###### Abstract
For instance, in [PERSON]'s [4] research, he developed an edge detection method based on an improved Canny operator to solve problems related to noise sensitivity, false edges, and the lack of self-adaptability on rebar thread heads. The filter we introduce in this paper resembles the traditional approaches, so it shares desirable characteristics, such as the advantage of exhibiting lower computational complexity because it relies on the linear convolution operator. In addition, these methods lead to a straightforward interpretation since they are based on well-understood mathematical principles while avoiding the burdens related to the development and deployment of machine learning models. Another field that converges to the topic discussed in this paper is fractional calculus (FC); FC is a branch of mathematics that studies a general framework of calculus where derivatives and integrals have a fractional or even complex order. Scientists are interested in finding new applications of the FC theory to solving engineering problems; in this regard, we will discuss some edge map computing algorithms based on FC in Section 2. Given the active research in the field of edge filters and their implementation using fractional calculus, and encouraged by the results achieved in our previous works [5; 6], we are interested in applying these results to other signal processing tasks. The first work [5] presented a digital watermarking scheme that embeds a binary signal called the watermark into an image, resulting in a watermarked image; the watermark has to be detected later from the watermarked signal for copyright enforcing applications using a FC-based model the authors derived, which they called the fractional cross-correlation. The authors of [5] extended their research in [6] to the case of Gaussian watermarks, that is to say, for watermarks as sequences of numbers with Gaussian distribution. In both cases, the fractional cross-correlation watermarking scheme they proposed, exhibited a higher performance in almost all tests, whereas the few unfavorable tests indicate that the performance of the proposed scheme equals the performance of typical watermark detection schemes for the worst-case scenario. We believe that this particular fractional model for watermark detection is applicable to other signal processing tasks, and thus, supported by evidence from our previous works, we are dedicated in this paper to developing an edge filter model based on the fractional cross-correlation equation. The main contributions reported in this paper are:  
* We introduce a new image filter designed for detecting edges in grayscale images using a model derived from the FC principles (Section 4). * We detail the methodology to calculate the parameters of the filter (Section 6). * We assess the performance of the proposed filter as an edge filter for grayscale images (Section 6). * We compare the proposed system with de facto standard edge filters (Section 6). Also, Section 2 covers a review of works closely related to our proposed scheme; Section 5 details the materials used for the experiments we conducted to evaluate the performance of the proposed filter and the validation criteria as well. We present our conclusions in Section 7; next to it, the references, and in the last part, relevant Appendices A-C.