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Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation

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Abstract

This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geometric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses fractional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of n×n any order fractional differential mask on negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discussion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.

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Authors and Affiliations

  1. School of Computer Science and Technology, Sichuan University, Chengdu, 610064, China

    YiFei Pu, JiLiu Zhou & HuaDing Jia

  2. School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    YiFei Pu & WeiXing Wang

  3. Academie des Sciences de l’Institue de France, 28, rue Saint-Dominique, 75007, Paris, France

    YiFei Pu

  4. Laboratoire de l’IADI ERI (INSERM-UHP) au CHU de Nancy Brabois, Université Henri Poincaré(Nancy I), 54511, Vandoeuvre les Nancy, France

    YiFei Pu

  5. School of Electronics and Information, Sichuan University, Chengdu, 610064, China

    JiLiu Zhou & YiYang Wang

Authors
  1. YiFei Pu
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  2. WeiXing Wang
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  3. JiLiu Zhou
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  4. YiYang Wang
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  5. HuaDing Jia
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Corresponding author

Correspondence to YiFei Pu.

Additional information

Supported by China Postdoctoral Science Foundation (Grant No. 20060401016), Fondation Franco-Chinoise Pour La Science Et Ses Applications (FFCSA), the National Natural Science Foundation of China (Grant No. 60572033), and the Doctor Foundation of China National Education Department (Grant No. 20060610021)

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Pu, Y., Wang, W., Zhou, J. et al. Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation. Sci. China Ser. F-Inf. Sci. 51, 1319–1339 (2008). https://doi.org/10.1007/s11432-008-0098-x

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  • DOI: https://doi.org/10.1007/s11432-008-0098-x

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