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Fractional Differential and Its Application in Image Texture Enhancement

ZHAO Jian(Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences, Changchun 130033,China)  
In order to enhance the edge and texture of the blurred image,making the details clearer,it is need to sharpen the image edge.The existing enhancement methods are integer-order differential sharpening and high-pass filter.As the enhanced effect of these methods is still not ideal,this paper introduces fractional differential operator.Fractional differential operator can greatly enhance the image edges and the texture details,can retain the smooth region information non-linearly and avoid large noise.The principle and the advantages and disadvantages of Tiansi fractional differential operator is studied and analyzed.This paper propose a new fractional differential operator,which can enhance the image edge and texture details better,while ensuring the image brightness balanced,and inhibiting the small noise.From the quantitative point of view,the average gradient of this improved fractional diffe-rential operator increases 3.8 times than original image.It verifies that the improved fractional differential operator has an advantage over the integer-order differential operator such as the Laplace operator and Tiansi fractional differential operator.And the algorithm is simple and easy to implement.It can be used for engineering applications in real-time image processing system.
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