# MODELING COLOR RENDITION AND COLOR DISCRIMINATION WITH AVERAGE FIDELITY, AVERAGE GAMUT, AND GAMUT SHAPE

Open Access

- Graduate Program:
- Architectural Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 28, 2016
- Committee Members:
- Kevin William Houser, Dissertation Advisor
- Kevin William Houser, Committee Chair
- Richard George Mistrick, Committee Member
- Stephen James Treado, Committee Member
- James Landis Rosenberger, Outside Member

- Keywords:
- color rendering
- color discrimination
- fidelity
- gamut area
- best-fit ellipse
- transposition
- Rdt
- preference
- naturalness
- vividness
- skin preference

- Abstract:
- ABSTRACT Background Color rendering and color discrimination are complex topics and have been the subject of many investigations. Only one color rendering metric, the CIE General Color Rendering Index (Ra), is widely accepted in the industry, despite its well-documented flaws. Despite numerous attempts by the International Commission on Illumination (CIE) to update/replace the metric, they have been largely unsuccessful. The Illuminating Engineering Society (IES) has recognized the industry need for more accurate and predictive color rendition measures and recently published TM-30-15 The IES Method for Evaluating Light Source Color Rendition. The technical memorandum (TM-30-15) outlines a two-metric system consisting of an average fidelity metric (Rf), an average gamut metric (Rg), a Color Vector Graphic (CVG), and a suite of other metrics. Rf and Rg were designed to utilize the same set of statistically selected color samples, reference source, and uniform color space such that a tradeoff between them can be explicitly demonstrated. The goal of this study was to explore these tradeoffs by modeling participant responses—various subjective ratings and FM100 hue test performance—under systematically varied light spectra. Methodology The IES TM-30-15 Rf-Rg space was partitioned into 12 bins whose centers were the target for spectral optimization. The nominal target Rf values were 65, 75, 85, and 95. The nominal target Rg values were 80, 90, 100, 110, and 120. Two SPDs were designated at each Rf-Rg combination to have conceptually orthogonal gamut shapes; one CVG generally oriented in the direction of hue angle bin 1 (‘CB1’) and one generally oriented in the direction of hue angle Bin 7 (‘CB7’). All spectra were created to be a metameric match to 3500 K blackbody radiation and calibrated to an illuminance of 600 lux. A single viewing booth was filled with 12 familiar objects with strong memory associations and which span the hue circle, as much as practically possible. Objects were chosen to fit nominally into 6 color groups: “Red,” “Orange,” “Yellow,” “Green,” “Blue,” and “Purple.” Objects were split into two categories: 1. Consumer Goods (6 objects); and 2. Natural Food (6 objects). Each of the 24 light spectra were evaluated by 20 participants. Experimentation was blocked such that 20 participants saw a randomly selected 12 of the 24 light spectra, and 20 different participants saw the other 12 light spectra. A total of 40 individuals participated in this experiment. There were 23 males and 17 females with ages ranging from 20 to 41 years and with a mean age of 26 years. The independent variables for this experiment were Rf, Rg, and gamut shape (specified with variable CB). The dependent variables were subjective ratings of naturalness, vividness, preference, and skin preference and objective measures of color discrimination (error scores from the Farnsworth-Munsell 100 hue test). Analysis Subjective ratings Using a combination of best subset and stepwise regression analyses, the best fitting models for each of the subjective rating scales were determined. It was discovered that the CB variable (the nominal orientation of the CVG) did not provide the granularity needed for model prediction. The visual observation that most of the experimental CVGs can be approximated by an ellipse suggested that a best-fit ellipse approach may be suitable to quantify the shape of the CVG. A direct least-squares fitting of an ellipse is proposed to approximate the CVGs of the 24 experimental SPDs. The resulting best-fit ellipses can be defined by the length of their semi-major axis (a), the length of their semi-minor axis (b), and their angular rotation (ψ). The best-fit models for each of the subjective rating scales follows: NAT = 1.464 + 0.02674 Rf + 0.188 Rcs,h1 - 15.41 (Rcs,h1)^2 (r-sq = 0.92) - 0.05305 ψ + 0.000602 Rf*ψ VIV = 3.332 + 4.594 Rcs,h16 (r-sq = 0.86) LIKE = 1.629 + 0.02686 Rf + 3.423 Rcs,h16 - 10.01 (Rcs,h16)^2 (r-sq = 0.86) - 0.04866 ψ + 0.000566 Rf*ψ SKIN = 0.128 + 3.758 b + 1.161 Rcs,h16 - 8.41 (Rcs,h16)^2 (r-sq = 0.85) Overall, the best-fit models demonstrate strong predictive power of the subjective responses. The bolded terms above are those which take a similar form to the models recently published by Royer and others [2016]. Every best-fit model includes some parameter extracted from the color vector graphic (either Rcs,hi and/or a best-fit ellipse parameter) and an ode to red rendering. The models presented here show marked consistency with the recent results of Royer and others. Color discrimination The standard scoring software for the FM100 hue test—which is often used when administering this test—assumes the order of colored caps to be their order under CIE Illuminant C (under which they were designed). Direct application of the standard scoring software, therefore, assumes that the test light source does not transpose caps relative to their order under illuminant C. By directly applying the scoring software to an experiment which purposefully varies the illuminant, errors could be miscounted and the results distorted. To decouple the error calculation from the standard illuminant, an adjusted Total Error Score (TESadj) was computed which compared participants’ responses to the correct order of colored caps under the experimental SPD (not their order under Illuminant C). Seventy percent of the experimental light sources (17 of the 24) exhibited at least one transposition relative to CIE Illuminant C. No single metric—of the main TM-30 metrics and best-fit ellipse parameters—has a higher r2 than 0.57. Rg was a fairly poor predictor of TESadj (r2 = 0.47) and is consistent with recent studies that show average gamut indices are not strong indicators of color discrimination for LED light sources. The poor predictive power of the considered metrics prompted a post-hoc development of custom measures to predict TESadj based on two assumptions: (1) A light source which transposes the colored caps is more likely to cause difficulty discriminating between those caps (measured by the custom metric Rdt), and (2) A light source which compresses caps in color space will make it more difficult to discern between adjacent caps (i.e. smaller average hue angle difference, (∆h) ̅_i). This custom approach to modeling the adjusted total error score demonstrates strong predictive ability (r2 = 0.87) and is significantly stronger than any single metric or metric combination considered in this study. Conclusions Overall, the importance of the CVG and red rendering is apparent. It is evident that even a two-measure system of color rendition cannot fully encapsulate the complexity of color rendering and this work confirms that the CVG is primary information. The proposed best-fit ellipse approach to the CVG provides the granularity necessary for model prediction and an objective measure to quantify its shape. Distilling the graphic into few parameters can simplify its specification. The results of the present study, combined with past research, suggest that it is time for researchers to abandon average fidelity and average gamut measures for the prediction of color discrimination ability of LED sources. The robust predictive power of the proposed light source transposition error score (Rdt) provides strong evidence that a more nuanced approach to predicting color discrimination is viable. With accurate methods to predict color discrimination ability, an ordinal based rating scale should be developed for ease of specification.