Analysing observer metamerism in CIECAM02 using real observers

Given a fixed set of viewing conditions, a colour appearance model provides a method for transforming tristimulus values to perceptual attributes correlates, and vice versa. Current colour appearance models, like CIECAM02 [1], have been developed assuming the CIE31 Standard Observer. However a general model must adequately describe the colorimetric behaviour of a large enough set of real observers. In this work we analyse the variability of the different parameters defined by CIECAM02 when different sets of colour-matching functions associated with real observers are considered. All our sets of colour-matching functions are for small-size fields (smaller than 4). Our main goal is to evaluate the observer metamerism provided in CIECAM02 for a set of 13 real observers, when the reflectances of the 24 chips of the GretagMacbetch ColorChecker are illuminated under D65 and A illuminants. Preliminaries As it is well known, the colorimetric behaviour of an observer α is characterized by its corresponding set of colour-matching functions, ) ( ˆ λ α i x (i = 1, 2, 3). In order to check the influence of the inter-observer variability on the perceptual attribute correlates provided by CIECAM02, we have used the following sets of colour-matching functions: CIE1931 Standard Observer (α =1), those associated with the ten observers in Stiles-Burch’s Figure 1: Colour-matching functions ) ( 1̂ λ α x (α=1, ...,14) used in this work (upper graphic) and the corresponding percent standard deviation (lower graphic) Figure 3: Colour-matching functions ) ( ˆ3 λ α x (α=1, ...,14) used in this work (upper graphic) and the corresponding percent standard deviation (lower graphic) CGIV 2008 and MCS’08 Final Program and Proceedings 31 Figure 4: Coefficient of variance 65 D l CVQ (upper graphic) and A l CVQ (lower graphic). pilot research (α =2...11) [2], and the CF, JAM, and MM observers (α =12, 13, and 14) [3, 4]. In this way, α runs from 1 to 14. This number is large enough in order to provide significative statistical results. The previous mentioned sets of colour-matching functions are shown in Figures 1 to 3, referred to the CIE31 representation system. In these Figures the thin solid lines in the upper graphics represent the individual ) ( ˆ λ α i x colour-matching functions. The red thick solid line shows the average value of these functions and the blue dashed lines represent the average plus/minus the corresponding standard deviation. The lower graphics in these Figures exhibit the percent standard deviation associated with the average for the corresponding functions. The standard deviation in Figure 3 exhibit an anomalous behaviour for the larger wavelengths. This manner of acting has no importance due to the fact that the ) ( ˆ3 λ α x functions take no significative values in this spectral range. From the previous Figures it becomes obvious that functions ) ( ˆ2 λ α x show a lower standard deviation (lesser than 20%) in all the spectral range in which they take significative values. For the ) ( 1̂ λ α x and ) ( ˆ3 λ α x colour-matching functions the standard deviations are about 40-60% in the significative spectral regions. These results point out that the inter-observer variability is relevant. The different colour stimuli used to evaluate the behaviour of the CIECAM02 appearance model have been generated by using the 24 spectral reflectances of the GretagMacbetch ColorChecker. The measurements of these reflectances have been performed from 400 nm to 700 nm in steps of 5 nm. For each observer, the tristimulus values of the different reflectances have been computed by using the CIE standard illuminants D65 an A. These illuminants can be considered as representative of two very different conditions of lighting: outdoor and inside lighting. The categorical viewing and lighting conditions setting for the CIECAM02 model were those associated with condition named “Surface colour evaluation in a light booth” in Reference [1]. The present work is an extension consequence of a previous one carried out by the authors [5]. Results Given an observer α (α =1, ..., 14), a spectral reflectance l (l=1, ..., 24), and an illuminant m (m=D65, A), we have computed the following perceptual attribute correlates: brightness ( m l Q , α ), lightness ( m l J , α ), colorfulness ( m l M , α ), hue angle ( m l h , α ), and the Cartesian coordinates m l m a , ) ( α and m l m b , ) ( α . For each reflectance we have computed the average of the previous quantities over all the observers (it is done for both of the illuminants D65 and A). The corresponding coefficients of variance are also obtained: m l CVQ , m l CVJ , m l CVM , m l CVh , m l m a CV ) ( , and m l m b CV ) ( . In the case of the brightness an the illuminant D65, we have