Two New von Kries Based Chromatic Adaptation Transforms Found by Numerical Optimization

In this paper, two new von Kries based chromatic adaptation transforms are proposed. The numerical optimization procedure adopted for deriving them simultaneously exploits the whole sets of data available and the existing chromatic adaptation transforms. Experimental results report several statistics to prove the effectiveness of our proposals with respect to the state-of-the-art. INTRODUCTION Chromatic adaptation transforms (CATs) are able to predict corresponding colors. A pair of corresponding colors consists of a color observed under one illuminant, and another color that has the same appearance when observed under a different illuminant [5]. This research topic has been extensively studied given its importance for many industrial applications, such as the prediction of color inconstancy, the evaluation of the color rendering property of light sources, and the achievement of successful color reproduction under different light sources [5],[14]. A survey of several CATs are given by Fairchild in his book [14]. Luo and Hunt [2] proposed a modified Bradford transform [3], which is included in CIECAM97s. Finlayson and Süsstrunk [4] have derived a transform based on sharpened sensors. Li et al. [5] derived a transform, known as CMCCAT2000, by fitting all the available corresponding color data sets, instead of just the Lam and Rigg set. Moroney et al. [6] proposed a modified CMCCAT2000 to be used with the CIECAM02 model. In 2004, the CIE TC 1-52 “Chromatic Adaptation Transforms” [20] tested thirteen chromatic adaptation transforms indicating four possible candidates for future CIE recommendations giving quite similar performances. The members of the CIE TC 1-52 were unable to agree to a single CAT as some of them required that the adopted transform must be theoretically based. Other members still agreeing that such objective is desirable, considered that was important to indicate a single CAT that should work as well as possible, even if only applicable to a limited range of conditions. In this paper, we propose two von Kries based chromatic adaptation transforms that outperform or are statistically equivalent to the existing ones on all the corresponding color datasets available. These transforms are found by numerical optimization based on Particle Swarm Optimization. The key idea in our procedure is the simultaneous use of all the corresponding color data sets available and the predictions of the corresponding colors done using already defined CATs. One of the reviewers let us know that many of the datasets used to fit chromaticadaptation models are influenced by illuminant-induced changes of reflected-light tristimulus values, as well as by the desired measurand of visual adaptation. Because several works treat these data as arising solely from visual adaptation, we will do so here too. In the long run, however, adaptation models should be derived and/or tested by data sets based on experiments that keep the test-patch tristimulus values constant when the light is changed in the wider visual field. Only under such conditions can visual adaptation effects be separately inferred. For the first CAT proposed, to boost as much as possible the performances, objective function uses both Wilcoxon signed-rank tests and the perceptual error metrics Lab E ∆ and 94 CIE E ∆ . As shown in the experimental results section, the proposed CAT outperforms existing solutions. For the second CAT we add to the above mentioned terms in the objective function, a positivity constraint on its spectral responses in order to have stable color ratios across illuminants [21]. The fitting results are, in this case, only statistically equivalent to the best available CATs. CHROMATIC ADAPTATION TRANSFORMS Several chromatic adaptation transforms exist in the literature, most based on the von Kries model [1]. CIE XYZ tristimulus values [ ] Z Y X ' ' ' are linearly transformed by a 3x3 matrix CAT M to derive the post-adaptation cone responses under the first illuminant. The resulting values are independently scaled to get the post-adaptation cone responses under the second illuminant. This transform is usually a diagonal matrix based on the post-adaptation cone responses of the illuminants’ white-point. To obtain CIE XYZ tristimulus values under the second illuminant [ ] Z Y X ' ' ' ' ' ' , the post-adaptation cone responses under the second illuminant are then multiplied by the inverse of matrix CAT M [7]. This model is outlined in Equation (1):