The edge of an image holds important visual information

which plays an important role in the subsequent image understanding and scene perception. Edge detection is used to extract image edge information and eliminate irrelevant information

which significantly reduce the amount of data for the subsequent analysis. Numerous scholars have proposed various edge operators for different requirements. However

the detection accuracy of traditional edge detectors is slightly low when extracting edges. Furthermore

the texture details in an image

which include complex texture with a fractal structure and weak edges

and noise immunity capability

are also weak. A fractional order derivative has the advantage of strengthening and extracting the textural features and weak edges of digital images. A person can choose a different order for the fractional calculus according to various images and interesting features to improve high-frequency signals

nonlinearly enhance intermediate-frequency signals

and retain low-frequency signals. To address the aforementioned problem

this study proposes an improved Canny edge detector based on a fractional order derivative. The method calculates image gradient using the classical Grünwald-Letnikov (G-L) fractional order differential definition instead of the derivative of the Gaussian function. Furthermore

a new edge detection mask based on the G-L fractional order calculus is suggested. Then

the quantitative relation curves between edge detection accuracy and the tuning parameters ( and ) are presented

which are helpful when selecting the optimal parameters. In addition

three effective evaluation criterions are introduced to assess the proposed method performance. We design a new edge detection mask based on the G-L definition

which is flexible in choosing the degree of fractional order derivative and capable of adjusting the direction of difference

and thus

can have extensive applications. We obtain the quantitative relation curves between edge detection accuracy and the parameters ( and )

which can be a guide in obtaining optimal parameters to extract desirable edges. We take many experiments using synthesize and real images

and compare the proposed method with five traditional edge detecting methods and three kinds of methods based on fraction calculus. The detection accuracy

detection efficiency and the robustness of the new method proposed in this paper are improved. In a digital image

a high-frequency component corresponds to edges and noises

an intermediate-frequency component corresponds to the texture detail

and a low-frequency component corresponds to the smoothing area. Using a fractional order differential for edge detection can completely extract weak edges and texture detail. Moreover

using a fractional order differential with suitable parameters can improve noise immunity capability. Edge-detecting efficiency is improved compared with other methods. Thus

the proposed method can be used in many real-time image-processing systems. Considerable experiment results show that the proposed method is a valid edge detector for a textured image

and even exhibit an evident advantage over other techniques. The proposed method is a significant extension of the traditional Canny detector. Overall

the proposed method is a valid and effective edge detection technique.