Fractional Differential Analysis for Texture of Digital Image

This paper discusses the capabilities of the fractional differential approach for the detection of textural features in two-dimensional digital images and the involved Lateral Inhibition Principle, and fractional differential masks and algorithms of digital image. Firstly, the kinetic physical meaning of fractional differential and the relationship between fractional calculus and classical time-frequency analysis and the separability of two-dimensional fractional calculus on certain conditions are deduced. Secondly, the difference between two Gaussians receptive fields for fractional differential of digital image involved signal processing and biologic vision nerve model is discussed. An analysis of its Mach band is also included. Thirdly, the implements and parameters of eight n × n fractional differential masks, which are mutual central symmetric, on negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left lower diagonal, left upper diagonal, right lower diagonal, right upper diagonal respectively are discussed. Lastly, the numerical implementation algorithms of fractional differential mask for digital image are discussed. Numerical experiments show that the textural details enhance capabilities of fractional differential-based texture operator and are better than that of integral differential based one for rich-grained digital images.