0~1 Order Riemann-Liouville Fractional Differential Enhancing Mask of Digital Image

An image enhancement algorithm based on 0~1 order Riemann-Liouville fractional differential is presented in this paper. The Riemann-Liouville differential equation and its discretization form are deduced from the Riemann-Liouville definition. According to the discretization equation, the structures and parameters of eight fractional differential masks are constructed respectively. The numerical implementation algorithms of the eight differential masks are discussed too. Finally, the relationships between the entropies of enhanced images with the orders are discussed, then, the most optimal order is obtained. The computer experiments show that the algorithm has excellent feedback for nonlinearly enhancing the textural details of the digital image and it can obviously enhance texture details and edges, the enhanced images have markedly visual effect enhance capabilities of the Gaussian smoothed images are also obvious too.