Complex composite derivative and its application to edge detection - Pan, Xiang (2015)
In this paper, a detailed study on a composite derivative is performed. The composite derivative, which is formed from the combination of fractional integration and derivative and performs a $90^°$ phase shift as the traditional first derivative does, is applied to edge detection and the results are analyzed, emphasizing the compromise ability between selectivity and noise suppression. Both objective and subjective comparisons with other edge detectors are carried out, including evaluations through the use of the benchmark Berkeley Segmentation Dataset (BSDS500). In contrast with the classical first-order derivative, the composite derivative is order-steerable; one can adjust the orders of fractional integration and derivative to tune magnitude characteristic and reach a compromise between sensitivity to noise and detection accuracy.