关键词: 分数阶微分, Tiansi算子, 阶次自适应模型, 图像增强

Abstract: It is very ambitious to search the optimal degree of fractional order differential operator manually, lack of order adaptive in image enhancement. In order to tackle this problem, a mathematical model of adaptive degree for fractional order differential operator is presented, which takes the arctangent function as prototype and adopts local image information as independent variables, such as the image gradient information, local information entropy, brightness and contrast. Therefore, the relationship between the optimal degree and local image information can be built up, and the optimal degree at every pixel location can be calculated automatically according to the characteristics of image. And then, the model provided is applied to fractional order differential Tiansi operator in image enhancement. Images from standard library with texture are selected as the object for the experiment to verify the validity of the mode. The experimental results are analyzed qualitatively and quantitatively. In quantitative analysis, image information entropy, image average gradient, image definition and image contrast are selected to evaluate the enhancement effect and comparison results to Laplacian and Tiansi operator are also provided. Theoretical analysis and experimental results have shown that the model presented is effective and the gray image can be enhanced continuously to the optimal level of fractional order differential enhancement effect, satisfying people’s visual perception.

Key words: fractional order differential, Tiansi operator, adaptive degree model, image enhancement