数字图像的Riemann-Liouville分数阶微分增强方法  

Riemann-Liouville Fractional Differential Enhancement Method of Digital Image

作　　者：牛为华[1,2] 李宝树[2] 梁贵书[2] 

机构地区：[1]华北电力大学控制与计算机工程学院,保定071003 [2]华北电力大学电气与电子工程学院,保定071003

出　　处：《计算机辅助设计与图形学学报》2014年第12期2189-2195,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：中央高校基本科研业务费专项资金(2014MS133;13MS88)

摘　　要：针对传统图像增强过程中存在丢失细节且容易出现欠增强或过增强的不足,提出一种基于RiemannLiouville分数阶微分的图像增强方法.该方法利用基本分数阶微积分的形式,根据数字图像的自相关性对RiemannLiouville分数阶微分中常数分数阶微分不为0的情况进行改进;定义了新的微分增强模板系数,构造了8个方向的分数阶微分卷积模板,并将其应用于图像增强.实验结果表明,文中方法在对图像高频信息进行提升的同时能够有效地提升图像的中低频信息,使得图像的纹理细节,特别是边缘信息更加突出,图像的清晰度及信息熵等图像质量指标有明显的提高,增强后图像的视觉效果良好.To solve some problems on image enhancement, such as losing details and falling into a sub or over enhancement, a method of image enhancement based on fractional differentiation algorithm is proposed. According to the basic fractional differentiation form and auto-correlation of digital image, the situation is improved that the differentiation of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional differentiation. The method is used to define the coefficients of differentiation enhancement template. Then, a fractional differential convolution template is constructed in 8 directions. Experimental results show that the proposed method can greatly increase high frequency, effectively improve the low frequency, strengthen the textural detail of image and improve the mean value, definition and comentropy of image quality index. The enhanced images have better visual quality.

关 键 词：分数阶微分 改进Riemann-Liouville微分 图像增强 微分卷积模板 边界点 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]