Object-color-signal prediction using wraparound Gaussian metamers

Abstract

Alexander Logvinenko introduced an object-color atlas based on idealized reflectances called rectangular metamers in 2009. For a given color signal, the atlas specifies a unique reflectance that is metameric to it under the given illuminant. The atlas is complete and illuminant invariant, but not possible to implement in practice. He later introduced a parametric representation of the object-color atlas based on smoother "wraparound Gaussian" functions. In this paper, these wraparound Gaussians are used in predicting illuminant-induced color signal changes. The method proposed in this paper is based on computationally "relighting" that reflectance to determine what its color signal would be under any other illuminant. Since that reflectance is in the metamer set the prediction is also physically realizable, which cannot be guaranteed for predictions obtained via von Kries scaling. Testing on Munsell spectra and a multispectral image shows that the proposed method outperforms the predictions of both those based on von Kries scaling and those based on the Bradford transform.

Gaussian-Based Hue Descriptors

“…basing hue on the peak wavelength of a metameric Gaussian-like reflectance from Logvinenko's pseudo-color atlas as the representation of hue. Such Gaussian-like reflectances have been used previously as a tool for predicting how a color signal (i.e., cone response triple) changes with a change in illumination [7]. Similar, but somewhat different, Gaussian-based representations of hue have been proposed previously by Mizokami et al [8][9] and further explored by O'Neil et al [10] and shown to explain the class of hue shifts known as the Abney effect.…”

“…For the wraparound Gaussian, however, there is no such overlap (see Fig. 2(c) of [7]). The overlap for the subtractive Gaussians implies that for a given XYZ we might find metameric Gaussians of both type G + and G -.…”

“…In a previous study [7] we compared (see Fig. 2 of [7] page 1682) the gamuts of chromaticities in the CIE 1931 XYZ tri-stimulus space for subtractive Gaussians, inverse Gaussians, and wraparound Gaussians under illuminant CIE D65 and found that neither subtractive Gaussians nor inverse Gaussians can cover the entire chromaticity gamut when the functions are restricted to being reflectance functions (i.e., all values in [0,1]). On the other hand, wraparound Gaussians do cover the entire chromaticity gamut.…”

“…On the other hand, wraparound Gaussians do cover the entire chromaticity gamut. Given an XYZ, the parameters of the subtractive and wraparound Gaussians can be found via a two-parameter optimization [7] that is independent of the scaling parameter; however, in the case of inverse Gaussians such a decomposition is not possible, so a much more difficult, threeparameter optimization is required. Given that inverse Gaussians are more difficult to compute and do not cover the chromaticity gamut, we do not consider them further here.…”

On the properties of some low-parameter models for color reproduction in terms of spectrum transformations and coverage of a color triangle

“…Closure under addition allows us to describe the summation effect of several lighting sources correctly, and closure under multiplication allows us to describe multiple reflections of light from surfaces [16,17] and to approximate high-saturation spectra higher accuracy [14]. Also, an important property is the color set coverage [14,18,19]. As a rule, it is not always possible to satisfy all the properties simultaneously, so the question arises: "How many (and which) properties can a single model have?…”