# CIE94, History, Use, and Performance

**DOI:**https://doi.org/10.1007/978-1-4419-8071-7_13

## Synonyms

## Definition

The CIE94 color-difference formula [1] was developed by the CIE Technical Committee 1–29 “Industrial Color Difference Evaluation” chaired by Dr. D.H. Alman (USA). CIE94 is a CIELAB-based color-difference formula where CIELAB lightness, chroma, and hue differences are appropriately weighted by very simple “weighting functions” correcting CIELAB’s lack of visual uniformity, as well as by “parametric factors” accounting for the influence of illuminating/viewing conditions in color-difference evaluation. CIE94 may be considered a simplified version of the CMC color-difference formula [2], as well as a predecessor of currently CIE-recommended color-difference formula, the joint ISO/CIE standard CIEDE2000 [3, 4].

## Overview

In 1976, CIE recommended the CIELUV and CIELAB color spaces with their corresponding color-difference formulas, defined as Euclidean distances in such spaces. These two color spaces are only approximately uniform, and it was indicated that the use of different weighting for lightness, chroma, and hue differences may be necessary in different practical applications [5]. CIELAB has been widely accepted in many industrial applications [6], and in the past recent years, several CIELAB-based color-difference equations have been proposed to improve its performance. Among these formulas, we can mention, in chronological order, JPC79 [7], CMC [2], BFD [8], and CIE94. Nowadays, it is generally agreed that most of these formulas significantly improved CIELAB [9].

*E**

_{ 94 }(

*k*

_{ L }:

*k*

_{ C }:

*k*

_{ H }):

*S*

_{ L }), chroma (

*S*

_{ C }), and hue (

*S*

_{ H }) are defined as

*k*

_{ L },

*k*

_{ C },

*k*

_{ H }are set as 1.0 (i.e., do not affect the total color difference computation) under the next illuminating/viewing conditions, usually known as “reference conditions”:

Illumination: D65 source

Illuminance: 1000 lx

Observer: Normal color vision

Background field: Uniform, neutral gray with

L^{ * }= 50Viewing mode: Object

Sample size: Greater than 4 degrees

Sample separation: Direct edge contact

Sample color-difference magnitude: Lower than 5.0 CIELAB units

Sample structure: Homogeneous (without texture)

In the textile industry, it is common practice to set the lightness parametric factor *k*_{ L } to 2. Although the experimental conditions leading to this parametric correction to lightness difference are not yet well understood, it introduces important improvements in the performance of CIE94, which in this case must be designated as Δ*E**_{ 94 } (2:1:1) or CIE94 (2:1:1).

*E**

_{ 94 }value, Eq. 1 approximately represents [10] an ellipsoid with semiaxis lengths given by the denominators

*k*

_{ L }

*S*

_{ L },

*k*

_{ C }

*S*

_{ C },

*k*

_{ H }

*S*

_{ H }. Under reference conditions, the semiaxis lengths

*S*

_{ L },

*S*

_{ C },

*S*

_{ H }are often denominated lightness, chroma, and hue tolerances, respectively. Equation 6 indicates that lightness tolerance is the same for all color centers. However, Eq. 7 indicates that chroma tolerances increase with chroma; that is, human sensitivities to chroma differences are smaller for color centers with higher chroma, as earlier pointed out by McDonald [11]. Similarly, Eq. 8 also indicates that hue tolerances/sensitivities increase/decrease with chroma. In summary, assuming small color differences [10], the loci of constant CIE94 differences in CIELAB color space can be represented by ellipsoids with constant lightness semiaxes, which sections in the

*a**,

*b**plane are ellipses with their major axes pointing to the origin (i.e., ellipses radially oriented). The major and minor semiaxes of theses

*a**,

*b**ellipses linearly increase with the chroma of the ellipse centers (Fig. 1).

## Development

The development of CIE94 [12, 13] began with a selection of experimental visual datasets meeting the next main conditions: statistical significance (i.e., to represent a population average with its corresponding uncertainty), well-documented experimental conditions, and use of object color specimens. CIE TC 1–29 decided to use only three experimental datasets: Witt [14, 15], Luo and Rigg [16], and RIT-DuPont [17, 18]. The main goal was to use these datasets to find the best weighting functions *S*_{ L }, *S*_{ C }, *S*_{ H } correcting CIELAB. The analyses also considered the characteristics of the previous CMC color-difference formula, which was an ISO standard in textiles [19] and was successfully employed in different industries.

As indicated by Eqs. 7 and 8, it was found that simple linear chroma functions described the main trends in the experimental datasets analyzed. Both the lightness dependence of lightness tolerances and the hue angle dependence of hue tolerances proposed by the CMC color-difference formula were found not robust trends in the experimental datasets analyzed [13], and therefore they were disregarded in CIE94. It is possible that these two corrections proposed by CMC were influenced by some specific parametric factors. Anyway, it can be said that CIE94 was a conservative approach incorporating only the main corrections to CIELAB. Currently, the CIEDE2000 color-difference formula has incorporated additional corrections to CIELAB. For example, CIEDE2000 proposes a V-shaped function for the *S*_{ L } function, which is different to both the lightness function proposed by CMC and the simple *S*_{ L } = 1 adopted by CIE94.

CIE94 was the first CIE-recommended color-difference formula incorporating the influence of illuminating/viewing experimental conditions in color-difference evaluations through the use of the so-called parametric factors *k*_{ L }, *k*_{ C }, *k*_{ H } (see Eq. 1).

The work carried out by CIE TC 1–29 finished with the proposal of CIE94 and some guidelines for coordinated future work on industrial color-difference evaluation [20]. These guidelines updated those earlier given by Robertson [21], proposing a new set of 17 color centers to be studied in future research, considering the effects of changes from the “reference conditions,” and suggesting the development of a database of color-difference visual responses.

## Performance

From the combined dataset employed at CIEDE2000 development [22], the performance of different color-difference formulas has been tested using the *STRESS* index [23]. Low *STRESS* values (always in the range 0–100) indicate better color-difference formula performance. *STRESS* values for CIELAB, CIE94, and CIEDE2000 are 43.9, 32.1, and 27.5, respectively [24]. As we can see, the improvement achieved by CIE94 upon CIELAB was considerably higher than the one achieved by CIEDE2000 with respect to CIE94. From *STRESS* values, it can be also concluded that in CIE94 the *S*_{ C } function (which was also adopted in CIEDE2000) is a much more important correction to CIELAB than the *S*_{ H } function [24]. Besides CIE94 being proposed for object colors, it has been reported that this formula also performed satisfactorily for self-luminous color datasets [25].

Curiously, Eqs. 7 and 8 involve the geometrical mean of the CIELAB chroma of the two samples in the color pair, in place of the more simple arithmetical mean proposed in other color-difference formulas, for example, CIEDE2000. Strictly speaking, this implies that the locus of constant CIE94 differences with respect to a given color center is not an ellipsoid/ellipse, although deviations from ellipsoidal/elliptical contours can be considered negligible in most practical situations. CIE94 color differences computed using the geometrical and arithmetical means of the CIELAB chroma of the samples in the color pair are slightly different, in particular for colors with very low chroma [26].

In comparison with other recent formulas like JPC79, CMC, BFD, or CIEDE2000, it can be said that CIE94 was relevant because it was a very simple and versatile color-difference formula accounting for the main robust trends found in reliable color-difference visual datasets. CIE94 just proposes to use simple corrections to CIELAB provided by the weighting functions *S*_{ L }, *S*_{ C }, *S*_{ H } plus consideration of the influence of the illuminating/viewing conditions using the parametric factors *k*_{ L }, *k*_{ C }, *k*_{ H }. After the CIE94 proposal, CIE TC 1–47 continued further work leading to the last CIE-recommended color-difference formula, CIEDE2000, which significantly improved CIE94 for the experimental datasets used in its development [22].

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