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The proximity factor in colour-difference evaluations Sharpe, Lindsay Theodore 1975

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THE PROXIMITY FACTOR IN COLOUR-DIFFERENCE EVALUATIONS by LINDSAY THEODORE SHARPE B.A.(Hons.), University of Bri t i s h Columbia, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF . THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Psychology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September1975 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes i s for f i nanc ia l gain sha l l not be allowed without my wr i t ten permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT The effect of diyiding line width. Csample proximity) upon sensitivity to supra-threshold and threshold colour differences is explored by three methods involving ratio comparisons, liminal determinations, and repeated colour matchings. The results suggest, in general, that sample separation impairs lightness discrimination more than chromatlcness discrimination and that i t may by necessary to introduce a proximity factor into colour difference formulae when evaluating threshold or small-sized colour differences. i i TABLE OE CONTENTS Page ABSTRACT 1 LIST OF TABLES i l l LIST OF FIGURES i y ACKNOWLEDGEMENT ' V I . INTRODUCTION 1 I I . EXPERIMENTAL PROCEDURE 18 Apparatus ' . -18 Observers 20 Test Colours 20 Colour D i f f e r e n c e Comparisons 21 Di f f e r e n c e Limens 24 Colour Matching E l l i p s o i d s 27 I I I . "RESULTS 30 Supra-threshold Colour D i f f e r e n c e Comparisons 30 Threshold D i f f e r e n c e Limens 32 Colour Matching E l l i p s o i d s 36 IV. DISCUSSION 46 Methodological C r i t i c i s m s 46 Conclusion 47 FOOTNOTES 50 BIBLIOGRAPHY 55 i i i LIST OF TABLES Page Table I : Values of , the proximity factor suggested by Judd (taken from Hunter, 1942). 16 Table II : Equal value differences. 31 Table III: Attributive difference limens. for two conditions of f i e l d separation. 33 Table IV: Colour-matching ellipsoids and their cross sections of observer LTS for 0, 3.2, and 8.2 cm f i e l d separations conditions. 37 i v LIST OF FIGURES. Page Figure 1. Colour-matching functions x\, y"k, zXof 1931 CIE C 2 ° ) standard observer as compared" to colour-matching functions xigA, y - i Q ^ , ^ 1 0 ^ of 1964 CIE CIO ) standard observer. 5 Figure 2. 1931 CIE (xjyj-chromaticity- diagram as com-pared to 1964 C I E Cxio>yio) - c n r o m a t :' : c :'- ty diagram. 9 Figure 3. Array of the seven v i s u a l f i e l d s provided by the NRC colorimeter. 19 Figure 4. Configuration of the v i s u a l f i e l d used i n the f i r s t method. 22 Figure 5. CIE .1931 chromaticity diagram showing chroma-t i c i t y points- of test s t i m u l i used throughout this experiment. 25 Figure 6. Section of CIE 1931 chromaticity diagram showing cross sections^ of colour matching e l l i p s o i d s obtained i n (x,y,l) space. 38 Figure 7. Portion of the CIE 1931 chromaticity- d i a -gram showing cross sections of colour-matching e l l i p s o i d s obtained i n Cx,y,l) space for observer LTS. 40 Figure 8. Portion of the CIE 1931 chromaticity d i a -gram showing cross sections of colour-matching e l l i p s o i d s obtained i n Cx,y,l) space for observer LTS producing sets of colour matches at three different occa-sions but otherwise i d e n t i c a l observing conditions. 42 Figure 9. Portion of the CIE 1931 chromaticity d i a -gram showing cross sections of colour-matching e l l i p s o i d s obtained i n (x,y,l) space for the same colour centre 5 R 8.25/3 at three conditions of f i e l d separation. 43 Figure 10. Portion of the CIE 1931 chromaticity d i a -gram showing cross sections of colour-matching ellipsoids- obtained i n (x,y,l) space for the same colour centre N 6/. 44 V ACKNOWLEDGEMENT I was g r e a t l y a s s i s t e d i n research and d i s c u s s i o n by: Mr. C.X. Dodd, Dr. R. Lakowski, Mr. F.T. McNeely, Dr. A.R. Robertson, Dr. R. Tees, and.Dr. G. Wyszecki. 1 The measurement of colour or colorimetry" 1" i s based on the e x p e r i -mental laws of colour matching which are v a l i d f o r a l l human observers w i t h normal colour v i s i o n ( i . e . , normal t r i c h r o m a t s ) . These laws o r i g i n a l l y f o r -mulated by Grassmann i n 1853, may be s t a t e d as f o l l o w s : F i r s t , any colour may be expressed by a l i n e a r combination 2 of three primary colours ; Second, i d e n t i c a l primary colours produce i d e n t i c a l e f f e c t s i n colour mixtures regardless of t h e i r s p e c t r a l energy d i s t r i b u -3 txons ; T h i r d , i n a two-or-more primary colour mixture i f one (or more) primary i s continuously a l t e r e d (while the others remain constant) the colour of the mixture correspondingly a l t e r s . Grassmann's f i r s t law allows us to s p e c i f y an unknown colour stimulus i n terms of three primary l i g h t s whose s p e c t r a l c h a r a c t e r i s t i c s are 4 _ _ _ known. Thus i f we choose red, b l u e , and green p r i m a r i e s , l a b e l e d R, G, B r e s p e c t i v e l y , then an unknown co l o u r stimulus C can be represented by the equation: C S rR + gG + bB Eq. (1) ..." ~o The equivalent s i g n may be i n t e r p r e t e d as 'matches' or ' i s matched ' by';cande the c o e f f i c i e n t s r , g, b may be i n t e r p r e t e d as the t r i s t i m u l u s values of C w i t h respect to the s p e c i f i e d p rimaries R, G, B"\ These t r i s t i m u l u s values are the amounts of the primary colours used to match C and are d i r e c t l y obtained from some a r b i t r a r y l i n e a r s c a l e based on p h y s i c a l s p e c i f i c a t i o n of the 3 primary l i g h t s . The amounts may 2 be positive, negative or n i l . Grassman's second law entails that equation (1) holds true for any set of primary colours (that satisfy the restriction mentioned in foot-note 4) regardless, of their spectral power distributions. In other words, the colour synthesized by the combination of the matching primaries.does not need to have the same spectral energy distribution as C in order for i t to have the same tristimulus values as C. Indeed, unless C is generated by the same set of primaries, i t is almost certain that C and the synthesized colour w i l l differ in their spectral energy distributions. 8 This fact introduces the concept of metamerism which may be defined as: the identity of colour appearance between stimuli of different 9 spectral energy distributions for certain specified conditions (Wright, 1969). The degree of metamerism between any two matching colour stimuli may be*taken as a function of the differences between their respective . ' 10 ' spectral energy dxstributions. Finally, Grassman's third law implies that colour space, where colours may be expressed as points with tristimulus values as their reference coordinates, i s a continuum without any disruptions or discontinuities. In sum, the concepts of three primary colour matching and meta-merism (Grassman's f i r s t two laws) provide a simple and direct method for specifying and arranging colour in a continuous.colour space (Grassmann's third law). However certain factors have to be standardized for this system to provide results that are consistently yalid for the group of normal t r i -chromats , including: 3 i) the state of adaptation of the observer's eye; i i ) the colour matching properties of the observer; i i i ) the illumination and observation conditions under which the two colour stimuli are matched; and iv) the reference set of matching primaries. Changes or anomalies in any of these factors may upset the accuracy and pre-cision of colour measurement. Therefore the Commission Internationale de l'Eclairage ( C L E . ) has established in detail a colorimetric system for ob-taining an accurate and precise set of tristimulus values for any given colour (within a certain range of observation conditions). This system, universally adopted in industrial and scie n t i f i c laboratories, i s formally called the C L E . Standard Observer and Coordinate System of Colour Mea-surement. It i s defined by two sources of information: f i r s t , the rela-tive amounts of three primary lights required by an averaged group of observers to match the colours of the spectrum under certain specified conditions and second, a set of reference primary stimuli for suitably ex-pressing these average responses. The f i r s t of these sources, the average colour matching response i s determined from detailed empirical investiga-tions; whereas, the second i s decided from considerations of practical and technical convenience. So far, the CIE has approved two standard observer and coordinate systems for use in applied colorimetry. The f i r s t , generally known as the CIE 1931 Standard Colorimetric Observer i s defined by 3 independent functions of wavelength, x(X), y(X), and z(A), which characterize the ideal or average observer's colour matching functions^ when colour matches, are made in photo-4 pically illuminated visual fields subtending between 1° to4° visual angle. These functions are based on experimental data for actual observers. who matched the colours of the spectrum i n foveal visual fields (2° centrally viewed). The i n i t i a l colour matching data were obtained by Guild (1931) and Wright (1928-1929), but were linearly transformed into an all-positive 12 reference system with non real primaries X, Y and Z. The second ideal observer, generally known as the CIE 1964 Sup-plementary Standard Colorimetric Observer i s defined by 3 similar but d i f -ferent functions of wavelength, x^Q^) , yi0(A)> and I^GA), which characterize the ideal or average observer's colour matching functions when colour matches are made i n photopically illuminated visual fields subtending between 4° to 10° of visual angle. These functions are based on experimental data for actual observers who matched the colours in the spectrum in visual fields allowing both foveal and parafoveal vision (10° angular subtense centrally viewed). The original data were obtained by Stiles and Burch (1959) and Speranskaya (1959), but were also linearly transformed into an a l l -reference system with non real primaries X^^, y J Q , and (that -V3 ei;«'T?.'".-".i;.at>3S for spactral colours).' Although the 2° and 10° standard observer systems are basically similar i n structure, they differ significantly in the values of their colour matching functions. For instance, i n the wavelength range from 400 to about 510 nanometers, the values of the Y-^QOO function are considerably higher than the corresponding values of the y("A) function (see Figure 1). These differences account for the greater sensitivity of the extra-foveal rod 13 receptors to the shorter wavelengths. 5 2.0 0 / Vx ——2° observe - ° - 10° observ (CIE) er Xx V 400 500 .600 700 Wavelength, mn Figure J . Colours-matching functions xX, yA, zX of J.931 CIE (2°1 standard observer as compared to colour-matching functions XJQ^> yj.0^ » ^10^ °^ -1964 CLE G 0 ° ) standard observer. The two sets of data are based on similar coordinate systems. (Dia-gram from Judd and Wyszeckl, 1963). 6 In sum, the basic operation in applied colorimetry- is, to specify an unknown colour stimuli in terms of standard tristimulus values. The CIE recommended 2° and 10° standard observer systems allow: the determination of these values according to the average colour matching properties of normal trichromats for either small or large viewing field conditions. The calcu-lations of the values differ, however, dependinggon whether the colour stimulus is presented in self-luminous or object mode. For self-luminous 14 colours, specified by their spectral distribution of radiant flux PAd\, the tristimulus walues are given by the three following integrals: X or X 1 Q =Ky/?Ax Q\)dx Y or Y 1 Q --. K ^PAyCx)dx Z or Z 1 Q _K y PAzCx)dA where ^ is calculated usually over the visible wavelength-range from 380 to 780 nanometers; where d\ is the wavelength interval over which-the radiant flux in calculated; where the colour matching functions x(^ )_, y(^)_, zQ\). are either those of the 1931 or 1964 standard observers; and where the constant K is a normalizing factor to which a value may be assigned arbitrarily, provided i t is kept constant throughout. On the other hand, for object colours,^ specified by their spectral distributions PAHAAA (for reflecting object colours) or TA**AAA (for transmitting object colours), the tristimulus values are given by the three following integrals: X or X 1 Q = K £ pA HA xA AA or K £ TA HA xA AA, Y or Y 1 Q = K £ pA HA yA AA or K £ TA HA yA AA, Z or Z l f ) = K £ pA HA zA' AA or K £ TA HA ZA AA, 7 where pX i s the spectral reflectance of the object colour or where T X i s the spectral transmittance of the object colour; where HX/CV is the spectral distribution of the flux irradiating the object (usually provided by one of the standard CIE illuminants A, B, C, or D 6 5 Q 0 defined so as to represent the spectral energy distribution of natural daylight for various sky condi-tions); where the colour matching functions may be either those of the 1931 CIE or 1964 CIE standard observers; and where K, again, is a normalizing factor. Although the CIE tristimulus values ( X Y Z ) or :(X^,„YY R„. Z, N ) alio J<]JO. 10 describe uniquely any given colour stimulus, they usually-are transformed to chromaticity coordinates (xyz) or ^XJO^10Z10^ w n-*- c n a r e m o r ^ convenient for the description of colour stimuli. These chromaticity coordinates are derived simply by normalising, the tristimulus values to unit sum: . x = X/CX + Y + Z) or x J 0 = X 1 0 / C X I 0 + Y 1 Q + Z^l y - Y / ( X • Y + Z) or y 1 Q -Y1(J/(*_<,• • Z ^ ) z - Z/CX • Y , Z ) or z 1 Q = Z 1 Q / ( X 1 0 + Y 1 Q * Z ^ ) 16 Once the, chromaticity coordinates are obtained, the chromaticity of a colour stimulus can be represented by a point in the CIE chromaticity diagram.^ Basically this diagram is obtained by plotting the x or x ^ chromaticity coordinate horizontally against the y or y^Q chromaticity coordinate vertically in a graph with rectangular coordinates. If the d i -agram is based on the 1931 CIE Standard Observer data i t is called the 1931 (x, y)-chromaticity diagram, and i f i t is based on the 1964 CIE Supplementary Standard Observer, data i t is called the 1964 CIE CX-^Q, y^^)-chromaticity diagram. 8 When the chrbmati.clti.es. of the spectrum-colours"''0 are plotted in the appropriate diagram they form the so-called spectrum locus (see Figure 2) which defines the region of the chromaticity diagram outside which. 19 no physical stimulus can be located. The .straight line, alchyne, joining the red and violet extremities of this locus represents- the chromaticity points of the most saturated, purples (non—spectral colours). Although very convenient for representing colours, the CIE chro-maticity diagrams have one clear disadvantage. The, individual regions within the diagrams are non-uniformiy•spaced with respect to colour perception (see e.g., MacAdam, 1942; Wright, 1941). This means that the distance apart of any two colours in the diagrams does not correspond to the perceived colour differences between them; or inoother words, that equal distances within the diagrams do not correspond to equal sized colour differences. Such non-uniformity occurs because no psychological aspects of colour vision (e.g., colour discrimination data) were considered when developing the CIE colour system (Wyszecki, 1958, p.30). The non-uniformity,.however, may be improved by either analytical or projective transformation of the CIE chromaticity diagrams. . In the f i r s t approach, the objective i s to find by non-linear transformation, a coordinate system (i.e., new chromaticity diagram) for the CIE standard observer data that yields essentially the same chromaticity spacing as that-provided by some colour appearance system accepted as psychologically uniform. The Munsell colour system based on material standards (colour chips) selected by 20 21 observer judgements to represent uniform scales of constant hue , saturation , 9 Figure 2. 1931 CIE (x,y)-chromaticity diagram (solid dots) as compared to 1964 CIE C x i o , y i o ) ~ c a r o m a t i c i t ^ d i a e r a m Copen ci r c l e s ) . The two diagrams are based on similar coordinate systems. (Diagram from Judd and Wyszecki, 1963,) 10-and l i g h t n e s s ^ is. w i dely considered the outstanding example of such a p s y c h o l o g i c a l l y uniform system. When the Munsell chips are c a l i b r a t e d i n terms of the CIE 1931 chr o m a t i c i t y coordinates . ( w i t h respect to s p e c i f i e d c o n d i t i o n s of i l l u m i - ^ n a t i o n and observation) and are p l o t t e d i n the CIE 19.31 c h r o m a t i c i t y diagram' t h e i r network of po i n t s form l i n e s of constant chroma and constant hue f o r 24 d i f f e r e n t Munsell v a l u e s . I f the CIE diagram w e r e * p e r f e c t l y uniform the l i n e s of constant chroma would be co n c e n t r i c c i r c l e s , the l i n e s of con-stant hue would be s t r a i g h t , and the spacing of the po i n t s along both the c i r c l e s and l i n e s would be uniform. However, s i n c e i t i s not uniform, "the l i n e s of constant chroma are ovoids, the l i n e s of constant hue are curved, and the spacing of the po i n t s along these l i n e s changes s y s t e m a t i c a l l y " (Wyszecki, 1973, p. 42). C l e a r l y , the o b j e c t i v e i s to de r i v e a n a l y t i c a l (non-linear) ex-, pressions f o r transforming the CIE t r i s t i m u l u s values - of the Munsell chips to three new v a r i a b l e s so that when the new v a r i a b l e s are used as rectangu-l a r coordinates they define a new diagram of more uniform spacing, which renders the Munsell chip p o i n t s i n t o a n e a r l y uniform network. Needless to . say, various n o n - l i n e a r a n a l y t i c a l expressions have been found by numerical o p t i m i z a t i o n techniques f o r improving the u n i f o r m i t y of the' CIE diagram (e.g., Adams, 1942; Saunderson and M i l n e r , 1946; Gla s s e r et a l . , 1958). In the second approach to u n i f o r m - s c a l i n g , the o b j e c t i v e i s to 25 l i n e a r l y arrange the p o i n t s of the CIE c h r o m a t i c i t y diagram so that equal displacements w i t h i n the transformed c h r o m a t i c i t y diagram, correspond to per-c e p t u a l l y equal colour d i f f e r e n c e s (Wyszecki and S t i l e s , 1967, p. 455). Thi 11 involves: a transformation which may be represented algebraically by the following nonhomogeneous equations: 1 .1 y a n x *,a 1 2y . + a13 a31 x t a 3 2y -t- a33 a2.1x taa 2 2y + a23 a31 X * a32y a33 where x,y are the 1931 or 1964 chromaticity coordinates of .the CIE chroma-t i c i t y diagram; where ,y"^  are the coordinates of the new chromaticity d i -agram; and where 4^k(i ?k = 1,2,3) are the transformation coefficients — o f which the determinant l a , k l = A is not equal to zero. Since only colours of constant luminance are considered in such a transformation, the new chro-maticity diagram is usually used in conjunction with some index scale of •2!6 luminous reflectance (or transmittance) or luminance. Once a more perceptually uniform has been obtained by either analytical or linear transformation of the CIE chromaticity diagram i t can be used as the basis for evaluating colour differences. In a perfectly uniform chromaticity diagram, the total colour difference (lightness plus chromaticness) perceived between any two colours, C^  and C 2, is given by a 27 straightforward sum of squares relation: A E = (xj - h1/ • ( YJ. - y\)2 • CLX - L 2 ) 2 ^ where AE signifies the total colour difference and where (xj, y^, L^) and x2' ^2' ^2^ a r e t* i e u n i f o r m chromaticity coordinates and lightness values of C^  and C 2 respectively. Unfortunately, to date both, analytical and projective transfor-12 mations, of the CIE chromaticity diagram proyide only crude approximations of a UCS diagram and therefore their associated AE formulae provide only crude predictions of perceived colour differences. , Nevertheless the urgent need for colour difference specification i n many practical applications has guided many attempts to .develop a more uniform chromaticity diagram Cor space) and to write an associated colour difference formula. As yet, no conclusions about the relative merits of these.colour difference formulae can be drawn with any assurance. Currently, however, the Colorimetry Committee TC-1.3 of the CIE is studying two uniform colour spaces and their associated colour-difference formulae as part of i t s program to promote uniformity of practice in the evaluation of colour differences. The f i r s t colour space, tentatively labeled the CIE 1976 (L*u*v*) space i s produced by plotting i n rectangular coordinates the quantities L*,u*,v* defined by: L* = 25(100Y/yo) 1 / 3 - 16, 1 < Y < 100 u* = 13L*(\i^ - uo''"), v* = lSI / H v 1 - vo 1) where, in turn, the quantities u 1, v"*", uo 1, vo 1 are defined by a linear 28 transformation of the CIE tristimulus values XYZ: u l = 4X , v 1 ^ 9Y X + 15Y + 3Z , X + 15Y -t^ 3Z uo 1 = Xo 4X6 , v o 1 = 9Y6 Xo t 15Yo + 3Zo Xo + 15Yo + 3Z& -The total perceived difference AE„T„CL*u*v*) between two colours r CIE specified by the points (L*^, -u*j, v*p and (L* 2, u*2» v*2^ respectively in this space is then calculated from the formula: 13 AE C I E. (L*u*v*) - (L* 1 r. L * 2 ) 2 + (u*1 - u * 2 ) 2 + ( y ^ - v * 2 ) 2 h = CAL*)2 + CAu*)2 + CAv*)2 1 5 The second uniform colour space, tentatively labeled the CIE 1976 (L*a*b*) space, is produced by plotting in rectangular coordinates the quantities L*, a*, b* defined by an analytical transformation of the CIE tristimulus values XYZ: Clii tristimulus values XYZ:.. L* •= 25(100Y/Yo) ' -16, 1 < Y < 100 a* = 500 (X/Xo) 1 / 3 - CY/Yo) 1 / 3, b* = 200 (Y/Yo) 1 / 3 - fe'AZo)1/3 . The total perceived difference AE_,T1_,(L*a*b*) between two colours C i t corresponding to the points (L*^, a*j> b*^) and Cl*2> a*2> b* 2) respectively in this space is then calculated from the formula: AE C I E(L*a*b*) = CL*j_ - L * 2 ) 2 + (a* 1 - a * 2 ) 2 + Q>*1 - b * 2 ) 2 = CAL*)2 + (Aa*) 2 + CAb*)2 ^ The parameters values of the equations defining both these spaces and their associated colour-difference formulae are intended to apply to the observing conditions ideally found i n practice; "Field size: 4 degrees or more. Nature of surround: uniform. _ 2 Luminance of surround: 100 to 1000 cd«m . Chromaticity of surround: equivalent to chromaticity of one of the CIE D illuminants from 5000 to 7500 K. Luminance of sample: 5 to 500% of surround luminance, such as to produce a surface mode of perception. Dividing line between samples: approaching zero width. Observers: normal colour vision and capable of judging the perceptibility of the colour differences without any acceptability bias." CWyszecki, 1974, p. 897) However, the colour difference formulae may be modified to include 14 new factors or new; parameters that are appropriate for certain obserying, situations departing from those normally- employed. In particular, "the weight of the perceived lightness difference between two given colours relative to the per-ceived chromaticness difference between the same, two colours may, under certain observing conditions, be different from the unit-weight implied in the, two colour-difference formulae. To account for the possibly.idifferent weight, a factor c may be i n -troduced in the colour difference formulae, AE C I E C c )(L*u*v*) = [ ( c ^ L * ) 2 + (Au*) 2 + (Av*) 2]^ AE^ ( c )(L*a*b*) = [(c 2AL*) 2 + (Aa*) 2 + (Ab*) 2]^." (Wyszecki, 1974, p. 897). One observing condition believed to cause a different weight between perceived lightness and perceived chromaticness differences is width of dividing line between samples. Intuitively i t seems obvious that as the angular separation between two colours increases, the noticeability of their colour difference should correspondingly decrease. At large separations where the observer must shift his gaze or turn his head to compare samples, the perceptibility of even large colour differences should be impaired. Indeed Judd (1930, 1939a, 1939b) did find that the presence of a conspicuous dividing line interferes with the perception of colour d i f -ferences but that i t reduces sensitivity to lightness difference much more than sensitivity to chromaticness differences. To compensate for this effect, he introduced separate luminance, k^, and chromaticity, k 2, weighting factors into his colour difference formula (1939a, 1939b); their function being to adjust the relative importance of lightness to chromaticness di f -ferences as sample separation is varied. 1 5 On the basis of a few. preliminary experiments (mostly-unpublished). Judd fixed the value of at 6 0 0 , but chose several tentative values for k^. A quick comparison of these values listed in Table I indicates that k^ weights perceived lightness differences less importantly as sample sepa-ration is increased. For instance, Judd suggested a value for of J . 2 0 when comparing samples separated by a very narrow dividing line, but he suggested a value of 3 0 or 4 0 when comparing samples separated by a broad contrasting area. When Hunter ( 1 9 4 2 ) revised Judd's formula he retained k^ (or proximity factor) as part of Judd's expression for luminance differences, but he presented no new evidence supporting i t s retention. Presumably he j u s t i f i e d i t s inclusion on the basis of Judd's unpublished studies and his own o!b'seBvat<3)onsyations, Some ten years later Traub ( 1 9 5 2 ) alerted by the fact that the functional relationship between proximity factor and sample separation was not known, deduced a continuous analytic expression for relating values of k^ to angular width of dividing line. According to his own psychophysical observations, the following function provided the best f i t with visual dis crimination: kx(6) = J 3 0 * 1 8 / CO. 2 + eS| where 0 is the angular separation measured in degrees, of the surface areas being compared for colour difference. The upper limit of this function (i.e., for 9 = 0 ° ) was arbitrarily fixed at 1 2 0 to accord with Judd's maxi-mum tentative value, but i t s lower limit (i.e., for 0 = wide angular sepa-ration) was determined independently by Traub to be equal to 3 0 . A value TABLE I: Values of K], the proximity factor, suggested by Judd (taken from Hunter, 1942) Conditions of observation giving equivalent visual estimates of color difference k l Samples separated by a very narrow or non-existent dividing line 120 Samples separated by a contrasting, but narrow dividing line 90 Samples separated by a broad patterned area different from the areas being compared 40-Samples evaluated for whiteness without visual reference to other samples 20 (Convenient value for use when samples are separated • by a narrow line) 100 17 corresponding closely to Judd's minimum tentative yalue. Traub. attempted to deduce a si m i l a r expression for r e l a t i n g the chromaticity constant, k^, to angular width of dividing l i n e , but he f a i l e d to. f i n d any consistent change i n chromaticity discrimination as a function of sample separation. Since Traub's investigation l i t t l e attention has been paid to the proximity.rfactor. In f a c t , no colour difference equation other than Hunter's-modified Judd formula, includes such a parameter. This poses a problem. When applying colour difference formulae under conditions of sample separation, i s a proximity factor necessary for adjusting the. r e l a -t i v e importance of lightness differences to chromaticness differences? Obviously Judd believed so. Yet on the basis of the scant evidence he pub-lished, no unequivocal answer to this question i s possible. Therefore i t would seem worthwhile to examine the effect of angular separation i n some d e t a i l . Especially since any data, so provided, would help to determine i f a proximity factor merits inclusion i n the two colour difference formulae now being studied by the CIE, 18 EXPERIMENTAL PROCEDURE This experiment i s a s e r i e s of t e s t s to determine the e f f e c t of sample s e p a r a t i o n upon s e n s i t i v i t y to supra-threshold and th r e s h o l d colour d i f f e r e n c e s . Three methods were used: one i n v o l v e d equating supra-thre-shold c olour d i f f e r e n c e s by the technique of Robertson (1975); another i n -volved d e r i v i n g d i f f e r e n c e limens by the method of constant stimulus d i f -ferences ( G u i l f o r d , 1954); and the t h i r d i n v o l v e d determining colour mat-ching e l l i p s o i d s i n the manner of Wyszecki and F i e l d e r (1971). Apparatus The apparatus used throughout the e n t i r e course of t h i s e x p e r i -ment was the NRC s e v e n - f i e l d c o l o r i m e t e r . The s t r u c t u r e and o p e r a t i o n of t h i s instrument i s described by Wyszecki (1965b). Therefore only i t s s a l i e n t f e a t u r e s w i l l be mentioned here. This unique c o l o r i m e t e r c o n s i s t s of seven juxtaposed photometric f i e l d s (see Figure 3) which may be s i n g l y or grouply presented to the ob-server f o r b i n o c u l a r viewing. Each f i e l d i s a re g u l a r hexagon, measuring 6 cm i n outside diameter and subtending about 3° of v i s u a l angle at the eye of an observer seated 120 cm away. The colour of each f i e l d i s produced by mixing three primary l i g h t s ( red, green, and blue) generated by a common 1000-watt quartz-halogen source i n conjunction w i t h three coloured g l a s s f i l t e r s . Three v a r i a b l e s h u t t e r s enable the observer to c o n t r o l the amount of l i g h t f l u x passing through the gl a s s f i l t e r s and hence to c o n t r o l i n -dependently the amounts of each primary l i g h t c o n t r i b u t i n g to the a d d i t i v e 19 Figure 3. Array of the seven visual fields provided by the NRC colorimeter. 20 mixture in any particular photometric f i e l d . The spectral transmittance of each shutter (21 in a l l ) and the spectral energy distribution of each primary light have been painstakingly calibrated so may be readily converted to CIE 1931 colour coordinates x, y, Y and vice versa. Fortunately, the spectral radiance distributions of the corres-ponding primaries of the 7 colorimetric fields are almost identical. There-fore, for each colour presented in one f i e l d , a matching colour can be ob-tained in an adjacent f i e l d whose spectral radiance distribution i s near-identical or practically non-metameric with the original colours. Such an arrangement avoids any invariances in colour matching caused by differences between colour-matching functions of different observers (Wyszecki and Fielder, 1971). Observers Five male observers, CD., F.M. , A.R. , L.S., and G.W. took part in the f i r s t phase of the experiment. Their ages ranged from 23 to 49 years. Only L.S., aged 23, took part in the second and third phases of the experi-ment. A l l observers were normal trichromats and were previously experienced with colour matching and colour difference assessments. Test Colours Colours based on the Munsell colour-order system were chosen as test stimuli. This is because the Munsell system provides convenient scales of perceptually uniform surface colours arranged along 3 separate visual dimensions: hue, chroma, and value. Since the Munsell notation of any colour 21 selected or interpolated from these uniform scales can be readily converted to CIE 1931 standard observer colour coordinates and i n turn to 7-field 29 colorimetric shutter readings , the experimenter could set up various pairs of colour s t i m u l i d i f f e r i n g by only uniform amounts i n a single colour attribute. This enabled him to compare the r e l a t i v e influence of sample separation upon discrimination of various kinds of colour differences. Colour Difference Comparisons In the f i r s t method, the 7-field colorimeter was used with 4 of i t s hexagonal f i e l d s i n operation. These were f i e l d s 3, 4, 5, and 6 i n Figure 3. The f i e l d s were masked during the experiment so that they sub-tended approximately 2° at the position of the observer who used both eyes i n viewing. Surrounding the f i e l d s wasaa 20° grey annulus enclosed within a 40° white one. The chromaticity of the grey surround was that of Munsell value N6/ and the chromaticity of the white surround was that of CIE stan-dard illuminant 0 5 5 . Throughout the observations, the surrounds were il-luminated by 2 common sources of high-pressure xenon arc lamps modified to provide CIE daylight illuminant Dg^. The luminance of the white surround _2 was maintained at approximately 100 cd«m , and that of the grey surround -2 at 30 cd-m . The projected l i g h t was masked so that none of i t f e l l on the colorimetric f i e l d s . The configuration of the f i e l d s and surrounds as they were pre-sented to the observers i s depicted i n Figure 4. As can be readily seen, the l e f t pair of f i e l d s (4 and 5) was separated by only an extremely fine dividing l i n e , p r a c t i c a l l y 0- cm or 0° of v i s u a l angle i n widthiy but the right pair of f i e l d s (3 and 6) was separated by a s i g n i f i c a n t distance, approxi-22 Figure 4, Configuration of the visual field used in the first method. Hatched area is the grey surround, cross-hatched is the white surround (not to scale). 23 mately 8.2 cm or 4.1 of v i s u a l angle i n width. Two t e s t colours were used. T h e i r Munsell s p e c i f i c a t i o n s were 7.5 R 6/6 and 7.5 G 6/6. Figure 5 i l l u s t r a t e s the CIE c h r o m a t i c i t y p o i n t s (x,y) of these t e s t colours as w e l l as the surrounds. In g e n e r a l , the t e s t colours were set i n f i e l d s 3 and 4; f o r part of the experiment the same t e s t colour was set i n both f i e l d s , but f o r the remainder d i f f e r e n t t e s t colours were set i n the two f i e l d s . Colours d i f f e r i n g from the t e s t colours by s m a l l amounts of e i t h e r hue, chroma, or value were set i n f i e l d s 5 and 6. The step s i z e of the v a r i a t i o n was i n i t i a l l y s e t at 1.0 Munsell s t e p , but t h i s was found to be too la r g e f o r accurate assessment of colour d i f f e r e n c e s , so p r o g r e s s i v e l y smaller Munsell steps of .5, .25, and .125 were used. Each of the 5 observers i n t u r n was given the two f o l l o w i n g i n s t r u c t i o n s : i ) The purpose of t h i s experiment i s to estimate the t o t a l colour d i f f e r e n c e between p a i r s of c o l o u r s . State which p a i r of c o l o u r s , the l e f t or the r i g h t e x h i b i t s the l a r g e r t o t a l colour d i f f e r e n c e . Since t h i s i s a forced choice s i t u a t i o n , the answers, " I cannot t e l l " or "They are equal", are d i s a l l o w e d . i i ) Estimate the r a t i o of the l a r g e r colour d i f f e r e n c e to the sm a l l e r colour d i f f e r e n c e . Answers are to be given to one decimal p l a c e . Therefore the sma l l e s t permissable answer i s e i t h e r 1.1 L e f t or 1.1 Right. Supposedly i f the two p a i r s had the same magnitude of colour d i f f e r e n c e , the observer's judgements would be 1.1 L e f t or R i g h t , at random. Once a l l the observers had judged the r e l a t i v e s i z e of the 2 p a i r s of colour d i f f e r e n c e , the geometric mean f a c t o r was c a l c u l a t e d . I f the mean of judgements d i f f e r e d a ppreciably from 1.0, the colour d i f f e r e n c e i n one p a i r of f i e l d s was increased or decreased by an appropriate f a c t o r and the judgements were repeated. This process was continued u n t i l the mean r a t i o judgement was $i.2L or R i n d i c a t i n g that the two colour d i f f e r e n c e s had p r a c t i c a l l y the same perceptual magnitude. U s u a l l y t h i s occurred by the second or t h i r d judgement when the observers were d i v i d e d as to whether the r i g h t or l e f t d i f f e r e n c e was l a r g e r . D i f f e r e n c e Limens In the second method, d i f f e r e n c e limens (DL) were s e p a r a t e l y measured i n terms of Munsell hue, v a l u e , and chroma steps around a few colours whose Munsell s p e c i f i c a t i o n s were: 7.5 R 6/6, 7.5 G 6/6, 5 B 4/4, 5 Y 8/8, and N 6/. Figure 5 i l l u s t r a t e s the d i s t r i b u t i o n of the c h r o m a t i c i t y p o i n t s of these c o l o u r s . For each colour c e n t r e , DL's were c a l c u l a t e d at two cond i t i o n s of stimulus d i v i d i n g l i n e , 0-cm and 8.2 cm sep a r a t i o n . During the 0-cm sep a r a t i o n c o n d i t i o n f i e l d s 5 and6 of the NRC co l o r i m e t e r were i n ope r a t i o n , whereas during the 8.2 cm se p a r a t i o n c o n d i t i o n , f i e l d s 6 and 3 were used. For the most p a r t , the c o n d i t i o n s of observation ( i . e . , surround luminance and c h r o m a t i c i t y , surround and f i e l d s i z e ) were the same as used i n the previous method. However, l i m i n a l determinations were repeated f o r the achromatic s t i m u l i , N 6/ using l e s s favourable c o n d i t i o n s of observation. S p e c i f i c a l l y , the f i e l d s i z e was reduced from 2° to 1° v i s u a l angle, the l i g h t grey d i v i d i n g l i n e was replaced by a b l a c k one, and the surround 25 Figure 5. CIS 1931 chromaticity diagram showing chromaticity points of test stimuli used throughout this experi-ment. .The numbers correspond to ;the following Munsell notations: (1) 5 R 8.25/3, (2) 7.5 R 6/6, (3) 5 Y 8/8, (4) 7.5 G 6/6, (5) 5 B 4/4, (6) N 6/. Points RGB represent the chromaticities of the instrumental primaries, SQ the grey surround, and S W the white surround. The broken line represents the gamut of the NRC seven-field colorimeter. 26, luminance was lowered from 100 cd-m ^ to 2.5 cd-m ^ (or l e s s ) . This was done to approximate more c l o s e l y the co n d i t i o n s of Traub's experiment (1952) and to determine i f observation c o n d i t i o n s l e s s favourable than those nor-mally a p p l i e d i n p r a c t i c a l c o l o r i m e t r y would increase the s i z e of the DL. The o b s e r v a t i o n a l data was c o l l e c t e d i n the f o l l o w i n g manner. A l a r g e number of s t i m u l i , u s u a l l y between 50-75, were s e l e c t e d on the b a s i s of p r e l i m i n a r y experiments and were presented to the observer 50 to 100 times each i n a random order. The s t i m u l i were chosen so that they d i f f e r e d only by sm a l l amounts i n e i t h e r Munsell hue, v a l u e , or chroma steps from the t e s t colour which was l o c a t e d near the centre of the stimulus range. Each stimulus was presented simultaneously w i t h the t e s t c olour (always f i x e d i n f i e l d 6) and the observer (who had been dark adapted) reported whether the former stimulus was perceived as greater or l e s s than the l a t t e r i n the appropriate colour a t t r i b u t e . The terms of judgement were "weaker or stronger" i n the case of chroma, " l i g h t e r or darker" i n the case of v a l u e , and "bluer or greener", e t c . i n the case of hue. The observers made h i s judgements q u i c k l y and c o n f i d e n t l y to avoid wavering or guessing. He i n t e n t i o n a l l y r e s t r i c t e d h i s judgements to the p a r t i c u l a r c olour a t t r i b u t e i n q u e s tion even though the other two colour a t t r i b u t e s d i d not always remain p e r c e p t u a l l y constant. When a l l the judgements were completed the DL's were computed from the cumulative proportions of the two-category comparisons by the f o l l o w i n g procedure ( c f . , G u i l f o r d , 1954, p. 126). F i r s t , the cumulative p r o p o r t i o n a l judgements were converted to u n i t normal deviates or Z-values. This conversion, based on the phi-gamma hypothesis, assumed that the r e l a -tionship of proportional judgements to Munsell colour steps (S^-values) closely follows the normal cumulative d i s t r i b u t i o n function. Second, a least squares solution of the form z = a + b s was found such that the para-meters a (y-intercept) and b Cslope) described a l i n e from which the devi-ations of the z-values were minimized (in the sense that the sum of squares of the z deviations were a minimum). The parameters a and b are derived from the transformed observational data by the following equations: a = z - bs b = n L sz - (X,s) (Ez) n E s 2 - (£s)2 where n i s the number of pairs of s and z values. Third, the standard deviation (a), the point of subjective quality (P.S.E.) or mean, and the probable error (P.E.) of this best f i t t i n g normal d i s t r i b u t i o n function ( i . e z = a + bs) were estimated by solution of the formulae; a = 1/b P.S.E.= s - z a P.E.= 0.6745a F i n a l l y , the DL was taken as the value of either the a or the P.E. Colour Matching E l l i p s o i d s In the t h i r d method, colour matching e l l i p s o i d s were obtained for 6 test colours — the 5 used i n the previous method plus a s i x t h whose closest Munsell s p e c i f i c a t i o n was 5 R 8.25/3. Its chromaticity point i s shown i n Figure 5. The f i e l d sizes and luminances of these test s t i m u l i as w e l l as the chromaticities and luminances of the surrounds were the same as i n the other two methods, 28 Each t e s t colour was f i x e d s u c c e s s i v e l y i n f i e l d 6 and the ob-server produced i t s colour match i n an adjacent f i e l d ( e i t h e r 3 or 5) by manipulating the s h u t t e r s e t t i n g s of that f i e l d ' s 3 p r i m a r i e s . The i n s t r u -mental s e t t i n g s of the match were a u t o m a t i c a l l y recorded and stored on computer tape f o r l a t e r s t a t i s t i c a l a n a l y s i s . A f t e r the recording was com-p l e t e d , the observer randomly destroyed the sh u t t e r s e t t i n g s of h i s match and repeated the task. T h i r t y such colour matches c o n s t i t u t e d one observing s e s s i o n . For a l l s i x t e s t c o l o u r s , the observer made 30 colour matches at 3 separate observing sessions and at two separate widths of d i v i d i n g l i n e between t e s t and matching f i e l d : 0 cm and 8.2 cm. Therefore a complete set of observing sessions f o r any given colour c o n s i s t e d of 90 matches made at 0 cm separation and 90 matches made at 8.2 cm sep a r a t i o n . These b a s i c colour matching observations were supplemented by two a d d i t i o n a l sets of measurements. F i r s t , f o r the achromatic s t i m u l u N 6/ a second set of ob-ser v i n g s e s s i o n was obtained under thesleasofav/ouEabnieeob'sef^ ation:.•.„,. cdocin^d r i d t i i ohn srevious method). Second, f o r the s i x t h c o l o u r , 5 R 8.25/3, a set of 90 matches was obtained at a d i v i d i n g width of 3.2 cm Cl;6°) between f i e l d s . When a l l the o b s e r v a t i o n a l data had been c o l l e c t e d , the 90 matches from the three separate observing sessions were combined to c a l c u l a t e a com-p o s i t e e l l i p s o i d i n (x, y, 1)-space f o r each colour and f o r each w i d t h of d i v i d i n g l i n e . This was accomplished by using the standard s t a t i s t i c a l t e c h -niques o u t l i n e d i n Wyszecki and S t i l e s (1967, pp. 536-541) and i n Wyszecki and F i e l d e r (1971). By these techniques, the equation of the colour-matching 29 e l l i p s o i d i s given as; 2 2 2 2 (ds) = -guCx - x Q) 4 - g 2 2 ( y - y Q) + g 3 3 C l - 1 Q) r 2 g 2 3 ( y - y 0 ) C l - l 0 ) = 7.81 where ( X Q , yQ, 1Q) and(x, y, 1) are respectively the reference coordinates of the test chromaticity and any random match on i t and where the metric coefficients g^, result from s t a t i s t i c a l analysis of the observational data. i f c 2 The value of (ds) was set equal to 7.81 because this ensured that, on the average, the e l l i p s o i d contained 95% of a random set of colour matches made on the test colour. For convenTeoce oc onroepcamr-aging the different sets of colour matches made on the same test colour, the in d i v i d u a l points (x^, y , 1^) of each set of observations were shifted so as to make their respective mean point (<x , y , 1 ) coincide exactly with (x , y , 1 .). This trans-o o' o J o' o o formation suggested by Wyszecki and Fielder (1971) corrects for small st a -t i s t i c a l discrepancies of the means as w e l l as for small c a l i b r a t i o n errors of the seven-field colorimeter without apparently affecting the v a l i d i t y of intercomparison between e l l i p s o i d s . 30 RESULTS Supra-threshold Colour D i f f e r e n c e Comparisons P r e l i m i n a r y experiments d i d not provide any r e l i a b l e evidence that chroma or hue d i s c r i m i n a b i l i t y changes s y s t e m a t i c a l l y as a f u n c t i o n of sample p r o x i m i t y . However the same experiments d i d suggest that s e n s i t i v i t y to value d i f f e r e n c e s decreases s l i g h t l y w i t h i n c r e a s i n g w i d t h of d i v i d i n g l i n e . Therefore f u r t h e r s t u d i e s were conducted only w i t h p a i r s of Munsell samples d i f f e r i n g by supraSthreshold value steps. Table I I presents 19 p a i r s of mean value d i f f e r e n c e s that were judged to be equal by four observers Ca f i f t h observer took p a r t only i n the p r e l i m i n a r y experiments). N o t i c H o;hrit f o r each p a i r the l a r g e r value d i f -ference i s always a s s o c i a t e d w i t h the wid e l y separated colour p a i r . In the f i r s t p a i r , f o r i n s t a n c e , the observers c o l l e c t i v e l y judged that a colour d i f f e r e n c e of .10 Munsell value steps when viewed w i t h an extremely f i n e d i v i d i n g l i n e between samples was p e r c e p t u a l l y equal i n magnitude to one of .15 Munsell step when viewed w i t h a 8.2 cm d i v i d i n g l i n e between samples. In other words the colour d i f f e r e n c e between the wid e l y separated f i e l d s had to be greater than the colour d i f f e r e n c e between the juxtaposed f i e l d s by a f a c t o r of 1.5 i n order f o r the two colour d i f f e r e n c e s to be perceived as equal. M i s s i n g from t h i s t a b l e , however, are 35 p a i r s of colour d i f f e r e n c e s f o r which no n o t i c e a b l e p r o x i m i t y i n f l u e n c e could be found w i t h any degree of confidence. In many cases these untabulated p a i r s of colour d i f f e r e n c e s 31 TABLE II: EQUAL VALUE DIFFERENCES Difference in Munsell Value Steps between Left Pair of Color Samples (0 cm dividing line width) Difference in Munsell Value Steps between Right Pair of Color Samples (8.2 cm dividing line width) Ratio of Right Pair Value Differ-ence to Left Pair Value Difference 1 0.10 0.15 1.50X 2 0.50 0.75 1.50X 3 1.00 1.50 1.50X 4 0.35 0.50 1.43X 5 0.35 0.50 1.43X 6 1.00 1.40 1.40X 7 0.75 1.00 1.33X 8 1.00 1.30 1.30X 9 1.00 1.25 1.25X 10 2.00 2.50 1.25X 11 2.00 2.50 1.25X 12 0.20 0.25 1.25X 13 1.00 1.25 1.25X 14 0.40 0.50 1.25X 15 0.20 0.25 1.25X 16 0.40 0.50 1.25X 17 0.40 0.50 1.25X .18 0.20 0.25 1.25X 19 4.00 4.50 1.13X MEAN: 1.32X 32 are of the same order of magnitude as those presented i n the t a b l e . Perhaps then the i n f l u e n c e of the p r o x i m i t y f a c t o r i s r e l a t i v e l y weak and e a s i l y masked by such f a c t o r s as observer v a r i a b i l i t y , c o l o r i m e t r i c f i e l d c a l i b r a -t i o n e r r o r s , and s m a l l c o l o r matching e r r o r s . Therefore, although, t h i s r a t i o comparison method was u s e f u l f o r q u a l i t a t i v e l y demonstrating the i n f l u e n c e of sample p r o x i m i t y upon value d i s c r i m i n a t i o n , i t was considered i m p r a c t i c a l f o r q u a n t i t a t i v e l y measuring the e f f e c t . Threshold D i f f e r e n c e Limens Table I I I presents the DL's f o r hue, v a l u e , and chroma limen which were determined at each of f i v e colour centers. They are based on separate a n a l y s i s of juxtaposed viewing f i e l d comparisons and wid e l y separa-ted (8.2 cm) viewing f i e l d comparisons. Each DL i s expressed i n terms of the standard d e v i a t i o n (cr) of the best f i t t i n g normal d i s t r i b u t i o n r e l a t i n g the observer's comparative judgements to the appropriate Munsell colour u n i t s . For instance the f i r s t row of e n t r i e s i n Table I I I i n d i c a t e s that at the l o c a t i o n of 5 Y 8/8 i n colour space (based on juxtaposed colour f i e l d ob-ser v a t i o n s ) the chroma limen was .161 Munsell chroma steps; the hue limen was .298 Munsell hue steps; and the value limen was .051 Munsell value steps. S i m i l a r l y the corresponding e n t r i e s i n the second row i n d i c a t e that f o r the same colour l o c a t i o n (based on widely separated f i e l d observations) the chroma limen was .218 Munsell chroma st e p s , the hue limen was .301 Munsell hue steps and the value limen was .113 Munsell value steps. A l s o presented i n t h i s t a b l e are the probable e r r o r (PE.) and the TABLE III: Attributive difference limens for two conditions of f i e l d separation TEST FIELD COLOUR SEPARATION (MUNSELL (CM.) x NOTATION) COLOUR CENTRE D.L.(a) D.L.(P.E.), P.S.E. CHROMA HUE VALUE CHROMA HUE VALUE CHROMA HUE VALUE 5Y 8/8 5B 4/4 N 6/ N 6/c 0.0 8.2 0.0 8.2 7.5G 6/6 0.0 8.2 7.5R 6/6 0.0 8.2 0.0 8.2 0.0 8.2 .4158 .4378 .3543 .2362 .2782 .2158 .2662 .3672 .2956 .4000 .3340 .2956 .3102 .3164 .2963 .3102 .3164 .2963 .1605 .2128 .2981 .3008 .0505 .1133 RATIO RATIO 1. 3600 1.0100 2.2400 1985 .4099. .0420 2652 .4828 .0871 1. 3400 1.1800 2..0700 1699 .2608 .0335 2747 .3059 .0790 1. 6200 1.1700 2.3600 0779 .0998 .0255 . 1452 .1249 .1005 1. 8600 1.2500 3.9400 .0239 .0774 3.2400 .0385 .0231 6.0100 .1082 ,1472 ,1339 ,1789 .2010 .2029 .2765 .3256 .0340 .0764 .0283 .0588 ,1146 .1759 .0226 ,1853 .2064 .0533 .0525 .0673 .0172 .0979 .0842 .0678 .0161 .0522 .0260 .1560 8.011 5.097 7.996 8.016 5.101 7.998 4.004 4.007 5.008 3.993 5.014 3.993 5.990 7.553 6.000 5.997 7.554 5.996 6.077 7.564 5.968 6.068 7.565 5.949 5.996 5.991 5.999 5.996 Expressed in terms of the standard deviation (a) of the best f i t t i n g normal distribution r e l a t i n g dichotomous observer judgements to the appropriate Munsell colour units. D.L. obtained under less favourable observing conditions, see note in text. 34 point of subjective equality Q?SE) of the best f i t t i n g normal distribution. The PE may be considered as a more conservative estimate of the DL. It is related to the a by the function PE = 0.6745a. The PSE may be interpreted as the mean of the stimulus range used in determining the DL. Any discre-pancies between the Munsell notations of the test colour and the PSE are due to samll unavoidable colour matching and colorimetric calibration errors which may be ignored. The DL's resulting from analysis of juxtaposed colour fields may be readily compared with attributivee Munsell limens obtained by Bellamy and Newhall (1942). On the basis of 34 chromatic plus 7 achromatic origins, Bellamy and Newhall found a mean hue limen of 0.5 Munsell hue steps with- a range of 0.05-1.40; a mean chroma limen of 0.17 chroma step with a range of 0.03-0.85; and a mean value limen of 0.021 value steps with a range of 0.002-0.049. On the other hand, in this study on the basis of 4 chromatic origins plus 1 achromatic origin, wi found a mean hue limen of .27 Munsell hue step with a range of .01-.41; a mean chroma limen of .15 Munsell chroma step with a range of .08-.20; and a mean value limen of .035 Munsell value step with. 30 a range of .026-0.51. Obviously there is considerable v a r i a b i l i t y between the mean hue and value limens evaluated in terms of the Munsell scales by the two d i f f e -rent studies. These discrepancies are probably due to the non-perceptual equivalence of the Munsell attributive scales, the smaller number of sample colours and observers used in the present study, and the different instru-mentation (Bellamy arM Newhall used spinning disks). They are not especi-ally disturbing because other investigators^ (e.g. , Davidson, 1951). using 35 -different observational procedures have also found markedly higher mean Munsell value limens and lower mean hue limens than those obtained by Bellamy and Newhall. An examination of the corresponding pairs of DL's presented i n Table I I I indicates that i n a l l cases a wide separation increases the size of the DL; influencing lightness discrimination the most and hue discrimination the least. For instance, the mean average increase in the value limen i s about 3x with a range of 2 - 4x, i n the chroma limen i s about 1.5x with a range of 1.3 - 1.9x, and i n the hue limen i s about 1.2x with a range of 1.0 - 1.3x The influence of sample separation upon value discrimination becomes somewhat more pronounced when poor or impractical observation conditions are employed such as reduced f i e l d s i z e , dark surround, and dark contrasting dividing l i n e . Under good observation conditions, the value limen determined for sample N 6/ increased i n size from 0.239 to 0.774 when wide f i e l d measurements were made, but under less favourable conditions i t increased from .0385 to .2313. This corresponds to a porportional increase i n the value limen from a factor of about 3.3 to one of about 6.0. A finding corroborating i n part Judd's observa-tion (1930) that a dark dividing l i n e between samples interferes more with the perception of chromaticity differences (when making colour temperature measurements)than a l i g h t grey dividing l i n e . .36 Colour Matching E l l i p s o i d s To supplement the difference limen data, various colour matching observations were made on the same f i v e test colours. The results obtained under both juxtaposed and widely separated matching f i e l d conditions (8.2 cm) and analysed i n terms of colour matching e l l i p s o i d s are presented i n Table IV. This table also includes data obtained for a s i x t h colour (5R 8.25/3) at f i e l d separations of 0 cm, 3.2 cm, (1.6° angular subtense), and 8.2 cm. Each colour matching e l l i p s o i d i s described by i t s colour centre (Xq, y o > l 0 ) coinciding with the test colour, i t s s i x cj-coe£ficients, and i t s e l l i p t i c a l x,y cross section or e l l i p s e whose relevant parameters include angle of orinetation 9 , length of major a and minor b semi-axes, shape a/b. and size A (where A = ITab) . The e l l i p s o i d s derived from analysis of juxtaposed f i e l d colour matches can be readily compared with the Wyszecki and Fielder (1971) com-posite e l l i p s o i d s (Robertson, 1975b) based on colour matching observations made with the same instrument. Examination of the corresponding e l l i p t i c a l cross sections of the two sets of e l l i p s o i d s (plotted i n Figure 6) indicates for s i m i l a r locations i n the CIE chromaticity diagram they agree reasonably well i n orientation and shape, but not i n size. The discrepancy i n size between the two sets of e l l i p s e s i s not unexpected because: i ) colour mat-ching data of this sort has low repeatability and high v a r i a b i l i t y and i i ) the Wyszecki-Fielder e l l i p s o i d s were obtained at a constant test f i e l d luminance l e v e l (1 = 0.2158) whereas mine were not (ranging from 1 = 0.21 to 1 = 0.36). 3 1 TABLE IV: Color-matching e l l i p s o i d s and t h e i r cross sections of observer LTS f o r 0, 3.2, and 8.2 cm f i e l d separation conditions. FIELD COLOR CENTRE q COEFFICIENTS H O ' 3 ) , NO. OF COLOR SEPARATION x Q y Q (cm. ] 5R 8.25/3 0 .3345 .3198 3.2 , 8.2 7.5R 6/6 0 .4000 .3340 8.2 5Y 8/8 0 .4158 .4378 8.2 7.5G 6/6 0 .2662 .3672 8.2 58 4/4 0 .2363 .2782 8.2 N6/ 0 .3102 .3164 8.2 N6/a 0 .3102 .3164 8.2 9 l l 912 g 2 2 g23 933 9l3 o(deg.) a-(103) b-(10) 3 a/b l o g ] 0 A OBSERVED POINTS AY/Y 3604 83 29 1319 -799 3371 83 19 2.7 1.5 1.87 -4.898 90 .019 10 -5 784 -70 1022 -25 15.3 3.2 2.7 1.17 -4.560 90 .034 25 -22 724 -87 993 53 16.4 3.4 2.8 1.21 -4.536 90 .035 2956 443 -7 293 -334 1984 90 10.8 5.8 2.0 2.99 -4.446 92 .025 96 -45 62 -11 368 24 2.1 11.2 4.6 2.06 -3.789 91 .057 ,3543 861 -65 761 -471 1275 -571 30.7 4.0 2.2 1.8 -4.548 90 .031 131 -115 344 -110 335 -77 46.1 5.8 4.2 1.4 -4.117 90 .060 ,2956 548 143 517 83 476 -283 128.1 4.4 3.7 1.19 -4.300 90 .050 107 48 214 130 306 -22 144.7 8.0 4.4 1.81 -3.953 90 .063 .2158 547 -94 576 -542 718 79 41.3 8.8 2.6 4.43 -4.149 90 .041 471 -172 441 -360 . 375 155 47.6 13.0 3.2 4.07 -3.887 90 .057 .2963 725 219 975 -423 938 86 46.3 3.8 2.4 1.61 -4.543 90 .035 348 -317 1498 -906 905 417 54.1 5.6 1.9 2.95 -4.474 90 .036 .2963 78 -23 593 -438 524 27 47.3 8.1 2.8 2.89 -4.148 90 .048 29 -37 251 -151 231 28 47 9.3 4.5 2.09 -3.883 90 .072 a Color matching e l l i p s o i d obtained under less favorable observing conditions, see note i n text. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x Figure 6. Section of the CIE 1931 chromaticity diagram showing cross sections (2.5 times enlarged) of colour matching ellipsoids obtained in (x,y,l) space. Solid line ellipses represent mean results obtained by Wyszecki and Fielder three observers (after Robertson^), Broken line ellipses represent results obtained by observer LTS for 0-cm f i e l d separation condition. The numbers correspond to the Munsell notations given in Figure 3. Points R,G,B re-present the chromaticities of the instrumental primaries. -39 The e f f e c t of f i e l d s e p aration upon colour matching p r e c i s i o n can be measured by two separate methods. The f i r s t i n v o l v e s c a l c u l a t i n g the p r o p o r t i o n a l change i n area of the e l l i p t i c a l cross s e c t i o n of the colour matching e l l i p s o i d i n the x,y plane. This technique provides a comparative measure of the observer's p r e c i s i o n of matching the c h r o m a t i c i t y of the t e s t colour under the two c o n d i t i o n s of f i e l d s eparation. The second method i n v o l v e s c a l c u l a t i n g the corresponding change i n len g t h of rad i u s of the colour matching e l l i p s o i d perpendicular to t h i s cross s e c t i o n . The l e n g t h of radius i s found by s o l v i n g the f r a c t i o n AY/Y = 34.6(g^^)^ (Wyszecki and S t i l e s , 1967). This technique provides a measure of the observer's pre-c i s i o n of matching the luminance of the t e s t c o l o u r . Figure 7 g r a p h i c a l l y i l l u s t r a t e s the l o s s i n p r e c i s i o n of chro-maticness s e n s i t i v i t y . For the same colour c e n t r e , the composite of e l l i p s e i s always l a r g e r when there i s a wide p h y s i c a l separation between the t e s t - f i e l d and the matching f i e l d . N u m erically, t h i s corresponds to an:.increase i n e l l i p s e area or l o s s i n chromaticness s e n s i t i v i t y by an 32 average f a c t o r of approximately 1.5, w i t h a range of 1.1 - 2.1. Concomitant w i t h the increase i n e l l i p s e area there i s an average increase i n the 33 luminance radius of approximately 1.6x w i t h a range of 1.02x - 2.3x when a wide f i e l d s e p aration i s employed. However i t must be emphasized that these f i g u r e s are based on averaged data ( i . e . , composite e l l i p s o i d s ) and there i s considerable f l u c t u a t i o n between the values of the e l l i p s e area and luminance radius AY/Y X Figure 7. P o r t i o n of the CIE 1931 c h r o m a t i c i t y diagram showing cross sections of c o l o u r -matching e l l i p s o i d s obtained i n ( x , y , l ) space f o r observer LTS. S o l i d l i n e e l l i p s e s are f o r the 0-cm separation c o n d i t i o n and broken l i n e e l l i p s e s are f o r the 8.2-cm separation c o n d i t i o n . The numbers correspond to the Munsell n o t a t i o n s given i n Figure 3. P o i n t s R,G,B represent the c h r o m a t i c i t i e s of the i n s t r u m e n t a l p r i m a r i e s . The axes of the e l l i p s e s are f i v e times a c t u a l s i z e . 41 as. estimated by- the three i n d i v i d u a l sets of observational data. Typical examples of the v a r i a b i l i t y i n cross sectional area of the e l l i p s o i d s are plotted i n Figure 8. This graph shows remarkable discrepancies between el l i p s e s obtained by the same observer at three different occasions but otherwise i d e n t i c a l observing conditions. Although the bulk of the colour matching observations were made at two widths of sample separation, observations were made on one test colour 5 R 8.25/3 at an additional width of separation, 3.2 cm. This set. 2 of measurements iremcd iceiaetceits; that precision of both chromaticity and luminance matching f a l l s off most rapidly at intermediate levels of dividing l i n e width and less so at increasing wider le v e l s . For instance, Figure 9 i l l u s t r a t e s that between the 0 cm and 3.2 cm separated f i e l d matching condi-tion there i s a s i g n i f i c a n t increase i n e l l i p s e area .0-.5x), but between the 3.2 cm and 8.2 cm condition there i s only a small one O.03x). S i m i l a r l y , the r a t i o increase i n AY/Y between the 0 cm and 3.2 cm condition i s large 0-8x), but between the 3.2 cm and 8.2 cm condition i s small G.Olx). How-ever i t would take further experimentation at various widths of angular separation to v e r i f y t h i s hypothesis. The colour matches made for the N6/ test colour under the less favourable observation conditions strengthenes the finding made with, the DL method. Namely, precision of both chromaticity matching Csee Figure 10) and lightness matching Csee Table IV) as measured by e l l i p s e size and AY/Y, respectively, decreases not only with the width, of the dividing l i n e , but also with the degree of contrast between the colorimetric f i e l d and the d i -viding l i n e . Under good observation conditions with: a l i g h t grey dividing 42 0.4 X .Figure;8. P o r t i o n of the CIE 1931 c h r o m a t i c i t y diagram showing cross sec-t i o n s of colour-matching e l l i p s o i d s obtained i n ( x , y y l l space f o r observer LTS producing s e t s of colour matches at three d i f f e r e n t occasions but otherwise i d e n t i c a l observing c o n d i t i o n s . The numbers correspond t o the Munsell n o t a t i o n s given i n F i g u r e 3. The axes of the e l l i p s e s are 2.5 times a c t u a l s i z e . 43 3350 3200 h 3050 3200 3350 3500 Figure 9. Portion of the CIE 1931 chromaticity diagram showing cross sections of colour-matching ellipsoids obtained in (x,y,lX space for the same colour centre 5 R 8.25/3 at three conditions of f i e l d separa-tion. The numbers indicate width; of dividing line in centimeters. 44 3350 3200 h 3050 3200 3350 3500 Figure 10. Portion of tne CIF 1931 chromaticity diagram showing cross sections of colour-mat ching ellipsoids, obtained in (x,y,l)_ space for the same colour centre center N 6/. Solid line ellipses represent colour matches made with: 4° f i e l d and light dividing line and surround. Broken line ellipses represent colour matches made with 2° f i e l d and dark dividing line and surround. The angular separation for each ellipse i s given in centimeters. 45 line, the ellipse area only increased by a factor of 1.1 and the luminance radius by a factor of 1.02 when wide field measurements were made (8.2 cm). But under poor observation conditions with a black dividing line and with wide field measurements, v.the ellipse area increased by a factor of 1.35 and the luminance radius by a factor of 1.51. 46 DISCUSSION Methodological C r i t i c i s m s A number of change s i n experimental design would extend the g e n e r a l i t y of these r e s u l t s and e l i m i n a t e some sources of experimenter b i a s . F i r s t the experiments should be repeated w i t h more observers.and at more widths of d i v i d i n g l i n e . The suprathreshold colour d i f f e r e n c e comparisons are based on the judgements of only four observers ( i n c l u d i n g the experimenter) and the th r e s h o l d measurements are based on only the experimenter's observations. L i k e w i s e , measurements were made at only two c o n d i t i o n s of d i v i d i n g l i n e w i d t h : 0 cm and 8.2 cm. Thus the data does not provide s u f f i c i e n t i n f o r m a t i o n to determine the f u n c t i o n a l r e l a t i o n s h i p of the pr o x i m i t y f a c t o r to angular separation of samples. Second, the measurements should be repeated w i t h surface colours i n s t e a d of w i t h aperture c o l o u r s . The aperture mode of co l o u r appearance was chosen i n t h i s study because i t a l l o w s continuous v a r i a t i o n o f the s t i -mulus c o l o u r dimensions (something not p o s s i b l e w i t h s u r f a c e c o l o u r s ) . How-ever the r e s u l t s are meant to apply to colour d i f f e r e n c e e v a l u a t i o n s made between surface c o l o u r s . U n f o r t u n a t e l y , there e x i s t s an obvious d i f f e r e n c e between seeing an object i n an i l l u m i n a t e d space (surface colour) and seeing a patch o f co l o u r f i l l i n g a photometric f i e l d (aperture c o l o u r ) . However the problem was somewhat lessened by the c o n f i g u r a t i o n of the t e s t f i e l d which causes aperture presented c o l o u r s to .resemble surface presented ones. These above m o d i f i c a t i o n s would c e r t a i n l y i n c r e a s e the v a l i d i t y 47 of the results and decrease the likelihood of experimental error in this study. However there are a number of other possible sources of experimenter bias which cannot be as readily eliminated. For instance, when making liminal determinations, the difference threshold i s a transi-tory phenomenon, varying from moment to moment and influenced by fatigue, practice, systemic and metabolic conditions. Consequently the difference threshold may be an unreliable or inaccurate measure of the observer's discriminability especially i f the above-mentioned sources of variance are augmented by asymmetries in the series of test stimuli being judged or by non-random patterns in the observer's sequence of comparative judge-ments.. Similar parameters reduce the repeatability of colour matching data and may not be eliminated by the s t a t i s t i c a l procedure used to evalu-ate such data (Wyszecki and Fielder, 1971). Conclusions Both the preliminary experiments >of Judd (1930) and a number of observations in the literature suggest that angular separation of 48 comparison samples conspicuously reduces s e n s i t i v i t y to colour d i f f e r e n c e s . Although, "hue and chroma comparisons do not s u f f e r as much, as l i g h t n e s s comparisons..." (Bellamy and Newhall, 1942). Judd, i n f a c t Q.939.a, 1939b). considered the l o s s i n l i g h t n e s s d i s c r i m i n a t i o n l a r g e enough, i n magnitude to i n c l u d e i n h i s colour d i f f e r e n c e formula a p r o x i m i t y f a c t o r whose purpose was to weight the r e l a t i v e importance of perceived l i g h t n e s s to perceived chromaticness d i f f e r e n c e s as a f u n c t i o n of sample p r o x i m i t y i n space. How-ever no other colour d i f f e r e n c e formula w i t h the exception of the Hunter 34 modified Judd equation (1942) inc l u d e s such a f a c t o r . This f a c t zmmedi-a t e l y suggested the question which prompted t h i s research: should a p r o x i -mity f a c t o r be introduced i n t o colour d i f f e r e n c e formulae when they are used to evaluate the colour d i f f e r e n c e between samples separated by a conspicuous d i v i d i n g l i n e ? The answer to t h i s question must be a q u a l i f i e d "yes". C e r t a i n l y the t h r e s h o l d colour measurements ( i . e . , d i f f e r e n c e limen and colour matching e l l i p s o i d determinations) made i n t h i s study imply that f i e l d s e p a r a t i o n a f f e c t s both l i g h t n e s s and chromaticness d i s c r i m i n a t i o n \ reducing s e n s i t i v i t y to perceived l i g h t n e s s d i f f e r e n c e s more. A wide d i v i d i n g l i n e between comparison samples may under good observing c o n d i t i o n s impair l i g h t n e s s d i s c r i m i n a t i o n by as much as a f a c t o r of three and under l e s s f a -vourable observation c o n d i t i o n s by as much as a f a c t o r of s i x . Thus a l u -minance weighting constant of the s o r t proposed by Judd (1939a, 1939b.l and explored by Traub ('1952) should be introduced i n t o c olour d i f f e r e n c e formulae a p p l i e d to t h r e s h o l d or s m a l l - s i z e d colour d i f f e r a n c e evaluations.. Howeyer many more t h r e s h o l d colour d i f f e r e n c e comparisons, would have to be conducted at v a r i o u s d i v i d i n g l i n e w i d t h s before the f u n c t i o n a l r e l a t i o n s h i p between 49 proximity factor and angular separation could be deduced. On the other hand, i t may be unnecessary- to apply- a weighting factor derived from highly specialized threshold measurements- to the f i n i t e colour comparisons: often involved in practical colorimetry. The supra— threshold colour difference assessments-made in-this experiment indicated no measurable loss in chromaticness discrimination, and only a small but highly unstable loss i n lightness discrimination when the test f i e l d and comparison f i e l d were physically separated by as much as 4.1° of visual angle (a^distance greater than the diameter of the combined colorimetric comparison f i e l d s ) . In fact, in more than 65% of these colour difference comparisons no notice-able influence of dividing linewidth on lightness discrimination could be ascertained with any degree of certainty. Presumably the magnitude of the effect was washed out by the large observer v a r i a b i l i t y encountered when making f i n i t e colour comparisons. Indeed, Wyszecki (1965a) points out that; "the phenomena and concepts associated with; threshold judgements differ in various ways from those inyolyed in the assessment of small but clearly perceived colour differences. It is quite coneeiyaMeefchatdin the latter case the action of the cortex as a part of the visual mechanism becomes a predominant factor making the ob-server's judgement highly subjective and f l e x i b l e . " In sum, therefore, a proximity factor would seem to be a neces^ sary parameter to introduce into colour difference formulae i f they are used to predict the perceived magnitude of threshold or small-sized colour d i f -ferences, but not i f they are applied to large-sized colour differences (those typical of the Munsell Book of Colour). However more experiments with more observers|Jcandrfcmor.e)robsepvingisc'6n;dMi6n's^,s shouUdefrejaper-forme'd'. to'"confirm 35 this condu'siomrmg conditions 9 should be performed to make -,r 35 - "..r.^i are indeed valid. 50 FOOTNOTES 1. S p e c i f i c a l l y , measurement of colour serves as a generic term f o r any procedure by which, colours are measured i n one way- or another; whereas-, colorimetry Implies the association of the physically-measureable pro-pe r t i e s of a colour with, the relevant colour perception of normal trichromats (cf. Thurner, 1962,. p.5). 2. Primary colours are the colours of three reference l i g h t s by whose additive mixture nearly a l l other colours may be produced.• These colours are often chosen to be e i t h e r red-f green, and blue, or red, green, and v i o l e t (Wyszecki and S t i l e s , 1967, p. 230). 3. The s p e c t r a l concentration at a given wavelength of radiant f l u x i s given by the amount of radiant f l u x , having wavelength i n an i n f i n i t e -simal i n t e r v a l containing the given wavelength, divided by the width of the i n t e r v a l . The v a r i a t i o n of the s p e c t r a l concentration of r a d i -ant f l u x with wavelength i s termedithe s p e c t r a l energy d i s t r i b u t i o n (or s p e c t r a l power d i s t r i b u t i o n ) and a corresponding graph i s termed the s p e c t r a l energy d i s t r i b u t i o n . c u r v e ( c f . , Wyszecki and S t i l e s , 1967). 4. The choice of primaries i n colour matching i s a r b i t r a r y , except f o r the r e s t r i c t i o n that no one of the primaries may produce a colour which can be matched by any combination of the other two primaries (Burnham, Hanes, and Bartleson, 1963, p. 119). 5. To c l a r i f y , R, G, B, C ar.enquaiita^ Be%ghmixedoor."JcmatGhea^sigDxfigf,nb?. endrerq uualntfctiTt- aysbi^l? e symb.qls, i ddennifyif.Ieyrdssnegtthe respective amountsloftt h e s e •.•=;-MghtstJusedcal s i g n i f i c a n c e and are quantitative symbols. Thus the equation Eq.(l)may be read as follows: the unknown colour C i s matched by an additive mixture of r parts of the primary R, g parts of the p r i -mary colour G, and b parts of the primary colour B. 6. The sum of the t r i s t i m u l u s values may be said to produce the same colour sensation as the unknown colour stimulus C. But i t must be recognized that such a t r i s t i m u l u s colour s p e c i f i c a t i o n merely expresses an. equi-^ valence between p h y s i c a l s t i m u l i i n t h e i r capacity to arouse a colour sensation, and that the s p e c i f i c a t i o n i t s e l f i s a p h y s i c a l s p e c i f i c a t i o n of s t i m u l i , not of a sensation (Wright, 1969, c f . p. 70). 7. Colour equations f o r s p e c t r a l radiations i n terms of three primaries R, G, B sometimes involve negative q u a n t i t i e s . This i s because, a l -though many colours can be matched by a mixture of a l l three primaries, i n p o s i t i v e or n i l amounts, other colours have to be mixed with s u i t a b l e amounts of one or two primaries before a match can be made with the remaining primaries or primary. In such cases, the colour matching 51 equation s t i l l holds, i f the quantity of the primary-mixed with, the given colour is. assigned a negative value. For example, i f r amounts, of R have to be mixed with C to_yield a match, with, the mixture, g amounts of G plus b amounts of B, then the equation of the match may be expressed as : C r-R = gG + bB or C -rR -r gG + bB or C rR gG + bB with r assigned a negative quantity- (Wyszecki and S t i l e s , 19.67, p. 232).. 8. The complementary term is. isomerism which may be defined as the i d e n t i t y of colour appearance and spectral energy d i s t r i b u t i o n between s t i m u l i . Hence isomeric colours are colour s t i m u l i of i d e n t i c a l tristimulus values and spectral energy d i s t r i b u t i o n . 9. Any change i n illuminating or observation conditions, such as a different illuminant or observer, w i l l generally upset the metameric match between 2 colour s t i m u l i . The.coloursswill then appear different and are con-sequently said to exhibit a metameric difference. 10. A quantitative measure for the degree of metamerism may be obtained by taking the square root of the sum of the squares of differences between the spectral energy di s t r i b u t i o n s (R ), and (R )^ of the two given meta-meric colours for the specified conditions. That i s , the degree of metamerism may be expressed as: (Judd and Wyszecki, 1963, p. 152-153). 11. Colour, matching functions, or colour mixing functions are the tristimulus values, with respect to three given primary colours of monochromatic lights, of equal radiant energy, regarded as functions of the wavelength (Wyszecki and S t i l e s , 1967, p. 230). 12. In accordance with the laws of additive colour mixture nonreal primaries can be defined which have the useful property that; any r e a l colour can . be represented by an additive mixture of positive amounts of the p r i -maries (Wyszecki and S t i l e s , 1967, p. 230). The use of such a, system of nonreal primaries avoids the problems of negative.coefficients .(see , footnote 7).. 1 3 . The r e t i n a l image of the large- f i e l d unavoidably- covers areas that con-tain rod receptors. When the s t i m u l i presented to the observer are of s u f f i c i e n t l y low intensity the scofcopic mechanism may contribute- to the 52 match in such a way as to upset the predictions of/the standard ob- , server. Upsets of this kind are described as arising from rod intru-sion (Wyszecki and Stiles, 1967). 14. Self-luminous colours are light sources producing energy that-travels ' directly to the retina tosserve as a colour stimulus. 15. Object colours are colour stimuli arising by the reflection or trans-^ mission of incident flux by objects. 16. The chromaticity of a colour is the colour quality of a light-definable by i t s chromaticity coordinates CWyszecki and Stiles, 1967, p. 230). Roughly speaking the .chromaticity of a colour stimulus correlates with the chromatic, appearance of a colour stimulus under ordinary observing conditions. However the term chromaticity does not account for the brightness of lightness of a colour stimulus. In order to f u l l y specify a colour stimulus the Y or Yj_-value computed on the basis of the 1931 or the 1964 CIE system must be added to the chromaticity coordinates Cx,y or x ^ , ^ IO^' a s ^ o r ^10 §-i-ves t n e luminance or luminous reflectance Cor transmittance) of the stimulus. Luminance is often considered a correlate to a brightness index and luminous reflectance a correlate to a lightness index Csee e.g., Wyszecki, 1966a, p. 174.) 17. A diagram in which any one of the three chromaticity coordinates is plotted against any other is called a chromaticity diagram. In this diagram the chromaticity of a colour plots as a point called the chro-maticity point (Wyszecki and Stiles, 1967, p. 230).• 18. A spectrum colour is the colour of a monochromatic light, that i s , light of a single frequency (Wyszecki and Stiles, 1967, p. 229). The chro-maticities of the spectrum colours for the 1931 Standard Observer sys-tem were determined from the Wright and Guild data, whereas those for the 1964 Standard Observer system were determined from the Stiles arid Burch and Speranskaya data. 19. Since the locus is always straight or convex, but never concave, i t follows that: "the colour resulting from the mixture of any two wave-lengths (or spectral primaries) must be either on the locus or within the area bounded, by the locus, but never outside i t . " (Wright, 1969, p. 122). 20. Hue is the attribute of a colour perception.denoted by blue, green, yellow, red, purple, and so on (Wyszecki and Stiles, 1967, p. 229JL. 21. Saturation is the attribute of a colour perception determining the degree of i t s difference from the achromatic colour perception most resembling i t (Wyszecki and Stiles, 1967, p. 229). In the: Munsell system this attribute corresponds to chroma. NOTE: The attribute 53 of a colour perception composed of the' attributes hue and saturation is called chromaticness. 22. Lightness (of an object perceived as non^-self luminous 1 is the a t t r i - . bute of a colour perception permitting'to be classed .as-equivalent to some member'of the-series of achromatic object-colour perceptions ranging for light-diffusing obj ects from black - to white,"~and ranging for regularly transmitting objects from black to perfectly clear and colourless (Wyszecki and Stiles, 1967, p. 229). In the-Munsell system • this attribute.is called value.. 23. Obviously this could be done for the 1964.CIE Standard Observer system as well. 24. Chromaticity edOBdinates do not account for the lightness of a colour stimulus so only Munsell chips of constant value (or lightness) can be plotted in any one chromaticity diagram. However a series of chro-maticity diagrams each set at a different Munsell value or Y-value can be used to represent the complete series of Munsell chips, with each diagram of different Munsell value representing a different set of equi-luminous Munsell chips. 25. That i s , those points lying in a plane of constant luminance of the 1931 or 1964 CIE tristimulus space. 26. An index i s chosen which gives' approximately- uniform lightness ; (or brightness) spacing for colours of the same chromaticness or the same chromaticity. Suitable scaling factors for both the chromaticness scale and.the lightness scale are selected to make the unit of chro-maticness difference closely equivalent to the unit of lightness difference (Wyszecki, 1965, p. 295). 27. The magnitude of the perceived colour difference between any two colours is given in terms of some convenient unit of measure. Usually the unit i s the just noticeable difference or some multiple of i t . 28. Xo, Yo, Zo are the CIE tristimulus values defining the colour of the . nominally white-colour (or standard illuminant).stimulus. 29. A special computer program based on the elaborate calibration of the 7-field colorimeter allows any colour specified in terms of CIE co-ordinates (within the colorimeter's gamut) to be set in any one of the 7 colorimetric fields by suitable mixture of the corresponding red,, green, and blue instrumental primaries. 30. It is d i f f i c u l t to draw any finer comparisons.between the two studies because the same Munsell colours were not employed as stimuli. There are two exceptions, however, two common colour centers, 5 Y 8/8 and N 6/, were used in both studies. For the former, Bellamy and Newhall 54 obtained a hue limen of .67, a chroma limen of .31,-and a yalue limen of .04. In this study, we obtained a hue limen of .30, a chroma limen of .16, and a value limen of .05. The agreement therefore in . this case is poor. For the achromatic sample, Bellamy and Newhall obtained a value limen of .023 and we obtained one of .024. The agreement therefore in this case is very good. .31. The size of e l l i p t i c a l cross-section of ellipsoids probably changes with test f i e l d luminance level. . For instance, the observations of Brown 0-951) suggest that ellipses increase in size as test f i e l d luminance decreases. 32. These values actually correspond to the average proportional increase. in the square root of the ellipse area. The square root of the ellipse area was. taken so that the area increase Can area change) could be roughly compared with the luminance increase Ca linear change). , 33. Only a small increase in ellipse area and AY/Y size was found for the N 6/ colour centre. This may be due to a crispening effect since i t s tristimulus values were almost identical to those of the surround colour. Or, perhaps the surround counterbalanced the effect of the dividing line width by appearing as an extended f i e l d of the test colour. 34. MacAdam (Am. Inst. Phys. Handbook, 2nd ed., pp. 6-149, 1963) does make allowances for sample proximity in his colour difference formula. The.constant g^o takes on different values depending upon the width and constrast or dividing line between samples: "For sharp dividing line and samples subtending about 2 deg. , g„„ -= 1. For less well-defined dividing line, g ^ may be considerably less; e.g., for 5-deg. separation between large samples g-jo - 0.005. For extremely small samples, contrasted with colour of their background, g^ 3 = 0.5..." 35. Pvecently Witzel, Burnham, and Onley (1973) obtained colour matching ellipses averagedly three times larger than ones predicted from graphical interpolation of the PGN data (MacAdam, 1943) for the same colour location. These authors speculated that the difference in size resulted from discrepancies between their's and MacAdam's observing conditions; specifically, that they maintained an angular separation of 5.14° (actually 3.72°) between the test and matching fields whereas MacAdam did not. However the results of this experiemnt suggest, on the contrary, that the magnitude of the proximity effect cannot account for the large difference between the two sets of ellipses. This con-clusion i s substantiated by Witzel et al.'s own report Cp. 620) that even for a series of juxtaposed-surround matches Convolving no separa-tion between matching and test field) the difference in ellipse area between the MacAdam predicted ellipse and their own was of a 'comparable magnitude'. Perhaps then the difference in size between the two sets of ellipses reflects other 'subtle differences' of viewing'conditions' between thettwo colour matching procedures Csee e.g., Wyszecki and Fielder, 1971, p. 1149$. 55 BIBLIOGRAPHY Adams, E.Q. - X-Y -planes in the 1931 TCI system of colorimetry-. J_. Opt. Soc. Am., 1942, 32, 169. Bellamy, B.R. and Newhall, S.M. Attributive- limens in selected regions of the Munsell colour solid. J. Opt. Soc. Am,, 1942, 32, 465-473. Brown, W.R.J. The influence of luminance level on visual sensitivity to to colour differences. J. Opt. Soc. Am., 1951, 41, 684-688. Brown, W.R.J. The effect of f i e l d size and chromatic surroundings on colour discrimination. J. Opt. Soc. Am., 1952, 42, 837-844. Brown, W.R.J, and MacAdam, D.L. Visual sensitivities to combined chromaticity and luminance differences. J. Opt. Soc. Am., 1949, 39, 808-834. Burnham, R.W., Hanes, R.M., and Bartleson, C.J. Colour: A Guide to  Basic Facts and Concepts. New York: John Wiley and Sons, 1963. Davidson, H.R. Visual sensitivity to surface colour differences. J. Opt. Soc. Am.,1951, 41, 104-111. Glasser, L.G. , McKinney, A.H. , Reilley, CD. , and Schnelle, P.D. Cube-root colour coordinate system. Jo.Opt. Soc. Am.,1958, 48, 736. Grassman, H.G. Theory of compound colours (1853) i n MacAdam, D.L. (ed.) Sources of Colour Science. Cambridge: The MIT Press, 1970, p. 53-60. Guild, J. The colorimetric properties of the spectrum. Phil. Trans.  Roy. Soc. (London), 1931, A, 230, 149. Guilford, J.P. . Psychometric Methods, 2nd ed., New York: McGraw-Hill Book Company, Inc., 1954. Hunter, R.S. Photoelectric tristimulus and colorimetry with, three f i l t e r s . J. Opt. Soc. Am., 1942, 32, 509-538. Judd, D.B. Precision of colour temperature measurements under various observing conditions; a new colour comparator for incandescent lamps. Bur. Stand. J. Res., 1930, 5, 1161-1177. 56 Judd, J.B. A Maxwell triangle yielding uniform chromaticity scales. J. Opt. Soc. Am., 1935, 25, 24-35. Judd, D.B. Specification of uniform colour tolerances for textiles. Textile Res., 1939(a), X, 253-268, 292-307. Judd, D.B. . Specification of colour tolerances at the National Bureau of Standards. . Am. J. Psych., 1939(b), 52, 418-428. Judd, D.B. Ideal Colour Space. Palette, No. 29, .1968/ 30, 1968/ .31, 1969. Judd, D.B., and Wyszecki, G.W.. Colour in Business, Science and Industry (2nd ed.). New York: John Wiley and Sons, 1963. MacAdam, D.L. Visual sensitivities to colour differences in daylight. J. Opt. Soc. Am., 1942, 32, 247-274. MacAdam, D.L. Specification of small chromaticity differences. J. Opt. Soc. Am., 1943, 33, 18-26. MacAdam, D.L. Colorimetry i n Gray, D.E. (coordinating ed.), Am. Inst. Phys. Handbook (2nd ed.). New York: MacGraw-Hill Book Co., 1963, 6, 139-152. Marcus, R.T. and Billmeyer, F.W.Jr. Step size in the Numsell colour-order system by pair comparisons near 5Y 7.5/1 and bisections near 10R 7/8. J. Opt. Soc. Am., 1975, 65, 208-212. Robertson, A.R. Comparison of the two uniform colour spaces proposed by CIE TC-1.3 for study. CIE proceedings, London, 1975. Robertson, A.R. (private communication). Saunderson, J.L. and Milner, B.Q. Modified chromatic value colour space. J. Opt. Soc. Am., 1946, 36, 36. Silberstein, L. Investigations on the instrinsic properties of the colour domain.II. J. Opt. Soc. Am., 1939, 63-J-85.10. Silberstein, L. Investigations on the intr i n s i c properties of the colour domain II. J. Opt. Soc. Am., 1943, 33, 1-10/ Speranskaya, N.I. Determination of spectrum colour coordinates for twenty-seven normal observers. Optics and Spectroscopy, 1959, 7, 424. Stiles, W.S. and Burch, J.M. N.P.L. colour-matching investigations: f i n a l report (1958). Optica Acta, 1959, 6,1. 57 Thurner, K. Colorimetry and Colorimetric Methods. Communication from the Textile Laboratory of Badische Anilin & Soda-Fabrik A.C. 1962. Traub, A.C. The proximity factor in Judd's colour difference formula. PhD thesis, University of Cincinnati, 1952. Traub, A.C. and Balinkin, I. Proximity factor in the Judd colour difference formula. . J. Opt. Soc. Am., 1961, 51, 755-760. Witzel, R.F., Burnham, R.W., and Onley, J.W. Threshold and supra-threshold perceptual colour differences. J. Opt. Soc. Am., 1973, 63, 615-625. Wright, W.D. A re-determination of the trichromatic coefficients of the spectral colours. Trans. Opt. Soc, 1928-1929, 30, 141. Wright W.D. The sensitivity of the leye to small colour differences. Proceedings Phys. Soc, 1941, 53, 93-112. Wright, W.D. The Measurement of Colour (4th ed.). London: Hilger & Watts Ltd., 1969. Wyszecki, G. On projective transformations of the CIE-chromaticity diagram. J. Opt. Soc. Am., 1956, 46, 982-986. Wyszecki, G. Colour: Its Measurement and Specification. A summary of five lectures given at the National Research Council in Ottawa from January 22 to 24, 1958. Wyszecki, G. The measurement of £olour differences. Farbe, 1965(a), 14, 67-79. Wyszecki, G. Matching colour differences. J. Opt. Soc. Am., 1965(b), 55, 1319-1324. Wyszecki, G. Contemporary tools and methods of colorimetry. 10th Seminar Book of Papers. August, 1966(a), .172-177. Wyszecki, G. The measurement of brightness and colour. Metrologica, 1966(b), 2, 111-125. Wyszecki, G. Colour matching and colour-difference matching. J.  Opt. Soc. Am., 1972, 62, 117-128. Wyszecki, G. Recent developments on colour-difference evaluation in Proc. Helmholtz Memorial Symposium on Colour Metrics, Driebergen, The Netherlands, September, 1971; eds.: Vos, J.J. , Friele, L.F.C. , 58 and Walraven, P.L., AICI Holland, c/o Institute for Perception TNO, So.es terherg, 1972. Wyszecki, G. Current developments in colorimetry in Colour 73 , Sym-posium of the International Colour Association, 2-6 July 1973 York, England, Adam Hilger Publisher, London 1973, pp. 21-51, Wyszecki, G. Proposal for study of colour spaces and colour-difference evaluations. Technical Notes. J. Opt. Soc. Am., 1974, 64, 896-897. Wyszecki, G. and Stiles, W.S. Colour Science: Concepts and Methods, Quantitative Data and Formulas. New York: John Wiley and Sons, Inc., 1967. Wyszecki, G. and Fielder, G.H. New colour-matching ellipses. J. Opt. Soc. Am., 1971, 61, 1135-1152. 

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