A method for image edge detection based on interval-valued fuzzy sets

Abstract

 A method for image edge detection is proposed, which employs interval-valued fuzzy (IVF) sets such that each pixel has an interval membership constructed from its original and neighboring intensities. This method relies on triangular norms and co-norms to develop operators generating lower (LIB) and upper (UIB) interval bounds, which are employed in a novel membership function. This membership function is then applied to the image represented as fuzzy singletons to generate an image containing the edges associated with the original image. The proposed method is applied to medical images for edge detection and the results are compared with those obtained based on application of other fuzzy methods as well as a classical method for implementation of edge detectors. The quantitative comparison of the edge binary images determined by each method is performed by employing a metric based on the Hausdorf distance as well as a metric based on the local refinement error known as global consistency error (GCE). The proposed method consistently produced lower values of Baddeley’s Delta metric as well as lower values of GCE. The proposed method was also characterized by values of Pratt’s figure of merit closer to unity as compared with the other methods. Furthermore, the proposed method outperforms a number of commonly employed edge detectors in terms of the processing time required for edge detection.