Research On Image Processing Using Fractional Calculus

In the information society, with the continuous improvement of living standards,people often need to access information through the image, and the demand of imagewith high resolution and rich detail is urgent. But it is difficult for people to get richtexture and apparent contrast about weak details of image in general. Then, we needto enhance the image details to improve the resolution quality and the weakcharacteristics of the image. This thesis will further explore and study the theory andmethods of image enhancement.Image enhancement is the most simple and the most attractive areas in thedigital image processing. In recent years, researchers have already introduced thetheory of fractional calculus mathematics from purely theoretical research into theapplication of digital image processing, so that the study of fractional calculus hasmade breakthrough progress. It is emerging field with little research in the Worlduntil now. Compared with traditional image processing approaches based on integerorder differential, the application of fractional differential has remarkable advantagesin image processing.This paper firstly studied the existing methods. Because of the directionalcharacteristic of different fractional differential mask processing image, we combinedfractional differential with Taylor formula and directional derivative. So it made fulluse of information of pixels close to the processing pixel. The paper analyzed thisimproved method of fractional differential, and the structure and transformationprocess of the fractional differential masks were the focus of reasoning，and it wasused for image enhancement.Finally, doing simulation in the Matlab simulation platform to verify the resultsof the above provided methods, and figure out the quality parameters of the resultingimages from the experiment. Then we compared it with results of existing typicalimage enhancement methods. From the comparison results, the improved imageenhancement method in this paper was effective in aspect of enhancing texturecharacteristic of gray image.