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中文摘要：
图像边缘细节包含重要的视觉感知信息，是进一步进行图像理解与场景感知的基础。针对常用的边缘梯度检测方法难以有效提取类似于分形纹理结构的复杂图像边缘问题，提出一种基于分数阶微分的图像边缘检测方法。该方法首先基于分数阶微分的性质进行图像拐点检测，并进一步结合拉格朗日多项式插值和Grumwald-Letnikov （G-L）分数阶微分的定义，推导出具有非整数步长像素信息的图像边缘检测算子。实验表明，该方法能有效提取图像中的边缘细节（拐点）特征。对被噪声严重污染的具有复杂边缘细节的图像，该算子同样具有较好的边缘细节检测能力，获得更好的视觉效果。
英文摘要：
The edge details in images involve significant visual perception information ,which play an important role in the further image understanding and scene perception .An image edge detection and extraction method is presented based on the fraction-al differentiation theory aiming at solving the problems of inaccurate edge detection like fractal structures in the images by the tradi-tional edge detection methods .Firstly ,the inflexion points in the images are detected based on the characteristics of fractional differ-entiation ;then ,an image edge detail detection and extraction operator with sub-pixel interpolation is derived from the Grumwald-Let-nikov （G-L ） definition of fractional differentiation combining with the Lagrange interpolation polynomials .The experimental results demonstrate that the proposed operator is capable of extracting image edge details （inflexion points ） efficiently .Furthermore ,it is able to detect the useful object edge details from image with serious noise to achieve better visual effect.
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