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Symmetry properties of halftone images I : Scattering symmetry and pattern symmetry

Previous work has shown that the mechanism of color and tone reproduction in halftone imaging systems can be described quantitatively by modeling functions for mean level probability, P ij , for light scattering from region i to region j, where regions i and j may be, for example, regions of the printed paper covered by different inks in the halftone process. The value of P ij has been shown to be a function of the area fractions of the regions, f i and f j . In the past, the P ij functions were written empirically to fit observed data or determined by convolution calculations involving the paper point spread function, PSF, and the transmittance geometry of the halftone pattern, T(x,y). In the current work it is shown that characteristics of the P ij functions can be deduced from symmetry properties of light scattering in paper and symmetry properties of the halftone pattern. This allows some P ij functions to be derived directly without the need to carry out a convolution with the point spread function of the paper. Models of these symmetry properties and methods for experimental analysis are presented.