Grassmann's second law indicates that two lights or two stimuli may match in color appearance even though their spectral radiance (or power) distributions differ. This kind of condition is referred to as âmetamerismâ and the stimuli involved are called metamers. More precisely, metamers are color stimuli that have the same color appearance in hue, saturation, and brightness under a given illumination, but a different spectral composition. Metamers and color mixing are at the heart of CIE colorimetry. The CMFs that specify the human color stimulus derive from the metameric color matching by the fact that many colors are matched by additive mixtures of three properly selected primaries. This makes it possible for the tristimulus specifications of colors such as the one given in Eq. (1.1). Note that metamers of spectral colors are physically unattainable because they possess the highest intensity. To get around this problem, a primary is added to the reference side to lower the intensity so that the trial side can match. This is the reason that there are negative values in the original CMF, before transformation to have all positive values (see Section 1.4).
This chapter presents the types of metameric matching, the vector-space representation of the metamerism, and Cohen's method of object spectrum decomposition into a fundamental color stimulus function and a metameric black, often referred to as the spectral decomposition theory or matrix R theory. In addition, several other metameric indices are also reported.
3.1 Types of Metameric Matching
A general description of the metameric match for a set of mutual metamers with Î·1(Î»), Î·2(Î»), Î·3(Î»), â¦, Î·m(Î») stimulus functions can be expressed as follows: â«Î⋅ 1 (Î»)x Â¯ (Î»)dÎ»=â«Î⋅ 2 (Î»)x Â¯ (Î»)dÎ»=â¦=â«n m (Î»)x Â¯ (Î»)dÎ»=X, â«Î⋅ 1 (Î»)y Â¯ (Î»)dÎ»=â«Î⋅ 2 (Î»)y Â¯ (Î»)dÎ»=â¦=â«n m (Î»)y Â¯ (Î»)dÎ»=Y, â«Î⋅ 1 (Î»)z Â¯ (Î»)dÎ»=â«Î⋅ 2 (Î»)z Â¯ (Î»)dÎ»=â¦=â«n m (Î»)z Â¯ (Î»)dÎ»=Z. For the convenience of the formulation, we drop the constant k as compared to Eq. (1.1), where the constant k is factored into function Î·.
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