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Fractional Directional Differentiation and Its Application for Multiscale Texture Enhancement

机译：分数阶方向差分及其在多尺度纹理增强中的应用

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摘要

This paper derives the directional derivative expression of Taylor formula for two-variable function from Taylor formula of one-variable function. Further, it proposes a new concept, fractional directional differentiation (FDD), and corresponding theories. To achieve the numerical calculation, the paper deduces power series expression of FDD. Moreover, the paper discusses the construction of FDD mask in the four quadrants, respectively, for digital image. The differential coefficients of every direction are not the same along the eight directions in the four quadrants, which is the biggest difference by contrast to general fractional differentiation and can reflect different fractional change rates along different directions, and this benefits to enlarge the differences among the image textures. Experiments show that, for texture-rich digital images, the capability of nonlinearly enhancing comprehensive texture details by FDD is better than those by the general fractional differentiation and Butterworth filter. By quantity analysis, it shows that state-of-the-art effect of texture enhancement is obtained by FDD.
机译：本文从一元函数的泰勒公式推导了二元函数的泰勒公式的方向导数表达式。此外，它提出了一个新的概念，分数方向微分（FDD）和相应的理论。为了实现数值计算，本文推导了FDD的幂级数表达式。此外，本文还讨论了分别在四个象限中用于数字图像的FDD掩模的构造。在四个象限中，沿着八个方向的每个方向的微分系数都不相同，与一般的分数微分法相比，这是最大的差异，并且可以反映沿不同方向的不同分数变化率，这有利于扩大两个方向之间的差异。图像纹理。实验表明，对于纹理丰富的数字图像，通过FDD非线性增强综合纹理细节的能力要优于一般的分数微分和Butterworth滤波器。通过数量分析，它表明通过FDD获得了最新的纹理增强效果。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第8期|325785.1-325785.26|共26页
  • 作者

    Chaobang Gao; Jiliu Zhou; Weihua Zhang;

  • 作者单位

    College of Information Science and Technology, Chengdu University, Chengdu 610106, China;

    School of Computer Science, Sichuan University, Chengdu 610064, China;

    School of Computer Science, Sichuan University, Chengdu 610064, China;

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