8 September 1993 Mean-preserving multilevel halftoning algorithm
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In multilevel halftoning, the appearance of intermediate shades of gray is created by the spatial modulation of more than two tones, i.e., black, white, and one or more gray tones. Periodic multilevel halftoning can be implemented similarly to bitonal halftoning by using N-1 identically sized threshold matrices for N available output levels. The amount of modulation in the output image is dependent on both the number of output levels and the spatial arrangement of threshold values. A method is presented for assessing the modulation resulting from a periodic multilevel halftone algorithm. The method is based on the constraint that the digital output of the halftone process be mean-preserving with respect to the input. This constraint is applied to the tone transfer functions of each pixel in the halftone cell, producing the result that the sum of the derivatives of all the unquantized tone transfer functions must equal the number of pixels in the halftone cell for all input values. This rule leads to a simple graphical technique for evaluating the modulation in a halftone algorithm as well as suggesting an infinite number of ways to vary the modulation. The application of this method to traditional as well as alternate halftone architectures is discussed.
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Rodney L. Miller, Rodney L. Miller, Craig Smith, Craig Smith, } "Mean-preserving multilevel halftoning algorithm", Proc. SPIE 1913, Human Vision, Visual Processing, and Digital Display IV, (8 September 1993); doi: 10.1117/12.152710; https://doi.org/10.1117/12.152710

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