24 Halftoning_error_diffusion - 2011

24 Halftoning_error_diffusion - 2011 - Advanced Digital...

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Unformatted text preview: Advanced Digital Halftoning – 2 October 2011 3.1 3. Error Diffusion Advanced Digital Halftoning – 2 October 2011 3.2 Synopsis • Error diffusion architecture • Error diffusion textures • Edge enhancement effect of error diffusion • Spectral analysis of error diffusion • Variations on a theme • Tone-dependent error diffusion • Efficient implementation of error diffusion • Clustered-dot error diffusion Advanced Digital Halftoning – 2 October 2011 3.3 Error Diffusion Architecture Advanced Digital Halftoning – 2 October 2011 3.4 Description of the Algorithm Advanced Digital Halftoning – 2 October 2011 3.5 1-D Example Advanced Digital Halftoning – 2 October 2011 3.6 2-D Error Diffusion Weighting Filters Advanced Digital Halftoning – 2 October 2011 3.7 Error Diffusion Examples Texture cliques Worms Advanced Digital Halftoning – 2 October 2011 3.8 Error Diffusion Characteristics • At each step, error diffusion preserves local average over part of image that has been binarized and part that is yet to be binarized • No fixed number of quantization levels • Requires more computation than screening • Excellent detail rendition (sharpens image) • Generally good texture with some exceptions: – Texture contouring – Worm-like patterns in highlights and shadows – Texture cliques in midtones – Texture used to render a given gray level may be context-dependent Advanced Digital Halftoning – 2 October 2011 3.9 Two Views of Error Diffusion Advanced Digital Halftoning – 2 October 2011 3.10 Fourier Analysis • Combining (1) and (3), • In Fourier domain, • Rearranging, we get where is a high-pass filter • This shows that the spectrum of the binary image consists of the spectrum of the continuous-tone image plus a high-pass filtered version of the spectrum of the quantization error. e Q [ m , n ] = g [ m , n ] − f [ m , n ] + w [ k , l ] e Q [ m − k , n − l ] l ∑ k ∑ E Q ( μ , ν ) = G ( μ , ν ) − F ( μ , ν ) + W ( μ , ν ) E Q ( μ , ν ) W ( μ , ν ) = 1 − W ( μ , ν ) G ( μ , ν ) = F ( μ , ν ) + W ( μ , ν ) E Q ( μ , ν ) (4) Advanced Digital Halftoning – 2 October 2011 3.11 Knox’s Empirical Model for Quantization Error* • We cannot find an analytical expression for • Knox proposed the following model Correlation coefficient – Residual – (generally some image-dependence) *K. T. Knox, “Error Image in Error Diffusion,” SPIE Vol. 1657 (1992) E Q ( μ , ν ) c R ( μ , ν ) ED Weights c 1-D 0.0 Floyd and Steinberg 0.55 Jarvis, Judice, and Ninke 0.80 E Q ( μ , ν ) = cF ( μ , ν ) + R ( μ , ν ) (5) Advanced Digital Halftoning – 2 October 2011 3.12 Application to Fourier Analysis • Combining (4) and (5), we get • The first term shows the origins of the sharpening effect that is characteristic of error diffusion....
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This note was uploaded on 02/19/2012 for the course ECE 638 taught by Professor Staff during the Fall '08 term at Purdue University.

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24 Halftoning_error_diffusion - 2011 - Advanced Digital...

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