### BibTeX

@MISC{_localcriterion,

author = {},

title = {Local Criterion of Quality for Color Difference Formula},

year = {}

}

### OpenURL

### Abstract

It is important to be equipped with criterion of correspondence between color difference formula and experimental data of color discrimination of standard observer considering a quality of color printing or measuring. Such criterion is used to distinguish whether applied color difference formula is good enough. A well-known criterion is the value of ellipticity of MacAdam ellipses. In this paper we introduce a criterion based on newer and more thorough experimental data obtained by Wyszecki & Filder. We compare some well known color difference formulas using proposed criterion and show that they are not optimal for metering of color printing and measuring quality. Also we state that CIE XYZ should not be thought as an orthonormal space. Introducing a Cohen metric allows us to calculate a color difference more precise compared with CIE standard formulas (including CIE L*a*b * ∆E, ∆E 1994 and CIE DE 2000) with a great simplification of computation procedure. Criterion of Local Non-Uniformity Every time we talk about precision of color reproduction and there is a necessity to numerically evaluate a value of error, we have to calculate a color difference. Since it was introduced in 1976, color difference formula was modified several times. However, it is still not convenient enough from practical point of view. In this article we show, that XYZ and Lab systems are not the best choice for establishing a color difference formula. Most of colorimetric experiments allow a vector space approach for stimuli description, so we discuss several metrics based on distance definition traditional for vector algebra. To evaluate metric quality we use criteria of local non-uniformity based on Wyszecki & Fielder experiments. The shape of Wyszecki & Fielder ellipsoids can serve as a criterion of the chosen metric quality. From a practical point of view, the closer Wyszecki & Fielder ellipsoids ’ shape approximate the spheres with the same radius, the better the corresponding metric, the better it reflects the peculiarity of human color perception. In this paper, the ratio of the largest distance to the smallest distance between the center of ellipse and its ’ surface was used as the criterion of imperfection of metric:

### Keyphrases

color difference formula local criterion color difference color printing practical point colorimetric experiment color discrimination thorough experimental data wyszecki fielder experiment color reproduction wyszecki filder applied color difference formula several metric cie xyz measuring quality local non-uniformity every time standard observer computation procedure metric quality local non-uniformity lab system well-known criterion cie de several time wyszecki fielder ellipsoid macadam ellipsis stimulus description closer wyszecki fielder ellipsoid shape orthonormal space human color perception chosen metric quality great simplification distance definition experimental data vector space approach cie standard formula vector algebra