Image edge detection and fractional calculation

Abstract

Fractional calculus has begun to play a significant role in various research domains, including image and signal processing. Within image processing, fractional calculus offers intriguing possibilities for filtering and edge detection, presenting a novel approach to enhance image quality. Fractional calculus involves the generalization of differentiation and integration to non-integer orders. As debated by numerous researchers, the term "generalized calculus" might be more suitable than "fractional calculus," which is the prevalent terminology. In this study, we aim to elucidate and delve into two pivotal articles: "A Novel Edge Detection Operator Based On Fractional Gaussian Differential" [1] and "Fractional Differentiation Based Image Processing" [2]. These articles elucidate how fractional calculus can confer advantages to image processing. Specifically, we will explore its application in image edge detection and image quality enhancement. The detection of image edges is of paramount importance within image processing, meriting thorough investigation. The objective of edge detection is to identify points within a digital image that correspond to abrupt changes in luminance intensity. These alterations in image properties often reflect significant events or changes in the world's characteristics. They encompass discontinuities in depth, surface orientation, material properties, and scene illumination. Edge detection constitutes a research field situated within image processing and computer vision, particularly within the realm of feature extraction. Consequently, we shall meticulously examine the utilization of fractional calculus for image edge detection, offering comprehensive insights into its application and presenting the outcomes of this endeavor. Additionally, we shall provide MATLAB programs developed during this research.