基于分数阶微分的图像增强

Image Enhancement Based on Fractional Differentials

通过理论分析得出分数阶微分可以大幅提升信号高频成分,增强信号的中频成分、非线性保留信号的甚低频,据此得出分数阶微分应用于图像增强将使图像边缘明显突出、纹理更加清晰和图像平滑区域信息得以保留的增强图像;然后由经典的分数阶微分定义出发,推导出了分数阶差分方程,构建了近似的Tiansi微分算子.通过图像增强的实验表明:采用基于分数阶微分算子的图像增强方法,其增强图像的视觉效果明显优于传统的微分锐化(整数微分)方法.文中方法为拓展分数阶微分的应用领域进行了有意义的探索.

The theoretical analysis shows that fractional differentials can greatly increase high frequency, reinforce medium frequency and non-linearly preserve low frequency of signals, hence they could be used for edge and texture enhancement as well as smooth area preservation. In this work, from classical fractional differential G-L definition, fractional order differential difference function is derived and an approximate fractional order differential Tiansi module is constructed. Experimental results show that image enhancement methods based on fractional differential are markedly superior to those based on integer differential in visual effects.