Generalized antisymmetric filters for edge detection

A large number of filters has been proposed to compute local gradients in grayscale images, usually having as goal the adequate characterization of edges. A significant portion of such filters are antisymmetric with respect to the origin. In this work we propose to generalize those filters by incorporating an explicit evaluation of the tonal difference. More specifically, we propose to apply restricted dissimilarity functions to appropriately measure the tonal differences. We present the mathematical developments, as well as quantitative experiments that indicate that our proposal offers a clear option to improve the performance of classical edge detection filters.