Skip to Main Content
Error diffusion halftoning is a popular method of producing frequency modulated (FM) halftones for printing and display. FM halftoning fixes the dot size (e.g., to one pixel in conventional error diffusion) and varies the dot frequency according to the intensity of the original grayscale image. We generalize error diffusion to produce FM halftones with user-controlled dot size and shape by using block quantization and block filtering. As a key application, we show how block-error diffusion may be applied to embed information in hardcopy using dot shape modulation. We enable the encoding and subsequent decoding of information embedded in the hardcopy version of continuous-tone base images. The encoding-decoding process is modeled by robust data transmission through a noisy print-scan channel that is explicitly modeled. We refer to the encoded printed version as an image barcode due to its high information capacity that differentiates it from common hardcopy watermarks. The encoding/halftoning strategy is based on a modified version of block-error diffusion. Encoder stability, image quality versus information capacity tradeoffs, and decoding issues with and without explicit knowledge of the base image are discussed.