Research On Application Of Fractional Calculus In Image Enhancement

Fractional calculus is mainly an integer-order calculus operations to promote it based onordinary differential and integral operations. As the gradual development in many fields andapplication of fractional calculus operators gradually in-depth research, application offractional calculus in all fields has become a hot research question.The sharpness of the image is affected by outside information and many other factors inthe image acquisition process, details of the image are so blurred that can not accurately bewell to extract or identify information. In order to adaptively decide the differential order andthe more effectively enhance the edge and texture information of the image, an edge detectionoperator based on the gradient mode can not effectively identify the characteristics of theimage pixels. On the basic theory of fractional calculus and the existing image enhancementalgorithm, fractional differential operator construction method based on a combination of localquadratic differential and directional mask is proposed in this thesis, thereby achieving anadapative image enhancement algorithm based on fractional differential. In the algorithm,quadratic differential operator in local coordinate system is introduced to detect the nature ofeach pixel first, then a piecewise function between the operator and the fractional differentialorder to map it to a proper order adaptively. After that, a group directive masks with small sizewill be employed to calculate the weighted means of sub-templates in different directionsaround the center pixel, then the maximum of all means is treated as filtering result tostrengthen the edge, texture direction and spatial correlation between the neighbor pixels.The experiment results and analysis show that the algorithm not only can effectivelystrengthen the edge and texture, but also improve the amount of information and the clarity ofenhanced image greatly. At the same time, experimental analysis according to structuralsimilarity show that a better integral order and denoising effect are obtained based on imagedenoising of fractional order integral, and the image with noise of different variances shouldtake better order and size are summarized in the application based on fractional order integral.