This dissertation was presented to the Faculty of the Graduate School of The University of Texas at Austin in partial fulfillment of the requirements for the degree of

Ph.D. in Electrical Engineering

Digital halftoning is the process by which a grayscale or color continuous-tone image is quantized to a limited number of discrete graylevels for printing or display. In halftoning by error diffusion, the quantization error at each image pixel is diffused to the unprocessed pixels in a neighborhood around the current quantized pixel via an error filter. This process aims at shaping the quantization noise power into the high frequency regions where the human eye is least sensitive. Such noise shaping results in a high-quality halftone reproduction of the continuous-tone image.

This dissertation extends error diffusion halftoning to operate on vector valued images. Vector valued images arise naturally as color images (e.g. RGB images) or synthetically as grayscale images. Vector-valued grayscale images have been subjected to a "blocking" operation, which divides the image into blocks and stores each block as a vector. In each case, the quantization error at a given component of the vector at the current location is not only diffused to the corresponding components of the neighboring vectors but rather to all of their components. This requires that the error filter is no longer a conventional filter with scalar-valued coefficients but rather a "multifilter" whose coefficients are matrices.

This dissertation develops a linear matrix "gain" model for the quantizer for the analysis and design of vector error diffusion halftoning systems. Design strategies for the matrix-valued error filter are presented for both the vector color halftoning and the block error diffusion halftoning cases to achieve specific goals, such as minimizing visual quantization error in color halftoning, and producing dot-clusters with user controllable properties in block error diffusion. Efficient parallel implementations of vector error diffusion halftoning are also described.