do common mechanisms of adaptation mediate color...

1CFbtautmwmfe

apomciowccv

tptfso

2090 J. Opt. Soc. Am. A/Vol. 22, No. 10 /October 2005 J. M. Hillis and D. H. Brainard

Do common mechanisms of adaptation mediatecolor discrimination and appearance?

Uniform backgrounds

James M. Hillis and David H. Brainard

University of Pennsylvania, Department of Psychology, 3401 Walnut Street 302C,Philadelphia, Pennsylvania 19104

Received February 8, 2005; revised manuscript received April 14, 2005; accepted April 18, 2005

Color vision is useful for detecting surface boundaries and identifying objects. Are the signals used to performthese two functions processed by common mechanisms, or has the visual system optimized its processing sepa-rately for each task? We measured the effect of mean chromaticity and luminance on color discriminability andon color appearance under well-matched stimulus conditions. In the discrimination experiments, a pedestalspot was presented in one interval and a pedestal + test in a second. Observers indicated which interval con-tained the test. In the appearance experiments, observers matched the appearance of test spots across achange in background. We analyzed the data using a variant of Fechner’s proposal, that the rate of apparentstimulus change is proportional to visual sensitivity. We found that saturating visual response functions to-gether with a model of adaptation that included multiplicative gain control and a subtractive term accountedfor data from both tasks. This result suggests that effects of the contexts we studied on color appearance anddiscriminability are controlled by the same underlying mechanism. © 2005 Optical Society of America © 2005Optical Society of America

OCIS codes: 330.1690, 330.4060, 330.7720.

nspraotoatf

pttsewhrv

ssptbltst

. INTRODUCTIONolor signals support two important visual functions.irst, color is useful for discriminating objects from theirackground (i.e., for segmenting the image into regionshat correspond to physically distinct surfaces). Second,s the perceptual correlate of surface reflectance, color isseful for identifying objects. These functions are concep-ually distinct, and each function may place different de-ands on visual processing. In this paper, we askhether color discrimination and color appearance areediated by the same mechanisms of adaptation. We re-

er to this proposition as the common mechanism hypoth-sis.

Both sensitivity to color differences and color appear-nce depend on the context in which the stimulus islaced. Color difference sensitivity is revealed by thresh-ld measurements. Thresholds for detecting a monochro-atic spot presented against a spatially uniform mono-

hromatic background vary with the wavelength andntensity of the background.1 The dependence of thresh-ld on context reveals a form of chromatic adaptation,herein the processing of a focal stimulus changes with

ontext. There is an extensive literature examining howhromatic adaptation affects visual sensitivity (for re-iews see Refs. 2–6).

Chromatic adaptation is also revealed by experimentshat assess color appearance. For example, the judged ap-earance of a test spot varies with the spectral composi-ion of the background against which it is seen.7 The ef-ect of adaptation on the appearance of stimuli is also theubject of an extensive literature found under the rubricsf both color appearance8–10 and color constancy.11,12

1084-7529/05/102090-17/$15.00 © 2

Research examining effects of context on color discrimi-ation and color appearance has often proceeded alongeparate paths. It is relatively rare for a single empiricalaper to report results from both paradigms. Nonethelessesults from discrimination and appearance experimentsre typically accounted for within the same general modelf color processing and adaptation.13,14 In broad outline,his model incorporates encoding of light by three classesf cone photoreceptors, recombination of cone signals intoluminance and two color-opponent channels, and sensi-

ivity regulation at sites both preceding (first-site) andollowing (second-site) the signal recombination.15,16

Numerous variants of the general model have been pro-osed to account for specific features of both discrimina-ion and appearance data.3,17–22 It is not clear whetherhe variations reflect fundamental differences between vi-ual processing for discrimination and appearance, differ-nces in stimulus conditions studied, or differences in theay individual investigators have treated their data. Weave thus undertaken a systematic investigation of theelation between mechanisms of visual processing re-ealed by discrimination and appearance.

We are, of course, not the first to consider the relation-hip between color discrimination and appearance. A fewtudies have explicitly tested the idea that specific as-ects of color discriminability and appearance are con-rolled by a common set of mechanisms.23–25 If weroaden attention to intensity discrimination andightness/brightness perception, additional studies haveested Fechner’s hypothesis26 that the rate of apparenttimulus change is inversely proportional to discrimina-ion thresholds. This hypothesis may be used to derive a

005 Optical Society of America

vficeooc

utt

A

1Wttboev�gorfit

mtdcipetad

apeata

2TtlFftlaacEds

tcptcficpsrpitc

matccbbeMtpltdppttIcp

Frbsanrtad

J. M. Hillis and D. H. Brainard Vol. 22, No. 10 /October 2005 /J. Opt. Soc. Am. A 2091

isual response function from discrimination data;27–32

or review see Ref. 33. This response function relates annferred perceptual dimension to stimulus magnitude andan be used to predict appearance. We adopted this gen-ral approach. Our formulation is very close to that devel-ped by Heineman,34 but subsequent advances in modelsf early visual processing and numerical data fitting pro-edures allow us additional leverage.

This paper describes the experimental paradigms wesed and develops our formal analysis. Here we reporthe results of investigations for adaptation to changes inhe luminance and chromaticity of uniform backgrounds.

. Methods Overview and Formal Model

. Experimental Paradigmse conducted two types of experiments: color discrimina-

ion and asymmetric matching. In the color discrimina-ion experiments, test stimuli were excursions from theackground color that isolated either the L and M conesr the S cones. The test stimuli may be represented by thexpression �Lbg Mbg Sbg�+I�Ltest Mtest Stest� where theectors indicate LMS cone coordinates.35 More specificallyLbg Mbg Sbg� indicates the cone coordinates of the back-round and �Ltest Mtest Stest� represents the color directionf the excursion. For example, �Ltest Mtest Stest�= �0 0 1�epresents and S-cone isolating test. The value of I speci-es the intensity of the stimulus excursion in units yokedo �Ltest Mtest Stest�, and we refer to it as the test intensity.

We used a two-interval-forced-choice (2IFC) task toeasure the probability that observers could discriminate

wo stimuli with intensity parameters I and I+�. Theseata provide the probability that two stimuli can be dis-riminated as a function of the value of the pedestal I andntensity difference �. Measurements were made for testsresented against a number of backgrounds, and observ-rs’ performance as a function of the test direction, pedes-al intensity, and intensity difference were used to char-cterize the effect of chromatic adaptation on coloriscrimination.In the asymmetric matching experiments, observers

djusted a matching spot against one background to ap-ear the same as a test presented against another. Differ-nces between the LMS coordinates of observers’ matchesnd those of the corresponding tests were used to charac-erize the effect of chromatic adaptation on color appear-nce.

. Modelhe core idea underlying the model of mechanisms con-rolling appearance and discrimination judgments is il-ustrated in Fig. 1 and described more completely withig. 2. The two curves in Fig. 1 are stimulus-response

unctions of the same mechanism in two different con-exts. Each curve defines the relationship between stimu-us intensity and response magnitude for one state of ad-ptation. Given these response functions, we can predictppearance matches across the context change and dis-rimination thresholds measured within each context.quality of appearance across the context change is pre-icted by equality of mechanism response. In Fig. 1, thetimuli indicated by the downward arrows are predicted

o match in appearance across the change in context. Dis-rimination thresholds are predicted to be inversely pro-ortional to response function slope. For example, givenhe two stimuli indicated by the downward arrows, dis-rimination thresholds would be higher for the responseunction on the right (black curve) because equal changesn the stimulus intensity yield smaller expected responsehanges (i.e., the slope of the white line segment superim-osed on the black response function is lower than thelope of the white line segment superimposed on the grayesponse function). As will be detailed below, smaller ex-ected response changes translate into a diminished abil-ty to discriminate I and I+�. In our work, we make bothypes of measurement and ask whether they may be ac-ounted for by the same pair of response functions.

To link data from the 2IFC discrimination and asym-etric matching tasks, we relied on Fechner’s

ssumption26 that sensitivity to changes in stimulus in-ensity is proportional to the rate of apparent stimulushange. Figure 2D shows two hypothetical psychometricurves from the discrimination task for a single choice ofackground. To stage ideas tangibly, imagine that thisackground appears green and that the test spots are anxcursion along a color direction that modulates the L and

cones together. The two curves show performance forwo different pedestals I1 and I2 (indicated above theanel). Consider the left curve, which corresponds to theess intense pedestal I1. The x axis on the graph showsest intensities, while the y axis is probability of correctiscrimination. Each point on the curve represents therobability that the observer correctly discriminates aair of tests, one with intensity I1 and the other with in-ensity I1+�. The value of I1+� is specified by the posi-ion on the x axis. Similarly, the right curve is for pedestal2. This curve has a shallower slope, indicating that dis-rimination performance declines with the increase ofedestal intensity.

ig. 1. Two hypothetical response functions. Each function cor-esponds to a different context (e.g., different chromaticity ofackground) and plots a mechanism’s response as a function oftimulus strength (e.g., test spot contrast). Equality of appear-nce across the context change is predicted by equality of mecha-ism response, so that the stimuli indicated by the downward ar-ows would be predicted to match in appearance. Discriminationhresholds (i.e., test increment required to discriminate betweenpedestal presented alone and a pedestal plus the test) are pre-

icted to be inversely proportional to response function slope.

snpif

gtbo“


Conventionally, one point from the psychometric curveshown in Fig. 2D is selected and identified as a just-oticeable difference (JND). The 75% JNDs from the twosychometric curves in Fig. 2D are plotted as open circlesn Fig. 2E. In this plot, it is clear that discrimination per-
ormance is worse at pedestal I2 than at pedestal I1. More e
enerally the black line in Fig. 2E shows JNDs as a func-ion of pedestal intensity, measured against the greenackground. Such curves are typically called tvi (thresh-ld versus intensity) curves. The tvi curve shown has thedipper” shape often found in this type of

29,31,36,37

Fig. 2. Intensity response model with expectedasymmetric matches and discrimination perfor-mance. The x axes in panels A,C,D, and E teststimulus intensity. Panel C shows the responsemodel [Eq. (2)]. The y axis is the magnitude ofthe response. The two curves in Panel C are theresponse functions for one mechanism in twoadapted states. The gray curve represents ex-pected response in a gray context and the blackcurve represents expected response in a greencontext. The difference between the two curves isa difference in the gain-and-subtractive param-eters [g and s in Eq. (2)]. Panel B shows theGaussian response distributions for four test in-tensities (I1 ,I1+�I1,75,I2 ,I2+�I2,75 where �Ii,75 isthe incremental intensity that yields 75% correctperformance) presented in the green context.The x and y axes are probability and responsemagnitude, respectively. Panel D shows two psy-chometric curves for pedestals I1 and I2. Thesecurves are the expected discrimination perfor-mance derived from the model characterized inpanels B and C for the response functionadapted to the green context. Panel E shows theincrements expected to yield 75% correct (JNDs)as a function of pedestal intensity derived fromthe response model in B and C. Finally, Panel Ashows the expected performance in an asymmet-ric matching task with the tests presented in thegreen context and the matches set in the graycontext. The height of the shaded rectangle run-ning the width of the x axis represents absolutethreshold for a spot presented against a graybackground (JNDgray

0 , which is equivalent to thepoint where the JNDgray curve in Panel E inter-sects the y axis). The width of the shaded rect-angle running the height of the y axis representsabsolute threshold for a spot presented againstthe green background JNDgreen

0 . Any test-matchpairs in this gray shaded region would be ex-tremely difficult to obtain.

xperiment. The gray curve in Fig. 2E shows a

hbg

uaprnmitpeinpt

atasetdatat

p

watslmts

gofi(feflrta

pt

sttad

HmoasbTdt

tftrt

mtsaFbiaagpac

atbrrkqautmTsa

2ATa


ypothetical tvi curve for tests presented against a secondackground, one that appears gray. The change in back-round induces a change in the tvi curves.

What do such data reveal about the mechanisms thatnderlie performance? We followed earlier authors28–32

nd adopted a functional equation solution28 to Fechner’sroposal that JNDs along a single stimulus dimensionepresent equal changes in response. Equivalently, in sig-al detection theoretic terms, we assumed that perfor-ance at all intensity levels is limited by additive Gauss-

an noise of fixed variance. Along with the assumptionhat a single mechanism mediates performance for alledestals, differences in JNDs at I1 and I2 reflect differ-nces in the slope of the response function at these twontensities. Thus if we know the response function andoise standard deviation, we can predict JNDs for anyedestal. More generally, we can predict the probabilityhat any pair of tests I and I+� will be discriminated.

Figures 2B and 2C show this logic graphically. The yxis of both panels represents inferred response magni-ude. The x axis in Fig. 2C is stimulus intensity and the xxis in Fig. 2B is probability (of obtaining a particular re-ponse magnitude). The distribution of responses to ped-stal I1 is represented by the lowest Gaussian distribu-ion (thick black line) in Fig. 2B. For this noiseistribution, we can calculate the probability that any �dded to I1 will give a higher response. These probabili-ies correspond directly to the y axis of Fig. 2D: the prob-bility that an increment will be detected. The probabilityhat I1 yields a smaller response than I1+� is

�Rgreen�I1� � Rgreen�I1 + ��

= p�Rgreen�I1� − Rgreen�I1 + �� 0�

= p�n�r̄green1,�2� − n�r̄green1+�,�2� � 0�

= p�n�r̄green1 − r̄green1+�,2�2� � 0�

=�−�

0

n„r̄green1 − r̄green1+�,2�2…, �1�

here Rgreen represents the response function when testsre presented against a green background, n representshe normal distribution function, r̄greeni is the mean re-ponse to increment i, and �2 is response variance. Theast line of this equation is a cumulative Gaussian with

ean r̄green1− r̄green1+� and variance 2�2. When integratedo 0, this yields the probability that I1 yields a smaller re-ponse than I1+�.

The above logic tells how to predict discrimination dataiven a response function. Our interest is in going thether way: using discrimination data to infer the responseunction.26,28–32 In Fig. 2C, JND1 and JND2 represent testntensities �� that yield, on average, a fixed probability0.75 in this example) that the observer discriminates I1rom I1+JND1 and I2+JND2. These JNDs correspond toqual average changes in the neural response and there-ore reflect the local slope of the response function (whiteine segments through the intersections of the lines rep-esenting �R75 and JND1&2 in Fig. 2C show the slopes ofhe response curves that would be inferred at pedestals I1nd I ). Thus using discrimination performance, we can
2
iece together local estimates of response function slopeso infer the shape of the stimulus-response function.

Since in practice discrimination data sample the inten-ity dimension fairly coarsely, inferring the response func-ion is done most effectively using a parametric descrip-ion. We chose a parametric form previously shown toccount for both psychophysical and physiologicalata:29,31,38,39

R = M�gI + s�p

�gI + s�q + 1. �2�

ere M controls the height of the curve, p and q deter-ine the rate of expansion at low intensities and the rate

f saturation at high intensities, g is a gain parameter,nd s is a subtractive term. Given this form, numericalearch can be employed to find parameter values thatest account for observed discrimination performance.he parameter M trades off perfectly with noise standardeviation, so we fixed noise standard deviation at unityhroughout.

The response curve labeled Rgreen in Fig. 2C representshe response function [Eq. (2)] that would be inferredrom the green background tvi curve in Fig. 2E. Similarly,he response curve labeled Rgray in Fig. 2C represents theesponse function [Eq. (2)] that would be inferred fromhe gray background tvi curve.

Inferred response functions allow us to predict asym-etric matching data. We use the linking hypothesis that

wo tests will appear the same when they produce theame mechanism response. Consider again Fig. 2C. Whentest stimulus, TESTgreen (indicated on the top axis of

ig. 2C; note that the subscript refers to the color of theackground), is presented against the green backgroundt yields an expected response of r̄eq (shown on the rightxis of Fig. 2C). Under the linking hypothesis statedbove, observers will set the intensity of a spot against aray background to yield the same response. This ex-ected intensity may be found from Fig. 2C by finding theppropriate point on the response curve Rgray and is indi-ated by MATCHgray.

Figure 2A plots the intensities of spots that matchcross a change in background. The gray circle representshe expected TESTgreen:MATCHgray pair as determinedy the response functions in Fig. 2C. The thick black lineepresents the locus of TEST : MATCH pairs obtained byepeating this procedure for different response levels. Theey point is that the inferred response functions provide auantitative link between discrimination data (Figs. 2Dnd 2E) and asymmetric matching data (Fig. 2A). Wesed this link to determine whether the mechanisms con-rolling adaptation to background chromaticity are com-on to both discrimination and appearance judgments.his analysis assumes that all tests are processed by theame mechanism. Our stimuli were chosen to make thisssumption reasonable.

. METHODS. Observerswo observers participated. Observer JMH was an authornd observer QRS was a paid volunteer. Observer QRS

wlBI

BSp(vaf

sm�w

CTaectatPbrwsad

fpwbatTvtfirp

g�Pss

btcgTt

Fsmrwpt


as unaware of the experimental hypotheses and hadittle previous experience in psychophysical experiments.oth observers had normal color vision as assessed by an

shihara test for color blindness.

. Apparatustimuli were presented on a calibrated RGB monitor (HP1110) with 14-bit intensity resolution for each channelprovided by a Cambridge Research System BITS�� de-ice) operating at a 75 Hz refresh rate. Gamma functionsnd phosphor spectral power distribution were measuredor each CRT phosphor with a Photo Research 650

Table 1. Properti

CIECondition Name Color Name x

GRAY Gray 0.310Gray+LM Pale green 0.313Gray−LM Pale red 0.306Gray+S Blue-purple 0.280Gray−S Brownish-yellow 0.365

ig. 3. Spatial and temporal profiles of test spots. The top panelhows the spatial profile of test spots in the discrimination andatching experiments. The bottom panel shows the temporal pa-

ameters of a trial in the discrimination experiment. The smallhite spots indicate frame timing (vertical blanking). The tem-oral profile in the matching experiment was the same excepthat only one interval was used.

pectra-radiometer. At the 40 cm viewing distance, theonitor subtended 45 deg�37 deg (each pixel subtended0.041 deg). The observer’s head position was stabilizedith a chin rest.

. Stimuliest stimuli were spots (1.5 deg diameter) convolved with2D Gaussian to produce a smooth intensity ramp at the

dge (as shown in the top panel of Fig. 3). They were lo-ated 3 deg, on average, horizontally from a central fixa-ion point. One test spot was located to the left of fixationnd the other to the right. To avoid adaptation to theests, their locations were perturbed from trial to trial.erturbations were selected from a uniform square distri-ution, and the same perturbations were used for left andight tests on each trial, so that the the locations were al-ays symmetric with respect to a vertical axis. The xy po-

ition of the left and right tests were thus �−3 0�+ ��x �y�nd �3 0�+ �−�x �y�, respectively, where �x and �y were ran-om draws from a uniform distribution:

P�� = �0 for � � − 1.513

for − 1.5 � � � 1.5·

0 for � � 1.5�

On every trial, test locations were indicated by squarerames composed of sparse black points. The frame had 8oints per side, including the corner points. Each pointas 0.041 deg in diameter and the points were separatedy 0.23 deg. The frames appeared 13 ms before each trialnd were extinguished 13 ms after the test appeared. In-ensity of the test spots was ramped on and off gradually.he ramp was a cumulative Gaussian with standard de-iation =40 ms (3 frames) such that the total duration ofhe ramp was 133 ms (11 frames). The test intensity wasxed for 200 ms (15 frames) between the on and offamps. The bottom panel of Fig. 3 shows spatial and tem-oral profiles of the test spots.The test spots were modulations relative to the back-

round. That is, test modulations were defined asLbg Mbg Sbg�+I�Ltest Mtest Stest�. We used the Smith–okorny estimates40 of cone spectral sensitivities andtandard methods41 to convert between cone coordinatepecifications and video DAC settings.

Test spots were presented in various contexts definedy a uniform background. We used five backgrounds inhe experiments reported here. Table 1 provides the CIEhromaticity and LMS cone coordinates of the back-rounds, along with a descriptive color name for each.he gray background served as a reference with respect

o which the other backgrounds were defined. These differ

Test Backgrounds

dinates Cone Isomerizations ��106�Y L M S

10 22.5 2.72 1.01 0.0368 31.1 4.03 1.59 0.0325 13.3 1.42 0.44 0.0340 22.5 2.72 1.01 0.0137 22.5 2.72 1.01 0.05

es of

Coory

0.30.30.20.20.4

foagiibcr

tclscafcowL

wicT

DWviggrvvdimwwsteoTepep

d(os

tg

FmppaiGitto−fElstdepmh


rom the gray background by steps that modulate the LMr S cones as specified in the table. LMS units in the tablere the expected number of isomerizations from the back-round light for the area and duration of test stimuli. Testntensities will be reported as the expected number ofsomerizations independent of the background. Thus theackground LMS coordinates in Table 1 can be used toompute a contrast for the test intensities reported in theesults:

C =test isomerizations

background isomerizations.

Test spots were increments or decrements modulated inwo color directions. One direction modulated the L and Mones together and in equal amounts, with S cone stimu-ation held constant. That is, �Ltest Mtest Stest�=I�1 1 0�uch that L and M isomerization rates for individualones varied by the same amount. The total number of Lnd M cone isomerizations will differ when there are dif-erent numbers of each cone type in the stimulus area. Toompute isomerization totals, we used an L:M cone ratiof 2:1, which means that for this test direction thereould be twice as many L-cone isomerizations as M-cone.- and M-cone contrasts for this test direction are

CL =2

3Itest Ibg,L, CM =

1

3Itest Ibg,M,

here Ibg,L and Ibg,M are listed in Table 1 and Itest are testsomerization totals. The other direction modulated the Sones while the L- and M-cone stimulation was constant.hat is, �Ltest Mtest Stest�=I�0 0 1�.

. Procedure: Discriminatione used a pedestal + test paradigm to measure threshold

ersus pedestal intensity (tvi) curves for spots modulatedn different color directions against different back-rounds. The definition of the pedestal and test is shownraphically in the lower panel of Fig. 3. On the trial rep-esented, the pedestal alone was shown in the first inter-al and the pedestal + test was shown in the second inter-al. The test and pedestal were always in the same colorirection. Observers were instructed to select the intervaln which they saw the more “intense color.” Before experi-

ental trials began, observers were given practice trialsith auditory feedback (used throughout the experiment)here the test was clearly visible. Observers were in-

tructed to run practice trials until they were certain ofhe apparent color change that corresponded to the ped-stal + test. Once they were certain, they pressed a buttonn a game pad that initiated a 90 s adaptation period.here was a minimum of 2 s between each trial. One ped-stal direction and intensity were selected for each ex-erimental session. The number of pedestals tested forach background and test/pedestal color direction de-ended on limits imposed by the gamut of the monitor.Of particular concern was matching the stimulus con-

itions to those used in the asymmetric matching taskdescribed below) as closely as possible. This introducesne uncommon aspect of the procedure: there were twopots presented on each stimulus interval. In one interval

he pedestal was presented alone in the left and right tar-et locations. In the other interval, the pedestal was pre-

ig. 4. JMH’s results from discrimination and matching experi-ents for LM tests and backgrounds that varied in their LM in-

ut. The top six panels are discrimination thresholds (JNDs)lotted as a function of pedestal intensity. The three left panelsre JNDs for decrements and the three right panels are JNDs forncrements presented on, from top to bottom, the Gray+LM,ray and Gray−LM backgrounds. Error bars are 95% confidence

ntervals. The bottom panel shows asymmetric matching data forhe same set of conditions. The x axis is the test excursion (i.e.,he number of isomerizations expected from the test independentf the background) against the Gray+LM (circles) and the GrayLM (triangles) backgrounds. The y axis is the match excursion

rom the gray background against which the matches were set.rror bars are standard error of the mean. Dashed and solid

ines are results of model fits with parameters selected on the ba-is of both discrimination and matching data. These are fits forhe gain-and-subtractive model of adaptation. Increments andecrements were fit independently but the p ,q, and M param-ters in Eq. (2) were yoked across adapting conditions. The rawsychometric and matching data underlying the points andodel fits shown in this figure and Figs. 4–7 can be obtained atttp://color.psych.upenn.edu/supplements/com_uniform/.

swwtbicws2ceen

tk

ptdttfep

EWftutatr

Fmi

FmSc


ented alone at one target location and the pedestal + testas presented in the other interval. Observers indicatedith a key press which interval they believed contained

he test, independent of which side it appeared on. A feed-ack tone indicated when observers selected the incorrectnterval. The intensity of the test was controlled by stair-ase procedures. Four randomly interleaved staircasesere used in each experimental session: two for tests

hown on the right and two for tests on the left. We used-down–1-up and 3-down–1-up staircase rules to ensureomprehensive sampling of psychometric functions forach pedestal. Typically, one session was run for each ped-stal intensity. In cases where the data were particularlyoisy, an additional session was run.To reduce the number of sessions, we put the same con-

ext on both the left and right halves of the display. Toeep the same split-field conditions as in the matching ex-

ig. 5. QRS’s results from discrimination and matching experi-ents for LM tests and adapting fields that varied in their LM

nput. Results are plotted in the same format as Fig. 4.

eriment would require that each observer run in twicehe number of sessions per context (because half of theata would always be against the neutral context). A con-rol experiment, presented below, compared discrimina-ion performance for split-field and uniform-field contextsor a subset of conditions. The results indicate no differ-nces that would affect the analyses presented in this pa-er.

. Procedure: Appearancee used an asymmetric matching task to measure the ef-

ect of context on color appearance. Observers adjustedhe color of one of two simultaneously displayed test spotsntil they appeared identical. We gave observers full con-rol over the three-dimensional LMS coordinates of thedjustable match spot. One spot appeared on the left andhe other on the right of fixation. One half (either left oright; 22.5 deg�37 deg) of the monitor was filled with the

ig. 6. JMH’s results from discrimination and matching experi-ents for S-cone tests and adapting fields that varied in their-cone input. Results are plotted in the same format as Fig. 4 ex-ept that values correspond to expected S-cone isomerizations.

ggptr

sbppcweC�pcjeowactma

ststmmfir

3Fi+ds�myuftafrattguAi

Gt

mPrtJmrpbss

ptrtf4

FmS


ray background. The other half had the adapting back-round. Observers were instructed to fixate a small blackoint at the border of the two backgrounds throughouthe experiment. There was an initial 90 s adaptation pe-iod prior to the first time the test spots were displayed.

Each time the test spots were displayed, the fixed testpot, called the standard, appeared against the adaptingackground and the adjustable spot, called the match, ap-eared against the gray background. The spatial and tem-oral profiles of the test spots were the same as in the dis-rimination experiment, with the exception that the spotsere flashed once per exposure rather than twice. Observ-rs used a game controller to adjust the match in theIELAB L*a*b* coordinates. Approximately red–green

a*� and blue–yellow �b*� adjustments were made byressing correspondingly colored buttons on the gameontroller. Luminance �L*� adjustments were made with aoystick. The standard and match were displayed afterach adjustment with a minimum interstimulus intervalf 2 s. The standard and match could also be displayedithout making an adjustment by pressing an appropri-te key on the game pad. Observers could, at any time,hoose any one of four step sizes for the adjustments. Af-er completing a match, observers rated the quality of theatch with a value between 0 (couldn’t make the match)

nd 3 (perfect match).Four matches were completed in a single experimental

ession (typically lasting 20 min). Each match was madeo a different standard, but the standards used withinession were always selected from the same color direc-ion. For each direction in LMS color space, we measuredatch settings for eight standard tests. Two to four totalatches were made for each standard color for each of the

ve contexts. To the extent possible, stimuli were left–ight counterbalanced across sessions.

. RESULTSigure 4 shows one of JMH’s discrimination and match-

ng results for LM tests presented on the Gray, GrayLM, and Gray−LM backgrounds. The top six panels plotiscrimination thresholds as a function of pedestal inten-ity. The left column shows thresholds for decrements−LM� and the right column shows thresholds for incre-ents �+LM�. Note, therefore, that points intersecting theaxis are detection thresholds for decrements (left col-

mn) and increments (right column). The three rows,rom top to bottom, correspond to three adapting condi-ions: Gray+LM, Gray, and Gray−LM. Units on abscissand ordinate are the expected number of isomerizationsor the pedestal and test, respectively (i.e., the x axes rep-esent the expected number of isomerizations attribut-ble to the pedestal independent of the background, andhe y axis represents the expected number of isomeriza-ions attributable to the test independent of the back-round and pedestal). The quantities and calculationssed to estimate isomerizations are detailed in Appendix. Contrast units can be computed using the background

somerizations in Table 1 as specified in the methods.Data points (circles, squares, and triangles for the

ray+LM, Gray, and Gray−LM backgrounds, respec-ively) are JNDs determined by fitting the raw psycho-

etric data with separate cumulative normal functions.arameters were selected by a maximum-likelihood crite-ion. Data points shown in the top six panels are test in-ensities that yield 75% correct on the fitted curves (i.e.,NDs). Error bars are 95% confidence intervals deter-ined by a bootstrapping of the maximum-likelihood pa-

ameters with trial number and test intensities set by thesychometric data.42 The increase in the size of the errorars with pedestal intensity may result from suboptimalampling of points on the psychometric function by ourtaircase algorithm.

The curves shown in Fig. 4 are a result of selecting thearameters for the response function [Eq. (2)] that led tohe best account of the data. The exact optimization crite-ia are described in Subsection 3.A below. The curves inhese six panels are the 75% correct points (JNDs) in-erred from the fitted response model (see Fig. 2). In Fig., the dashed black curve, solid black curve, and solid

ig. 7. QRS’s results from discrimination and matching experi-ents for S-cone tests and adapting fields that varied in their-cone input. Results are plotted in the same format as Figs. 4–6.

gGJecp

ddtJtdepttatcps

JtmsadsGtGbmtorrjcTc

satootmttfth

AOtnfi

fiasfhwv

dffnema

ttta

wsce=dt

aetwtstcrm

tlm

fi(npcmaaaafi


ray curves are JNDs against the Gray+LM, Gray, andray−LM backgrounds, respectively. Response modelND curves for each adapting condition are repeated inach panel to provide a common reference; the curves thatorrespond to the adapting condition represented by eachanel are thickened.There are three notable trends in the discrimination

ata. First, consistent with many studies of contrastiscrimination,29,37,43 there is a dip in JNDs at low (sub-hreshold) pedestal values and a subsequent increase inNDs as pedestal intensity increases. Under the assump-ion that fixed-variance additive Gaussian noise limitsiscriminability, the dip reflects an accelerating nonlin-arity at low contrasts29,37,43 while JND increases at highedestals reflect response saturation (Fig. 2C). Second,here is a clear effect of background color on JNDs, par-icularly at low pedestals. JNDs for the LM tests increases the intensity of the LM background is increased. Third,here is good agreement between JNDs determined by theonventional method of fitting cumulative normals to thesychometric data and the JNDs determined by the re-ponse model fit.

The response model parameters that determine theND curves in the top six panels of Fig. 4 were also usedo derive performance for the corresponding asymmetricatching data. The bottom panel of Fig. 4 shows the re-

ults of the asymmetric matching task for the samedapting conditions represented by the top six panels ofiscrimination data. The x axis represents intensity of thetandard presented against either the Gray+LM orray−LM background. The y axis represents intensity of

he match set against the gray background (circles,ray+LM background; triangles, Gray−LMackground).44 Error bars are 1 standard error of theean. Observers’ ratings of the quality of the match (be-

ween zero and four) were used to reject trials where thebserver could not find an adequate setting. Any settingated 0 or 1 was rejected from the data set (no trials wereejected for observer JMH and 6 out of 120 trials were re-ected for QRS). The dashed black curve and solid grayurve are predictions derived from the response model.he correspondence between predictions and data is ex-ellent.

Figure 5 shows data for QRS for the same conditionshown in Fig. 4. Figures 6 and 7 show, respectively, JMH’snd QRS’s discrimination and matching data for S-coneests presented against adapting backgrounds that variednly in their S-cone input. Each figure shows data fromne observer in the same format as Figs. 4 and 5. The bot-om panel again shows results from the asymmetricatching task for S-cone tests. The agreement between

he model and data in Figs. 4–7 is good: Almost all sys-ematic trends are well predicted by the inferred responseunctions. The raw psychometric and matching data usedo obtain points shown in Figs. 4–7 can be downloaded atttp://color.psych.upenn.edu/supplements/com_uniform/.

. Error Trade-Off Analysisur broad goal is to determine whether both discrimina-

ion and appearance are mediated by the same mecha-isms of adaptation. The fits in Figs. 4–7 suggest an af-rmative answer for the conditions studied here. These

ts were obtained by leveraging both discrimination andppearance data simultaneously to determine the re-ponse function parameters. It remains possible, there-ore, that considerably better fits to each data set couldave been obtained had we fitted the two separately. Heree investigate this by fitting the response function witharying emphasis on discrimination and matching data.

Figure 8 illustrates the analysis for JMH’s −LM testata presented against Gray and Gray+LM backgroundsor observer JMH. The center panel shows model fit erroror discrimination and matching data. The x axis is theormalized negative log-likelihood of the model param-ters given the discrimination data. The y axis is the nor-alized sum-of-squared error between the model and the

symmetric matching data.The normalizing term for the negative log-likelihood of

he discrimination data was the likelihood of observinghe data if the probability p of every binomial variable inhe psychometric data was equal to the proportion of tri-ls the observer got correct for that test intensity, or

L = i=1

N1�Nped � Nitrials

Nicorrect�pi

Nicorrect

�1 − pi�Nitrials−Ni

correct,

here Nitrials is the number of trials for a given test inten-

ity, Nicorrect is the number of 2 IFC trials the observer got

orrect, NI is the number of test intensities for each ped-stal, Nped is the number of pedestals, and piNi

correct /Nitrials. To calculate likelihoods for models of the

iscrimination data, p is replaced by the probability de-ermined from the model.

The normalizing term for the squared error of thesymmetric matching data was the sum-of-squared differ-nce between the mean of the observer’s settings andheir actual settings: Err= i=1

N1 j=1Ntrials�matchj,i−i�2,

here matchi,j is the observer’s setting on the jth trial forest intensity I ,i is the mean of settings for test inten-ity I ,Ntrials is the number of trials completed for test in-ensity I, and NI is the number of test intensities. To cal-ulate the sum of squared errors for the model fits, i iseplaced by the value of the match determined by theodel for test intensity I.For these error metrics, no model could do better than

he values of the normalizing terms. Thus the normalizedikelihoods and normalized sum of squared errors for any

odel will be greater than or equal to 1.Consider the normalized likelihoods for different model

ts to the discrimination data only. The data pointsJNDs) in Figs. 4–7 were determined from cumulativeormal fits to the discrimination data. Characterizingsychometric data with cumulative normal parameters isommon and assumes, as our model does, that perfor-ance is limited by additive Gaussian noise. Such char-

cterization of psychometric data makes no assumptionsbout the relationship between data across pedestals anddapting conditions. We therefore consider it a baselinegainst which we can compare the quality of other modelts.

itp2GbnWpedtmsswt

nfidGfig

tearmo

mlfdnact

gwcwtrp

p

Fel(caFetgcsatml


The thick vertical gray line in the center panel of Fig. 8s the normalized negative log-likelihood for the cumula-ive normal fits to the psychometric data (i.e., a 40-arameter model given the two parameters for each of the0 −LM test psychometric functions from the Gray andray+LM backgrounds). The shaded (lighter) gray regionordering this line is the 95% confidence interval of theegative log-likelihood for these cumulative normal fits.e determined these confidence intervals by a bootstrap-

ing procedure using the maximum-likelihood param-ters (i.e., binomial probabilities for data resampling wereetermined by model fits, not the data trial numbers, andest intensities from the original data set. We performedaximum-likelihood fits to each of 1000 resampled data

ets to determine the range of likelihoods indicated by thehaded regions. This region therefore gives us an idea ofhat range of likelihoods we could reasonably expect for

his baseline fitting method.The thick, vertical, black, dashed line is the normalized

egative log-likelihood for the response model where allve parameters in Eq. (2) were allowed to vary to fit theiscrimination data for the −LM tests in the Gray andray+LM backgrounds (i.e., a 10-parameter model withve for the Gray and five for the Gray+LM). Finally, theray star with the black outline is the normalized nega-

ig. 8. Error trade-off analysis for JMH’s −LM test data in the Grror trade-off analysis described in the text for the gain-and-subikelihood �−LL� of model parameters given the full complement owe plot the negative log likelihood so small values correspond toriterion for the matching data). The y axis is the normalized leadapting conditions. The two left panels show the data that undeig. 4. The two right panels show the same data. The model fits ixclusively by the discrimination data. The gray star in the centhese fits. The model fits in the two right panels are fits where moray diamond in the central error trade-off panel is the −LL, LSEentral panel are −LL, LSE combinations where both data setsents a −LL, LSE combination for a specific combination of weighre from fits where more weight was given to maximize the likelihe sum-of-squared error for the model parameters given the maore weight was given to minimize the sum-of-squared error for

ikelihood of the parameters given the discrimination data.

ive log-likelihood for the response model fits with param-ters M ,p, and q yoked across Gray and with Gray+LMdapting conditions and parameters g and s chosen sepa-ately for each adapting condition (i.e., a 7-parameterodel that we refer to as the gain-and-subtractive model

f adaptation).There is little cost in fitting the data with the responseodel rather than independent cumulative normals; like-

ihood of the data given the response model parametersor both unyoked and yoked fits falls within the confi-ence range of likelihoods for unconstrained cumulativeormal fits. There is also little cost in yoking the M ,p,nd q parameters across adapting conditions (as indi-ated by the negligible horizontal shift in the star relativeo the vertical dashed line).

The two panels on the left show the results of the yokedain-and-subtractive model fits when the parametersere fitted to the discrimination data. The fit to the dis-

rimination data is good, but here the model does not doell in predicting the matching data. This is reflected in

he relatively high, normalized sum-of-squared error thatesults from these model parameters (star in the centeranel).Now consider the fits to the matching data only. Model

redictions for the asymmetric matching data require pa-

d Gray+LM adapting condtions. Central panel are results of thee model of adaptation. The x axis is the normalized negative log

imination data from the Gray and Gray+LM adapting conditionsr fits, consistent with the sum-of-squared error metric used as aared error (LSE) of model fits for the matching data in the samee analysis presented in the central panel and are replotted fromwo left panels are fits where model parameters were determinedor trade-off panel is the −LL, LSE combination corresponding torameters were determined exclusively by the matching data. Theination corresponding to these fits. The filled gray circles in thesed to determine the model parameters. Each gray circle repre-e matching and discrimination error. Higher points in the graph

f the parameters given the discrimination data than to minimizedata. Similarly, the more rightward points are from fits where

del parameters given the matching data than to maximizing the

ray antractivf discrbette

st-squrlie thn the tral errdel pa

combwere uts to thhood otching

the mo

ryce(obptsmiuaisstyc

coptp

fbbftretmbbtb

FlTW(


ameters for both backgrounds. When no parameters areoked, there are 10 model parameters for every adaptingondition (five for Gray, five for Gray±X). These param-ters are vastly underconstrained by the matching databottom panels of Figs. 4–7). However, the error for fitsbtained using this many parameters provides a goodaseline. The horizontal black dashed line in the centeranel of Fig. 8 is the normalized sum of squared error forhis 10-parameter fit to the matching data. We generatedimulated data from these model parameters to deter-ine the range of sum-of-squared errors we could expect

f those model parameters accurately characterized thenderlying response function. The gray shaded regionround the horizontal dashed line is the 95% confidencenterval for the sum-of-squared error derived from theseimulations. The gray diamond with black outline repre-ents errors from fits of the gain-and-subtractive adapta-ion model to the matching data (when M ,p, and q areoked across adapting conditions). Again there is little

ig. 9. Error trade-off analysis for LM tests and adapting fieldseft to right, JMH’s results from +LM tests on Gray and Gray−LMhe bottom two panels are from the same conditions for QRS. Ploe have included results of the error trade-off analysis for the ga

gray symbols) model.

ost to yoking parameters M ,p, and q across adapting e

onditions. The two panels on the right show the resultsf these yoked gain-and-subtractive model fits. With thearameters selected on the basis of the matching data,he model provides a good fit to the matching data and aoor fit to the discrimination data.Finally consider the error trade-offs possible when data

rom both tasks are used to constrain the model fits. Thelack-outlined gray star in Fig. 8 represents the loweround for the negative likelihoods and the upper boundor the squared error for the gain-and-subtractive adapta-ion model. Similarly, the black-outlined gray diamondepresents the lower bound for the matching squared-rror and the upper bound for the negative likelihoods forhe gain-and-subtractive adaptation model. If perfor-ance in matching and discrimination tasks is controlled

y common mechanisms of adaptation then there shoulde little cost in terms of the likelihoods of the discrimina-ion data and squared errors for the matching data whenoth data sets are used to constrain the model param-

aried only in their LM component. The top two panels are, fromting fields and −LM tests on Gray and Gray+LM adapting fields.onventions are the same as those for the central panel in Fig. 8.(open white symbols) model as well as the gain-and-subtractive

that vadap

tting cin-only

ters. That is, the likelihoods and squared errors for the

watgwmtliesa

iewtdscs

t

TertttwcwlpfbGbddfwggsg


eighted fits should follow the contour of the horizontalnd vertical dashed black lines with some points closeothe intersection of these two lines. The black-outlinedray circles are likelihoods and squared errors foreighted fits with the gain-and-subtractive adaptationodel. Using both data sets, we found model parameters

hat gave errors close to both lower bounds. Further theikelihood and squared error for these fits fell within thentersection of the confidence intervals established forach error metric. These results establish, for this dataet, that both matching and discrimination data can beccounted for by common mechanisms of adaptation.We also examined the quality of the fits by eye, compar-

ng fits when both data sets were factored into the param-ter selection and fits where only one or the other data setas employed. Differences between the fits with errors in

he lower left corner of the error trade-off plots and thoseetermined by each data set in isolation were vanishinglymall (i.e., the fits determined by appearance and dis-rimination data independently essentially looked theame as the yoked fits shown in Figs. 4–7).

Figures 9 and 10 show the results for all the data setshat could be subjected to this error trade-off analysis.

Fig. 10. Same as Fig. 8 except for S-cone tests and

he conventions in Figs. 9 and 10 are the same as thosestablished in Fig. 8 with two exceptions. First, we addedesults of the analysis for a simpler model of adaptationhat allows only the gain [g in Eq. (2)] to vary across con-exts. For this gain-only model (shown as open symbols),he subtractive term [s in Eq. (2)] was set to zero. Second,e plot only the extremes of the fits (fits to either the dis-

rimination or matching data) and the one result of theeighted fits that came closest to the lower bounds estab-

ished by the fits to each data set in isolation. The top twoanels in Fig. 9 are results of this error-trade-off analysisor JMH for −LM tests presented against the Gray+LMackground (left panel) and +LM tests presented on theray−LM background (right panel, same as Fig. 8). Theottom two panels are results from QRS for the same con-itions. The white stars are from fits to the discriminationata of the gain-only adaptation and the gray stars arerom the gain-and-subtractive model of adaptation. Thehite diamonds are from fits to the matching data of theain-only adaptation, and the gray diamonds are from theain-and-subtractive model of adaptation. The whitequare and gray circle are the best weighed fits for theain-only and gain-and-subtractive adaptation models,

ng fields that varied only in their S-cone component.
adapti

raFfmm

aweteettitd

ccitp

4DSIpcthccytwt

pooOse

ocuen

ceTbftiia

5VIwopKd

mfibnvsw

odgttgofiti

adgSwm

Fc−(afa−t


espectively. Figure 10 shows results for the S-cone testsnd adapting conditions using the same conventions asig. 9. The parameters that determined the error values

or the gray circles (gain-and-subtractive adaptationodel) in Figs. 9 and 10 are the parameters used in theodel fits shown in Figs. 4–7.Three important trends are revealed through the

nalysis depicted in Figs. 8 and 9: (1) in all cases, theeighted fits come very close to the lower bounds of therror established by considering each data set in isola-ion; (2) there is essentially no cost in terms of the modelrror to yoking parameters M ,p, and q across the rel-vant adapting conditions for either the discrimination orhe matching data; and (3) there are several cases wherehe gain-and subtractive model provides a clear reductionn the model error relative to the gain-only model (thoughhis error reduction is observed primarily in the matchingata).Our error tradeoff analysis confirms the impression

onveyed by Figs. 3–6: Effects of adaptation on both dis-rimination and appearance can be explained by a changen response function common to both. Before discussinghe results and their implications further, we brieflyresent two control experiments.

. CONTROL EXPERIMENT 1:ISCRIMINATION PERFORMANCE ONPLIT FIELDS

n the asymmetric matching experiment, test spots wereresented against a split field, one on either side of theolor discontimuity. To obtain the discrimination data, onhe other hand, tests were presented against a field thatad the same color across the entire display. We used aompletely uniform field in the discrimination task be-ause, with this arrangement, each experimental sessionielded twice as much data for the given adapting condi-ion. The control data presented here indicate that thereere no unexpected interactions between the two sides of

he split-field context.Methods were identical to the main discrimination ex-

eriment except that tests and pedestals were presentedn a split field. One half of the field was Gray and thether half was Gray−LM. Pedestals and tests were +LM.ne pedestal intensity was tested in each experimental

ession. One observer was tested with four staircases forach background–pedestal combination.

For our purposes, it is sufficient to show that the ratiof JNDs between the split versus uniform field adaptingonditions is constant. In Appendix B we show that such aniform shift would not have affected any fitting param-ters in Eq. (2) except for M, and that a change in M doesot affect the predictions for the asymmetric matches.The ratio of JNDs from the first experiment and this

ontrol experiment are shown in Fig. 11. The x axis is thexpected number of isomerizations for the +LM pedestal.he y axis is the ratio JNDuniform/JNDsplit. Different sym-ols denote different adapting conditions: Open circles arerom the Gray background and filled circles are data fromhe Gray−LM background. Error bars are 95% confidencentervals determined by a bootstrapping procedure. Theres no systematic difference in the JND ratios for thesedapting conditions.

. CONTROL EXPERIMENT 2: TESTING THEON KRIES HYPOTHESIS

n the main experiment, tests and adapting field shiftsere in the same color direction. We also examined effectsf LM background shifts on the discriminability and ap-earance of S tests, and vice versa. This tests the vonries hypothesis that each cone type adapts indepen-ently for both appearance and discrimination.Methods were identical to those of experiment 1. Weeasured detection thresholds and asymmetric matches

or S and LM tests against Gray±LM and Gray±S adapt-ng fields, respectively. That is, S tests were presented onackgrounds that varied in their L- and M-cone coordi-ates and LM tests were presented on backgrounds thataried only in the S-cone coordinates. The same two ob-ervers who participated in the first experiment, alongith one other observer, participated in this experiment.Detection thresholds and asymmetric matches for one

bserver are shown in Fig. 12. The top left panel showsetection thresholds for ±LM tests as a function of S back-round intensity. The filled black circles are test intensi-ies that gave 75% correct for a cumulative normal fit tohe data by a maximum-likelihood criterion. The solidray lines provide a reference for no changes in thresh-lds as a function of background intensity. Similarly, thelled black circles in the top right panel are absolutehresholds for ±S tests as a function of LM backgroundntensity.

The bottom two panels of Fig. 12 are results from thesymmetric matching experiment: In the left panel areata for LM tests when the S-cone component of the back-round was varied, and in the right panel are data for-cone tests when the LM component of the backgroundas varied. The filled black squares are a symmetricatching condition (both the fixed test and adjustable

ig. 11. JMH’s JND ratios for the split field versus uniform fieldonditions for LM increments presented against Gray and GrayLM backgrounds. The x axis is isomerizations of the pedestal

same as lower right and middle right panels in Fig. 4). The yxis is the JND ratio for discrimination data collected on a uni-orm and split field. Open circles are JND ratios from the Graydapting field and filled gray circles are ratios from the GrayLM adapting field. Error bars are 95% confidence intervals de-

ermined by a bootstrap analysis.

mptatn

ttslbt

6Wcajtaact

lwsettaaccHhmbocra

atpshppaamwfrmfsFtpojtida

tuTsse

FtpotttgrgitibtttttfGJstbwGrst


atch were presented against the Gray background) androvide an indication of any bias in the observer’s set-ings. The slight systematic trend for the +LM matchesnd +S matches to be lower than the baseline settings inhe Gray−S and Gray−LM conditions, respectively, wasot evident for two other observers.Results from both the asymmetric matching and detec-

ion task are generally consistent with the hypothesishat, for uniform fields, cones adapt independently. Re-ults from two other observers (not presented) were simi-ar. The lack of interaction between cones observed inoth discrimination and appearance judgments is consis-ent with the results of several previous studies.45–48

ig. 12. JMH’s detection and matching results for LM-coneests presented on adapting fields that varied only in their S com-onent and S-cone tests presented on adapting fields that variednly in their LM component. The top two panels are detectionhresholds plotted as a function of background intensity. The bot-om two panels are results of the asymmetric matching task. Thewo left panels are results from LM-cone tests presented on back-rounds that varied only in the S-cone components. The twoight panels are results from S-cone tests presented on back-rounds that varied only in their LM-cone component. The x axisn the top left panel is the expected number of S-cone isomeriza-ions from the background light for the same area and temporalnterval as the test stimuli, and the y axis is the expected num-er of isomerizations for an LM-cone test. Similarly, the x axis inhe top right panel represents background LM-cone isomeriza-ions and the y axis S-cone test isomerizations. Data points inhese top two panels are the 75% thresholds determined by fit-ing the detection data with a cumulative normal. The x axis inhe bottom left panel is the expected number of isomerizationsor fixed LM-cone tests presented on either the Gray+S, Gray, orray−S adapting fields. The y axis is S-cone isomerizations forMH’s match settings against the gray background. Filledquares are from the symmetric matching conditions (where bothhe fixed test and adjustable match were presented on the Grayackground). Open circles and filled diamonds are conditionshere the fixed tests were presented against the Gray+LM andray−LM conditions, respectively. Error bars are standard er-

ors of the mean. The convention for the bottom right panel is theame as for the bottom left panel except that the axes correspondo the expected isomerizations of S-cone tests.

. DISCUSSIONe have tested the assumption that effects of background

hromaticity and luminance on color discriminability andppearance are mediated by mechanisms common to bothudgments. This common mechanism hypothesis holds forhe conditions we examined. Our general conclusiongrees with that of earlier authors who have studied ad-ptation of discrimination and appearance with respect tohanges in uniform backgrounds.24,34,49–52 Our work ex-ends previous studies in several ways.

First, we measured full tvi curves and used these toearn how adaptation affects discriminability across aide range of stimulus intensities. In this regard, we

hare much with Heinemann.34 Most earlier work, how-ver, characterized adaptation with changes in detectionhreshold and relied on gain-control models of adaptationo extrapolate predictions to the intensity range whereppearance was studied. Use of detection thresholds isdequate only for stimulus conditions where the gain-ontrol model is valid. Some of our conditions required in-lusion of a subtractive term in the adaptation model.ad we relied only on detection thresholds, we wouldave drawn erroneous conclusions about the commonechanism hypothesis. We expect this consideration to

ecome increasingly important as we extend our work tother adapting contexts that include contrast and moreomplex spatial structure. There is good evidence thaticher models of adaptation are required to account fordaptation effects for such contexts.22,36,53

A second novel feature of our work is the error tradeoffnalysis presented in Figs. 8–10. This analysis showshat fitting a model to discrimination data alone leads tooor predictions of appearance and vice versa. Such a re-ult could arise either because the common mechanismypothesis is false, or because measurement variabilityropagates to the model fits in a manner that leads tooor extrapolation across tasks. These two possibilitiesre distinguished by the error tradeoff analysis. For ad-ptation to uniform fields, the case studied here, the com-on mechanism hypothesis holds. Under other conditionse might expect the common mechanism hypothesis to

ail. For example, Nerger et al.54 found that “filling-in” ofetinally stabilized images affected appearance judg-ents but not detectability. While this result suggests dif-

erent mechanisms mediating detection and appearance,uch a conclusion would be premature for two reasons.irst, our results show the importance of measuring the

vi function and not just detection thresholds when com-aring threshold and suprathreshold performance. Sec-nd, the common mechanism hypothesis should be sub-ected to the kind of statistical test provided by the errorradeoff analysis presented here. Further, error tradeoffs important to bear in mind when evaluating conclusionsrawn from comparisons of data that were collected andnalyzed in different laboratories.A third important feature of our work was the attempt

o match as carefully as possible the stimulus conditionssed in the discrimination and appearance experiments.hus the same observers viewed spots flashed with theame temporal and spatial profiles. Careful matching oftimulus conditions rules out the possibility that differ-nces between discrimination and appearance occur sim-

padouCf

fa(iassspafaecthdd

emtlmtaswaWcwgt

cibthmbetmito

oaccpnsegttcsf

APTisiwilip=

P

PPLM

PL�IOPPQ


ly because the visual system is in a different state of ad-ptation across the two paradigms. The one majorifference that persisted in our experiments was the usef split backgrounds in the appearance experiments andniform backgrounds in the discrimination experiments.ontrol measurements, however, indicated that this dif-

erence was not of consequence for our comparisons.At the core of our modeling is an inferred response

unction common to both discrimination andppearance.34,49 This function explains discriminationtvi) data through the linking hypothesis that sensitivitys proportional to its slope.55 The same function explainsppearance through the linking hypothesis that twotimuli appear the same when they lead to the same re-ponse. We chose a particular parametric form for the re-ponse function [Eq. (2)]. This function is consistent withrevious studies of both discrimination29–32 andppearance.51,57 A parametric response function sets theorm of the common mechanism hypothesis and providesway to aggregate data collected at discrete intensity lev-

ls. For the conditions studied here, Eq. (2) allowed an ex-ellent description of both tvi and matching data. Underhe assumption that the common mechanism hypothesisolds, the parameters of the response function are betteretermined using both discrimination and appearanceata than by using either data set alone.In addition to testing the common mechanism hypoth-

sis, our data also speak to models of adaptation. Theost general model we considered was one in which all of

he parameters of the response function [Eq. (2)] were al-owed to vary across adapting conditions. More restrictive

odels yoke some of the model parameters across condi-ions and thus account for adaptation through changes of

subset of the parameters. We considered two specificubset models, one in which only the gain (parameter g)as allowed to change and one in which subtraction waslso allowed (both parameters g and s allowed to vary).e found cases where the gain-only model failed to ac-

ount for the data while the gain-and-subtractive modelorked well. Previous authors25,30,32,58,59 have also ar-ued that models of adaptation must include a subtrac-ive term61 (but see Ref. 60).

There are obvious practical reasons why testing the

Table 2. Conventions Us

roperty

osterior nodal point distance 1upil diameter 3.5ens densityacular pigment optical density

hotoreceptor density 1.6�1cone: M-cone ratio

L+M� cone: S-cone rationner segment length 2uter segment diameterhotopigment axial densityhotopigment spectral sensitivityuantal efficiency

aFor the purposes of calculating isomerizations, pupil diameter was fixed to its e

ommon mechanism hypothesis is important: (1) Model-ng adaptation is simplified for conditions where data ofoth discrimination and appearance experiments revealhe same mechanisms, and (2) predictions about the be-avior of the neural substrate from the psychophysics areore straightforward under these conditions. More

roadly, however, the status of this hypothesis is of inter-st as we consider the utility of color vision. Cases wherehe hypothesis fails are cases where separate mechanismsediate the role of color in scene segmentation and object

dentification. Such cases would provide important clueso differences in the information processing requirementsf these two tasks.

The data presented in this paper do not reveal failuresf the common mechanism hypothesis, but represent onlylimited set of stimulus conditions: We consider contexts

onsisting only of uniform backgrounds. In addition, wehoose the color directions of the tests to maximize therobability that they would isolate individual mecha-isms, as indicated by a large literature on how the visualystem processes color.3,11,16,22 Clearly it will be of inter-st to determine how the common mechanism hypothesiseneralizes. Of particular interest to us are conditionshat include contrast adaptation,17,19,62,63 intermediateest color directions, and spatial structure in theontexts.64 We believe that the basic methods and analy-is presented here will allow sharp tests of the hypothesisor this wider range of conditions.

PPENDIX A: ESTIMATING CONEHOTOPIGMENT ISOMERIZATIONSable 2 lists the conventions we used to estimate the

somerizations for the data presented in this paper. Theoftware used to perform isomerization rate calculationss available at www.psychtoolbox.org. Test intensitiesere presented in terms of the total expected number of

somerizations independent of the background. To calcu-ate the total expected number of isomerizations, isomer-zation rates were integrated for the spatial and temporalrofiles of the test (Fig. 3). Specifically, Rtotal

*

x y tRrate* f�x ,y , t�, where f is the function defining the

Estimate Isomerizations

Source

Ref. 65a Ref. 66

Ref. 67Ref. 68; scaled by estimates of relative

density at 3 deg eccentricity from Ref. 69mm2 Ref. 70

——

Ref. 65Ref. 65Ref. 65Ref. 40Ref. 65

value for the Gray background.

ed to

Value

6.1 mm2 mm——

04 per2:1

20:1.9 mm

33 m0.5—

2/3

xpected

ssittatu

ASHssJsJcF

TcWmme

cem

AWcg

e

R

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

2

2

2

2


timulus, and x and y correspond to the assumed conepacing. As we noted in Section 2 the conversion fromsomerization rates (per cone per second) to isomerizationotals incorporates differences in the cone ratios. Thus ifhere are more L than M cones, there will be proportion-lly more total L-cone isomerizations when the isomeriza-ion rates are the same. The cone densities and ratiossed to calculate these totals are included in Table 2.

PPENDIX B: EFFECTS OF UNIFORMHIFTS IN JNDS ON MODEL PARAMETERSere we show that effects on JNDs we observed in the

plit field versus uniform field conditions will not sub-tantively affect model parameter estimation. Recall thatNDs are inversely proportional to the slope of the re-ponse function (i.e., JND1/R�). How would a shift inNDs by a factor common to all pedestals and adaptingonditions, as we observed, affect parameter estimation?irst we note that

JND 1

R�=

1

M

��gI + S�q + 1�2

g��gI + S�p−1��gI + S�q�p − q� + p��.

hus any multiplicative shift in JNDs common across allonditions would be reflected by a common change in M.hat is important is, such a change does not affect theatch predictions. Recall that we assume matches areade when the responses of the relevant mechanisms are

quated, that is, when

RiA = Ri

B

MA

�gAI + sA�p

�gAI + sA�q + 1= MB

�gBI + sB�p

�gBI + sB�q + 1

.

Because both sides of this equation can be divided by aommon change in MA and MB without affecting thequality, the magnitude of this change does not influenceatch predictions.

CKNOWLEDGMENTSe thank Jack Nachmias for helpful comments and dis-

ussion. This research was supported by NIH throughrant R01 EY10016.

Corresponding author J. M. Hillis can be reached by-mail at [email protected].

EFERENCES AND NOTES1. W. S. Stiles, “Color vision: the approach through increment

threshold sensitivity,” Proc. Natl. Acad. Sci. U.S.A. 45,100–114 (1959).

2. G. Wyszecki and W. S. Stiles, Color Science—Concepts andMethods, Quantitative Data and Formulae, 2nd ed. (Wiley,1982).

3. R. T. Eskew, J. S. McLellan, and F. Giulian, “Chromaticdetection and discrimination,” in Color Vision: FromMolecular Genetics to Perception, K. Gegenfurtner and L. T.Sharpe, eds. (Cambridge U. Press, 1999), pp. 345–368.

4. D. C. Hood and M. A. Finkelstein, “Senstivity to Light,” inHandbook of Perception and Human Performance: Sensory

Processes and Perception, K. R. Boff, L. Kaufman, and J. P.Thomas, eds. (Wiley, 1986).

5. P. Lennie and M. D’Zmura, “Mechanisms of color vision,”Crit. Rev. Neurobiol. 3, 333–400 (1988).

6. P. K. Kaiser and R. M. Boynton, Human Color Vision, 2nded. (Optical Society of America, 1996).

7. R. W. Burnham, R. M. Evans, and S. M. Newhall,“Prediction of color appearance with differentadaptation illuminations,” J. Opt. Soc. Am. 47, 35–42(1957).

8. S. K. Shevell, “Color appearance,” in The Science of Color,2nd ed., S. K. Shevell, ed. (Optical Society of America,2003).

9. G. Wyszecki, “Color appearance,” in Handbook ofPerception and Human Performance: Sensory Processesand Perception, K. R. Boff, L. Kaufman, and J. P. Thomas,eds. (Wiley, 1986), pp. 9.1–9.56.

0. Q. Zaidi, “Color and brightness inductions: from Machbands to three-dimensional configurations,” in Color Vision:From Genes to Perception, K. R. Gegenfurtner and L. T.Sharpe, eds. (Cambridge U. Press, 1999), pp. 317–344.

1. D. H. Brainard, “Color Constancy,” in The VisualNeurosciences, L. Chalupa and J. Werner, eds. (MIT Press,2004), pp. 948–961.

2. D. H. Foster, “Does colour constancy exist?” Trends Cogn.Sci. 7, 493–443 (2003).

3. L. M. Hurvich and D. Jameson, “An opponent-processtheory of color vision,” Psychol. Rev. 64, 384–404 (1957).

4. W. S. Stiles, “Mechanism concepts in colour theory,” J.Colour Group 11, 106–123 (1967).

5. D. H. Brainard, “Color vision theory,” in InternationalEncyclopedia of the Social and Behavioral Sciences, N. J.Smelser and B. P. Baltas, eds. (Elsevier, 2001), pp.2256–2263.

6. M. A. Webster, “Human colour perception and itsadaptation,” Network Comput. Neural Syst. 7, 587–634(1996).

7. J. Krauskopf, D. R. Williams, and D. W. Heeley, “Cardinaldirections of color space,” Vision Res. 22, 1123–1131 (1982).

8. J. Krauskopf, D. R. Williams, M. B. Mandler, and A. M.Brown, “Higher order color mechanisms,” Vision Res. 26,23–32 (1986).

9. M. A. Webster and J. D. Mollon, “Changes in colourappearance following post-receptoral adaptation,” Nature(London) 349, 235–238 (1991).

0. C. C. Chen, J. M. Foley, and D. H. Brainard, “Detection ofchromoluminance patterns on chromoluminance pedestalsII: Model,” Vision Res. 40, 789–803 (2000).

1. P. B. Delahunt and D. H. Brainard, “Control of chromaticadaptation: signals from separate cone classes interact,”Vision Res. 40, 2885–2903 (2000).

2. M. D’Zmura and B. Singer, “Contrast gain control,” inColor Vision: From Molecular Genetics to Perception, K.Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press,1999), pp. 369–385.

3. J. M. Loomis and T. Berger, “Effects of chromaticadaptation on color discrimination and color appearance,”Vision Res. 19, 891–901 (1979).

4. E. N. Pugh and J. Larimer, “Test of the identity of the siteof blue/yellow hue cancellation and the site of chromaticantagonism in the �1 pathway,” Vision Res. 20, 779–788(1980).

5. J. Walraven, “Perceived color under conditions of chromaticadaptation: Evidence for again control by �- mechanisms,”Vision Res. 21, 611–620 (1981).

6. G. T. Fechner, Elements of Psychophysics, Henry HoltEdition in Psychology (Holt, Rinehart & Winston, 1966).

7. D. H. Krantz, “Integration of just-noticeable differences,” J.Math. Psychol. 8, 591–599 (1971).

8. R. D. Luce and W. Edwards, “The derivation of subjectivescales from just noticeable differences,” Psychol. Rev. 65,222–236 (1958).

9. G. E. Legge and J. M. Foley, “Contrast masking in humanvision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

5

5

5

5

5

5

5

5

5

5

6

6

6

6

6

66

6

6

6

7


0. E. H. Adelson, “Saturation and adaptation in the rodsystem,” Vision Res. 22, 1299–1312 (1982).

1. J. M. Foley, “Human luminance pattern-visionmechanisms: masking experiments require a new model,”J. Opt. Soc. Am. A 11, 1710–1719 (1994).

2. W. S. Geisler, “Mechanisms of visual sensitivity:backgrounds and early dark adaptation,” Vision Res. 23,1423–1432 (1983).

3. D. Laming, The Measurement of Sensation, 1st ed., Vol. 30of Oxford Psychology Series (Oxford U. Press, 1997), p. 262.

4. E. G. Heinemann, “The relation of apparent brightness tothe threshold for differences in luminance,” J. Exp.Psychol. 61, 389–399 (1961).

5. D. H. Brainard, “Cone contrast and opponent modulationcolor spaces,” in Human Color Vision, 2nd ed., P. K. Kaiserand R. M. Boynton, eds. (Optical Society of America, 1996),pp. 563–579.

6. C. C. Chen, J. M. Foley, and D. H. Brainard, “Detection ofchromoluminance patterns on chromoluminance pedestalsI: Threshold measurements,” Vision Res. 40, 773–788(2000).

7. J. Nachmias and R. V. Sansbury, “Grating contrast:discrimination may be better than detection,” Vision Res.14, 1039–1042 (1974).

8. K. I. Naka and W. A. Rushton, “S-potentials from colourunits in the retina of fish (Cyprinidae),” J. Physiol.(London) 185, 536–555 (1966).

9. M. J. Valeton and D. v. Norren, “Light adaptation ofprimate cones: an analysis based on extracellular data,”Vision Res. 23, 1539–1547 (1983).

0. V. Smith and J. Pokorny, “Spectral sensitivity of the fovealcone photopigments between 400 and 500 nm,” Vision Res.15, 161–171 (1975).

1. D. H. Brainard, D. G. Pelli, and T. Robson, “Displaycharacterization,” in Encylopedia of Imaging Science andTechnology, J. Hornak, ed. (Wiley, 2002), pp. 72–188.

2. F. W. Wichmann and N. J. Hill, “The psychometric function:II. Bootstrap-based confidence intervals and sampling,”Percept. Psychophys. 63, 1314–1329 (2001).

3. J. M. Foley and G. E. Legge, “Contrast detection andnear-threshold discrimination in human vision,” VisionRes. 21, 1041–1053 (1981).

4. Note that matches varied along only the color direction ofthe test for this and other conditions examined in thispaper. Thus, plotting intensity is sufficient.

5. J. Krauskopf and K. Gegenfurtner, “Color discriminationand adaptation,” Vision Res. 32, 2165–2175 (1992).

6. E. J. Chichilnisky and B. A. Wandell, “Photoreceptorsensitivity changes explain color appearance shifts inducedby large uniform backgrounds in dichoptic matching,”Vision Res. 35, 239–254 (1995).

7. S. M. Wuerger, “Color appearance changes resulting fromiso-luminant chromatic adaptation,” Vision Res. 36,3107–3118 (1996).

8. A. R. Wade and B. A. Wandell, “Chromatic light adaptationmeasured using functional magnetic resonance imaging,” J.Neurosci. 22, 8148–8157 (2002).

9. P. Whittle and P. D. C. Challands, “The effect ofbackground luminance on the brightness of flashes,” VisionRes. 9, 1095–1110 (1969).

0. P. Whittle, “Increments and decrements: luminancediscrimination,” Vision Res. 26, 1677–1691 (1986).

1. P. Whittle, “Brightness, discriminability and the�crispening effect’,” Vision Res. 32, 1493–1507 (1992).

2. O. Rinner and K. R. Gegenfurtner, “Time course ofchromatic adaptation for color appearance anddiscrimination,” Vision Res. 40, 1813–1826 (2000).

3. A. G. Shapiro and Q. Zaidi, “The effects of prolonged

temporal modulation on the differential response of colormechanisms,” Vision Res. 32, 2065–2075 (1992).

4. J. L. Nerger, T. P. Piantanida, and J. Larimer, “Colorappearance of filled-in backgrounds affects huecancellation, but not detection thresholds,” Vision Res. 33,165–172 (1993).

5. This linking hypothesis is equivalent to assuming thatperformance is limited by additive noise of fixed variancefollowing the nonlinearity. An alternative model includessignal-dependent noise. For a subset of the data, weexamined parametric fits to the discrimination andappearance data that included signal-dependent noise(with variance proportional to the expected response). Theprecise shape of the inferred nonlinearity is different for asignal-dependent noise model, but the quality of the fits tothe discrimination and appearance data was not affected(see Ref. 56 for an analysis of the power of discriminationdata to test these alternative noise models).

6. G. E. Legge, D. Kerstein, and A. E. Burgess, “Contrastdiscrimination in noise,” J. Opt. Soc. Am. A 4, 391–404(1987).

7. H. Takasaki, “Lightness change of grays induced by changein reflectance of gray background,” J. Opt. Soc. Am. 56,504–509 (1966).

8. D. Jameson and L. M. Hurvich, “Color adaptation:Sensitivity, contrast, and afterimages,” in Handbook ofSensory Physiology, L. M. Hurvich and D. Jameson, eds.(Springer, 1972), pp. 568–581.

9. J. Walraven, “Discounting the background: The missinglink in the explanation of chromatic induction,” Vision Res.16, 289–295 (1976).

0. S. K. Shevell, “Unambiguous evidence for the additiveeffect in chromatic adaptation,” Vision Res. 20, 637–639(1980).

1. In the literature on subtractive adaptation, some authorsapply the subtractive term to the incremental/decrementalstimulus, as we have done here. Others apply it to the sumof the background and the increment/decrement. These twoformulations are equivalent except in the interpretation ofwhat a subtractive term of zero means.

2. Q. Zaidi and A. G. Shapiro, “Adaptive orthogonalization ofopponent-color signals,” Biol. Cybern. 69, 415–428 (1993).

3. R. O. Brown and D. I. A. MacLeod, “Color appearancedepends on the variance of surround colors,” Curr. Biol. 7,844–849 (1997).

4. J. M. Hillis and D. H. Brainard, “A shadowy dissociationbetween discriminability and identity,” J. Vision 4, 56a(2004).

5. R. W. Rodieck, The First Steps In Seeing (Sinauer, 1998).6. J. Pokorny and V. C. Smith, “How much light enters the

retina?” in Colour Vision Deficiencies XIII, C. R. Cavonius,ed. (Kluwer Academic, 1997), pp. 491–511.

7. A. Stockman, L. T. Sharpe, and C. C. Fach, “The spectralsensitivity of the human short-wavelength cones,” VisionRes. 39, 2901–2927 (1999).

8. R. A. Bone, J. T. Landrum, and A. Cains, “Optical densityspectra of the macular pigment invivo and invitro,” VisionRes. 32, 105–110 (1992).

9. A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey,G. E. Holder, F. W. Fitzke, A. C. Bird, and F. J. van Kuijk,“Macular pigment density and distribution: comparison offundus autofluorescence with minimum motionphotometry,” Vision Res. 43, 1765–1775 (2003).

0. C. A. Curcio, K. R. Sloan, Jr., O. Packer, A. E. Hendrickson,and R. E. Kalina, “Distribution of cones in human andmonkey retina: individual variability and radialsymmetry,” Science 236, 597–582 (1987).

do common mechanisms of adaptation mediate color...

Documents