Edge representation with fuzzy sets in blurred images

This paper proposes a representation of edges in blurred images using the concept of fuzzy sets when the images are degraded by various asymmetric and local blurring factors. The proposed representation is expressed by fuzzy membership functions, and it can serve as a relative index of blur. The membership function is derived from the distribution of intensity gradients and the symmetricity of gradient magnitudes, and the function is calculated directly from the blurred image without identifying the point spread function or restoring image. In this way, the fuzzy edge representation describes edges with their degradation states by fuzzy memberships instead of the binary description of edges. The index of fuzziness reflects the average amount of ambiguity presented in a fuzzy set, and the moments denote an object in the image quantitatively. These measures are adopted to illustrate the effectiveness of the representation in locally blurred images.