非整数步长的分数阶微分滤波器在图像增强中的应用

Application of Non-integer Step and Fractional Order Differential Filter in the Image Enhancement

为了改善图像增强的效果,根据图像具有高度自相关性的特性(越接近目标像素的像素点其两者的相似性越高),构造了基于非整数步长的分数阶微分滤波器,打破了Grümwald-Letnikov定义中分数阶微分数值计算取单位步长的思想,即在传统的分数阶微分的基础上再增加一个自由度参量步长。在一定范围内适当调节v和n的大小来构造相应的掩模算子,并利用线性加权的拉格朗日多项式的分段插值方法来确定非整数步长像素点的灰度值,在一定程度上起到降噪的作用。实验结果表明,提出的方法在增强图像细节和抗噪方面取得了较好的平衡点。

In order to improve the effect of image enhancement,the fractional order differential filter based on non-integer step was constructed according to the image with the characteristics of high autocorrelation,which broke the idea that the step in the numerical calculation based on Grümwald-Letnikov definition was taken unit one.This method added a parameter named step on the basis of the traditional fractional order differential definitions.A good performance mask operator was attained by appropriately adjusting the size of step and order.The gray value of non-integer step pixel was got by the linear weighted method based on Lagrange interpolation polynomial,so it could play a role of denoising in the process of image enhancement.The experimental results showed that the method can make a better balance between enhancing image details and denoising.