On the Generalization of the Fuzzy Morphological Operators for Edge Detection

The morphological gradient is a widely used edge detector for grey-level images in many applications. In this paper, we generalize the definition of the morphological gradient of the fuzzy mathematical morphology based on t-norms. Concretely, instead of defining the morphological gradient from the usual definitions of fuzzy dilation and erosion, where the minimum and the maximum are used, we define it from generalized fuzzy dilation and erosion, where we consider a general t-norm and t-conorm, respectively. Once the generalized morphological gradient is defined, we determine which t-norm and tconorm have to be considered in order to obtain a high performance edge detector. Some t-norms and their dual t-conorms are taken into account and the experimental results conclude that the t-norms of the Schweizer-Sklar family generate a morphological gradient which outperforms notably the classical morphological gradient.