Theoretical analysis of inter-observer variability in the determination of luminance thresholds

Theoretical Analysis of Inter-Observer Variability in theDetermination of LuminanceThresholds

Fernando Carreno,* Jose Miguel Ezquerro,Jesus M. ZoidoEscuela Universitaria de Optica, Universidad Complutense de Madrid, C/ Arcos de Jalon s/n, Madrid 28037, Spain

Received 22 December 2004; revised 11 February 2006; accepted 17 March 2006

Abstract: We present an analytical method to analyze, froma theoretical point of view, the influence of color-matchingfunctions on the perception of luminance thresholds. Weshow that the thresholds depend on the spectral responsivi-ties of each observer. We also analyze the influence ofluminance level on the thresholds: a strong inter-observervariability is found at low or moderate luminance levels(0.02 � Y � 1 ft�L) whereas at high intensities (1 � Y �7 ft�L) the thresholds are observer-independent. © 2006

Wiley Periodicals, Inc. Col Res Appl, 31, 468–474, 2006; Published

online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/

col.20259

Key words: color vision; luminance thresholds; variabilityof color-matching functions

INTRODUCTION

Colors can be specified in terms of color matching functions(cmf’s) associated to a given observer and the spectralcharacteristics of the physical stimuli �(�) (spectral radiantflux). It is well-known that tristimulus values are given by

Xi� � k�

�1

�2

�� xi��d�, i � 1,2,3, (1)

xi� (�) being the i-th color matching function associated to

observer � in the selected colorimetric system, and k is anormalization constant. In the CIE 1931 system, the con-stant factor k is equal to 683 lm/W. In Eq. (1) [�1, �2] is the

visible spectral range. Most authors take �1 � 400 nm and�2 � 700 nm. All the color stimuli perceived by observer �can be represented by the vectors belonging to the subset ofR3 defined as

R� � ��X1�, X2

�, X3�� for all �� 3. (2)

Subset R� contains all the vectors of tristimulus valuesassociated to the colors perceived by observer �.

It is evident from Eq. (1) that the same physical stimulus�(�) will be perceived as a different color stimulus by twoobservers (� and �) with different sets of cmf’s, i.e., subsetsR� and R� are different from each other. Besides, there is noone-to-one correspondence between these subsets. Note thatalthough R� and R� are nonisomorphic from a global pointof view, we could ask ourselves whether a certain degree ofsimilarity exists between the observers when judging col-orimetric or luminance thresholds. The comparison of theperception of a given set of spectral distributions by differ-ent observers allows us to obtain valuable information con-cerning the influence of variability of cmf’s on the absoluteperception of colors. Several works have been carried out inorder to gain further insight into this effect.1–4 The influenceof cmf’s on the specification of color discrimination thresh-olds were analyzed by Melgosa et al.1 They found that theparameters characterizing the thresholds presented a weakvariability. They also found significant displacements of thecenters of the ellipses when considering several sets ofcmf’s. This fact is an indication that the absolute perceptionof a color depends dramatically on the cmf’s. The colori-metric behavior of different observers has been analyzed forseveral color centers by considering the distance betweenthe so-called “characteristic matrices” associated with theobservers under study.2 The similarities were analyzed bycomparing how a given set of metameric spectral distribu-

*Correspondence to: F. Carreno (e-mail: [email protected])© 2006 Wiley Periodicals, Inc.

468 COLOR research and application

tions are perceived by different observers.3 In addition, thediscrepancies in specifying colors for different observerswas also addressed in Ref. 4 where it was shown that thereis no reciprocity between the colorimetric behavior of agiven pair of observers.5

Several studies of visual sensitivity of the human eye tocolor differences have been carried out by analyzing thedistribution of color-matching mismatches around severalcolor centers. The elliptical geometry was adopted by Mac-Adam in order to represent the threshold of chromaticdiscrimination6: He considered that the luminance wasmaintained constant during the course of the experiment.

In subsequent investigations, the thresholds were consid-ered to be ellipsoids when carrying out color matchingsinvolving the simultaneous variations of chromaticity andluminance in the experiments.7–9 From these pioneeringworks up to now this field of research has been a subject ofintense activity.10–20

It is interesting to analyze the sets of color-discriminationthresholds obtained by different observers (inter-observervariability). This will help us in determining the averageability of a normal observer. This analysis can also be usefulin order to evaluate the validity of a given standard ob-server. Color discrimination thresholds for twelve observerswere reported for several color centers,8 although the authoronly provided the averaged results. Wyszecki and Fielderalso addressed this problem11 (see also Ref. 21 for a recentreview). In this article, we are interested in the theoreticalevaluation of how cmf’s influence the average ability of aset of observers when judging luminance thresholds. Wealso address the influence of luminance level on the thresh-olds. The study could allow us to elucidate to what extentsensitivity to luminance changes depends on chromaticity.For these purposes we will use the set of data supplied inRefs. 7 and 22, since the authors of these studies haveprovided the complete set of data required for our analysis.In the next section, we present a description of the theoret-ical background. The numerical results and the discussionsare presented in the section entitled “Inter-observer variabil-ity in the judgment of luminance thresholds.” Finally, wediscuss the major conclusions.

THE EVALUATION OF THE WEBER FRACTION

Let {xi�(�)} (i � 1, 2, 3) be the set of cmf’s associated with

observer �. For a given spectral radiant flux, �(�), thecorresponding tristimulus values are given by Eq. (1). Theintegral of Eq. (1) is usually approximated by the sum

Xi� � k ��

j�1

N

xi��j��j�, i � 1,2,3, (3)

�� being the spectral width of the sampling interval and Nis the number of wavelengths at which functions �(�) andxi

�(�) have been sampled.Let us consider the thresholds of color-differences around

a given set of color centers (color centers are labeled with m,

and m runs from 1 to S). Each threshold can be specified interms of an ellipsoid with the corresponding coefficients.The parameters needed to characterize a threshold are thetristimulus values of the center and the matrix of covari-ances obtained from the analysis of the data of the color-matching experiment (see Refs. 7 and 19). The chromaticitycoordinates associated to color center m for the referenceobserver (labeled with superindex st) are (x0

st,m, y0st,m) and

the mean luminance Y0st,m. For this color center, we can

determine the upper/lower (Yust,m/Yl

st,m) threshold limits ac-cording to the statistical procedure developed in Ref. 23.

In this article we will take CIE1931 as the referenceobserver. We also propose an analytical method to evaluatehow luminance thresholds are perceived by a given set ofobservers. These observers are not directly involved in thecolor-matching experiments but we assume that we knowtheir cmf’s.

The method proposed by us proceeds as follows:

1. For a given a color center m with mean luminanceY0

st,m, and its corresponding threshold of color-differ-ences, we have computed the upper/lower threshold ofluminance Yu

st,m/Ylst,m for the reference observer by

using the statistical method described in Ref. 23. Theconfidence level used to obtain the luminance thresh-olds was 0.16 in accordance with Ref. 23. The thresh-olds derived by these procedures for the reference ob-server serve us as a starting point in the currentinvestigation.

2. By using the software tool described in Refs. 24 and 25,a spectral distribution �0

st,m(�) has been generated. Thisspectral distribution reproduces the tristimulus values ofthe m color center for the reference observer: Xi,0

st,m (i �1, 2, 3). In the (x, y, Y) space, the coordinates are givenby (x0

st,m, y0st,m, Y0

st,m) (Y0st,m ' X2,0

st,m).3. We have also generated with the aid of the software tool

two additional spectral distributions, �ust,m(�) and

�lst,m(�), which reproduce for the reference observer the

chromaticity of the color center but with luminancesgiven by the upper/lower value (Yu

st,m/Ylst,m), i.e., in the

(x, y, Y) space these spectral distributions provide thefollowing coordinates: (x0

st,m, y0st,m, Yu

st,m) / (x0st,m,

y0st,m, Y l

st,m). These distributions will exactly reproducethe Weber fraction for the reference observer, which hasbeen previously determined by the statistical methoddescribed in Ref. 23.

4. By considering the previously mentioned distributions�0

st,m(�), �ust,m(�), and �l

st,m(�) and by using Eq. (3), thecorresponding luminances Y0

�,m, Yu�,m, and Yl

�,m arecomputed for each one of the set of cmf’s available,{xi

�(�)}. In this way, we can estimate for observers whoare not directly involved in the color-matching experi-ment the values of the Weber fraction, or the degree ofluminance mismatch with regard to those associated tothe reference observer.

5. For all the considered color centers (m � 1, . . . , S) theWeber fraction (W F�,m � (Yu

�,m�Yl�,m)/Y0

�,m) is eval-uated for each set of cmf’s.

Volume 31, Number 6, December 2006 469

6. To determine the similarity among the observers whenevaluating luminance thresholds, a statistical analysis ofthe set of data W F�,m has been carried out. For each oneof the observers available labeled as �, we have com-puted the mean value W F� and the standard deviation ��

by averaging the data over the considered color centers.7. To analyze the influence of the color center in the per-

ception of luminance thresholds, the average value overall the observers W Fm and the corresponding standarddeviation �m have been computed for each of the con-sidered color centers.

INTER-OBSERVER VARIABILITY IN THEJUDGMENT OF LUMINANCE THRESHOLDS

In this section, we analyze how different observers evaluatethe relative luminance thresholds (Weber fraction) for agiven set of color centers by using the procedure describedin the previous section. The color centers used in ouranalysis are those reported in Ref. 7. The sets of cmf’s usedin this research are those associated with the ten observersof Stiles-Burch26 (� � 1, . . . , 10) and they had not beendirectly involved in the determination of color-differencethresholds, i.e., these observers did not participate in theinvestigation reported in Ref. 7, thus up to now we were notable to evaluate the Weber fraction for these observers.These cmf’s were determined for visual fields of 2°.

We present in Fig. 1 the Weber fraction W F�,m obtainedfor all the color centers (m � 1, . . . , 37) and the consideredobservers together with the corresponding average fractionW F� (open circles). A single inspection of this figure re-veals that, for each observer, the Weber fraction presents ahigh scattering of the data. The average Weber fraction

W F� and the corresponding standard deviation �� are verysimilar for all the observers. This result can be numericallychecked with the data listed in Table I, and it points out howthe average Weber fraction, and its corresponding standarddeviation, can be considered to be nearly independent of theconsidered observer.

The influence of the color center in the perception ofluminance thresholds is shown in Fig. 2. In this figure, theWeber fraction W F�,m computed for all the observers ineach color center is displayed. The average Weber fractionW Fm obtained by averaging the data over the observers isalso shown for each color center. We can see that theaverage Weber fraction and the corresponding standarddeviation strongly depends on the considered color center,i.e., the luminance thresholds depend on the color stimulusperceived by the observer. This result is an expected one: asit is well known, the ellipsoids of color discrimination havedifferent size and orientation depending on the color centerunder study, thus the chromaticity thresholds and the lumi-nance thresholds should also depend on the considered colorcenter. Table II provides the average Weber fraction W Fm

and the corresponding standard deviation �m for all thecolor centers. These data quantitatively confirm the conclu-sions derived by inspection of Fig. 2. In summary, theprevious results point out that the perception of the lumi-nance thresholds slightly depend on the cmf’s of the ob-server under consideration but they strongly depend on theconsidered color center.

The results displayed in Figs. 1 and 2 seem to be in anapparent contradiction, although it is not actually the case. Theanalysis of Fig. 1 reveals that for any of the observers consid-

FIG. 1. Weber fraction W F�,m obtained for all the colorcenters (m � 1, . . . , 37) for each observer together with thecorresponding average fraction W F� (open circle).

TABLE I. Average values (W F� ) and standard deviations (��) of Weber fraction for the different observers. Thefourth row provides the values for the coefficient of variation (CV� � ��/W F� ).

SB1 SB2 SB3 SB4 SB5 SB6 SB7 SB8 SB9 SB10 CIE1931

W F� (10�2) 4.79 4.59 4.71 4.88 4.76 4.86 4.84 4.80 4.81 4.79 4.70�� (10�2) 1.54 1.30 1.42 1.50 1.75 1.46 1.44 1.42 1.45 1.41 1.32CV� (10�1) 3.21 2.84 3.01 3.07 3.68 3.00 2.99 2.95 3.007 2.94 2.80

FIG. 2. Weber fraction W F�,m obtained for all the observ-ers at each color center. The average Weber fraction W Fm

obtained when averaging the data for all the observers isalso shown for each color center as an open circle.


ered by Stiles-Burch, the value of W F� is nearly observer-independent, although very different values of �� are found inthe numerical analysis. It is to be noted that the results dis-played in Fig. 2 clearly reveal that the average observer abilityin determining luminance thresholds depends strongly on thecolor center under consideration (W Fm ). In other words, theresults derived from the statistical descriptors W F� and W Fm

are very different among them due to the different ways usedto group the data, thus there is no contradiction between theresults obtained in both figures.

Furthermore, we have qualitatively analyzed how theluminance thresholds depend on the observer and the colorcenters. To analyze these dependencies qualitatively it isdesirable to define a parameter which would allow to esti-mate the discrepancies in evaluating the relative luminancethresholds. One way to do this is by comparing the devia-tions in the perception of the thresholds with regard to thereference observer. For this purpose we compute the fol-lowing magnitude

da��st,m �|WFst,m � WF�,m|

WFst,m � 100. (4)

Eq. (4) provides a local estimation of the similarity ofluminance thresholds at a given color center between theobserver � and the standard one (st).

If we consider two different observers � and �, from aformal point of view, quantities W F� and W F� are asso-ciated with different statistical populations since �� .In this case, it is not possible to use these average quantitiesin order to carry out an absolute comparison between agiven pair of observers, or between a given observer and thestandard one. Thus, quantity (4) does not allow the perfor-mance of global comparisons among the different observ-ers. Besides, the average values W� F� present a high scat-tering in the corresponding standard deviations �� (seeTable I), thus they cannot be considered by themselvesadequate statistical descriptors in evaluating the global dif-ferences between the different observers. The adequate sta-tistical descriptors are the corresponding coefficients ofvariation CV� and CV�, which involve both the averagevalues and the corresponding standard deviations. Thismagnitude is defined as

CV� ��

WF�. (5)

The difference between quantities CV� and CV� provides aglobal estimator of the similarity between the observers �and � when evaluating relative luminance thresholds. Themore similar the coefficients of variation, the more similarare the perception of the relative luminance thresholds.

Now we are interested in evaluating the global degree ofsimilarity when perceiving relative luminance thresholdsbetween each observer and the standard one. We haveassumed that the tristimulus values of color-matchings re-ported in Refs. 7 and 22 for observer WRJB were computedwith the CIE1931 set of cmf’s. We will compute the dif-

FIG. 3. Percentage of deviations da2�st,m (E) and da5�st,m

(�).

TABLE II. The first column provides the number of thecolor center (CC) according to the notation in Ref. 7.Average values (W Fm) and standard deviations (�m) ofWeber fraction for the different observers in columns 2and 3, respectively. The fourth column provides the val-ues for the coefficient of variation (CVm � �m/W Fm).

CC W Fm �m CVm

1 0.052 0.0213 0.4092 0.053 0.0252 0.4733 0.059 0.0271 0.4604 0.065 0.0216 0.3305 0.039 0.0178 0.4506 0.038 0.0141 0.3697 0.041 0.0187 0.4568 0.050 0.0255 0.5109 0.065 0.0288 0.442

10 0.066 0.0221 0.33812 0.047 0.0159 0.33513 0.067 0.0224 0.33614 0.055 0.0222 0.40615 0.041 0.0661 1.60816 0.046 0.0173 0.37717 0.066 0.0222 0.33818 0.056 0.0224 0.40219 0.038 0.0167 0.43920 0.039 0.0133 0.34421 0.040 0.0259 0.64222 0.040 0.0229 0.56823 0.041 0.0179 0.43724 0.046 0.0287 0.62825 0.036 0.0231 0.65126 0.058 0.0191 0.33027 0.050 0.0168 0.33528 0.042 0.0252 0.59329 0.045 0.0257 0.57030 0.027 0.0095 0.35631 0.026 0.0089 0.34232 0.033 0.0122 0.36733 0.034 0.0126 0.37634 0.055 0.0193 0.35435 0.032 0.0127 0.40136 0.035 0.0266 0.75737 0.040 0.0135 0.33938 0.038 0.0377 0.996


ferences between the coefficients of variation CVst and CV�

(� � 1, . . . , 10).Now we will analyze the results obtained by using ex-

pressions (4) and (5). Concerning the first one, Fig. 3displays the magnitude da��st,m for observers SB2 (� � 2)and SB5 (� � 5). We have chosen these observers since thedifference CVSB5�CVst/CVSB2�CVst is the higher/lower ob-tained for all the observers according to the data listed inrow 4 in Table I and, in this way, observer SB5/SB2 is themore different/similar to the observer CIE1931 when per-ceiving relative luminance thresholds. Figure 3 reveals thatthe magnitude da��st,m presents deviations as high as 40%when estimating luminance-differences for many of thecolor centers considered in Ref. 7.

Note that for observer SB2 the percentage of deviation isaround 8% for many color centers and, at a certain value ofm, the percentage is increased up to 26%. This variation inthe percentage of deviations is an indication that the lumi-nance thresholds for observer SB2 and the standard ob-server highly differ in magnitude with each other. Thisdifference is strongly enhanced for the case of observerSB5.

The results previously found provide a further confirma-tion concerning the nonreciprocity between the colorimetricbehavior of two real observers.5 Furthermore, they providea convincing demonstration on how the variability of cmf’snot only influences the absolute perception of physicalstimuli, but the evaluation of luminance-differences.

We have also analyzed how Weber fraction depends onchromaticity coordinates (x, y): the plots produced (notshown) reveal that the thresholds of luminance are notindependent on chromaticity as first suggested by Brown.22

The high degree of scattering in the data does not allow aquantitative prediction of this dependence in a easy way forany of the observers considered in the current investigation.Furthermore, there is no apparent relationship between theWeber fraction (W F�,m) and luminance level (Y0

�,m), overthe range of luminance considered in Ref. 7.

When evaluating the global degree of similarity betweenobservers in perceiving relative luminance thresholds, wewill use the quantity given by Eq. (5). This statisticaldescriptor is provided for all the observers in row 4 of TableI, and it can be used to arrange the observers in order oflikeness with regard to the reference observer. This task canbe done by analyzing the differences between CV� and CVst:the lesser the difference, the more similar are the observers� and CIE1931. The results obtained by analyzing thesedifferences for all the Stiles-Burch observers are given inTable III. It is a surprising fact that the order of likenessobtained by using this method differs from that reported inRef. 4. The reason for this discrepancy relies in the fact thathere we are concerned with the evaluation of discrepanciesbetween pairs of observers for a single color attribute (lu-minance threshold at a fixed chromaticity), whereas in Ref.4 the evaluation of similarities between pairs of observerswas concerned with the three color attributes.

Finally we address the problem of how Weber fraction

TABLE III. Order of likeness according to the valuesof CV� listed in row 4 of Table I.

Observer Order

SB2 1SB10 2SB8 3SB7 4SB6 5SB9 6SB3 7SB4 8SB1 9SB5 10

TABLE IV. Weber fraction for the different observers and the color centers considered in Ref. 22. The firstcolumn provides the number of the color center according to the notation used in Table II in Ref. 22. The lastcolumn provides the Weber fraction for the reference observer determined according to the method reported inRef. 23.

No SB1 SB2 SB3 SB4 SB5 SB6 SB7 SB8 SB9 SB10 CIE1931

1 0.0475 0.0458 0.0429 0.0503 0.0504 0.0505 0.0500 0.0516 0.0484 0.0498 0.0432 0.0424 0.0471 0.0424 0.0435 0.0404 0.0490 0.0470 0.0484 0.0451 0.0482 0.0403 0.0302 0.0315 0.0326 0.0282 0.0309 0.0232 0.0260 0.0253 0.0289 0.0265 0.0274 0.0293 0.0241 0.0248 0.0309 0.0251 0.0409 0.0374 0.0391 0.0308 0.0327 0.0214 0.0628 0.0677 0.0683 0.0569 0.0646 0.0539 0.0544 0.0563 0.0623 0.0566 0.0505 0.0279 0.0287 0.0289 0.0278 0.0263 0.0300 0.0292 0.0291 0.0274 0.0277 0.02819a 0.0110 0.0136 0.0128 0.0127 0.0065 0.0194 0.0160 0.0163 0.0161 0.0167 0.01719a 0.0239 0.0251 0.0275 0.0241 0.0243 0.0164 0.0165 0.0167 0.0236 0.0176 0.01619a 0.0390 0.0376 0.0408 0.0351 0.0431 0.0325 0.0326 0.0339 0.0370 0.0332 0.03319a 0.0881 0.0852 0.0882 0.0793 0.0960 0.0718 0.0762 0.0768 0.0814 0.0773 0.05031a 0.0024 0.0077 0.0031 0.0066 0.0040 0.0124 0.0101 0.0097 0.0072 0.0117 0.01331a 0.0142 0.0156 0.0166 0.0141 0.0112 0.0197 0.0167 0.0180 0.0173 0.0165 0.01731a 0.0141 0.0147 0.0133 0.0140 0.0142 0.0148 0.0156 0.0151 0.0133 0.0156 0.01831a 0.0157 0.0141 0.0165 0.0165 0.0154 0.0182 0.0168 0.0170 0.0166 0.0143 0.02134a 0.0145 0.0151 0.0157 0.0097 0.0198 0.0049 0.0071 0.0077 0.0115 0.0091 0.00934a 0.0102 0.0106 0.0102 0.0091 0.0110 0.0060 0.0085 0.0074 0.0086 0.0090 0.00934a 0.0123 0.0127 0.0096 0.0115 0.0142 0.0104 0.0128 0.0115 0.0102 0.0141 0.01434a 0.0125 0.0122 0.0100 0.0137 0.0122 0.0140 0.0148 0.0134 0.0126 0.0153 0.01634a 0.0185 0.0180 0.0189 0.0202 0.0163 0.0213 0.0211 0.0202 0.0204 0.0206 0.02534a 0.0358 0.0356 0.0359 0.0359 0.0358 0.0359 0.0358 0.0358 0.0358 0.0357 0.036


depends on the luminance level. In Ref. 22, Brown analyzedthe variations of the color-difference thresholds as a func-tion of the luminance level. The data reported in Ref. 22were also used in Ref. 23 to derive the Weber fraction forobserver WRJB. It was concluded in Ref. 23 that the Weberfraction depends on the luminance level. To further explorethe inter-observer variability of Weber fraction, we haveapplied the procedure described earlier in this article to thedata reported in Refs. 22 and 23. We call the attention to thefact that luminances used in Ref. 22 are provided in ft�L(see the corresponding abstract in Ref. 22). The resultsobtained are shown in Table IV. An inspection of this tablereveals that the Weber fraction at a fixed color center m, sayfor example color center 19a with the highest value ofluminance (row 8 in Table IV), strongly varies from oneobserver to another. It should be remarked that for thosecolor centers with very low level of luminance (Y � 0.02ft�L), i.e., color centers 4, 19a, and 31a, the Weber fractionpresents a high inter-observer variability.

The average ability of each observer to perceive relativeluminance thresholds is presented in Table V together withthe corresponding standard deviations and coefficients ofvariation. Note also that the different observers have inaverage a similar value for the relative luminance thresh-olds. Finally, it should be pointed out that the values ob-tained by us are close to those reported in Ref. 27 for thedifferent observers.

Further to compare the results obtained in this article withthose given in Ref. 27 we have fitted, for each observer �and for all the considered color centers, the values of W F�,m

listed in Table IV to the formula

�Y

Y� c�1 �kY��1/ 2 2. (6)

The values of c and k (in ft-L�1) computed for the different

observers are listed in Table VI. Note that according to Ref.23, c � 0.012 and k � 30.3 for the reference observer.Besides, the values for constant c are nearly similar for allthe considered observers. This fact indicates that the asymp-totic value of Weber fraction is nearly equal for all theobservers. However, the values for k present a great scat-tering of the data. Furthermore the values for k stronglydiffer from the value for the reference observer. In sum-mary, the previous analysis points out how, in the regime oflow and intermediate luminance levels considered in Ref. 22(0.02 � Y � 1), there are significative inter-observer dif-ferences when evaluating luminance mismatches. However,the influence of the variability in the set of cmf’s on theluminance thresholds becomes negligible when high enoughluminance levels are considered (1 � Y � 7 in the unitsused in Ref. 22).

CONCLUSIONS

In this work, we have analyzed how luminance mismatchesare dependent upon the characteristic spectral responsivitiesof the visual system, thus variations in the cmf’s willproduce variations in the luminance thresholds. We haveshown that, as a consequence of observer’s variability incmf’s, a certain luminance mismatch perceived by oneobserver may appear to be a significantly different mis-match to another observer. In this article, we have provideda method to estimate the degree of luminance mismatch byusing information concerning to color-difference thresholdstogether with a software tool to generate metameric spectraldistributions.24,25 This procedure allows the estimation ofWeber fraction for observers who are not directly involvedin color-matching experiments although their correspondingcmf’s must be known. Finally, it is found that in the regimeof low and moderate luminance levels (0.02 � Y � 1 ft�L),cmf’s strongly influence the perception of luminance thresh-olds (see Table VI), whereas at high intensities (1 � Y � 7ft�L) the luminance thresholds are essentially independenton cmf’s.

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TABLE VI. Values of k and c defined in Eq. (6) for thedifferent observers analyzed in Ref. 26.

Observer k C

SB1 5.0 0.006SB2 6.0 0.006SB3 5.0 0.006SB4 6.2 0.007SB5 3.2 0.005SB6 10.4 0.008SB7 9.0 0.008SB8 8.3 0.007SB9 7.0 0.007SB10 9.1 0.008

TABLE V. Average values, standard deviations and coefficients of variation of Weber fraction listed in Table IVfor the different observers are provided in rows 2, 3, and 4 respectively.

SB1 SB2 SB3 SB4 SB5 SB6 SB7 SB8 SB9 SB10 WRJB

W F 0.028 0.028 0.028 0.027 0.028 0.027 0.027 0.028 0.028 0.027 0.025�W F 0.021 0.020 0.021 0.019 0.023 0.018 0.018 0.019 0.020 0.018 0.013CV 0.751 0.725 0.756 0.699 0.828 0.661 0.669 0.686 0.702 0.666 0.509


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NEWS

David Brainard Receives theISCC Macbeth AwardThe Inter-Society Color Council (ISCC) honored ProfessorDavid Brainard with the presentation of the Macbeth Awardduring its Annual Meeting held in Ottawa, Ontario, Canada.The Macbeth Award, which was established in 1970 inmemory of Norman Macbeth, is presented biannually to amember, or former member, of the ISCC for recent impor-tant contributions in the field of color. Professor Brainard,Chair of the Psychology Department and Co-Director of theVision Research Center at the University of Pennsylvania,was recognized for his application of Bayesian methods toproblems in color appearance and for his contribution as aprincipal author of the Psychophysics Toolbox, a set ofsoftware tools that assists vision researchers in performingvision experiments and color modeling.

He received his undergraduate education at Harvard andhis graduate degrees from Stanford, an M. S. in ElectricalEngineering and a Ph. D. in Psychology. Before joining thefaculty at the University of Pennsylvania in 2001, he had

been a Professor of Psychology at the University of Cali-fornia at Santa Barbara since 1991. Prof. Brainard’s re-search interests include human vision, machine vision, andcomputational modeling of visual processing, with a pri-mary focus on how the visual system uses the informationavailable in the light signal incident at the eye to estimateobject properties. His published work is notable for itscontributions to both color science and color engineering.Brainard is probably best known for his fundamental workon color appearance. In particular, a 1997 paper he co-authored introduced a statistical framework for thinkingabout color perception as a Bayesian estimate of the prop-erties of the light spectral power distribution and the surfacereflectance functions. This has been an influential paper andhas been cited over 200 times.

Prof. Brainard is a Fellow of the Optical Society ofAmerica and a member of the board of editors of theJournal of Vision.

Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/col.20270


Documents

Theoretical analysis of inter-observer variability in the determination of luminance thresholds