A type-2 fuzzy edge detection method is presented in this paper. The general process consists of first obtaining the image gradients in the four directions—horizontal, vertical, and the two diagonals—and this technique is known as the morphological gradient. After that, the general type-2 fuzzy Sugeno integral (GT2 FSI) is used to integrate the four image gradients. In this second step, the GT2 FSI establishes criteria to determine at which level the obtained image gradient belongs to an edge during the process; this is calculated assigning different general type-2 fuzzy densities, and these fuzzy gradients are aggregated using the meet and join operators. The gradient integration using the GT2 FSI provides a methodology for achieving more robust edge detection, even more if we are working with blurry images. The experimental evaluations are performed on synthetic and real images, and the accuracy is quantified using Pratt’s Figure of Merit. The results values demonstrate that the proposed edge detection method outperforms other existing algorithms.
Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral
