3 template as approximate value of denoised image,a novel image denoising approach based on two improved fractional integral masks is also proposed. The experimental results of Lena and Cam era show that the improved method can effectively enhance image edge and texture information and remove noise respectively. Furthermore,its advantages include good visual effects.

关 键 词：分数阶微积分 图像增强 图像去噪 边缘和纹理 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TP391.41[自动化与计算机技术—控制科学与工程]