Design of Fractional Calculus based differentiator for edge detection in color images

Edge detection has many applications in engineering and medical field. Edge detection in color images is getting the attention of the researchers due to the reason that color images have more information as compared to gray scale images. Different differential methods have been proposed in the literature for edge detection. Some of them required smoothing due to high sensitivity of differential methods towards noise. In the present manuscript, fractional order differentiation operator is defined to find out the gradient of the image which is further used for edge detection. Considering the input image as a reconstructed image, optimal threshold selection method is defined which is based on an error in image reconstruction assuming thatthe input image isa reconstructed image. Fractional edge detection improves the thin edge detection. It has more details of edges as compared to integer order based fractional differentiation. Fractional differentiation based edge detector does not require additional smoothing. Optimal threshold selection based on an error in a reconstructed image enhances the texture information as compared to normal threshold selection.