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The properties of multiple CMF determinations using alternative primary sets Part II: A data unification methodology

The properties of multiple CMF determinations using alternative primary sets Part II: A data... The spectral power values representing Thornton's “alternative primary” PC, NP, and AP colour matching functions (CMF) are compared with the power values representing the 49‐observer Stiles–Burch average definition. The Thornton measurements are first converted by matrix transformation into a data set expressed in terms of spectral power at the Stiles–Burch primary wavelengths. Graphs and power ratios are used to compare the definitions for two alternative matches to the same visual stimulus. A triplet of n:n spectral‐power ratios (one in each dimension, R, G, and B) is used to quantify the differences between the alternative matches. The relationship between the Thornton PC and Stiles–Burch match‐definitions is then found to deviate from the expected power‐ratio of 1:1 after matrix transformation. The revealed relationship is an internally consistent and smooth function of matched wavelength, which has a different nonlinear characteristic in each R, G, and B dimension relative to the Stiles–Burch reference model. The “Thornton bow‐tie” phenomenon is also demonstrated between a pair of maximum saturation CMF definitions made with alternative primaries. The implicit differences in neutral axis definition represented by the bow‐tie diagram are linked to differences in trichromatic unit (T‐unit) definition. In this case, the conventional CMF normalization process is postulated to be inaccurate at the wavelengths concerned, resulting in incompatibility between the T‐unit definitions of the two primary sets being compared. The conventional N→3 T‐unit definition of visual neutrality equating Illuminant SE to a single R:G:B power ratio is extended, by adding an extra N→N mapping to the definition. The resulting N→N→3 mapping is in principle a fully determined redefinition of three‐dimensional T‐unit equivalence, in which many R:G:B ratios for a comprehensive set of visually neutral metamers can be mapped by N→N transformation onto the conventional single ratio. The effect of N→N mapping is to transform spectral power distributions (SPDs) into spectral effect distributions (SEDs) expressed in T‐units. The SPD/SED transform, thus defined, is proposed as a method for unifying CMF determinations made with alternative primaries. The expected outcome is that after transforming SPDs by N→N mapping into SEDs the definitions for all visually matching metamers will be demonstrably interconvertible by matrix product. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 438–450, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20069 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Color Research & Application Wiley

The properties of multiple CMF determinations using alternative primary sets Part II: A data unification methodology

Oulton, D. P.
Color Research & Application , Volume 29 (6) – Dec 1, 2004
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References (13)

Publisher
Wiley
Copyright
Copyright © 2004 Wiley Periodicals, Inc.
ISSN
0361-2317
eISSN
1520-6378
DOI
10.1002/col.20069
Publisher site
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Abstract

The spectral power values representing Thornton's “alternative primary” PC, NP, and AP colour matching functions (CMF) are compared with the power values representing the 49‐observer Stiles–Burch average definition. The Thornton measurements are first converted by matrix transformation into a data set expressed in terms of spectral power at the Stiles–Burch primary wavelengths. Graphs and power ratios are used to compare the definitions for two alternative matches to the same visual stimulus. A triplet of n:n spectral‐power ratios (one in each dimension, R, G, and B) is used to quantify the differences between the alternative matches. The relationship between the Thornton PC and Stiles–Burch match‐definitions is then found to deviate from the expected power‐ratio of 1:1 after matrix transformation. The revealed relationship is an internally consistent and smooth function of matched wavelength, which has a different nonlinear characteristic in each R, G, and B dimension relative to the Stiles–Burch reference model. The “Thornton bow‐tie” phenomenon is also demonstrated between a pair of maximum saturation CMF definitions made with alternative primaries. The implicit differences in neutral axis definition represented by the bow‐tie diagram are linked to differences in trichromatic unit (T‐unit) definition. In this case, the conventional CMF normalization process is postulated to be inaccurate at the wavelengths concerned, resulting in incompatibility between the T‐unit definitions of the two primary sets being compared. The conventional N→3 T‐unit definition of visual neutrality equating Illuminant SE to a single R:G:B power ratio is extended, by adding an extra N→N mapping to the definition. The resulting N→N→3 mapping is in principle a fully determined redefinition of three‐dimensional T‐unit equivalence, in which many R:G:B ratios for a comprehensive set of visually neutral metamers can be mapped by N→N transformation onto the conventional single ratio. The effect of N→N mapping is to transform spectral power distributions (SPDs) into spectral effect distributions (SEDs) expressed in T‐units. The SPD/SED transform, thus defined, is proposed as a method for unifying CMF determinations made with alternative primaries. The expected outcome is that after transforming SPDs by N→N mapping into SEDs the definitions for all visually matching metamers will be demonstrably interconvertible by matrix product. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 438–450, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20069

Journal

Color Research & Application – Wiley

Published: Dec 1, 2004

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