A novel image edge detection algorithm based on neutrosophic set

•This study proposes a novel method to detect edge on clear or noisy images.•The proposed approach performs well on images without noise or with different levels of noise.•Neutrosophic set is employed to deal with uncertain information on image edge detection.

Neutrosophic set (NS) theory is a formal framework to study the origin, nature, and scope of the neutral state. In this paper, neutrosophic set is applied in image domain and a new directional α-mean operation is defined. Based on this operation, neutrosophic set is applied into image edge detection procedure. First, the image is transformed into NS domain, which is described by three membership sets: T, I and F. Then, a directional α-mean operation is employed to reduce the indeterminacy of the image. Finally, a neutrosophic edge detection algorithm (NSED) is proposed based on the neutrosophic set and its operation to detect edge. Experiments have been conducted using numerous artificial and real images. The results demonstrate the NSED can detect the edges effectively and accurately. Particularly, it can remove the noise effect and detect the edges on both the noise-free images and the images with different levels of noises.