CIE S 014-6 E-2013 Colorimetry C Part 6 CIEDE2000 Colour-Difference Formula.pdf

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1、 International Standard Colorimetry Part 6: CIEDE2000 Colour-Difference Formula Colorimtrie Partie 6: Formule dcart de couleur CIEDE2000 Farbmessung Teil 6: CIEDE2000-Farbabstandsformel CIE International Standards are copyrighted and shall not be reproduced in any form, entirely or partly, without t

2、he explicit agreement of the CIE. CIE Central Bureau, Vienna CIE S 014-6/E:2013 Kegelgasse 27, A-1030 Vienna, Austria UDC: 535.65:006 Descriptor: Standardisation of colour measurement 535.643.2 Standard colorimetric systems CIE S 014-6/E:2013 CIE S 014-6/E:2013 II CIE 2013 - All rights reserved CIE

3、2013 This document is a CIE International Standard and is copyright-protected by CIE. All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permis

4、sion in writing from CIE Central Bureau at the address below. CIE Central Bureau Kegelgasse 27 A-1030 Vienna Austria Tel.: +43 1 714 3187 0 Fax: +43 1 714 3187 18 e-mail: ciecbcie.co.at www.cie.co.at CIE S 014-6/E:2013 CIE 2013 - All rights reserved III Foreword International Standards produced by t

5、he Commission Internationale de lEclairage are concise documents on aspects of light and lighting that require a unique definition. They are a primary source of internationally accepted and agreed data which can be taken, essentially unaltered, into universal standard systems. This CIE International

6、 Standard has been prepared by CIE Technical Committee TC 1-57*. It has been approved by the Board of Administration and Division 1 “Vision and Colour“ of the Commission Internationale de lEclairage and the CIE National Committees. The following ISO and IEC committees and working groups co-operated

7、in the preparation of this International Standard: IEC TC100/TA2 (Audio, video and multimedia systems) ISO TC6 (Paper, board and pulps) ISO TC35/SC9/WG22 (Paints and varnishes) ISO TC38/SC1/WG7 (Textiles) ISO TC42 (Photography) ISO TC130 (Graphic technology) ISO/IEC/JTC1/SC28 (Office systems) * The

8、chairperson of this TC was A.R. Robertson (CA), members were: P.J. Alessi (US), M. Brill (US), J. Campos Acosta (ES), E. Carter (US), R. Connelly (US), J.-F. Decarreau (FR), R. Harold (US), R. Hirschler (HU), B. Jordan (CA), C. Kim (KR), D. McDowell (US), P. McGi nley (AU), M. Melgosa (ES), Y. Ohno

9、(US), M.R. Pointer (GB), K. Richter (DE), G. Rsler (DE), J.D. Schanda (HU), R. Sve (FR), K. Witt (DE), H. Yaguchi (JP), J. Zwinkels (CA). CIE S 014-6/E:2013 IV CIE 2013 - All rights reserved CONTENTS Foreword III Introduction 1 1 Scope 1 2 Normative References 1 3 Definitions, Symbols and Abbreviati

10、ons 1 4 Reference Conditions . 3 5 Calculation Method . 3 6 Parametric Factors . 6 Annex A (Informative) Three-Component Micro-Spaces . 7 Bibliography . 8 CIE S 014-6/E:2013 CIE 2013 - All rights reserved 1 Colorimetry Part 6: CIEDE2000 Colour-Difference Formula Introduction The three-dimensional co

11、lour space produced by plotting CIE tristimulus values (X, Y, Z) in rectangular coordinates is not visually uniform, nor is the (x, y, Y) space nor the two-dimensional CIE (x, y) chromaticity diagram. Equal distances in these spaces and diagrams do not represent equally perceptible differences betwe

12、en colour stimuli. For this reason the CIE has standardized two more-nearly uniform colour spaces (known as CIELAB and CIELUV) whose coordinates are non-linear functions of X, Y and Z. Numerical values representing approximately the relative magnitude of colour differences can be described by simple

13、 Euclidean distances in these spaces or by more sophisticated colour-difference formulae that improve the correlation with the relative perceived size of differences. The purpose of this CIE International Standard is to define one such formula, the CIEDE2000 formula. The Standard is based on CIE Tec

14、hnical Report 142-2001. The formula is an extension of the CIE 1976 L*a*b* colour-difference formula (ISO 11664-4:2008(E)/CIE S 014-4/E:2007) with corrections for variation in colour-difference perception dependent on lightness, chroma, hue and chroma-hue interaction. Reference conditions define mat

15、erial and viewing environment characteristics to which the formula applies. 1 Scope This CIE International Standard specifies the method of calculating colour differences according to the CIEDE2000 formula. The Standard is applicable to input values of CIELAB L*, a*, b* coordinates calculated accord

16、ing to ISO 11664-4:2008(E)/CIE S 014-4/E:2007. The Standard may be used for the specification of the colour difference between two colour stimuli perceived as belonging to reflecting or transmitting objects. This includes displays, if they are being used to simulate reflecting or transmitting object

17、s and if the tristimulus values representing the stimuli are appropriately normalized. The Standard does not apply to colour stimuli perceived as belonging to areas that appear to be emitting light as primary light sources, or that appear to be specularly reflecting such light. 2 Normative Reference

18、s The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. CIE 142-2001. Improvement to industrial colour-

19、difference evaluation, 2001. CIE S 017/E:2011. ILV: International Lighting Vocabulary, 2011. ISO 11664-4:2008(E)/CIE S 014-4/E:2007. Joint ISO/CIE Standard: Colorimetry Part 4: 1976 L*a*b* Colour Space, 2008. 3 Definitions, Symbols and Abbreviations For the purposes of this International Standard, t

20、he terms and definitions given in CIE S 017/E:2011 (International Lighting Vocabulary), and the following symbols and abbreviations apply. CIE S 014-6/E:2013 2 CIE 2013 - All rights reserved L* CIELAB lightness a*, b* CIELAB a*,b* coordinates *abC CIELAB chroma abh CIELAB hue angle L CIEDE2000 light

21、ness L arithmetic mean of the CIEDE2000 lightnesses of two colour stimuli a, b CIEDE2000 a, b coordinates C CIEDE2000 chroma C arithmetic mean of the CIEDE2000 chromas of two colour stimuli h CIEDE2000 hue angle h arithmetic mean of the CIEDE2000 hue angles of two colour stimuli G switching function

22、 used in the modification of a* L CIEDE2000 lightness difference C CIEDE2000 chroma difference h CIEDE2000 hue-angle difference H CIEDE2000 hue difference E00 CIEDE2000 colour difference SL lightness weighting function SC chroma weighting function SH hue weighting function T T-function for hue weigh

23、ting RT rotation function hue dependence of rotation function RC chroma dependence of rotation function kL lightness parametric factor kC chroma parametric factor kH hue parametric factor CIE S 014-6/E:2013 CIE 2013 - All rights reserved 3 4 Reference Conditions The CIEDE2000 formula is intended to

24、be applicable to objects viewed under the following reference conditions: Illumination: source simulating the relative spectral irradiance of CIE Standard Illuminant D65. Illuminance: 1 000 lx. Observer: normal colour vision. Background field: uniform, neutral grey with L* = 50. Viewing mode: object

25、. Sample size: sample pair subtending a visual angle greater than 4. Sample separation: minimum sample separation achieved by placing the sample pair in direct edge contact. Sample colour-difference magnitude: 0 to 5 CIELAB units. Sample structure: homogeneous colour without visually apparent patter

26、n or non-uniformity. When conditions of use deviate appreciably from the reference conditions, parametric factors may be used to correct for the effects of material or experimental variables, as described in Clause 6. NOTE 1 A proposed Technical Report of CIE TC 1-63 “Validity of the Range of CIE DE

27、2000“ will discuss and may show some application limitations of CIEDE2000 for CIELAB colour differences 5 units and for the CIE 1931 standard colorimetric observer (CIE 2 degree observer). NOTE 2 A proposed Technical Report of CIE TC 1-81 “Validity of Formulae for Predicting Small Colour Differences

28、“ will discuss and may show some application limitations of CIEDE2000 for CIELAB colour differences 2 units. 5 Calculation Method All angular quantities in this Standard shall be evaluated in degrees. CIELAB L*, a*, b*, and *abC coordinates of the two samples shall be calculated according to ISO 116

29、64-4:2008(E)/CIE S 014-4/E:2007. Modified CIELAB coordinates shall be calculated according to equations (1) to (7). *LL (1) (1 ) *a G a (2) *bb (3) 2 2 1/2()C a b (4) CIE S 014-6/E:2013 4 CIE 2013 - All rights reserved a r cta n i f 0 a n d 0a r cta n 3 6 0 i f 0 a n d 0a r cta n 1 8 0 i f 09 0 i f

30、0 a n d 02 7 0 i f 0 a n d 0babababahbaaab (5) 0h if 0 a n d 0ab (6) where 7*ab7*7ab0 , 5 125CGC (7) and *abC is the arithmetic mean of the *abC values for the two samples of the colour-difference pair. Equation (5) ensures that h is the angular position of the point a, b in the range from 0 to 360

31、measured from the positive a axis in the a, b plane. In the case where a = b = 0, h is indeterminate and shall be assigned a value of zero as indicated in equation (6). NOTE 1 The L, a, b, C and h values should be used only for the calculation of colour difference and should not be used as an altern

32、ative uniform colour space. When reporting CIELAB colour space coordinates, L*, a*, b*, ab*C and hab values should be used. Differences between two samples denoted by subscripts 0 (usually the reference) and 1 (usually the test) shall be calculated as follows: 10L L L (8) 10CCC (9) 1 / 201 2 s in /

33、2H C C h (10) where 0h if 010CC (11) 10hhh if 010CC and 10180hh (12) 10 360hhh if 010CC and 10( ) 180hh (13) 10 360hhh if 010CC and 10( ) 180hh (14) CIE S 014-6/E:2013 CIE 2013 - All rights reserved 5 NOTE 2 Equations (11) to (14) avoid possible computational difficulties when 0h and 1h are in diffe

34、rent quadrants or when one of the chromas is zero. They are based on Sharma et al., 2005. NOTE 3 In information technology and other fields the subscripts r (for reference) and t (for test) are sometimes used instead of 0 and 1, respectively. Similarly in industrial evaluation of small colour differ

35、ences s (for standard) and b (for batch) are sometimes used. The CIEDE2000 colour difference, E00 between the two samples shall be calculated by 1 / 22220 0 TL L C C H H C C H H L C H C HERk S k S k S k S k S (15) where 2L20, 01 5 ( 50 )1 20 ( 50 )LS L(16) C 1 0,045SC (17) H 1 0,015S C T (18) 1 0 ,

36、1 7 c o s ( 3 0 ) 0 , 2 4 c o s ( 2 ) 0 , 3 2 c o s ( 3 6 ) 0 , 2 0 c o s ( 4 6 3 )T h h h h (19) TCsin(2 )RR (20) 2 3 0 e x p ( 2 7 5 ) / 2 5 h (21) 7C 7 72 25CRC (22) kL, kC and kH are parametric factors explained in Clause 6. NOTE 4 The L , C and h values used in equations (16) to (22) are the ar

37、ithmetic means of the corresponding values of the colour-difference pair. A consequence of this is that the total colour difference is reversible, that is, the total colour difference between a pair is the same whether the first or second sample is used as the standard for calculation of colour-diff

38、erence components. NOTE 5 The locus of points of equal total colour difference from a standard is not an exact ellipsoid and is not exactly centred on the standard. Users should take care in calculating the mean hue angle if the colour-difference pair has samples in different quadrants. For example,

39、 if a colour-difference pair has hue angles of 30 and 300, the simple mean, 165, is incorrect, the correct value being 345. To determine the mean correctly, the following equations (Sharma et al., 2005) shall be used. 01( ) / 2h h h if 01180hh and 010CC (23) 01( 3 6 0 ) / 2h h h if 01180hh and 01( )

40、 360hh and 010CC (24) CIE S 014-6/E:2013 6 CIE 2013 - All rights reserved 01( 3 6 0 ) / 2h h h if 01180hh and 01( ) 360hh and 010CC (25) 01h h h if 010CC (26) NOTE 6 Some worked examples of the calculations are given in CIE 142-2001, Luo et al., 2001 and Sharma et al., 2005. Sharma et al. also give

41、some useful implementation notes and mathematical observations. 6 Parametric Factors Experimental observation and material variables can have parametric effects that influence the visual colour-difference results (CIE, 1993). The parametric factors kL, kC and kH may be used to correct for these effe

42、cts. Under the reference conditions the parametric factors have assigned values of unity and do not affect the total colour difference. The parametric factors provide a method to correct for deviation in experimental conditions from the defined reference conditions. Users are cautioned against indis

43、criminate use of these parametric factors without thorough experimental validation. Industry groups may define parametric factors to correspond to typical experimental conditions for that industry. NOTE In the textile industry it is common practice to set the lightness parametric factor to 2. Howeve

44、r, the experimental conditions leading to this parametric correction to lightness-difference sensitivity are not yet well understood. CIE S 014-6/E:2013 CIE 2013 - All rights reserved 7 Annex A (Informative) Three-Component Micro-Spaces For certain applications, such as apportioning a colour differe

45、nce into lightness, chroma and hue components for shade sorting and attributing size and direction to a specific difference in recipe prediction, it is useful to have a three-term version of equation (15) valid in a micro-space around the reference. The following equations accomplish this (Nobbs, 20

46、02). C C H HT 22H H C C( ) ( )t a n ( 2 ) ( ) ( )k S k SR k S k S (A.1) with taken to be between 90 and 90. NOTE 1 If kHSH = kCSC, then 2 is equal to 90 and is equal to 45. c o s ( ) s in ( )C C H (A.2) c o s ( ) s in ( )H H C (A.3) HHC C C H H T C C2 ( )() 2 ( ) ( ) t a n ( )kSS k S k S R k S (A.4)

47、 CCH H H C C T H H2 ( )() 2 ( ) ( ) t a n ( )kSS k S k S R k S (A.5) 00 LL LL kS(A.6) 00 C CC S (A.7) 00 H HH S (A.8) 2 2 2 1 / 20 0 0 0 0 0 0 0 ( ) ( ) ( ) E L C H (A.9) NOTE 2 Equation (A.9) gives a value of colour differenceE00 identical to that calculated using equation (15). However, the definition of the three-dimensional “micro-space” is different for each colour centre. CIE S 014-6/E:2013 8 CIE 2013 - All rights reserved Bibliography CIE 101-1993. Parametric Effects in Colour-Difference Evaluation, 1993. LUO, M.R., CUI, G.,