Defining color tolerances numerically continues to be a topic of intense interest in colorimetry. A technique was developed to evaluate formula performance that incorporated visual uncertainty. In this technique, visual uncertainty was represented by randomized equal color-difference ellipsoids or randomized visual color differences. STRESS, a multivariate statistical tool, was employed to quantify these randomized equal color-difference ellipsoids or visual color differences. The STRESS clouds were composed of the STRESS values between the randomized equal color-difference ellipsoids and T50 equal color-difference ellipsoids, or between the randomized visual color differences and T50 visual color differences where T50 represented visually determined tolerances equivalent to an anchor-pair stimulus. These STRESS values clouds were taken as rulers to evaluate whether one color-difference formula over-, under- or well-fitted a specified color-difference dataset, based on an F-test. This technique is a necessary addition to the current deviation evaluation metrics, e.g., PF/3. In follow-on research, a Euclidean color space was developed with the color-difference formula based on IPT color space for supra-threshold color differences. The color-difference formula has similar chromatic modeling to CIE94. A lightness transformation function was applied to model color difference along lightness. A rotation matrix on the chromatic plane was also applied to achieve better characteristics of the color space. A step-wise optimization was performed to achieve better consistency and remove conflicts between different color-difference datasets. The evaluations include STRESS, F-test, hue constancy and equal color-difference ellipsoid shape. It was shown by the evaluation results that the Euclidean color space could be a potential candidate of a future color model useful for defining industrial color tolerances.
Library of Congress Subject Headings
Colorimetric analysis; Colorimetry--Mathematical models
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Berns, Roy S.
Shen, Shizhe, "Color difference formula and uniform color space modeling and evaluation" (2009). Thesis. Rochester Institute of Technology. Accessed from
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