A novel edge detector based on discrete t-norms for noisy images

Abstract

Image edge detection is one of the more fashionable topics in image processing and it is an important preprocessing step in many image processing techniques since its performance is crucial for the results obtained by subsequent higher-level processes. In this paper, an edge detection algorithm for noisy images, corrupted with salt and pepper noise, using a fuzzy morphology based on discrete t-norms is proposed. It is shown that this algorithm is robust when it is applied to different types of noisy images. The obtained results are objectively compared with other well-known morphological algorithms such as the ones based on the Łukasiewicz t-norm, representable and idempotent uninorms and the classical umbra approach. This comparison is addressed using some different objective measures for edge detection, such as Pratt’s figure of merit, the ρ -coefficient, and noise removal like the structural similarity index and the fuzzy DI -subsethood measure. The filtered results and the edge images obtained with our approach improve the values obtained by the other approaches.