Fractional Directional Differentiation and Its Application for Multiscale Texture Enhancement

Chaobang Gao; Jiliu Zhou; Weihua Zhang
January 2012
Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1
Academic Journal
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.


Related Articles

  • Stochastic Stability of Damped Mathieu Oscillator Parametrically Excited by a Gaussian Noise. Floris, Claudio // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1 

    This paper analyzes the stochastic stability of a damped Mathieu oscillator subjected to a parametric excitation of the form of a stationary Gaussian process, which may be both white and coloured. By applying deterministic and stochastic averaging, two Ito's differential equations are retrieved....

  • Precision and Accuracy in Scientific Imaging. Kirsch, Russell A. // Journal of Research of the National Institute of Standards & Tec;May/Jun2010, Vol. 115 Issue 3, p195 

    Digital images are commonly used to represent scientific data. Typically, high resolution images with many square pixels are considered to be necessary under the assumption that the increased precision of such images yields increased accuracy to the viewer. We question this assumption by...

  • A Novel Medical Image Registration Based on Contour Features and MultiScale information. Yang Yunfeng; Lin Chengxin; Wang Pengxiao; Li Jia; Li Bo // Applied Mechanics & Materials;2014, Issue 513-517, p3020 

    Medical image registration is the important technique in the clinical medicine field. A novel hierarchical registration method of the medical images based on multiscale information and contour line is proposed in the paper. At First, contour lines of the couple images are extracted based on the...

  • Reducing the Numerical Calculation in the Wave Iterative Method by Image Processing Techniques. Hrizi, H.; Sboui, N. // Applied Computational Electromagnetics Society Journal;Jun2012, Vol. 27 Issue 6, p524 

    The wave iterative method is a numerical method used to model electromagnetic circuits. It is based on the concept of waves in the place of electromagnetic fields. To study the electronic circuits having complex structures, this method requires much time. We propose in this article to improve...

  • TOPOLOGY PRESERVING BINARY CONTOUR SMOOTHING IN 2D IMAGES. PÉTER, BORBOLA // Agricultural Management / Lucrari Stiintifice Seria I, Managemen;Jan2011, Vol. 13 Issue 1, p157 

    Digital topology of images, objects deals with those mathematical characteristics which are not affected by certain deformations. For example stretching and sintering are admissible but shredding is not. Some fields of digital processing of images thinning, sintering, etc. may need the execution...

  • Image denoising and zooming under the linear minimum mean square-error estimation framework. Zhang, L.; Li, X.; Zhang, D. // IET Image Processing;Apr2012, Vol. 6 Issue 3, p273 

    Most of the existing image interpolation schemes assume that the image to be interpolated is noise free. This assumption is invalid in practice because noise will be inevitably introduced in the image acquisition process. Usually, the image is denoised first and is then interpolated. The...

  • A Remark on a Paper of I. V. Latkin. Leont’eva, M. N. // Algebra & Logic;Nov2013, Vol. 52 Issue 5, p429 

    The article offers the author's remark on the computational expressivity and recognition complexity of theories. The author mentions the primary theorem involving a Turing machine program along with the construction of its formula. An overview of the calculation of its value, variables and...

  • A Hybrid of Self Organized Feature Maps and Parallel Genetic Algorithms for Uncertain Knowledge. Gamal, Mona; Abo El-Fatoh, Ahmed; Barakat, Shereef; Radwan, Elsayed // International Journal of Computer Applications;2012, Vol. 60, p23 

    The need to handle uncertainty and vagueness in real world becomes a necessity for developing good and efficient systems. Fuzzy rules and their usage in fuzzy systems help too much in solving these problems away from the complications of probability mathematical calculations. Fuzzy rules deals...

  • Investigation of the process of drying of plane moist materials by the method of generalized variables. Ol'shanskii, A. // Journal of Engineering Physics & Thermophysics;Jan2013, Vol. 86 Issue 1, p69 

    Equations for calculation of the basic parameters of the kinetics of drying in the period of a dropping rate have been established. A graphoanalytical method of calculating the process of drying in the second period has been presented.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics