Wavelet representations of images are increasingly important as more image processing functions are shown to be advantageously executed in the wavelet domain. Images may be inverse halftoned, compressed, denoised, and enhanced in the wavelet domain. In conjunction with other wavelet processing, it would be efficient to halftone directly from the wavelet domain. In this paper we demonstrate how to perform error diffusion in the wavelet domain. The wavelet coefficients are modified by a normalization factor and re-arranged. Then, traditional feed-forward raster scan error diffusion is performed and quality halftones are shown to result. Error diffusing in the wavelet domain is noted to be non-causal with respect to the pixels, and thus the method is not reproducible by feed-forward raster scan error diffusion of pixels. It is shown that the wavelet halftones preserve the average value of the input for constant patches. The resulting halftones may appear smoother in smooth regions and sharper at edges than the corresponding pixel-domain halftones. Disadvantages may include a greater susceptibility to moire and false contouring. Error diffusion is a two-dimensional sigma-delta modulation, and the ideas presented may also be useful for one-dimensional sigma-delta modulation applications.
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