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

作　　者：PU YiFei WANG WeiXing ZHOU JiLiu WANG YiYang JIA HuaDing 

机构地区：[1]School of Computer Science and Technology, Sichuan University, Chengdu 610064, China [2]School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu610054, China [3]Academie des Sciences de I'lnstitue de France, 28, rue Saint-Dominique, 75007 Paris, France [4]Laboratoire de I'IADI ERI (INSERM-UHP) au CHU de Nancy Brabois, Universite Henri Poincare(Nancy I),54511 Vandoeuvre les Nancy France [5]School of Electronics and Information, Sichuan University, Chengdu 610064, China

出　　处：《Science in China(Series F)》2008年第9期1319-1339,共21页中国科学（F辑英文版）

基　　金：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);the Doctor Foundation of China National Education Department (Grant No. 20060610021)

摘　　要：This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric 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 frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, 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 discus- sion, 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.This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric 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 frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, 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 discus- sion, 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.

关 键 词：fractional stationary point fractional equilibrium coefficient fractional stable coefficient fractional grayscale co-occurrence matrix fractional differential mask 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]