数字图像的分数阶微分掩模及其数值运算规则

Fractional Differential Masks of Digital Image and Their Numerical Implementation Algorithms

研究目的是提出并论述数字图像的分数阶微分掩模及其数值运算规则.首先,从信号处理角度论述了数字图像分数阶微分掩模的特性.其次,详细论述了在x轴负、x轴正、y轴负、y轴正、左下对角线、左上对角线、右下对角线、右上对角线8个相互中心对称的数字图像n×n分数阶微分掩模的构造.最后,论述了数字图像分数阶微分掩模的数值运算规则.计算机数值实验结果表明,对于纹理细节信息丰富的图像信号而言,分数阶微分对灰度变化不大的平滑区域中的纹理细节信息的提取效果明显优于整数阶微分运算.

We mainly discuss the fractional differential masks of digital image and their numerical implementation algorithms. Firstly, we discuss the characteristics of the fractional differential masks from a signal processing point of view. Secondly, we discuss in detail the structures and parameters of eight n × n fractional differential masks on negative x-axis, positive x-axis, negative y-axis, positive y-axis, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively, which are centro-symmetric interdependently. Lastly, we discuss the numerical implementation algorithms of the fractional differential masks for digital image. Numerical experiments show that the textural details enhance capabilities of the fractional differential-based texture operator are better than those of the integral differential based one for rich-grained digital images.