###### Abstract  
In this paper, we propose a new sliding window edge-oriented filter that computes the output pixels using a cross-correlation-like equation derived from the principles of fractional calculus (FC); thus, we call it the \"fractional cross-correlation filter\" (FCCF). We assessed the performance of this filter utilizing exclusively edge-preservation-oriented metrics such as the gradient conduction mean square error (GCMSE), the edge-based structural similarity (EBSSIM), and the multi-scale structural similarity (MS-SSIM); we conducted a statistical assessment of the performance of the filter based on those metrics by using the Berkeley segmentation dataset benchmark as a test corpus. Experimental data reveal that our approach achieves higher performance compared to conventional edge filters for all the metrics considered in this study. This is supported by the statistical analysis we carried out; specifically, the FCCF demonstrates a consistent enhancement in edge detection. We also conducted additional experiments for determining the main filter parameters, which we found to be optimal for a broad spectrum of images. The results underscore the FCCF's potential to make significant contributions to the advancement of image processing techniques since many practical applications such as medical imaging, image enhancement, and computer vision rely heavily on edge detection filters. edge filter; fractional calculus; filtering model +
Footnote †: journal: _sciences_  
0000-0001-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-5000-50000-50000-5000-50000 The conventional approach to edge detection involves convolving the image with a specifically designed 2D kernel that is responsive to significant gradients. However, current research is shifting towards techniques utilizing machine learning and deep-learning-based algorithms specifically tuned for detecting edges in images. For instance, [PERSON] et al. [1] developed an edge detection algorithm based on an artificial neural network (ANN), expecting that the edges information the ANN computes might be useful for diagnosing illness from magnetic resonance images (MRI). Their algorithm was reported to be up to three times faster than traditional edge detection schemes; however, they noted that one drawback of the ANN-based approach they proposed is that it requires data preparation and cleaning, which imply a significant additional effort compared to approaches based on the Canny or Sobel operators. On the computer vision applications to the industry realm, [PERSON] et al. [2] developed a deep-learning-based edge detection to improve building footprint extraction from satellite images. A common issue in these target applications is that the resulting edge maps are sensitive to noise; thus, this study focused on reducing noise in the edges computed from images of buildings that may affect boundary resolution. They addressed this problem by utilizing detected edge bands. Another example is the work of [PERSON] et al. [3], who introduced a neural network-based hybrid filter that combines neural edge enhancers and bilateral filters. In this study, the neural filter works as a fusion operator, effectively eliminating quantum noise from an input image. A common drawback of these approaches is the requirement for an extensive dataset to train effective models and the significant computational power needed to fit the model. Scientists and engineers are making a transition towards machine learning and deep learning models to implement various image processing tasks; however, they must overcome the problems related to the construction of such models, especially for the late majority who prefer to work with more traditional approaches before they can adopt new trends in technology such as deep learning. For these reasons, researchers are still working with the most well-known methods for edge detection, such as the Robert's filter, Prewitt filter, Sobel filter, Canny filter, and Laplacian filter.