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INTRO2 The determination of the difference between the colours of two specimens is important in many applications, and especially so in those industries, such as textile dyeing, in which the colour of one specimen (the batch) is to be altered so that it imitates / duplicate that of the other (the standard). COMPILED BY TANVEER AHMED This is usually an iterative process.
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Reliability of visual colour-3 difference assessments the human visual system is excellent at assessing Whether two specimens match. If the supplier and customer assess its colour difference from standard visually, they are likely to disagree. COMPILED BY TANVEER AHMED
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Reliability of visual colour-4 difference assessments quantifying both the repeatability and reproducibility of visual assessments of colour differences repeatability :is a measure of the extent to which a single assessor reports identical results, Reproducibility: is the corresponding measure for more than one assessor. COMPILED BY TANVEER AHMED
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Reliability of instrumental colour-5 difference evaluation The results from instrumental methods are much less variable than those from visual assessments. COMPILED BY TANVEER AHMED
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Development of CIELAB and6 CIELUV colour-difference formulae The result was the publication, in 1976, Of two CIE recommendations, CIELAB and CIELUV, for approximately uniform colour spaces and colour-difference calculations. COMPILED BY TANVEER AHMED
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Calculation of CIELAB and CIELUV7 colour difference The colour difference between a batch (B) and its standard (S) is defined, in each space, as the Euclidean distance between the points (B and S) representing their colours in the relevant space. The formulae for the calculation of colour difference and its components in the two spaces are identical in all but the nomenclature of their variables. We shall therefore detail only those pertaining to the calculation of colour difference in CIELAB COMPILED BY TANVEER AHMED
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Calculation of CIELAB colour8 difference If L*, a* and b* are the CIELAB rectangular coordinates of a batch, and L*S, a*S and b*S those of its standard, substituting ∆L* = L* – L*S, ∆a* = a*B – a*S and ∆b* = b*B – b*S in Eqn 4.22 gives Eqn 4.23: COMPILED BY TANVEER AHMED
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Hue angle difference ∆h10 However, the hue angle difference ∆h is in degrees, and so is incommensurate with the other two variables: the substitution is mathematically invalid. COMPILED BY TANVEER AHMED
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Hue angle difference ∆h11 The definition of CIELAB colour difference includes two methods of overcoming the problem. The first uses radian measure to obtain a close approximation to a hue (not hue angle) difference ∆H* in units commensurate with those of the other variables (Eqn 4.26): COMPILED BY TANVEER AHMED
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12 Suppose there does exist a variable ∆H*ab representing, in units commensurate with the other variables of CIELAB colour difference, the hue difference between batch and standard, and that it is orthogonal to both ∆L* and ∆C*ab. Then ∆E*ab must be the Pythagorean COMPILED BY theseAHMED component sum of TANVEER three differences
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HUE Difference ∆H*ab (not hue13 angle) We know the value of each of the first three variables in Eqn 4.27------------- ∆E*ab from the output of Eqn 4.23, ----- ∆L* as one of the inputs to Eqn 4.23, and ∆C*ab ---------------------from Eqn 4.24, each without knowledge of ∆H*ab. By rearranging Eqn 4.27 we can define ∆H*ab (Eqn 4.28): COMPILED BY TANVEER AHMED
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Unfortunately, this method also has14 its problems. The other four components of CIELAB difference are defined as differences and are thus signed so that, for example, ∆L* > 0 if L*B > L*S but ∆L* < 0 if L*B < L*S, while ∆H*ab is defined (by Eqn 4.28) as a square root, the sign of which is indeterminate. COMPILED BY TANVEER AHMED
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Unfortunately, this method also has15 its problems. The CIE states that ‘∆H*ab is to be regarded as positive if indicating an increase in hab and negative if indicating a decrease’. This may be interpreted as implying that the sign of ∆H*ab is that of ∆hab, So that ∆H*ab > 0 if the batch is anticlockwise from its standard, and ∆H*ab < 0 if clockwise. COMPILED BY TANVEER AHMED
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Unfortunately, this method also has16 its problems. Thus, for example, for batch B1a and standard S1 where h,B1a = 30 and for hab,S1 = 10, ∆hab = 30 – 10 = 20 (greater than zero), so that the sign of ∆H*ab is positive. COMPILED BY TANVEER AHMED
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Unfortunately, this method also has17 its problems. Thus, for example, Now consider batch B1b where h,B1b = 350 and for hab,S1 = 10, ∆hab = 350 – 10 = 340, which is again greater than zero so that ∆H*ab is positive. The hue vector from S1 to B1b must, however, clearly be considered clockwise, so that ∆hab and ∆H*ab should be negative. This problem arises whenever ∆hab > 180. The definition therefore presents problems, but for many years it offered the only way of calculating ∆Hab. COMPILED BY TANVEER AHMED
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work of Huntsman.18 Another method was based on the work of Huntsman. Equating the right-hand sides of Eqns 4.23 and 4.27, followed by manipulation, yields Eqn 4.29 COMPILED BY TANVEER AHMED
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work of Huntsman.19 Although Eqn 4.29 provides a simpler method of calculating ∆H*ab, it still suffers from the disadvantage that it outputs the wrong sign of ∆H*ab when ∆hab > 180. The correct sign may, however, be determined without knowledge of the value of ∆hab, by testing the relative sizes of the two directed areas a*B b*S and a*S b*B; denoting the correct sign of ∆H* by s [23] gives Eqn 4.30: COMPILED BY TANVEER AHMED
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COMPILED BY TANVEER AHMED 20CMC(L:C)COLOUR-DIFFERENCEFORMULA
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CMC(l : c)21 formula was published in 1984 under the name of CMC(l : c), CMC being the abbreviation commonly used for the Colour Measurement Committee (Eqn 4.32) [24]: COMPILED BY TANVEER AHMED
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22 where ∆L*, ∆C*ab and ∆H*ab are respectively the CIELAB lightness, chroma and hue differences between batch and standard, l and c are the tolerances applied respectively to differences in lightness and chroma relative to that to hue differences (the numerical values used in a given situation being substituted for the characters l and c, for example CMC(2 : 1), whenever there be possible ambiguity), COMPILED BY TANVEER AHMED
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23 where the ki (i = 1, 2, 3) are as defined in Eqn 4.31, and L*S, C*ab,S and hab,S are respectively the CIELAB lightness, chroma and hue angle (in degrees) of the standard. COMPILED BY TANVEER AHMED
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The mathematics of the CMC(l : c)24 formula deserve examination Because they well illustrate the general principles of optimised formulae, currently so important in industrial applications. In CIELAB space, Eqns 4.27 and 4.28 define the shell containing all shades equally acceptable as matches to (or perceived as equally different from) a standard at a given colour centre. Arising from the non-uniformity of CIELAB space, the magnitudes of each of ∆L*, ∆C*ab and ∆H*ab are not usually equal, and ∆E*ab is therefore a variable which is assumed in CMC(l : c) and most other optimised formulae to define an ellipsoidal shell with its three axes orientated in the directions of the component differences. COMPILED BY TANVEER AHMED
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The non-uniformity of CIELAB25 space further dictates The non-uniformity of CIELAB space further dictates that an equally acceptable (or perceptible) ∆E*ab, at another colour centre, is unlikely to define a similar shell. For a formula to allow SNSP, however, we require the overall colour difference to be a constant, so that its locus describes a spherical shell of equal radius at all colour centres. The ellipsoid in CIELAB space may be converted into a sphere by dividing each of its attribute differences (∆L*, ∆C*ab and ∆H*ab), in turn, by the length of the semi-axis of the ellipsoid in the direction of the relevant attribute difference (SL for lightness, SC for chroma and SH for hue). COMPILED BY TANVEER AHMED
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26 The inclusion in Eqns 4.27 and 4.28 of the relative tolerances (l and c) yields the first line of the CMC(l : c) formula (Eqn 4.32). This line therefore converts a usually ellipsoidal tolerance volume in CIELAB space into a spherical one in a CMC(l : c) microspace. COMPILED BY TANVEER AHMED
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27 The principal difficulty in the design of optimised colour- difference formulae, however, is to derive mathematics allowing the generation of the systematic variation in the relative magnitudes of attribute differences judged equally acceptable (or equally perceptible) at different centres. These mathematics occupy the whole of the remainder of the formula. Their effect is demonstrated in Figure 4.9. COMPILED BY TANVEER AHMED
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