Many coloration applications require the match of a reference color under specific viewing and illuminating conditions (primary conditions). Such so called metameric matches are, however, unlikely in practice due to various noise sources in most production processes. As a result the match is not perfect and the real colors are rather grouped around the reference color. In this paper we investigate such so called parameric colors under the assumption that they follow a normal distribution with the reference color as expectation value. We analyze corresponding distributions of parameric reflectances and calculate the distribution of colors if the viewing and illuminating conditions change (secondary conditions). A paramer mismatch gamut can be defined by the 95% boundary ellipsoid of this distribution. Based on this definition a formula is proposed to calculate its volume in terms of CIELAB unit. In the experiments we compare the volumes of 95% boundary ellipsoids for primary and secondary conditions and analyze the properties of a mismatch quantity that is defined as the ratio of these volumes.
Philipp Urban, "Distributions of Paramers and Paramer Mismatch Gamuts" in Proc. IS&T 17th Color and Imaging Conf., 2009, pp 143 - 148, https://doi.org/10.2352/CIC.2009.17.1.art00027