We use color difference metrics to quantify the perceptual difference between colors. All of these metrics are based on L*a*b* color space, which was designed to be perceptually uniform. If it were truly uniform, perceptual color differences could be determined by the Euclidian distance between colors expressed as L*a*b* values (CIE 1976 metrics):

Δ

E*_{ab}= ( (L*_{2}-L*_{1})^{2}+ (a*_{2}-a*_{1})^{2}+ (b*_{2}-b*_{1})^{2})^{1/2}= (ΔL*^{2}+ Δa*^{2}+ Δb*^{2})^{1/2}

We are often interested in differences between color only, omitting luminance.

Δ

C*_{ab}= ((a*_{2}-a*_{1})^{2}+ (b*_{2}-b*_{1})^{2})^{1/2}= (Δa*^{2}+ Δb*^{2})^{1/2}

However, L*a*b* (sometimes referred to as CIE 1976) is not nearly as uniform
as its designers intended. In particular, the eye is a good deal less sensitive
to differences in chroma (*c** = (*a**^{2} + *b**^{2}
)^{1/2 }; i.e., intensity of color) for strongly chromatic colors than
it is to hues (hue angle = *h** = arctan(*b*/*a*) ). To
correct this deficiency several color metric formulas have been proposed.

**CIE 1994:**Δ*E**_{94}, which includes Luminance*L**, and Δ*C**_{94}, which omits*L**.**CMC:**Δ*E**_{CMC}, which includes Luminance*L**, and Δ*C**_{CMC}, which omits*L**. Widely used in the textile industry for matching bolts of cloth.**CIEDE2000:**Δ*E*_{00}, which includes Luminance*L**, and Δ*C*_{00}, which omits*L**. This is the emerging standard as well as the most accurate color difference metric. Its acceptance has been slowed by the complexity of its formula. Although it is less familiar that the other equations, it is the best choice in the long run.

Whichever metric you choose, remember that they give different numbers. It is important to be consistent and always specify which measurement you are using.

The Hue and Chroma differences, Δ*H** and Δ*C**, are
of interest for their own sake and because they are used in the CIE 1994 and CMC
color difference formulas, below.

Δ*H** = ( (Δ*E* _{ab }*)

Δ*c** = ( *a _{1}**

Δ*h* = *180/π (arctan( *b _{1}** /

Δ

Δ*h* = *0 where the hue angle is poorly defined: L* < 2 ; max(*a _{1
}*,

**CIE
1976**

The
L*a*b* color space was designed to be * relatively*
perceptually uniform. That means that perceptible color difference is
approximately equal to the Euclidean distance between L*a*b* values. For colors
{

ΔE*= ( ( Δ_{ab}L*)^{2}+ (Δa*)^{2}+ (Δb*)^{2})^{1/2}(DCIH (1.42, 5.35); (...)^{1/2}denotes square root of (...) ).

Although
Δ*E* _{ab}* is relatively simple to calculate and understand,
it's not very accurate especially for strongly saturated colors. L*a*b* is not
as perceptually uniform as its designers intended. For example, for saturated
colors, which have large chroma values (

**CIE
1994**

The
CIE-94 color difference formula, Δ*E**_{94},
provides a better measure of perceived color difference.

ΔE*_{94}= ( (ΔL*)^{2}+ (ΔC*/(DCIH (5.37); omitting constants set to 1 ), whereS)_{C }^{2}+ (ΔH*/S)_{H }^{2})^{1/2}

S= 1 + 0.045_{C}C* ;S= 1 + 0.015_{H}C* (DCIH (1.53, 1.54) )[

C* = ( (a*_{1}^{2}+b*_{1}^{2})^{1/2}(a*_{2}^{2}+b*_{2}^{2})^{1/2})^{1/2}(the geometrical mean chroma) gives symmetrical results for colors 1 and 2. However, when one of the colors (denoted by subscripts) is the standard, the chroma of the standard,C* = (_{s}a*_{s}^{2}+b*_{s}^{2})^{1/2}, is preferred for calculatingSand_{C}S. The asymmetrical equation is used by Bruce Lindbloom.]_{H}

The
CMC color difference formula is widely used by the textile industry to
match bolts of cloth. Although it's less familiar to photographers than
the CIE 1976 geometric distance Δ s denotes the standard (reference)
measurement. CMC is the Colour
Measurement Committee of the Society
of Dyers and Colourists (UK). |

ΔE*_{CMC}(l,c) = ( (ΔL*/lS)_{L}^{2}+ (ΔC*/cS)_{C }^{2}+ (ΔH*/S)_{H }^{2})^{1/2}(DCIH (5.37) ), where(That's the lowercase letter

lin (l,c) and the denominator of (ΔL*/lS)_{L}^{2}.) ΔE*_{CMC}(1,1) (l=c= 1) is used for graphic arts perceptibility measurements.l= 2 is used in the textile industry for acceptability of fabric matching. For now Imatest displays ΔE*_{CMC}(1,1).

S= 0.040975_{L}L* / (1+0.01765_{s}L*) ;_{s}L* ≥ 16 (DCIH (1.48) )_{s}= 0.511 ;

L* < 16_{s}

S= 0.0638_{C}c* / (1+0.0131_{s}c* ) + 0.638 ;_{s}S=_{H}S(_{C}T+ 1 -_{CMC }F_{CMC}F) (DCIH (1.49, 1.50) )_{CMC }

F= ( (_{CMC}c*)_{s}^{4}/ ( (c*)_{s}^{4}+ 1900 ) )(DCIH (1.51);^{1/2}

T= 0.56 + | 0.2 cos(_{CMC}h* + 168°) | 164° ≤_{s}h* ≤ 345° (DCIH (1.52) )_{s}= 0.36 + | 0.4 cos(

h* + 35 °) | otherwise_{s}

The
CIEDE2000 formulas (Δ*E*_{oo} and Δ*C*_{oo}
) are the upcoming standard, and may be regarded as more accurate than the
previous formulas. We omit the equations here because they are described very
well on Gaurav Sharma's CIEDE2000
Color-Difference Formula web page. Default values of 1 are used for
parameters *k _{L}*,

At the
time of this writing (February 2008) the CIE 1976 color difference metrics (Δ*E* _{ab}*...)
are still the most familiar. CIE 1994 is more accurate and robust, and retains a
relatively simple equation. Δ

Photographic
papers, especially matte papers, are not able to reproduce deep gray and black
tones well. This results in a large density difference that has a strong effect
on Δ*E* _{ab}*, Δ

ΔC*= ((Δ_{ab}a*)^{2}+ (Δb*)^{2})^{1/2}

ΔC*_{94}= ( (Δc*/S)_{C }^{2}+ (ΔH*/S)_{H }^{2})^{1/2}

ΔC*_{CMC}= ((Δc*/S)_{C }^{2}+ (ΔH*/S)_{H }^{2})^{1/2}

These
formulas don't entirely remove the effects of exposure error since *L**
is affected by exposure, but they reduce it to a manageable level.