scope:

Purpose and Scope

Ellipsoidal color difference equations are used to calculate a volume of acceptable color difference, based on the color of the Reference and the specified tolerance. CIEDE2000 and CMC (l:c) are both ellipsoidal color difference equations, and they may both be used for color evaluation of textile and other materials in many applications. The current data (see references 6.1 through 6.7) indicate that the CIEDE2000 metric performs slightly better in terms of agreement with visual evaluations. It is therefore being recommended as the primary color difference method to use for instrumental evaluations.

The CIEDE2000 formula is denoted as ΔE₀₀. The CMC (l:c) formula is generally shown as ΔE_cmc. Both CIEDE2000 and CMC (l:c) are extensions of the CIE 1976 L*a*b* color-difference formula with corrections for variation in color-difference perception dependent on lightness, chroma, and hue. CIEDE2000 additionally includes corrections for chroma-hue interaction.

The CMC (l:c) modification to CIELAB provides a unit of measurement for the acceptance volume about a reference color. This volume takes the shape of an ellipsoid whose base semi-axes are defined by SL, SC, and SH in the directions of lightness, chroma, and hue differences, respectively, in CIELAB color space. The actual size and shape of the ellipsoid is further controlled by modifying parametric factors l and c, see section 3.3. The CMC (l:c) formula varies the ratio of the lengths of these three semi-axes systematically throughout CIELAB color space according to the equality of lengths with perceptually equal color differences, regardless of both the color of the Reference and the direction of difference of any trial specimen from it. Around any given reference color, the ratio SL:SC:SH is fixed regardless of the industrial application. However, it should be noted that color difference evaluations may vary if the reference and trial specimen are switched. Note: The difference in the resulting total color difference computed in the two directions (reference to specimen vs. specimen to reference) is not significant for color differences of the magnitude that is relevant for textile applications (under 3.0 units).

The CIEDE2000 modification to CIELAB also provides an ellipsoidal acceptance volume about a reference color. It is analogous to CMC (l:c) in the use of three semi-axes for the lightness, chroma, and hue dimensions. CIEDE2000 was developed to improve on shortcomings identified in the performance of various color difference equations including CMC (l:c). CIEDE2000 differs from CMC (l:c) in an important application, however. CIEDE2000 determines the arithmetic mean between the Reference and Specimen and uses this as the point in CIELAB color space to determine the shape of the ellipsoidal space. This resolves the associated color differences encountered when the reference and the specimen are reversed. This also results in the boundary for the acceptance volume to be somewhat imprecise for a group of specimens compared to a single reference, since the calculations are based on the relation of each specimen to the reference,). Because of this difference in computing the acceptance boundary, CIEDE2000 may not be suited for some applications, especially when visual plotting is utilized.

Both CIEDE2000 and CMC(l:c) support the use of component color difference metrics, that is DL, DC, and DH values which are weighted for visual acceptance by the CMC (l:c) or CIEDE2000 internal math, respectively. These weighted values of DL, DC, and DH are correlated more strongly to visual color evaluation than legacy metrics such as DL*, Da*, Db*, DC*, DH*. For CMC (l:c), these component color difference terms are DL_cmc, DC_cmc, DH_cmc. For CIEDE2000, these terms are DL₀₀, DC₀₀, and DH₀₀.

In applications which require rating within or about a critical tolerance, multiple levels consisting of ellipsoidal volumes representing various levels of color difference may be generated in both ΔE₀₀ and ΔE_cmc. This will result in a set of concentric volumes/tolerances which provide a uniform grading system when correlated to and associated with a predefined set of terms. An example of this is the association of Gray Scale Grades with word descriptions as shown in Table III of AATCC EP9-2021.