An adaptive method based on the Atangana-Baleanu in the sense of Caputo fractional operator for improving edge detection accuracy in SEM images

Abstract Edge detection is a fundamental task in low-level image processing. Classical approaches such as the Roberts, Sobel, and Canny operators often perform poorly in the presence of noise and contrast variations, conditions that are common in scanning electron microscopy (SEM) images. To address these limitations, we propose ABC-AED, an adaptive edge detection method based on the Caputo-sense Atangana–Baleanu fractional operator. The associated Mittag–Leffler kernel introduces natural smoothing, non-local memory effects, and enhanced robustness to noise. The discrete fractional mask is constructed using finite-difference approximation combined with series expansion, allowing the fractional order to vary spatially. A bilateral filter preserves edge information while generating a local variance map that guides optimal block-wise assignment of fractional orders. ABC-AED is assessed against the Canny detector and a previously proposed fractional method using synthetic noisy images and real SEM data. Evaluations show that ABC-AED yields sharper and more continuous edges, maintains stability under noise, and ensures consistent detection across SEM images with varying contrast. Overall, ABC-AED outperforms competing methods, which exhibit edge distortion, fragmentation, or excessive blurring, although slight contour smoothing remains.