Edge detection using fractional derivatives and information sets

Abstract

The inherent memory effect of the Grunwald–Letnikov fractional derivatives is combined with the effectiveness of information sets for detecting edges in digital images. Fractional derivatives are utilized in the computation of fractional gradients, which are further processed using information sets for the proposed edge detector to extract more edges than possible with the traditional edge detectors. In the proposed approach, first the gradient operators of the Sobel mask are converted into the fractional form and convolved with the given gray image. In the next step, the histogram of the fractional gradients is fuzzified using the Gaussian membership function and the sigmoidal membership function. The optimal parameters for these membership functions are selected through a grid search method based on the information set-based edge strength factor ESf. In the final step, defuzzification is performed to obtain the final edge maps. By plotting the edge maps, analyzing the boundary information, and Pratt’s figure of merit scores for images in the Berkeley segmentation dataset, it is observed that the resulting edge maps of the proposed edge detector contain more quantitative and qualitative information than that of traditional edge detectors even in the presence of noise.