Edge detection using the Prewitt operator with fractional order telegraph partial differential equations (PreFOTPDE)

Detecting edges in image processing is an important process in image analysis or enhancement. Many methods detected edge information based on the differences in brightness values. Prewitt, the most widely used edge detection method, performs the extraction of edges by partial differential calculation. This study performed fractional order partial differential calculation with the Telegraph equation in the Prewitt method calculation. Filter coefficients are determined by using Grumwald-Letnikov series expansion for fractional partial differential equation calculation. To determine the most appropriate fraction value, five different coefficients were tried. The proposed method is compared with the conventional edge detection methods Sobel, Canny and standard Prewitt. The obtained result showed that the proposed method detects the edges more accurately. In addition, it has been compared with Prewitt fractional order edge detection (FOED) and edge detection method based on ant colony optimization (ACO) methods developed in recent years. Pratt's figure of merit (FOM) metric was used to compare these studies. It was realized that the FOM values calculated with the proposed method were more accurate than the others methods.