Robust Chroma and Lightness Descriptors

New descriptors for lightness and chroma are presented that are based on properties of a wraparound Gaussian metameric to the given XYZ tristimulus coordinates. For the 1600 samples of the Munsell glossy set, both descriptors are found to correlate to Munsell value and chroma at least as well as the corresponding CIECAM02 descriptors when the Munsell samples are under the CIE C illuminant. However, when the illuminant is changed the new descriptors were found to be considerably more consistent under the second illuminant than those of CIECAM02. Introduction Object colour can be described in terms of three main dimensions, which are often specified as hue, chroma, and lightness [1]. In terms of hue, Mirzaei et al. [2][3] propose using the peak wavelength of a metameric Gaussian-like function (called a wraparound Gaussian) as a hue descriptor and show that it correlates as well as CIECAM02 hue does to Munsell hue [4], NCS hue [5], and the hue names in Moroney’s color thesaurus [6][7][8]. The Gaussian-based hue descriptor is also shown to be significantly more stable than CIECAM02 when the illuminant differs from CIE Standard Illuminant C. Given a CIE XYZ and the spectrum of the illuminant, the key idea of the hue descriptor is to determine the wraparound Gaussian reflectance function that is metameric (i.e., leads to the same XYZ) under the given illuminant and then base the hue on a property of that reflectance, namely the wavelength at which the Gaussian peaks. This paper introduces Gaussian-based chroma and lightness descriptors and compares them to CIECAM02 in terms of (i) how well they each correlate with the chroma and value designators of the 1600 Munsell [4] papers, and (ii) how stable the respective descriptors are under a change in the illuminant. Logvinenko’s Wraparound Gaussians The Gaussian-like representation used here originates from Logvinenko’s illuminant-invariant object-color atlas [10]. In contrast to other popular color spaces such as CIELAB/CIECAM02, Logvinenko’s atlas provides a coordinate system that is independent of the illuminant. The atlas is defined in terms of a special set of optimal spectral reflectance functions, no pair of which becomes metameric under any all-positive illuminant. In a subsequent paper [11], he suggests a Gaussian parameterization of his color atlas. This Gaussian parameterization involves reflectances defined in terms of a 3-parameter wraparound Gaussian function ( ; , , ) g k    defined as follows. When ( ) / 2 max min      then for / 2 min        2 ( ; , , ) exp[ ( ) ] g k k          (1) for /2 max       2 ( ; , , ) exp[ ( ) ] g k k           (2) When ( )/2 max min      then for / 2 min        2 ( ; , , ) exp[ ( ) ] g k k           (3) for /2 max       2 ( ; , , ) exp[ ( ) ] g k k          (4) In these equations, max min      , θ 1/σ , and and are the wavelength limits of the visible spectrum. For 0 1 k   , min max      and positive , we have a Gaussian-like reflectance (i.e., it is in [0, 1] for all wavelengths) function. We will refer to the triple kσμ as KSM coordinates, where σ stands for standard deviation, μ for peak wavelength, and k for scaling. Figure 1 shows an example of a wraparound Gaussian metamer for the spectral reflectance of Munsell paper 5 YR 5/6 under D65. Based on these KSM coordinates, we define descriptors for lightness (called KSM lightness) and chroma (called KSM chroma) and compare them to CIECAM02 lightness and saturation. Our tests show two important properties of both KSM lightness and chroma. First, they correlate well with the value and chroma designators of Munsell papers. Second, KSM descriptors are much more stable under a change of illuminant than CIECAM02. Figure 1. The spectral reflectance of Munsell 5 YR 5/6 (dotted black) and its metameric wraparound Gaussian (solid black) spectrum under D65. Result is for the 1931 ̅ ̅ 2-degree standard observer. CIE Lightness The CIE defines lightness in terms of brightness, where brightness is “...a visual perception according to which an area appears to exhibit more or less light.” (p. 26 of [12]). Lightness is then defined as “...the brightness of an area judged relative to the 75 23rd Color and Imaging Conference Final Program and Proceedings brightness of a similarly illuminated reference white” (p. 26 of [12]). KSM Lightness Given the XYZ coordinates (CIE 1931 2-degree observer functions ̅ , , ̅) for light reflected from an object illuminated by light of known spectrum, the parameters k, σ, and μ of the metameric wraparound Gaussian reflectance are determined. Given these KSM parameters, the KSM lightness is defined by: