Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

• Published in: Advances in difference equations 2020-08, Vol.2020 (1), p.1-19, Article 435
• Main Authors: Ghanbari, Behzad, Atangana, Abdon
• Format: Article
• Language: English
• Subjects: Analysis; Applications of mathematics; Atangana–Baleanu fractional integration; Computer simulation; Difference and Functional Equations; Differential calculus; Digital imaging; Edge detecting; Fractional calculus; Fractional kernels; Functional Analysis; Image processing; Image segmentation; Kernels; Masks; Mathematics; Mathematics and Statistics; Operators (mathematics); Order parameters; Ordinary Differential Equations; Partial Differential Equations; PSNR
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02890-9

Computers and electronics play an enormous role in today’s society, impacting everything from communication and medicine to science. The development of computer-related technologies has led to the emergence of many new important interdisciplinary fields, including the field of image processing. Image processing tries to find new ways to access and extract information from digital images or videos. Due to this great importance, many researchers have tried to utilize new and powerful tools introduced in pure and applied mathematics to develop new concepts in imaging science. One of these valuable research areas is the contents of fractional differential calculus. In recent years, extensive applications to the new fractional operators have been employed in real-world problems. This article attempts to address a practical aspect of this era of research in the edge detecting of an image. For this purpose, two general structures are first proposed for making new fractional masks. Then the components in these two structures are evaluated using the fractional integral Atangana–Baleanu operator. The performance and effectiveness of these proposed designs are illustrated by several numerical simulations. A comparison of the results with the results of several well-known masks in the literature indicates that the results presented in this article are much more accurate and efficient. This is the main achievement of this article. These fractional masks are all novel and have been introduced for the first time in this contribution. Moreover, in terms of computational cost, the proposed fractional masks require almost the same amount of computations as the existing conventional ones. By observing the numerical simulations presented in the paper, it is easily understood that with proper adjustment for the fractional-order parameter, the accuracy of the obtained results can be significantly improved. Each of the new suggested structures in this article can be regarded as a valid and effective alternative for the well-known existing kernels in identifying the edges of an image.