GLF-ResFormer: Fractional Derivative-Guided Deep Learning for Computer Vision Edge Detection

Edge detection is an essential problem in computer vision and is used in applications such as object recognition, scene analysis, and medical imaging. Conventional edge detectors based on integer-order derivatives are computationally efficient but sensitive to noise, whereas modern deep learning approaches generally achieve higher accuracy at the cost of increased model complexity. This paper presents GLF-ResFormer a lightweight hybrid CNN–Transformer architecture incorporating Grünwald–Letnikov (GL) fractional preprocessing. The discrete GL operator is approximated using a finite-difference convolution with a truncation level of N=15, where the fractional order α∈(0,1] controls the spatial memory of the operator. We establish an upper bound for the truncation error of the discrete GL approximation, O(hN−α) (Theorem 1), and present a gradient-sensitivity analysis (Lemma 1) that provides theoretical support for the proposed preprocessing strategy. Extensive experiments using 10 independent random seeds on the MNIST dataset show that, at the optimal fractional order of α=0.01, GLF-ResFormer achieves a pixel-wise F1 score of 0.9967±0.0002 compared with 0.9891±0.0033 for a CNN baseline, while reducing the validation loss to 0.0043±0.0003. Additional experiments on the CIFAR-10 dataset and comparisons with the BSDS500 benchmark further demonstrate the effectiveness of the proposed framework across multiple edge detection evaluation settings while maintaining a lightweight architecture.