the Physical Reconstruction Function

Digital halftoning, also referred to as spatial dithering, is the method of render-ing the illusion of continuous-tone pictures on displays that are capable of only producing binary picture elements. This report addresses the problem of de-veloping such algorithms that best match the specific parameters of any target display device, modeled as the Physical Reconstruction Function, particularly for nonstandard grid geometries. Techniques are organized by computational complexity and according to the nature of the dots produced, dispersed or clus-tered. The point process of dispersed-dot ordered dither is generalized for both rectangular and hexagonal grids, by means of the Method of Recursive Tessella-tion, a sub-tiling algorithm. Hexagonal ordered dither proves to be the solution for asymmetric rectangular grids. The concept of blue noise-high frequency white noise-is introduced and found to have desirable properties for halftoning. Very efficient algorithms for dithering with blue noise are developed, based on perturbed error diffusion. The nature of dither patterns produced is extensivel