An application of fractal analysis in halftoning

— Although the error‐diffusion technique is widely accepted as providing a good balance of gray‐scale reproduction and edge fidelity in halftones, a general graininess of the image remains. Since the visual system is more sensitive to halftoning errors in low frequencies or smooth areas, graininess is most objectionable in these regions. It is less visible in rough areas of an image. In order to gain insight into the error‐filtering effects of various error‐diffusion weights, we first investigate error‐weight modifications in test images that contain only a few textures. Given that the fractal dimension of an image area can predict the area's perceived smoothness or roughness, we describe a novel error‐diffusion scheme where the error weights depend on the local fractal dimension of the gray‐scale image. The technique modifies the widely used Floyd and Steinberg four‐weight mask at each pixel. Results and a comparison with other error‐diffusion schemes are provided.