Fuzzy bidirectional flow for adaptive image sharpening

A growing amount of research concerning partial differential equations in image sharpening has been done for years, most of which, however, indicating edges by a binary zero-crossing decision process, produce a false result with piecewise constant regions. In this paper, a fuzzy bidirectional flow framework based on generalized fuzzy sets is proposed, which performs a fuzzy backward (inverse) diffusion along the gradient direction to the isophote lines (edges), while does a certain forward diffusion along the tangent direction on the contrary. The fuzzy membership function is controlled by the second order normal derivative of the image (or the smoothed one in the presence of noise). To preserve image features, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image.