Laplacian edge detection method based on a new approximation of the second-order fractional derivative in the Caputo-Fabrizio sense

Abstract

Edge detection is an important issue in image processing and computer vision problems. It includes all mathematical methods that aim to identify the discontinuous points in the image. This process leads to construct curves that indicate the boundaries of an object and therefore extract feature information. In recent years, this task has received great attention from researchers and scientists, as we find in the literature many methods with their different algorithms. Up to now, there are two methods, the gradient and Laplacian methods. The first depends on the first derivative, where pixels with a high gradient are considered edges, whereas the second depends on the second derivative, such as the pixel whose second derivative is zero, it is marked as an edge point. Although these methods have achieved remarkable success, they are sensitive to noise and sometimes produce false edges. For this reason, in this paper, we propose an efficient edge detection method based on the fractional Laplacian operator in the Caputo-Fabrizio sense. In this method we develop a new approximation formula to the second-order with the Caputo-Fabrizio fractional derivative. Then, we construct a new fractional mask to compute the Laplacian convolution. To check the effectiveness of our proposed method, we have provided some test images that are affected by a Gaussian noise. The numerical results and visual observation show that our proposed edge detection method gives better performance compared to the classical Laplacian method in terms of the peak signal to noise ratio (psnr) and fine details extraction.