Construction of Fractional differential Masks Based on Riemann-Liouville Definition

This paper analyses the fractional calculus's Riemann-Liouville definition and derives 1~2 order (2 ) ( 2) nn +×+ fractional differential mask of digital image, including x positive direction, x negative direction, y positive direction, y negative direction, left upper diagonal, left lower diagonal, right upper diagonal and right lower diagonal. Based this mask, the experiments show that this fractional differential calculation can not only maintain the low frequency contour information in the smooth area, but also nonlinear enhance the high frequency edge and texture part in the image. This property have special advantage and visual effect for the images whose texture information has important meaning.