Image Gradient Estimation with Wide Support Kernels

Gradient estimation using small support kernels is often used in edge detection algorithms. Small kernels such as Sobel and Roberts are often used in order to obtain gradient estimation in a short time. However, the limited number of samples that are used in the gradient estimation adversely affects the estimation performance under noise. Moreover, kernels larger than 3times3 cause interference of neighboring objects and localization problems. Another problem associated with small kernels is that they can not detect smooth edges. On the other hand, gradient estimation with large kernels at any image location yields better estimations due to more samples used in the computation. Also noise suppression can be handled in a better way. The goal of this paper is to devise a fuzzy topology based method that diminishes the problems of using larger kernels. The proposed method addresses the issues of interference of nearby objects and wide response area around edges for larger kennels. Results show that the proposed filter can be used instead of small support kernels since it reacts to both step and ramp edge models. Under heavy noise, topological gradient estimation is shown to perform superior to conventional gradient operators with same sizes.