FoGDbED: Fractional-order Gaussian derivatives-based edge-relevant structure detection using Caputo-Fabrizio definition

Abstract Edge-relevant structure features (ERSFs), e.g., object edges, boundaries and contours, junctions, etc. play an important role in low and middle level image processing tasks, such as image segmentation, as well as in higher-level computer vision tasks, such as scene analysis and content understanding. Commonly-used ERSF detection methods employ the integer-order differential-based methods, which are noise-sensitive and have less selectivity of ERSFs. Hence, they are difficult to effectively extract object edges or boundaries, especially in natural images with rich fractal-like structures. This paper presents a highly selective and noise-robust ERSF detection approach based on the fractional-order Gaussian derivatives (FoGDs) by using the definition of Caputo-Fabrizio derivative, termed FoGDbED. FoGDbED is constructed based on the concept of robust edge feature selection and inflexion point localization, whose detection mask can be designed with a close-form expression of FoGDs. Theoretical analysis and experimental results show that the proposed FoGDbED operator is capable of extracting complex ERSFs in natural images especially detecting object edges and junctions in natural images with serious noises to achieve a better visual effect.