QRFODD: Quaternion Riesz fractional order directional derivative for color image edge detection

Abstract

Edge detection is the prominent method to determine the discontinuities present in an image. There exists an issue of loss of information and correlation during the extraction of edges in color images. To resolve it, a novel quaternion domain based Riesz fractional order directional derivative approach is presented in this paper to extract more edge details in color images. The Riesz fractional masks obtained by utilizing Aitken interpolation are applied on color images in the quaternion domain for yielding the edge map as there is no need for recalculation of basis polynomials in case of the addition of any data point. The performance of the proposed quaternion based technique is analyzed on the benchmark BSDS300 and BSDS500 datasets in the terms of Figure of Merit and F-Score. The results obtained exhibit the efficiency of proposed technique over the classical and state-of-the-art edge detection approaches. The robustness of this approach is further established by taking into account uncontrolled conditions such as noise, JPEG compression, and varying illumination as it provided more features than the classical integer-order detectors. Moreover, the superiority of the proposed quaternion based technique is validated for medical images as well as its application in image enhancement.