Topological Gradient Operators for Edge Detection

Edge detection in image processing is the task of locating pixel value variations in images. First methods were directional derivative based linear filters. One of the most important problems of these methods that are based on computation of approximate derivative are their sensitivity to noise due to small kernel sizes. Small kernels are widely used to avoid the effect of nearby objects. In this work, we propose a fuzzy topology based method that allows the use of larger gradient kernels. This method produces thin gradient lines by limiting the support area of gradient kernels for slowly varying ramp-like edges. By applying the proposed method on synthetic and natural images, it is observed that it decreases the output area around the edge and has a better noise suppression compared to conventional gradient operators.