Colour Difference 2008

8/3/2019 Colour Difference 2008

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Colour Di f ferenc e

One m easure o f t he d if fe renc e in co lour

bet w een tw o st imu l i i s t he Euc l idean

d is tance

E bet w een t he t w o point s in t het hree-d im ens ional spac e.

E = { (X)2

+ (Y)2

+ (Z)2

}1/2

The t erm E is deri ved from t he Germ an

w ord for sensat ion Empf indung. Et herefore l i t era l ly m eans d i f ferenc e in

sensat ion.


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Differences in rectangular coordinates L *, a* and b* in the CIELAB space


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Tolerances in rectangular coordinates L*, a* and b* in the CIELAB space


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Tolerances in cylindrical co-ordinates L *, C* and h in the CIELAB space


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Som e Anom al ies

Major non-uni fo rm i ty i n c o lour spac e

w as c aused by an inc rease in t he

numer ic a l c o lour di f fe renc e as t he

c hrom a value of t he s t andard is

increased.

L ight ness t o leranc e w as biased in

t he t o leranc e t o t he fu l l s ide o f t hes tandard w as abou t t w i ce t hat t o the

t h in side of s t andard.


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Tow ards Sing le Num ber

Shade Passing Depending on the pos it i on of t he

s t andard in c o lour spac e t heLight ness, Chrom a and Huet o leranc es l im i t s c ou ld be di f fe ren t .

Toleranc e e l l ipsoid m ay be c reat ed ,w here t he sem i -ax es L t un it s fo r

L ightness, Ct uni t s for Chrom a and Htuni t s fo r Hue m ay be assessed andused.


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CMC (I:c )

hue

l igh tness


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J PC79 Equat ion

I t w as found t hat t he Chrom a t o le rance

inc reased rap id ly as t he Chrom a of s t andard inc reased; t he Hue t o lerance a lso

inc rease in a s imi lar fash ion t o Chrom a

t o lerance, but Hue to leranc e (H t ) w asabout ha l f t he Chrom a t o lerance (Ct ). The

l ight ness t o leranc e (L t ) inc reased only as

t he L ightness o f t he s tandard inc reased.


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Hunt er L,a,b

L = 100 (Y/Yn)1/2

a = Ka

[(X/XnY/Y

n)/ (Y /Y

n)1/2]

b = K b [(Y/Y n--Z /Zn)/ (Y/Yn)1/2]

X,Y,X and X n, Yn, Zn are t he t r i s t im u lusvalues of sam ple and sourc e.

K a and K b are t he c h romac i t y c oef fi c i en ts o f t he sourc e .


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J PC79 Equat ion

E = [ (L/Lt

)2 + (C/Ct

)2 + (H/Ht

)2]1/2

Where L t = 0.08195 L 1/(1+0.01765 L 1)

Ct

= 0.0638 C1

/(1+0.0131C1

) + 0.638

Ht = TCtT = 1 i f C1


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Calc u lat e Tot a lCa lc u lat e Tot a l ColourColourDi f ferenc e andDi f ferenc e and

d i f ferenc e in Chrom a, hue bet w eendi f ferenc e in Chrom a, hue bet w eenAA 1 & A& A 2 and be t w een Band be t w een B 1& B& B 2

L** a** b** C** H** EA1 56.706.70 37.107.10 46.906.90A2 57.257.25 36.506.50 47.407.40B1 61.701.70 -37.237.23 -20.150.15B2 61.101.10 -38.408.40 -21.951.95


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L* a* b* C* h0 E

A1 56.70 37.10 46.90 59.8 51.60

A2 57.25 36.50 47.40B1 61.70 -37.23 -20.15 42.33 208.40

(28.40+1800)

B2 61.10 -38.40 -21.95


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L* a* b* C* H * E

A1 56.70 37.10 46.90A2 57.25 36.50 47.40 -0.02 0.77 0.95

B1 61.70 -37.23 -20.15

B2 61.10 -38.40 -21.95 -1.9 1.0 2.23


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Lim i t a t ions of J PC79 Equat ion

For dark c olours L 1approac hes zero and L t alsoapproac hes zero. L/L t bec om es very la rge. For L 1below 16 L t = 1.022 so lves t he problem

Anom a li es w i t h near-neut r al sam p les

L a b ESTD 1 50 0.35 0.50

SAM1 50 -0.50 0.35 1.3

STD 2 50 0.367 0.525

STD 50 -0.525 0.367 3.7


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Acceptability tolerances in CMC in the CIEIAB space


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Group2

Sam ple K /S L* a* b* c * h* E 76

E CMC

1:1

E CMC

2:1

1 2.2 51.61 16.41 1.05 16.44 3.68 - - -

2 1.8 54.22 15.50 2.24 15.66 8.23 3.01 2.73 1.80

3 2.0 52.79 15.64 1.19 15.68 4.37 1.42 1.20 0.76

4 2.2 52.09 16.25 1.29 16.30 4.55 0.56 0.51 0.34

5 2.0 52.99 15.81 2.49 16.00 8.94 2.08 1.95 1.62

6 1.9 53.47 15.77 0.95 15.80 3.44 1.97 1.74 0.95

7 2.4 20.71 16.45 0.99 16.48 3.44 0.90 0.82 0.41

8 1.6 56.66 15.07 1.70 15.17 6.45 5.26 4.70 2.55

9 2.4 50.69 16.59 0.83 16.61 2.86 0.96 0.87 0.49

10 2.8 48.47 16.60 0.79 16.62 2.73 3.15 2.85 1.45


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Group2

Sam ple K /S L* a* b* c * h* E 76

E CMC

1:1

E CMC

2:1

1 2.2 51.61 16.41 1.05 16.44 3.68 - - -

2 1.8 54.22 15.50 2.24 15.66 8.23 3.01 2.73 1.80

3 2.0 52.79 15.64 1.19 15.68 4.37 1.42 1.20 0.76

4 2.2 52.09 16.25 1.29 16.30 4.55 0.56 0.51 0.34

5 2.0 52.99 15.81 2.49 16.00 8.94 2.08 1.95 1.62

6 1.9 53.47 15.77 0.95 15.80 3.44 1.97 1.74 0.95

7 2.4 20.71 16.45 0.99 16.48 3.44 0.90 0.82 0.41

8 1.6 56.66 15.07 1.70 15.17 6.45 5.26 4.70 2.55

9 2.4 50.69 16.59 0.83 16.61 2.86 0.96 0.87 0.49

10 2.8 48.47 16.60 0.79 16.62 2.73 3.15 2.85 1.45


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Group3

Sample K /S L* a* b* c * h* E 76

E CMC1:1

E CMC2:1

1 2.2 52.67 16.12 2.02 15.55 3.42 - - -

2 2.1 53.00 15.97 2.22 15.43 3.23 3.08 1.98 1.78

3 1.9 54.12 15.07 1.94 15.42 3.75 2.34 2.10 0.76

4 2.1 52.21 15.87 1.29 16.12 4.21 2.22 1.76 0.92

5 2.1 52.32 15.45 2.12 16.01 2.24 1.43 0.78 1.20

6 2.0 52.66 15.39 2.07 15.98 3.12 1.44 2.12 0.43

7 2.0 53.38 15.21 1.97 15.48 2.54 2.10 1.90 0.89

8 2.3 52.12 16.23 1.76 16.87 3.44 2.34 2.10 1.10

9 1.9 54.43 15.09 2.00 15.76 2.54 1.95 1.10 0.22

10 1.9 53.12 15.19 1.88 15.34 3.20 1.85 0.98 0.78

11 2.1 52.34 15.67 2.34 15.99 3.54 0.95 1.30 1.11

12 1.9 53.01 15.39 1.98 15.21 3.12 4.40 1.40 2.10


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Group3

Sample K /S L* a* b* c * h* E 76

E CMC1:1

E CMC2:1

1 2.2 52.67 16.12 2.02 15.55 3.42 - - -

2 2.1 53.00 15.97 2.22 15.43 3.23 3.08 1.98 1.78

3 1.9 54.12 15.07 1.94 15.42 3.75 2.34 2.10 0.76

4 2.1 52.21 15.87 1.29 16.12 4.21 2.22 1.76 0.92

5 2.1 52.32 15.45 2.12 16.01 2.24 1.43 0.78 1.20

6 2.0 52.66 15.39 2.07 15.98 3.12 1.44 2.12 0.43

7 2.0 53.38 15.21 1.97 15.48 2.54 2.10 1.90 0.89

8 2.3 52.12 16.23 1.76 16.87 3.44 2.34 2.10 1.10

9 1.9 54.43 15.09 2.00 15.76 2.54 1.95 1.10 0.22

10 1.9 53.12 15.19 1.88 15.34 3.20 1.85 0.98 0.78

11 2.1 52.34 15.67 2.34 15.99 3.54 0.95 1.30 1.11

12 1.9 53.01 15.39 1.98 15.21 3.12 4.40 1.40 2.10


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EXAMPLEEXAMPLE

The CIE L*a*b* values of a standardThe CIE L*a*b* values of a standard

colourcolour and a batch of material dyed toand a batch of material dyed to

match it are given in the table:match it are given in the table:

L*L* a*a* b*b*

StandardStandard

47.2247.22

--18.2218.22

17.6417.64

BatchBatch 46.0946.09 --17.8817.88 16.8316.83


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QuestionQuestion

1.1. Calculate theCalculate the colourcolour--difference between thedifference between the

standard and the batch usingstandard and the batch using CMC(CMC(l:cl:c))

equation, for both acceptability andequation, for both acceptability and

perceptibility conditions, given that theperceptibility conditions, given that thetolarancetolarance ellipsoid semiellipsoid semi--axis values of Saxis values of SLL,,

SSCC,S,SHH are 1.064,1.852 and 1.400 respectively.are 1.064,1.852 and 1.400 respectively.

2.2. Comment on the two values ofComment on the two values ofE obtained,E obtained,given that thegiven that the tolarancetolarance limit of acceptabilitylimit of acceptability

is = 1.000 unitis = 1.000 unit


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SolutionSolution

Calculate values of C* and hCalculate values of C* and h00 and then theand then the

differencedifference L* ,L* , C* andC* and H*H*

L* =L* = --1.130,1.130, C* =C* = -- 0.85,0.85, H* = 0.351H* = 0.351

Perceptibility (1:1)Perceptibility (1:1)

E = 1.83E = 1.83

Acceptability (2:1)Acceptability (2:1) E = 0.734E = 0.734


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Samples L* a* b* C* h0 E E E(CIE76) (CMC1:1) CMC2:1)

STD 31.79 43.83 24.8 50.36 29.51

1 33.24 45.53 26.89 52.87 30.57 3.11 2.21 1.522 30.96 44.03 25.92 51.09 30.49 1.41 1.21 0.86

3 31.85 44.92 26.02 51.91 30.09 1.63 0.71 0.71

4 30.90 41.96 24.07 48.38 29.84 2.20 1.33 0.96

5 32.79 44.32 25.51 51.13 29.93 1.32 1.27 0.72

6 39.09 44.21 24.52 50.55 29.02 0.56 0.46 0.377 31.89 44.82 26.11 51.87 30.22 1.64 0.76 0.75

8 32.43 45.31 26.70 52.59 30.51 2.49 1.33 1.16

9 31.02 44.10 25.21 50.80 29.76 0.91 0.95 0.52

10 32.92 45.87 27.15 53.30 30.62 3.31 1.92 1.52

11 32.23 44.79 26.01 51.80 30.14 1.61 0.87 0.74

12 32.06 45.61 26.82 52.91 30.45 2.71 1.22 1.18

13 32.85 45.55 26.33 52.61 30.03 2.53 1.58 1.13

14 32.08 45.07 27.07 52.57 30.99 2.60 1.35 1.31

15 32.28 44.52 26.32 51.72 30.59 1.74 1.08 0.93

16 33.12 46.06 27.10 53.44 30.47 3.49 2.08 1.59

17 31.45 45.19 26.08 52.17 29.99 3.47 2.09 1.57

18 32.07 44.82 26.02 51.82 30.13 1.90 0.87 0.80


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Samples Visual 555 b* c* h E E E(CIE76) (CMC1:1) CMC2:1)

STD

1 08.33 368 26.89 52.87 30.57 3.11 2.21 1.52

2 50.00 588 25.92 51.09 30.49 1.41 1.21 0.863 25.00 26.02 51.91 30.09 1.63 0.71 0.71

4 50.00 767 24.07 48.38 29.84 2.20 1.33 0.96

5 08.33 664 25.51 51.13 29.93 1.32 1.27 0.72

6 75.00 578 24.52 50.55 29.02 0.56 0.46 0.37

7 58.33 26.11 51.87 30.22 1.64 0.76 0.75

8 00.00 366 26.70 52.59 30.51 2.49 1.33 1.16

9 58.33 25.21 50.80 29.76 0.91 0.95 0.52

10 08.33 678 27.15 53.30 30.62 3.31 1.92 1.52

11 66.66 26.01 51.80 30.14 1.61 0.87 0.74

12 41.66 799 26.82 52.91 30.45 2.71 1.22 1.18

13 33.33 26.33 52.61 30.03 2.53 1.58 1.13

14 16.66 679 27.07 52.57 30.99 2.60 1.35 1.31

15 41.66 26.32 51.72 30.59 1.74 1.08 0.93

16 00.00 488 27.10 53.44 30.47 3.49 2.08 1.59

17 58.33 678 26.08 52.17 29.99 3.47 2.09 1.57

18 58.33 26.02 51.82 30.13 1.90 0.87 0.80


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1.The spec im ens are hom ogeneous in c o lour .

2 . The c o lour d i fferenc e (CIELAB) is 4 degrees

t o t he assessor , w hose co lour v is ion is norm al .

5 . They are i l lumina ted a t 1000 lux , and v iew ed

against a back ground of un ifo rm grey, w i t h L*

of 50, under i l luminat ion s im ulat ing D65.

The CIE 1994 Colou r Di f ferenc e Mode l

The CIE have def ined referenc e c ondi t ions under w h ic h the new m et r ic w i th de faul t pa ramete rs

c an be expec t ed to per fo rm w e ll .


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w here C* = va lue of

s t andard 's Chroma. I f ne i t her

c an be reasonab ly te rm ed thestandard , the geomet r ic m ean

of t he C va lues is used:C* = (C* 1.C* 2)1/2

The CIE 94 formula and acceptability


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Univers i t y o f Bradford - BFD (l :c )


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Univers i t y o f Bradford BFD (l :c)

EBFD = [ (LBFD/l)2 + (C*/cDc)

2 + (H*/DH)2 +

RT(C* . H*/Dc DH)]1/2

The new fo rm u la is sim i la r in st ruc t u re t o the

CMC(l :c). How ever , i t w as found tha t a new t e rm

w as requi red to tak e in to acc oun t t he fac t t hat

w hen c h romat ic i t y e l l i pses c a lc u lat ed from

ex perim enta l da ta a re ex perim enta l da ta a re

p lo t t ed in the CIELAB a* b* d iagram, t hey do not a l l

po int t ow ards the neut ra l po int as assumed in t he

CMC(l :c) form ula


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CIEDE 2000

E00

= [ (L /klS

l)2 + (C/ k

cS

c)2 + (H/ k

HS

H)2 +

RT(C/ kcSc .H/ kHSH)]1/2

L = L * , a = (1+G)a* , b = b *

C = (a 2 + b 2)1/2 , h = t a n -1 (b/a)


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CIELAB t o CIEDE 2000


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CIE2000 form ula inc ludes 5 c or rec t ions t oCIELAB:

1. A l ight ness w eight ing fac t or (SL)

2. A c hrom a w eight ing fac t or (SC)

3. A hue w eight ing fac t or (SH)

4. An int erac t ive t erm (RT) bet w een chromaand hue d i f ferenc es for im prov ing t he

per formanc e for b lue c o lours , and

5 . A fac t o r (1 + G) f or resc a li ng the CIELAB

a* sc a le fo r im prov ing t he per form anc e

for gray c o lours

Documents

Colour Difference 2008