Anti-Impulse-Noise Edge Detection via Anisotropic Morphological Directional Derivatives

Traditional differential-based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises. The morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise. In this paper, by combining the biwindow configuration with weighted median filters, anisotropic morphological directional derivatives (AMDDs) robust to impulse noise are proposed to measure the local grayscale variation around a pixel. For ideal step edges, the AMDD spatial response and directional representation are derived. The characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly. In terms of the AMDD spatial response and directional representation of ideal step edges, the spatial matched filter is used to extract the edge strength map (ESM) from the AMDDs of an image. The spatial and directional matched filters are used to extract the edge direction map (EDM). Embedding the extracted ESM and EDM into the standard route of the differential-based edge detection, an anti-impulse-noise AMDD-based edge detector is constructed. It is compared with the existing state-of-the-art detectors on a recognized image dataset for edge detection evaluation. The results show that it attains competitive performance in noise-free and Gaussian noise cases and the best performance in impulse noise cases.