David H. Foster, Kinjiro Amano, Sérgio M. C. Nascimento, and Michael J. Foster, "Frequency of metamerism in natural scenes," J. Opt. Soc. Am. A 23, 2359-2372 (2006)
Estimates of the frequency of metameric surfaces, which appear the same to the eye under one illuminant but different under another, were obtained from 50 hyperspectral images of natural scenes. The degree of metamerism was specified with respect to a color-difference measure after allowing for full chromatic adaptation. The relative frequency of metameric pairs of surfaces, expressed as a proportion of all pairs of surfaces in a scene, was very low. Depending on the criterion degree of metamerism, it ranged from about to for the largest illuminant change tested, which was from a daylight of correlated color temperature to one of . But, given pairs of surfaces that were indistinguishable under one of these illuminants, the conditional relative frequency of metamerism was much higher, from about to , sufficiently large to affect visual inferences about material identity.
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Centiles of Color Differences under the Second of Two Illuminants for Pairs of Surfaces with under the First Illuminant,a Calculated with Color-Difference Formula CIEDE2000[3, 27] and Adaptation Model CMCCAT2000[24]
Entries show means (SDs) of median and upper centiles evaluated over 29 predominantly vegetated scenes (e.g., trees, shrubs, grasses, flowers) and 21 predominantly nonvegetated scenes (e.g., buildings, painted or treated surfaces, rocks, stone) under successive daylight illuminants labeled by correlated color temperature. Number of pairs of surfaces sampled in each scene was 4,498,500. Data for were similar to those for and are not shown. The observer was the CIE 1964 standard observer.[3]
Table 2
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Entries show means (SDs) of relative frequency over 29 predominantly vegetated scenes and 21 predominantly nonvegetated scenes under successive daylight illuminants labeled by correlated color temperature. Number of pairs of surfaces sampled in each scene was 4,498,500. Entries for are for pairs of surfaces with subthreshold color differences, i.e., , under the first illuminant and any color difference under the second illuminant; those for are for pairs of surfaces with under the first illuminant and suprathreshold color differences under the second illuminant, i.e., , , , , respectively. Conditional relative frequencies are not defined for . The observer was the CIE 1964 standard observer.[3]
Table 3
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula ,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated With Color-Difference Formula [3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated from CIELAB[3] Alone, with Nominal Discrimination Threshold
Centiles of Color Differences under the Second of Two Illuminants for Pairs of Surfaces with under the First Illuminant,a Calculated with Color-Difference Formula CIEDE2000[3, 27] and Adaptation Model CMCCAT2000[24]
Entries show means (SDs) of median and upper centiles evaluated over 29 predominantly vegetated scenes (e.g., trees, shrubs, grasses, flowers) and 21 predominantly nonvegetated scenes (e.g., buildings, painted or treated surfaces, rocks, stone) under successive daylight illuminants labeled by correlated color temperature. Number of pairs of surfaces sampled in each scene was 4,498,500. Data for were similar to those for and are not shown. The observer was the CIE 1964 standard observer.[3]
Table 2
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Entries show means (SDs) of relative frequency over 29 predominantly vegetated scenes and 21 predominantly nonvegetated scenes under successive daylight illuminants labeled by correlated color temperature. Number of pairs of surfaces sampled in each scene was 4,498,500. Entries for are for pairs of surfaces with subthreshold color differences, i.e., , under the first illuminant and any color difference under the second illuminant; those for are for pairs of surfaces with under the first illuminant and suprathreshold color differences under the second illuminant, i.e., , , , , respectively. Conditional relative frequencies are not defined for . The observer was the CIE 1964 standard observer.[3]
Table 3
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula CIEDE2000,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated with Color-Difference Formula ,[3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated With Color-Difference Formula [3, 27] Adaptation Model CMCCAT2000,[24] and Nominal Discrimination Threshold a
Relative Frequencies and Conditional Relative Frequencies of Metameric Pairs of Surfaces in Natural Scenes, Calculated from CIELAB[3] Alone, with Nominal Discrimination Threshold