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文中提出并论述数字图像纹理细节的分数阶微分检测及其分数阶微分滤波器实现.首先,分别从信息论和动力学两个角度深刻阐述了分数阶微积分的几何意义和物理意义.然后,提出并论述了分数阶驻点、分数阶平衡系数、分数阶稳定系数、分数阶灰度共生矩阵的概念与理论,并详细论述了分数阶灰度共生矩阵对图像纹理细节特征的检测.然后,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个方向上的数字图像任意分数阶n×n的分数阶微分掩模的构造及其数值运算规则.最后,在此基础上,提出并论述了数字图像分数阶微分滤波器的理论与构造.仿真实验分别从定性和定量两方面证实了,对于纹理细节信息丰富的图像信号而言,分数阶微分具有非线性增强图像复杂纹理细节特征的独特优势与良好效果.
In this paper, the fractional differential detection of digital image texture details and its implementation of fractional differential filter are proposed and discussed.Firstly, the geometrical and physical meanings of fractional calculus are elaborated from two aspects of information theory and dynamics respectively.And then, The concept and theory of fractional order stationary point, fractional equilibrium coefficient, fractional stability coefficient and fractional grayscale co-occurrence matrix are discussed, and the detailed features of fractional grayscale co-occurrence matrix are also discussed. The digital image in the x-axis negative, x-axis positive, y-axis negative, y-axis positive, lower left diagonal, upper left diagonal, lower right diagonal, n fractional differential mask structure and its numerical rules.Finally, based on this, the theory and construction of digital image fractional differential filters are proposed and discussed.The simulation experiments prove from both qualitative and quantitative aspects, For texture-rich image signals, fractional-order differential has the unique advantage and good effect of non-linearly enhancing the complex texture details of images.