{"title": "Morton-Style Factorial Coding of Color in Primary Visual Cortex", "book": "Advances in Neural Information Processing Systems", "page_first": 221, "page_last": 228, "abstract": "", "full_text": "Morton-Style Factorial Coding of Color in\n\nPrimary Visual Cortex\n\nJavier R. Movellan\n\nInstitute for Neural Computation\nUniversity of California San Diego\n\nLa Jolla, CA 92093-0515\nmovellan@inc.ucsd.edu\n\nThomas Wachtler\n\nSloan Center for Theoretical Neurobiology\n\nThe Salk Institute\n\nLa Jolla, CA 92037, USA\n\nthomas@salk.edu\n\nThomas D. Albright\n\nTerrence Sejnowski\n\nHoward Hughes Medical Institute\n\nComputational Neurobiology Laboratory\n\nThe Salk Institute\n\nLa Jolla, CA 92037, USA\n\ntom@salk.edu\n\nThe Salk Institute\n\nLa Jolla, CA 92037, USA\n\nterry@salk.edu\n\nAbstract\n\nWe introduce the notion of Morton-style factorial coding and illustrate\nhow it may help understand information integration and perceptual cod-\ning in the brain. We show that by focusing on average responses one\nmay miss the existence of factorial coding mechanisms that become only\napparent when analyzing spike count histograms. We show evidence\nsuggesting that the classical/non-classical receptive \ufb01eld organization in\nthe cortex effectively enforces the development of Morton-style factorial\ncodes. This may provide some cues to help understand perceptual cod-\ning in the brain and to develop new unsupervised learning algorithms.\nWhile methods like ICA (Bell & Sejnowski, 1997) develop independent\ncodes, in Morton-style coding the goal is to make two or more external\naspects of the world become independent when conditioning on internal\nrepresentations.\n\nIn this paper we introduce the notion of Morton-style factorial coding and illustrate how it\nmay help analyze information integration and perceptual organization in the brain. In the\nneurosciences factorial codes are often studied in the context of mean tuning curves. A\ntuning curve is called separable if it can be expressed as the product of terms selectively\nin\ufb02uenced by different stimulus dimensions. Separable tuning curves are taken as evi-\ndence of factorial coding mechanisms. In this paper we show that by focusing on average\nresponses one may miss the existence of factorial coding mechanisms that become only\napparent when analyzing spike count histograms.\n\nMorton (1969) analyzed a wide variety of psychophysical experiments on word perception\nand showed that they could be explained using a model in which stimulus and context\nhave separable effects on perception. More precisely, in Mortons\u2019 model the joint effect of\nstimulus and context on a perceptual representation can be obtained by multiplying terms\n\n\fselectively controlled by stimulus and by context, i.e.,\n\u0001\u0013\u0007\u0014\t\u0015\u0003\u0016\r\n\u0011\u0018\u0017\n\u0001\u0013\u0007\n\t\u0019\u0003\u0016\r\n\u0011\n\u0012\n\n\u0002\u0001\u0004\u0003\u0006\u0005\b\u0007\n\t\f\u000b\u000e\r\u0010\u000f\n\n\u0011\n\u0012\n\u001a\u001c\u001b\n\n\u0001\u0004\u000b\u0016\t\u0019\u0003\u0016\r\n\u0001\u001d\u000b\u001e\t\u0019\u0003\u0016\r\n\u0011\n\u0017\n\n(1)\n\nis the empirical probability of perceiving the perceptual alternative \u0003\n\nwhere \u0002\u0001\u0004\u0003\u001f\u0005\u001e\u0007\n\t\u0015\u000b\u000e\r\nin\n\u0001\u001d\u0007\n\t\u0015\u0003\u001e\r represents the support of stimulus \u0007 for percept\nresponse to stimulus \u0007\nthe support of the context for percept \u0003 . Massaro (1987b, 1987a, 1989a) has\n\u0003 and \u0011!\u0017\nshown that this form of factorization describes accurately a wide variety of psychophysical\nstudies in domains such as word recognition, phoneme recognition, audiovisual speech\nrecognition, and recognition of facial expressions.\n\nin context \u000b , \u0011 \u0012\n\n\u0001\u001d\u000b\u001e\t\u0019\u0003\u0016\n\nMorton-style factorial codes used to be taken as evidence for a feedforward coding mech-\nanism (Massaro, 1989b) but Movellan & McClelland (2001) showed that neural networks\nwith feedback connections can develop factorial codes when they follow an architectural\nconstraint named \u201cchannel separability\u201d. Channel separability is de\ufb01ned as follows: First\nwe identify the neurons which have a direct in\ufb02uence on the observed responses (e.g., the\nset of neurons that affect an electrode). For a given set of response units, the stimulus\nchanel is de\ufb01ned as the set of units modulated by the stimulus provided the response spec-\ni\ufb01cation units are excised from the rest of the network. The context channel is the set of\nunits modulated by the context provided the response units are excised from the rest of\nthe networks. Two channels are called separable if they have no units in common. Chan-\nnel separability implies that the in\ufb02uences of an information source upon the channel of\nanother information source should be mediated via the response speci\ufb01cation units (see\nFigure 1). While the models used in Movellan and McClelland (2001) are a simpli\ufb01ca-\ntion of actual neural circuits, the analysis suggests that the form of separability expressed\nin the the Morton-Massaro model may be a useful paradigm for the study of information\nintegration in the brain. Indeed it is quite remarkable that the functional organization of\ncortex into classical/non-classical receptive \ufb01elds provides a separable architecture (See\nFigure 1). Such organization may be nature\u2019s way of enforcing Morton-style perceptual\ncoding. In this paper we present evidence in favor of this view by investigating how color\nis encoded in primary visual cortex.\n\nIt is well known that stimuli of equal chromaticity can evoke different color percepts, de-\npending on the visual context (Wesner & Shevell, 1992; Brown & MacLeod, 1997). Con-\ntext dependent responses to color stimuli have been found in V4 (Zeki, 1983). More re-\ncently the last three authors of this article investigated the chromatic tuning properties of\nV1 cells in response to stimuli presented in different chromatic contexts (Wachtler, Se-\njnowski, & Albright, 2003). The experiment showed that the background color, outside\nthe cell\u2019s classical receptive \ufb01eld, had a signi\ufb01cant effect on the response to colors inside\nthe receptive \ufb01eld. No attempt was made to model the form of such in\ufb02uence. In this\npaper we analyze quantitatively the results of that experiment and show that a large propor-\ntion of these neurons, adhered to the Morton-Massaro law, i.e., stimulus and context had a\nseparable in\ufb02uence on the spike count histograms of these cells.\n\n1 Methods\n\nThe animal preparation and methods of this experiment are described in Wachtler et al.\n(in press) in great detail. Here we brie\ufb02y describe the portion of the experiment relevant\nto us. Two adult female rhesus monkeys were used in the study. Extracellular potentials\nfrom single isolated neurons were recorded from two macaque monkeys. The monkeys\nwere awake and were required to \ufb01xate a small \ufb01xation target for the duration of each trial\n(2500 ms.). Ampli\ufb01ed electrical activity from the cortex was passed to a data acquisition\nsystem for spike detection and sorting. Once a neuron was isolated, its receptive \ufb01eld was\ndetermined using \ufb02ashed and moving bars of different size, orientation, and color. All the\n\n\fResponse\n\n Response\nSpecification\n Units\n\nStimulus Channel\n\nBackground Channel\n\nResponse Specification\n\n\u0010\f\u0010\f\u0010\f\u0010\f\u0010\n\u0011\f\u0011\f\u0011\f\u0011\f\u0011\n\u0010\f\u0010\f\u0010\f\u0010\f\u0010\n\u0011\f\u0011\f\u0011\f\u0011\f\u0011\n\u0012\u0001\u0012\u0001\u0012\n\u0013\u0001\u0013\u0001\u0013\n\u0012\u0001\u0012\u0001\u0012\n\u0013\u0001\u0013\u0001\u0013\n\u0012\u0001\u0012\u0001\u0012\n\u0013\u0001\u0013\u0001\u0013\n\u0014\u0001\u0014\u0001\u0014\n\u0015\u0001\u0015\u0001\u0015\n\u0014\u0001\u0014\u0001\u0014\n\u0015\u0001\u0015\u0001\u0015\n\n\u0001\u0001\n\u0002\u0001\u0002\u0001\u0002\n\u0001\u0001\n\u0002\u0001\u0002\u0001\u0002\n\u0001\u0001\n\u0002\u0001\u0002\u0001\u0002\n\u0001\u0001\n\u0002\u0001\u0002\u0001\u0002\n\u0001\u0001\n\u0002\u0001\u0002\u0001\u0002\n\n\u0005\u0001\u0005\u0001\u0005\n\u0006\u0001\u0006\u0001\u0006\n\u0005\u0001\u0005\u0001\u0005\n\u0006\u0001\u0006\u0001\u0006\n\u0005\u0001\u0005\u0001\u0005\n\u0006\u0001\u0006\u0001\u0006\n\nElectrode\n\n\u0003\u0001\u0003\u0001\u0003\n\u0004\u0001\u0004\u0001\u0004\n\u0003\u0001\u0003\u0001\u0003\n\u0004\u0001\u0004\u0001\u0004\n\u0003\u0001\u0003\u0001\u0003\n\u0004\u0001\u0004\u0001\u0004\n\u0003\u0001\u0003\u0001\u0003\n\u0004\u0001\u0004\u0001\u0004\n\u0003\u0001\u0003\u0001\u0003\n\u0004\u0001\u0004\u0001\u0004\n\n\u0007\u0001\u0007\u0001\u0007\n\b\u0001\b\u0001\b\n\u0007\u0001\u0007\u0001\u0007\n\b\u0001\b\u0001\b\n\u0007\u0001\u0007\u0001\u0007\n\b\u0001\b\u0001\b\n\u0007\u0001\u0007\u0001\u0007\n\b\u0001\b\u0001\b\n\u0007\u0001\u0007\u0001\u0007\n\b\u0001\b\u0001\b\n\nStimulus\n Relays\n\nContext\n Relays\n\nStimulus\n Sensors\n\nContext\nSensors\n\nStimulus\n\nContext\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\t\u0001\t\u0001\t\u0001\t\u0001\t\n\n\u0001\n\u0001\n\u0001\n\u0001\n\n\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\n\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\n\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\n\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\n\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\f\u000b\n\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\r\f\n\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\u0001\u000e\n\u000f\u0001\u000f\u0001\u000f\u0001\u000f\u0001\u000f\n\nInput\n\nBackground\n\nStimulus\n\nBackground\n\nFigure 1: Left: A network with separable context and stimulus processing channels. Right:\nThe arrows connecting the stimulus to the unit in the center represent the classical receptive\n\ufb01eld of that unit. External inputs affecting the classical receptive \ufb01eld are called \u201cstimuli\u201d\nand all the other inputs are called \u201cbackground\u201d. In this preparation the stimulus and back-\nground channels are separable.\n\nneurons recorded had receptive \ufb01elds at eccentricities between\n\nand\n\n.\n\n\u0016\u0018\u0017\n\n\u0019\u001a\u0017\n\nOnce the receptive \ufb01elds were located, the color tuning of the neurons was mapped by\n\ufb02ashing 8 stimuli of different chromaticity. The stimuli were homogenous color squares,\ncentered on and at least twice as large as the receptive \ufb01eld of the neuron under study. They\nwere \ufb02ashed for 500 ms. Chromaticity was de\ufb01ned in a color space similar to the one used\nin Derrington, Krauskopf, and Lennie (1984). Cone excitations were calculated on the basis\nof the human cone fundamentals proposed by Stockman (Stockman, MaCleod, & Johnson,\n1993). The origin of the color space corresponded to a homogeneous gray background to\n). The three coordinate axis of the\nwhich the animal had been adapted (luminance 48 cd/m\ncolor space corresponded to L versus M-cone contrast, S-cone contrast, and achromatic lu-\nminance. The 8 color stimuli were isoluminant with the gray background, had a \ufb01xed color\ncontrast (distance from origin of color space) and had chromatic directions corresponding\nto polar angles\n\n.\n\n\u001c\u0018\u0019\u001a\u0017\n\nAfter several presentations of the stimuli, the chromatic directions for which the neurons\nshowed a clear response were determined, and one of them was selected as the second\nbackground condition. In the second condition, the color of the background changed during\nstimulus presentation (i.e., for 500 ms) to a different color. This color was isoluminant with\nthe gray background, was in the direction of a stimulus color to which the cell showed clear\nresponse, but was of lower chromatic contrast than the stimulus colors. In subsequent trials\ncombinations of the 8 stimulus and 2 background conditions were presented in random\norder.\n\nFor each trial we recored the number of spikes in a 100 ms window starting 50 ms after\nstimulus onset. This time window was chosen because color tuning was usually more\npronounced in the \ufb01rst response phase as compared to later periods of the response and\nbecause it maximized the effects of context. Data were recorded for a total of 94 units. Of\nthese, 20 neurons were selected for having the strongest background effect and a minimum\nof 16 trials per condition. No other criteria were used for the selection of these neurons.\n\n\u001b\n\f2 Results\n\nFigure 2 shows example tuning curves of 4 different neurons. The thick lines represent\nthe average response for a particular color stimulus in the plane de\ufb01ned by the \ufb01rst two\nchromatic axis. The dark curve represents responses for the gray background condition.\nThe light curve represents responses for the color background condition. The boxes around\nthe tuning curves represent average response rates as a function of stimulus onset for the\ntwo background conditions.\n\nTesting whether a code is factorial is like testing for the absence of interaction terms in\nAnalysis of Variance (ANOVA). The complexity (i.e., degrees of freedom) of an ANOVA\nmodel without interaction terms is identical to the complexity of the Morton-Massaro\nmodel. When testing for interaction effects we analyze whether the addition of interac-\ntion terms provides signi\ufb01cant improvement on data \ufb01t over a simple additive model. In\nour case we investigate whether the addition of non-factorial terms provides a signi\ufb01cant\nimprovement on data \ufb01t over the factorial Morton-Massaro model. For each neuron there\nwere 8 stimulus conditions, 2 background conditions, and 10 response alternatives, one per\nbin in the spike count histogram. The probabilities of the spike count histogram add up to\none thus, there is a total of \u0002\u0001\nindependent probability estimates per neuron.\nIn this case the Morton-Massaro model requires \u0001\b\u0006\n\t\f\u000b\r\u0006\n\u0006 parameters\n(Movellan & McClelland, 2001), thus there is a total of 63 nonfactorial terms.\n\n\u0016\u0003\u0001\u0005\u0004\n\n\u000f\u0007\u0006\n\n\u000b\r\u0006\n\n\u001c\u001a\u001c\n\n\u000f\u000e\n\n\t\u0014\u0013\n\nmodel (chi-square test, 63 degrees of freedom, \u0010\u0012\u0011\n\nFor each neuron we \ufb01tted Morton-Massaro\u2019s model and performed a standard likelihood\ntest to see whether the additional nonfactorial terms improved data \ufb01t signi\ufb01cantly (i.e.,\nwhether the deviations from the Morton-Massaro factorial model where signi\ufb01cant). We\nfound that of the 20 neurons only 5 showed signi\ufb01cant deviations from the Morton-Massaro\n). While the Morton-Massaro\nmodel had 81 parameters many of them were highly redundant. We also evaluated a 30 pa-\nrameter version of the model by performing PCA independently on the stimulus and on the\ncontext parameters of the full model and deleting coef\ufb01cients with small eigenvalues. The\n30 parameter model provided \ufb01ts almost indistinguishable from the 81 parameter model. In\nthis case only 4 neurons showed signi\ufb01cant deviations from the model (chi-square, 124 df,\n). On a pool of 20 neurons compliant with the Morton-Massaro model one would\n\u0010\u0015\u0011\nexpect the test to mistakenly reject 1 neuron by chance. Rejection of 4 or more neurons out\nof 20 is not inconsistent with the idea that all the neurons were in fact compliant with the\nMorton-Massaro model (\u0010\u0015\u0016\n\nFigure 2 shows the obtained and predicted spike count histograms for a typical neuron. The\ntop row represents the 8 stimulus conditions with gray background. The bottom row shows\nthe 8 conditions with color background. Lines represent spike count histograms predicted\nby the Morton-Massaro model, dots represent obtained spike count histograms.\n\n\t , binomial test).\n\n\t\u0017\u0013\n\n\t\u0014\u0013\n\nIn order to test the statistical power of the likelihood-ratio test, we generated 20 neurons\nwith random histograms. The histograms were unimodal, with peak response randomly\nselected between 0 and 9, with fall-offs similar to those found in the actual neurons and\nwith the same number of observations per condition as in the actual neurons. We then \ufb01tted\nthe 81-parameter Morton-Massaro model to each of these neurons and tested it using a\nlikelihood ratio test. All the simulated neurons exhibited statistically signi\ufb01cant deviations\n\n) suggesting that the test was quite sensitive.\n\nfrom the model (chi-square, 63 df, \u0010\u0015\u0011\n\n\t\u0017\u0013\n\nFinally, for comparison purposes we tested a model of information integration that uses the\nsame number of parameters as the Morton-Massaro model but in which the stimulus and\ncontext terms are are combined additively instead of multiplicatively, i.e.,\n\n\u0002\u0001\n\n\u0005\u000e\u0007\n\t\f\u000b\u000e\n\n\u0001\u0013\u0007\u0014\t\u0015\u0003\u0016\r\n\u0001\u0013\u0007\u0014\t\u0015\u0003\u0016\n\n\u0011\u0018\u0017\n\n\u0001\u0004\u000b\u0016\t\u0019\u0003\u0016\r\n\u0001\u0004\u000b\u001e\t\u0015\u0003\u001e\n\n\u0011\n\u0012\n\u001a\u001c\u001b\n\n(2)\n\n\u0001\n\u0001\n\u0016\n\n\u000f\n\n\t\n\u0019\n\t\n\u0019\n\u0016\n\t\n\u0019\n\u0003\n\u000f\n\u000e\n\u0011\n\u0012\n\u000e\n\u0011\n\u0017\n\fFigure 2: Effect of the stimulus and background on the chromatic mean tuning curves of\n4 neurons. The thick dark and light lines show mean responses in the isoluminant plane\n(x axis: L-M cone variation; y axis: S cone variation) for the two background conditions.\nBlack: gray background; Light: colored background. The 8 boxes around each tuning\ncurve shows the average response rate as a function of the time from stimulus onset for the\ntwo background conditions.\n\n\fFigure 3: Predicted (lines) and obtained (dots) spike count histograms for a typical neuron.\nThe horizontal axis represents spike counts in a 100 ms. window. The vertical axis rep-\nresents probabilities. Each row represents a different background condition. Each column\nrepresents a different stimulus condition.\n\nAfter \ufb01tting the new model, we performed a likelihood-ratio test. 80 % of the neurons\n\nshowed signi\ufb01cant deviations from this model (chi-square, 63 df, \u0010\n3 Relation to Tuning Curve Separability\n\n\t\u0017\u0013\n\n).\n\nIn neuroscience separability is commonly studied in the context of mean tuning curves. For\nexample, a tuning curve is called (multiplicatively) separable if the conditional expected\nvalue of a neuron\u2019s response can be decomposed as the product of two different factors each\nselectively in\ufb02uenced by a single stimulus dimension. An important aspect of the Morton-\nMassaro model is that it applies to entire response histograms, not to expected values. If the\nMorton-Massaro model holds, then separability appears in the following sense: If we are\nallowed to see the response histograms for all the stimuli in background condition A and\nthe response histogram for a reference stimulus in background condition B, then it should\nbe possible to predict the response histograms for any stimulus in background condition B.\nFor example, by looking at the top row of Figure 1 and one of the cells of the bottom row\nof Figure 1, it should be possible to reproduce all the other cells in the bottom row.\n\n\u0011\n\t\n\u0019\n\fObviously if we can predict response histograms then we can also predict tuning curves,\nsince they are based on averages of response histograms. Most importantly, there are forms\nof separability of the tuning curve that become only apparent when studying the entire\nresponse histogram. Figure 4 illustrates this fact with an example. The curve shows the\ntuning curves of a particular neuron from an experiment \ufb01tted using the Morton-Massaro\nmodel. These curves were obtained by \ufb01tting the entire spike count histograms for each\nstimulus and background condition, and then obtaining the mean response for the predicted\nhistograms. The large open circles represent the obtained average responses. The dots\nrepresent 95 % con\ufb01dence intervals around those responses. Note that the two tuning\ncurves do not appear separable in a discernable way (it is not possible to predict curve B by\nlooking at curve A and a single point of curve B). Separability becomes only apparent when\nthe entire histogram is analyzed, not just the tuning curves based on response averages.\n\nFigure 4: Tuning curves for a typical neuron as predicted by the Morton-Massaro model.\nThe two curves represent the average response of the neuron to isoluminant stimulus, for\ntwo different background conditions. The elongated curve corresponds to the homogenous\ngray background and the circular curve to the colored background. The open dots are the\nobtained mean responses. The dots represent 95 % con\ufb01dence interval of those responses.\nNote that the predicted curves do not appear separable in a classic sense. However since\nthey are generated by Morton\u2019s model the underlying code is factorial. This becomes ap-\nparent only when one looks at spike count histograms, not just mean tuning curves.\n\n\f4 Discussion\n\nWe introduced the notion of Morton-style factorial coding and illustrated how it may help\nanalyze information integration and perceptual organization in the brain. We showed that\nby focusing on average responses one may miss the existence of factorial coding mecha-\nnisms that become only apparent when analyzing spike count histograms. The results of\nour study suggest that V1 represents color using a Morton-style factorial code. This may\nprovide some cues to help understand perceptual coding in the brain and to develop new\nunsupervised learning algorithms. While methods like ICA (Bell & Sejnowski, 1997) de-\nvelop independent codes, in Morton-style coding the goal is to make two or more external\naspects of the world become independent when conditioning on internal representations.\n\nMorton-style coding is optimal when the statistics of stimulus and background exhibit a\nparticular property: when conditioning on each possible response category (i.e., spike\ncounts) the empirical likelihood ratios of stimulus and background factorize. Our study\nsuggests that Morton coding of color in natural scenes should be optimal or approximately\noptimal, a prediction that can be tested via statistical analysis of color in natural scenes.\n\nAcknowledgments\n\nThis project was supported by NSF\u2019s grant ITR IIS-0223052.\n\n5 References\n\nBell, A., & Sejnowski, T. (1997). The \u2019independent components\u2019 of natural scenes are edge \ufb01lters.\n\nVision Research, 37(23), 3327\u20133338.\n\nBrown, R. O., & MacLeod, D. I. A. (1997). Color appearance depends on the variance of surround\n\ncolors. Current Biology, (7), 844\u2013849.\n\nDerrington, A. M., Krauskopf, J., & Lennie, P. (1984). Chromatic mechanisms in lateral geniculate\n\nnucleus of macaque. Journal of Physiology, 357, 241\u2013265.\n\nDomingos, P., & Pazzani, M. (1997). On the optimality of the simple Bayesian classi\ufb01er under\n\nzero-one loss. Journal of Machine Learning, 29, 103\u2013130.\n\nMassaro, D. W. (1987a). Categorical perception: A fuzzy logical model of categorization behavior.\n\nIn S. Harnad (Ed.), Categorical perception. Cambridge,England: Cambridge University Press.\n\nMassaro, D. W. (1987b). Speech perception by ear and eye: A paradigm for psychological research.\n\nHillsdale, NJ: Erlbaum.\n\nMassaro, D. W. (1989a). Perceiving talking faces. Cambridge, Massachusetts: MIT Press.\nMassaro, D. W. (1989b). Testing between the TRACE model and the fuzzy logical model of speech\n\nperception. Cognitive Psychology, 21, 398\u2013421.\n\nMorton, J. (1969). The interaction of information in word recognition. Psychological Review, 76,\n\n165\u2013178.\n\nMovellan, J. R., & McClelland, J. L. (2001). The Morton-Massaro law of information integration:\n\nImplications for models of perception. Psychological Review, (1), 113\u2013148.\n\nStockman, A., MaCleod, D. I. A., & Johnson, N. E. (1993). Spectral sensitivities of the human cones.\n\nJournal of the Optical Society of America A, (10), 2491\u20132521.\n\nWachtler, T., Sejnowski, T. J., & Albright, T. D. (2003). Representation of color stimuli in awake\n\nmacaque primary visual cortex. Neuron, 37, 1\u201320.\n\nWesner, M. F., & Shevell, S. K. (1992). Color perception within a chromatic context: Changes in\n\nred/green equilibria caused by noncontiguous light. Vision Research, (32), 1623\u20131634.\n\nZeki, S. (1983). Colour coding in cerebral cortex: the responses of wavelength selective and colour-\ncoded cells in monkey visual cortex to changes in wavelenght composition. Neuroscience, 9,\n767\u2013781.\n\n\f", "award": [], "sourceid": 2229, "authors": [{"given_name": "Javier", "family_name": "Movellan", "institution": null}, {"given_name": "Thomas", "family_name": "Wachtler", "institution": null}, {"given_name": "Thomas", "family_name": "Albright", "institution": null}, {"given_name": "Terrence", "family_name": "Sejnowski", "institution": null}]}