Generating fuzzy edge images from gradient magnitudes

The representation and processing of edges in images based on notions from fuzzy set theory has become popular in recent years. There are several reasons for this direction, from the vague definition of edges to the inherent uncertainty of digital images. Here, we study the transition from a gradient image, a popular intermediate representation, to a fuzzy edge image. We consider different parametric membership functions to transform the gradients into membership degrees. A histogram-based strategy is then introduced for automatically determining the value of those parameters, adapting the membership functions to the characteristics of each image. The functions are applied on the Canny method for edge detection, resulting in an improvement compared to the classical normalizing approach.