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Empirical colorant mixture models

Empirical colorant mixture models The color behavior of unconventional colorant systems and certain other mixtures cannot be described adequately by available theory. In such cases alternative approaches to formulation and shading need to be developed. In this article we investigate empirical models using Scheffé polynomials to describe color response surfaces for three‐ and four‐component olorant mixtures. We describe experimental designs that allow the efficient estimation of the coefficients of high‐order polynomial models over the full mixture‐design space and that also allow estimation of lower‐order models over subspace mixture regions. The experimental designs are applied to real colorant systems, and the accuracy of color response prediction from linear, quadratic, cubic, and quartic polynomial models is compared to that of theoretical models. The color response surfaces are visualized by preparing contour plots that depict color variation over a compositional region. These maps allow one to observe the relationship between color and composition, to assess the color gamut available with a given colorant set, and to estimate the formula or adjustments required to match a given color position. The effective use of model predictions to perform a sensitivity analysis on the compositional variables is also demonstrated in the context of manufacturing process control. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Color Research & Application Wiley

Empirical colorant mixture models

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References (8)

Publisher
Wiley
Copyright
Copyright © 1987 Wiley Periodicals, Inc., A Wiley Company
ISSN
0361-2317
eISSN
1520-6378
DOI
10.1002/col.5080120409
Publisher site
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Abstract

The color behavior of unconventional colorant systems and certain other mixtures cannot be described adequately by available theory. In such cases alternative approaches to formulation and shading need to be developed. In this article we investigate empirical models using Scheffé polynomials to describe color response surfaces for three‐ and four‐component olorant mixtures. We describe experimental designs that allow the efficient estimation of the coefficients of high‐order polynomial models over the full mixture‐design space and that also allow estimation of lower‐order models over subspace mixture regions. The experimental designs are applied to real colorant systems, and the accuracy of color response prediction from linear, quadratic, cubic, and quartic polynomial models is compared to that of theoretical models. The color response surfaces are visualized by preparing contour plots that depict color variation over a compositional region. These maps allow one to observe the relationship between color and composition, to assess the color gamut available with a given colorant set, and to estimate the formula or adjustments required to match a given color position. The effective use of model predictions to perform a sensitivity analysis on the compositional variables is also demonstrated in the context of manufacturing process control.

Journal

Color Research & Application – Wiley

Published: Aug 1, 1987

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