space error in color matching

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Space Error in Color Matching

R. W. BURNHAM, JOYCE R. CLARK, AND S. M. NEWHALLColor Technology Division, Eastman Kodak Company, Rochester, New York

(Received January 17, 1957)

Recent reports indicate that stimulus position affects appearance in some visual situations. The presentinvestigation was designed to yield information on the size of such a space error in color matching, theprecision of color matching as a function of positional relations of the test and matching fields, and matchingtime as a function of position. Differences caused by position were not obtained. This is a reassuring result,since it has usually been assumed that no space error exists when symmetrical foveal areas are used forcolor matching.

INTRODUCTION

COLORIMETRIC color matching is a tridimen-sional version of the psychophysical method of

average error.' A test color is matched when the threeprimaries of a colorimeter are varied continuously toproduce a physically specifiable mixture that has thesame appearance as the test color under some givenset of viewing conditions. The method of average error,oldest of the classical psychophysical methods, hastraditionally been applied to determine the differencein two physical stimuli required to make them phenom-enally equal, i.e., perceptually equivalent with respectto some criterion.

Generally speaking, in experiments designed toutilize the method of average error, the result ofprincipal interest is the physical difference betweenperceptually equal stimuli. This result, as Guilfordexpressed it, "is the main constant error in the experi-ment. A constant error is produced by a uniform condi-tion ... and it represents a deviation in a fixed directionand of a given extent."2 It should be made clear thatthe term "error" refers to the physical differencerequired for equal perceptions; there can be no errorsin perceptions as such. There may be a differentconstant error caused by the position of one stimulusin relation to another, the direction and kind of move-ment used in manipulating the variable stimulus, thetemporal interval between stimuli which must beseparated in time, or due to variations in other experi-mental conditions.

In color matching experiments the test color to bematched is typically closely juxtaposed to the contin-uously variable matching color, either above or belowit, or to the left or right of it. There is no obviousphysiological basis for expecting that the spatial relationof a test and matching color in the small bi-partitefields employed in visual color matching would producea differential position or space error. Consequently, sofar as the authors are aware, there has been no recordedsystematic attempt to determine the so-called spaceerror for visual color matching. There have, however,been several reports recently which indicate that

'J. P. Guilford, Psychometric Methods (McGraw-Hill BookCompany, Inc., New York, 1954), second edition, p. 86.

2 Reference 1, p. 88.

position does affect appearance in comparable viewingsituations.3

Constant errors resulting from movement areunlikely in a color matching situation, since a refinedbracketing technique is normally employed in manip-ulating the three color dimensions and repeatedmatches are begun from randomly varied startingpositions. Such errors are more likely to appear when aone-dimensional stimulus is varied from low to high(or from high to low) in approaching a perception ofequality, but without reversals in the direction ofstimulus variation or bracketing the "point of subjectiveequality."

Constant time-order effects have been investigatedseparately by the present authors. Striking andconsistent effects were found, and these have alreadybeen reported.4

The consistent time-order effects and the recentreports concerning a constant space error in relatedviewing situations suggested the desirability of in-vestigating directly the space error in visual colormatching, for all three color dimensions at once. Alsosuggested were the possibilities that there could benot only physical differences in color matches due toposition, but differences in the precision of repeatedmatches and differences in matching time. Given thisinformation, it would be possible to state the relativegenerality of color matching results for particularspatial relations of test and matching colors, to setdown optimal spatial relations for test and matchingcolors in order to achieve maximum precision (highestcolor discrimination), and to specify optimal spatialrelations for the most economical matching time.

The present experiment was designed to yield infor-mation on the size of the space error for a typicalcolor matching situation, the precision of repeatedmatches as a function of position, and on matching timeas a function of position.

APPARATUS

In general, an observer was asked to manipulate acalorimeter in order to match a test color which could

3 J. Weitz and D. Post, Am. J. Psychol. 61, 59 (1948); G. C.Higgins and K. Stultz, J. Opt. Soc. Am. 40, 135 (1950); J. A. S.Kinney, J. Opt. Soc. Am. 45, 507 (1955).

4 Newhall, Burnham, and Clark, J. Opt. Soc. Am. 47,43 (1957).

959

OCTOBER, 1957VOLUME 47, NUMBER 10

BURNHAM, CLARK, AND NEWHALL

tively, to the right, left, bottom, and top of the testcolor as shown in Fig. 2.

A preliminary calibration had shown small butconsistent mixture differences in different areas of theintegrating face of the colorimeter, of the order ofmagnitude that might be expected experimentally, sothe positional changes were accomplished optically topreclude any instrumental basis for an apparentconstant space error.

Except for the dove-prism eyepiece, and monocularviewing, the instrument was the same as that used inthe previously reported study of time-order errors.The integrating face of the colorimeter, as before, wasplaced far enough outside the sphere which producedthe surround (see Fig. 1) so that none of the surroundilluminant could contribute to the colorimetric mixtures,

FIG. 1. Over-all view of apparatus with observerin viewing position.

be made to appear in any one of four fixed positionsrelative to the matching mixture. The observer wasseated comfortably with his preferred eye at the eye-piece of a telescope, as shown in Fig. 1, and with hishead position fixed by a headrest mounted inside ablack shield which excluded all light from the other eye.Through the telescope (with natural pupil) he couldsee a 1-in. square bipartite field at an apparent distanceof 26 in., which produced a visual angle of about 2,surrounded by a circular source "C" white field sub-tending a visual angle of 710, and yielding a luminanceof about 25 foot lamberts. The test color was alwaysplaced in the left half of the bipartite instrumentfield. The right half of the field consisted of a rectangularaperture in the surround through which the face ofan integrating bar colorimeter5 could be seen as fillingthe aperture. The test color could be made to appearin either the left, right, top, or bottom of the bipartitefield by means of a dove-prism device mounted inthe telescope housing which was designed specificallyfor this purpose, and reported by Grant.6 For each testcolor position, the matching mixture appeared, respec-

1

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FIG. 2. Experimentaltest color and matchingcolor positions.

T test colorM matching mixture

6 R. W. Burnham, Am. J. Psychol. 65, 603 (1952).6 D. E. Grant, J. Opt. Soc. Am. 47, 256 (1957).

.40

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FIG. 3. Mean chromaticities of matches for observer RWBCross-hatched borders enclose areas enlarged in Fig. 4.

yet near enough so the full matching aperture appearedto be filled with the mixture color. The sphere wallwhich served as surround was coated with Middleton-Sanders white sphere paint.7 The test colors wereMunsell paper samples positioned in the test-coloraperture in the sphere wall, and the colorimetricmixtures appeared in the surface mode, juxtaposed toand in the same plane as the test colors when visualaccommodation was set for the distance of the testcolors. Variation in position of the test color andcalorimetric mixtures was achieved by rotating twoknobs on the dove-prism eyepiece to any of the fourpositions which were detented on the eyepiece housing.

A shutter that had the same spectral characteristics

7 W. E. K. Middleton and C. L. Sanders, Illum. Eng. 48, 254(1953).

960 Vol. 47

SPACE ERROR IN COLOR MATCHING

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FIG. 4. Mean chromaticities of matches for three observers, four test positions, and four test colors.

as the surround was used to maintain a source "C"adaptation in the observer's eye.

PROCEDURE

When the observer was in position to observe, thewhite shutter was closed and the observer's eye wasadapted for three minutes to the source "C" field. Atthe end of three minutes the shutter was opened sothat a test color and a juxtaposed random colorimetricmixture were visible in the bipartite field. The observerwas then told to rotate the knobs of the dove-prism

eyepiece until the test color was in some given positionfor the observation. When the test color was properlypositioned, the observer proceeded to make his match.The experimenter began timing the match when he sawthe observer's hands drop to the colorimeter knobsafter positioning the test color. When the observersignalled that his match was complete, the experimenterchecked the time and closed the shutter to re-establishadaptation of the observer's eye to the surround foran interval of 30 sec. The experimenter then reopenedthe shutter, whereupon the observer was allowed to

October 1957 961

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Vol. 47

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FIGS. 5(a)-(f). Half-axes representing MacAdam (l-) chromaticity discrimination ellipses for threeobservers, four test positions, and four test colors.

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FIGS. 5(g)-(k). Half-axes representing MacAdam (la) chromaticity discrimination ellipses for threeobservers, four test positions, and four test colors.

October 1957 963

BURNHAM, CLARK. AND NEWHALL

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FIG. 5(1). Half-axes representing MacAdam (la-) chromaticity discrimination ellipses for three observers,four test positions, and four test colors. [Figures 5(a)-5(k) are on preceding pages.]

make any adjustments required to improve the match.When the observer signaled the match, the shutter wasagain closed for 30 sec, reopened, and the observer wasallowed to make further adjustments in the match.Following these final attempts at improvement, theshutter was again closed by the experimenter who thenrecorded the scale readings of the instrument and thetime of the match in seconds. (Time was recorded oneach observation only for the matching period beforethe shutter was first closed.) The experimenter thenchanged the test color, reopened the shutter, andnotified the observer of the proper test-color positionfor that observation. The observer made the positionchange and proceeded as before with the next (double-checked) match.

Each of three observers made ten observations oneach of four test colors in each of the four positions. Inany one session an observer matched each of the fourcolors once in each of two of the four positions. Theobservations were fatiguing, so only eight matcheswere made in any one session. A session lasted from 20to 40 min. There were 60 experimental sessions spread

over a period of 5 weeks. Test colors and positions wererandomized in a prearranged sequence which wasdifferent for all observers. All three observers served asexperimenters for part of the time, but observer SMNto a very minor extent.

Because a color matching space error (if any) couldbe expected to be small and possibly obscured by therelatively low precision of color matches repeated ondifferent days, the above procedure of requiring theobserver to readapt twice to the surround with interven-ing checks on the match was adopted. A furtherattempt was made to keep precision high by using testcolors which did not depart too markedly in luminancefrom that of the surround. Three Munsell samples wereused, SYR 7/10, SP 8/4, and OG 8/2. The fourthtest color was a patch of the same Middleton-Sanderssphere paint used in the surround, and was separatedfrom the surround only by the hazy lines around theaperture in which it was presented. This fourth testcolor has been designated as N 10/ since the spherepaint has reflectance comparable to MgO.

Vol. 47964


SMN 5 YR 7/10

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3cr Ellipses

I I I I I I I I I I I I I I I I I I I I I I I I I.420 .430 .440 A50 .460 A70 .480 .490 .500 .510 520 .530 .540

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FIG. 6. Three a ellipses for the most variant set of data for one observer, one test color, and four test positions.

RESULTS

The colorimetric scale readings for each match weretransformed to CIE tristimulus values, based on aspectrophotometric calibration of the colorimeter.Mean tristimulus values and chromaticities were thencomputed for each observer, for each color and position.Mean chromaticities for observer RWB are shown inFig. 3, in a full chromaticity diagram, and on a muchlarger scale for all observers in Fig. 4. The cross-hatched borders in Fig. 3 enclose the areas enlarged inFig. 4. Vectors have been drawn in Fig. 4 between thematch specifications for the left-to-right positionchanges and between the top-to-bottom changes.There were no systematic shifts in specification due toposition changes either for particular colors or observers.Luminance changes were likewise irregular and sosmall as to make the match variations effectivelytwo dimensional.

Significance of the chromaticity shifts may beestimated by comparing their sizes to those of thecorresponding chromaticity discrimination ellipses com-puted from repeated matches. Before making anydetailed direct comparison, significance of the shiftswas tested by a multivariate form of analysis ofvariance using the covariance matrices computedfrom the trivariate data recorded for replicate matches.Significant differences among positions were found fortwo observers, as shown in Table I. Analysis of variance,however, constitutes an over-all test; significance could

accrue from a difference in mean match for only asingle pair of positions for one observer and color, butfor different pairs of positions from one color andobserver to another. For real significance to be demon-strated, it would be necessary to show general andsystematic trends in these differences. Consequentlya detailed check was made on the size of differences foreach pair of positions for all observers and test colors.

Chromaticity discrimination ellipses were computedfrom the covariance matrices. Figure 5 shows plots ofhalves of the major and minor axes of the MacAdamellipses8 that represent the standard deviation () ofrepeated matches for each observer, test color, andtest position. The full ellipse can be constructed byextending the axes, as shown in the example in Fig. 5 (a),and connecting the full axis extremes by an appropriateellipse. Such an ellipse would be expected on a probabil-

TABLE I. Analysis of variance. Over-all significance ofmatch differences resulting from position.

Test colorsObservers N 1O/ 10 G8/2 5 P 8/4 5 YR 7/10

JRC a a ... bSMN b b b bRWB ... ... ...

a Sgnficnc a 5%leel

b Significance at 5% level.b Significance at % level.

I D. L. MacAdam, J. pt. Soc. Am. 32, 247 (1942).

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October 1957 965


TABLE II. Precision as a function of position, expressed as rank ofr Ithe trace of the covariance (CIE x, y) (highest precision= 1).

PositionsTest Left Right Top Bottomcolor Observer (L) (R) (L+R) (T) (B) (T+B)

N 1O/ JRC 2 1 3 3 4 7SMN 1 3 4 2 4 6RWB 1 4 5 3 2 5

10G 8/2 JRC 2 1 3 3 4 7SMN 1 4 5 3 2 5RWB 4 1 5 2 3 5

5P 8/4 JRC 2 4 6 1 3 4SMN 3 2 5 4 1 5RWB 3 4 7 1 2 3

5YR 7/10 JRC 3 2 5 4 1 5SMN 1 4 5 2 3 5RWB 4 1 5 2 3 5Totals 27 31 58 30 32 62

ity basis to contain 39% of the repeated matches.9

This means that significant position differences would berepresented by relatively non-overlapping ellipses twoto three times the size indicated by the half-axes inFig. 5. Ellipses of 3 magnitude have been computedfor the most variant set of data and are shown in Fig. 6.

A detailed inspection of the half-axes in Fig. 5 andthe 3 ellipses in Fig. 6 shows that there were nosystematic differences from one test color or observerto another. Although a significant difference mayoccasionally be found for some pair of positions oranother, enough to account for the significance revealedby analysis of variance, the size of the replicate sample(10 observations per ellipse), plus the lack of a con-sistent trend, make it highly probable that no realdifferences resulting from position have beendemonstrated.

Comparative matching precision was assessed interms of the variability of repeated matches for eachtest position. The trace of the covariance matrix(representing ellipsoidal variability of repeated matches)is proportional to the volume of the ellipsoid representedby the matrix, and volume is an inverse measure ofprecision. Thus, the less the volume the higher theprecision. Traces were computed for each test-color,position, and observer combination, and the ranks ofthe traces are given in Table II. Greatest precision is

9 Brown, Howe, Jackson, and Morris, J. Opt. Soc. Am. 46, 46(1956).

shown by a rank of 1. These ranks show that no oneposition had preponderantly higher precision, nor wasa left-right or top-bottom orientation favored (as acomparison of the sums of ranks for the left and rightpositions with the sums of ranks for the top and bottompositions will show).

A "t" test was used to test the significance of differ-ences in mean matching time for each observer andcolor for all possible pairs of positions. There were nogenerally significant differences favoring one positionover another. One observer did, however, show signifi-cantly less matching time (1% level) for both topand bottom positions as compared to left and rightpositions for two of the four test colors.

DISCUSSION

The present experiment has given a reasonablyclear-cut indication that there is no space-error incolor matching, at least for symmetrically stimulatedareas of the central retina. It has also shown thatmatching precision and matching time are apparentlyunaffected by relative position of the test and matchingcolor.

Negative results in the present case do not precludethe possibility that a constant space-error might befound for particular observers or for largr fields whicchstimulate more peripheral retinal areas. There mightbe retinal inhomogeneities which could provide abasis for observer space-error. The generally negativeresults are nevertheless reassuring, since colorimetricmatching has usually assumed no space-error. Theysuggest that, where evidence for a space-error is found,the instrument should be checked as a probable sourceof the bias. Incidentally, if a parafoveal 10° field shouldbecome standard for the CIE observer, this experimentaffords a technique for finding out whether the standardobserver should give different results for differentpositions of the test and matching fields.

ACKNOWLEDGMENTS

For expert technical help in preparing for the experi-ment and reducing the data, we are particularlyindebted to W. N. Fitzgerald, D. E. Grant, J. EdwardJackson, and E. H. Sprague, all of the Color TechnologyDivision.

966 Vol. 47

space error in color matching

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