The principle of color reproduction by the superimposition of halftone dots in printing process being essentially subtractive mixture, the necessity of the correction of optical dot gain, and the corrective term of optical dot gain into Pollak equation concerning C, M, Y, Bk halftone dots imposed on paper were already introduced by Nonaka, et al., in 1999. This paper presents the numerical output method of the C, M, Y and Bk dot areas converted from the image singal R, G, B harvested from continuous tone color original by scanner using proportional tone compression. The dot area of black by gray component replacement (GCR) was fixed and other C, M, Y dot areas were determined so that the optical reflectance through color filter (R, G, B) was to be equalized with the optical reflectance by prepositional tone compression. The dot areas were determined by the simultaneous quadratic equations with three unknowns (c, m, y). These equations were constructed with Pollak equation containing the corrective terms of optical dot gain and solved by the succesive approximation devised or the method of Newton-Raphson. The conversion contained gray balance, optical and mechanical dot gain, GCR, masking (color correction) and the effect of paper used. The process work has been dealt with empirically. While LUT is one of the empirical methods, the proposed treatment presented in this paper is to construct the numerical model of color image made up of dot areas superimposed, and by this treatment the fractions of dot areas required are calculated numerically.
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