A feature-dependent fuzzy bidirectional flow for adaptive image sharpening

In this paper, a fuzzy bidirectional flow framework based on generalized fuzzy set is presented to sharpen image by reducing its edge width, which performs a fuzzy backward (inverse) diffusion along the gradient direction to the isophote line (edge), while does a certain forward diffusion along the tangent direction on the contrary. Gaussian smoothing to the second normal derivative of an image is used to decide its zero-crossing, which results in a robust sharpening process against noise. Controlled by the image gradient magnitude, the fuzzy membership function guarantees a natural transition across different areas. To preserve image features, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experiments on real images demonstrate that the algorithm substantially improves the visual quality of the enhanced image over some relevant equations.