A Model of Color Vision Based on Cortical
Reentry
Jonathan Wray and Gerald M. Edelman
It is known that the perceived color of an object depends on the
context in which it is viewed, its reflectance properties and the
spectral distribution of the illuminating light. What is not known,
however, is how the visual system functions so that color percepts
depend upon the integration of local and contextual cues. While
phenomenological theories of color vision exist, robust neurally
based theories consistent with psychophysical observations are
sparse. In the present study we develop such a theory and establish
its self-consistency by computer simulations of cerebral cortical
areas involved in color perception. The simulations test the
hypothesis that long-range reciprocal connections within and
between cortical areas mediate a dynamic process of reentry that
integrates contextual cues into the color percept When stimuli
similar to those used in psychophysical testing of contextual
influence were used, firing patterns consistent with psychophysical
data on color constancy and color induction in humans were
observed. Selective disruption of reciprocal inter- or intra-areal
connections reduced the correspondence between the model's
responses and the psychophysical data. The findings are consistent
with the proposal that reentrant interactions within and between
cortical areas provide a major basis for the context-sensitive
aspects of color vision.
1986; Brainard and Wandell, 1992), psychophysical studies of
lesion patients (Land et al, 1983) and normal subjects (Arend
and Reeves, 1986; Valberg and Jange-Malecki, 1990) clearly
implicate cortical processes in this phenomenon.
Studies of the visual cortex have revealed the existence of
functionally segregated areas and a high degree of intra- and
inter-areal connectivity (Zeki and Shipp, 1988; Felleman and Van
Essen, 1991). It has been demonstrated by means of lesion
studies (Heywood et al, 1987; Zeki, 1990; Walsh et al., 1992),
electrophysiology (Livingstone and Hubel, 1984; Ts'o and
Gilbert, 1988) and psychophysics (Livingstone and Hubel, 1987)
that color is analyzed to some degree in a segregated manner
from other visual attributes such as form, motion and depth.
These and other studies (Schiller et al, 1990; Heywood et al,
1992; Merigan and Maunsell, 1993; Barbur et al 1994) provide
considerable evidence that the chromatic and achromatic
aspects of the color percept have different cortical locations. The
chromatic aspect of color vision has been associated with a
specific visual pathway starting with the parvocellular layers of
the LGN and continuing via the cytochrome oxidase-rich blobs
of VI and thin stripes of V2 into area V4 (e.g. Zrenner et al,
1990). The evidence suggests that regions up to V2 are involved
with the local aspects of color vision (Livingstone and Hubel,
1984; Ts'o and Gilbert, 1988; Lennie et al., 1990; Walsh et al,
1992) and that area V4 plays a role in constructing the
contextual effects of color (Zeki, 1983a,b; Schein and Desimone,
1990; Walsh et al 1993). In addition to the pathways up to V4,
area IT has been shown to be involved in color vision (Dean,
1979; Heywood etal, 1988; Komatsu et al, 1992; Horel, 1994;
Heywood et al, 1995), although its exact functional role is not
known. These various observations give rise to two main
questions: (i) Given that the contextual aspects of color vision
have a major cortical component, what is the role of the
extensive collections of intra- and inter-areal connections in
mediating contextual influences? (ii) What role does area IT play
in chromatic vision? In the present paper we provide a
theoretical analysis aimed at clarifying answers to these
questions.
The perception of the color of an object is not solely dependent
upon the wavelength distribution of light reflected from it.
Rather, it is synthesized within the central nervous system as a
result of the interaction of this distribution with the wavelength
distribution of reflected light from surrounding parts of the
visual scene. Two examples of this context dependency of color
perception are color constancy, in which the perceived color of
an object remains approximately constant independent of the
wavelength distribution of the illuminant, and color induction,
in which the perceived color of an object can be changed by
surrounding it with an object of another color. Traditional
investigations of color vision have focused intensively on the
local properties of the visual system concerned with color.
Among the major contributions to this aspect of the theory of
color vision was the postulation, by Young and Helmholtz, that
our color vision is based upon three basic receptors (now known
to be the three cone types) and the demonstration by Hering that
we perceive color based on three opponent axes of red-green,
blue-yellow and white-black. In both of these major
contributions, the effect of context was not explicitly taken into
consideration. However, since the striking demonstration of
color constancy effects by Land (1964), various investigators
have concerned themselves increasingly with the contextual
aspects of color vision. This has led to a number of
computational or algorithmic approaches to the study of color
constancy (Land and McMann, 1971; Buchsbaum, 1980;
Hurlbert and Poggio, 1988; Gershon and Jepson, 1989; Forsyth,
1990). Although several authors have presented models of color
constancy based on retinal adaptation (D'Zmura and Lennie,
The Neurosciences Institute, 10640 John Jay Hopkins Drive,
San Diego, CA 92121, USA
It has previously been proposed that the dense, reciprocal
connectivity within and among areas of the cerebral cortex
subserves a dynamic process of reentry which consists of
ongoing, parallel signaling between and within brain areas
(Edelman, 1987, 1993). Previous modeling studies have shown
how this process can subserve properties such as the
synchronization of firing between distant neurons (Sporns etal,
1989), figure-ground segregation (Sporns et al, 1991) and
cortical integration and binding (Tononi et al, 1992). The
proposal on which the present theoretical study rests is that
reentry also leads to the integration of context during the
construction of the color percept. Using images obtained via
a CCD camera and video digitizer as input to computer
Cerebral Cortex Sep/Oct 1996:6:701-716; 1047-3211/96/$4.00
simulations, we describe and analyze a model incorporating
anatomical and physiological properties of certain parts of the
visual cortex. We show how reciprocal connections within and
among areas can give rise to neuronal responses consistent with
the properties of human color vision. In simulations performed
using the model, we show how color can be represented by
firing patterns within a population of neurons, each neuron of
which is broadly tuned with respect to color and responds to
white. These results indicate that the representation of a large
number of colors does not require neurons having sharply tuned
chromatic response functions and a null response to white. The
model can generate unique firing patterns for stimuli unique in
their hue or saturation, and these firing patterns vary in a
continuous manner when hue and saturation are continuously
varied. The response of the model to a set of psychophysically
based tests concerned with color constancy and color induction
illustrates that the neural circuits simulated in the model are
sufficient to mediate the integration of contextual cues into the
color percept. Selective perturbations of the different reciprocal
pathways illustrate their role in producing color constancy and
color induction. Taken together, these experiments illustrate
that, within the context of the model, reentry mediated by the
modeled cortical circuitry produces firing patterns consistent
with the phenomena of color constancy and color induction.
Materials and Methods
All simulations were run on Neumachine, a special-purpose
transputer-based parallel computer, built at the Neurosciences Institute,
using the Cortical Network Simulator (Reeke et at, 1990). This program
allows the user to design models consisting of multiple areas representing
different brain regions. Each region contains multiple neural units of
different types. Each unit, modeled as a leaky integrator, is assumed to
represent a group of interconnected neurons, and is characterized by a
specific set of parameters. The level of activity corresponding to each unit
can be viewed as representing the average firing rate of this collection of
cells, and its response properties can be considered as representative of a
typical response of a cell within the group. The model contained a total of
-65,000 units and 7,000,000 connections. General features of the model
are presented here; specific details are given in Appendix A.
Dynamics
At each computer iteration or cycle, the state of each unit is characterized
by an activation variable sKf). Each unit i receives individual connections
of one or more connection types from other units. Connections can be set
to be either voltage-dependent or voltage-independent. The total
contribution of input to unit i from voltage-independent connections,
At^if), is given by
where gi is a scale factor applied to all connections of type I, Mis the total
number of different connection types projecting to unit i, Cy is the
strength of the connection between a presynaptic unit j and unit /
(negative values imply an inhibitory hyperpolarizing, as opposed to a
shunting, connection), s/f) is the activity level of unity at time t and N, is
the total number of connections to unit / of type /.
The total contribution from voltage-dependent connections, 4/ r a (/), is
given by
/=1
j=\
where 0) is a decay coefficient which determines how much activity is
carried from one simulation step to the next and o"i(x) = 1.0 - sech (x/Ti)
is an increasing sigmoidal function whose slope is determined by 7). This
function assures a connection whose effect depends upon the
postsynaptic voltage: as the postsynaptic voltage increases, the
702 Cortically Based Model of Color Vision • Wray and Eddman
connection has an increasing effect, but if the postsynaptic voltage is
zero, the connection has no effect.
The activity level of unit / is given by
s, (f +1) = HA!" (0 + A™ (0 + OK,. (0 + n, (/))
(1)
where nKf) is a noise value added to the activity level at each cycle and <j>
is a limiting function given by
if
x>\
if
0<x <1
otherwise
A cycle of the simulation consists of calculating the current value of si for
each unit within the model according to Equation 1. Each stimulus was
presented to the model for 40 simulation cycles. This was empirically
determined as sufficient to allow the activity levels (ft) to settle to
relatively stable values. After each stimulus presentation, the model was
allowed to run for five cycles with no input, a period adequate to allow
the units' activation levels to decay to the resting noise level.
Stimuli
All stimuli presented to the model were obtained as signals from a CCD
camera and video digitizer. To approximate the spectral properties of the
cone photoreceptors, three sets of spectral filters were used in front of
the camera while acquiring the stimuli. [The filters used were all from the
Kodak photographic range. The L cone response was approximated by
filter number 102, the M cone response by the collection of filters CC50G,
CC50C and CC10G, and the S cone response by filters 1A and 39. These
were chosen empirically by matching the cone spectral responses
(Wyszecki and Stiles, 1982) to the spectral responses of the filters given
by the Kodak technical manual (Eastman Kodak, 1990).] This produces
three gray level images for each stimulus, each one corresponding to the
response of one of the cone types. The properties of the filters were
chosen to match the spectral absorption properties of human cones.
Although the filters do not match the cone absorption exactly, they have
approximately the same peaks and amounts of overlap between the
different cone types. After obtaining the raw images, several steps were
involved in producing the images used as input to the model. First, the
center portions (448 x 448 from 638 x 478) of the raw images were
spatially averaged to produce three images of size 64 x 64 pixels. After
spatial averaging, the images were scaled by a factor determined by each
channel's response to an achromatic stimulus (Munsell N6) such that each
channel had the same response to the achromatic stimulus.
The stimuli used consisted of various shapes made from Munsell matte
paper illuminated using two 500W quartz halogen lights. The color of the
illuminant was changed using lighting filters from the Bogen Cine range
of cool colors (FP207) and warm colors (FP208). This enabled a wide
range of stimuli, varying in both reflectance and illumination, to be used
and reported. As mentioned earlier, there is considerable evidence
concerning the separation of chromatic and achromatic aspects of the
color percept within the brain. Although the brain regions thought to be
involved in the construction of the chromatic axis are reasonably well
characterized, the neural basis of achromatic perception is not as well
localized. For example, a lesion study of specific layers of the LGN
(Schiller et aL, 1990) indicates that brightness perception can be
mediated by both the parvocellular and magnocellular layers of the LGN.
For this reason, it was decided to ignore the achromatic axis in the study
and use isoluminant stimuli. This was achieved by preparing stimuli made
from Munsell papers of a specific value 6, using stimuli from a plane of
constant value through the Munsell color solid, and by assuring, with a
light meter, that all iUuminants used had the same luminance. Gross
adjustments in luminance were achieved by using neutral density filters
(Bogen Cine-FP204) or, for small changes, by altering the voltage supply
to the lights. The specific form of the stimuli used will be discussed in the
presentation of each experiment.
General Architecture and Major Features
A major goal of the present study was to investigate the possible role of
reentrant interactions within the visual cortex in mediating context
LGN
V1/V2
m
64x64
64 x 64
32 x 32
16 x 16
Figure 1. Diagram of gross connectivity in the full model. Each box represents a particular modeled area. Lines represent patterns of connections; straight lines refer to
cortico-cortical connections both forward and backward, and circular lines represent long-range, intra-areal connections. The local circuitry within each area is not represented in this
figure (see text and Appendix A for details). Riled arrowheads refer to voltage-independent connections and open arrowheads to voltage-dependent connections. The size of the filled
triangles connected to the arrows represents the degree of convergence of the forward and backward connections between V1/V2 and V4. The size of the filled squares represents
the spread of the modeled long-range, intrinsic connections in both cortical regions. The data constraining the extent of these various connections are summarized in Table 5 of
Appendix A. The spatial dimensions of each area are in units; differences in these values from area to area are discussed in Appendix A.
dependent phenomena. Although there is evidence implicating V4 in
mediating long-range effects of color vision, the involvement of earlier
areas and backward connectivity from V4 to earlier areas cannot be
excluded. A detailed anatomical model of the cortical hierarchy up to V4
was therefore constructed and analyzed. The gross connectivity of the
model is shown in Figure 1.
As can be seen, the model consists of a number of areas, each
corresponding to an area within the visual cortex. Obviously, this does
not imply that the modeled areas have structural and functional
characteristics identical to those in the primate visual system. Instead,
only those properties assumed to be directly related to color vision were
modeled. To reflect this simplification, we adopt the convention of
indicating real areas in Roman type (e.g. V4) and modeled areas in italics
(e.g. V4).
The LGN contains six cell types corresponding to the color opponent,
center-surround cells seen in the parvocellular layers of the LGN
(Derrington et al, 1984). Region V1/V2 can be considered as modeling
the functional role of areas VI and V2 in color vision. Regions VI/V2 and
V4 are each modeled as containing four maps of excitatory and inhibitory
units, with units in the individual maps being tuned respectively to
respond maximally to red, yellow, green or blue stimuli. Note that while,
for descriptive purposes, these maps are considered in the model as
separate collections of units, in reality, the maps would be interspersed
and their units would spatially coexist within the cortex. The method by
which chromatic receptive field tuning is achieved is still an open
question and as this study was not explicitly concerned with this
problem, the proposal of De Valois and De Valois (1993) was utilized. The
justification for this choice is examined further in Discussion.
The four maps in V1/V2 and V4 are linked via extensive patterns of
reciprocal connectivity both within and between themselves. It is this
pattern of reciprocal connectivity that subserves the reentrant
interactions proposed to underlie contextual integration. The connection
patterns were such as to replicate the functional connectivity observed in
V4 (Schein and Desimone, 1990). This implies large, silent surrounds
with chromatic specificities giving rise to isochromatic inhibition and
opponent facilitation (e.g. a cell excited by red in its classical receptive
field is inhibited by red and facilitated by green in its non-classical
surround). To achieve this functional connectivity, excitatory units
receive long-range intrinsic connections from units of the opposite
chromatic specificity and inhibitory units receive long-range connections
from excitatory units of the same chromatic specificity. In addition, all
intrinsic excitatory connections are voltage-dependent. Thus cells are
only affected by stimulation of the surround when they are driven by a
stimulus in their receptive field. The anatomical arrangement of these
connections within V1/V2 and V4 corresponds to the long-range patchy
connections observed in the supragranular layers of visual cortex
(Yoshioka etal., 1992; Lund etal, 1993; Levitt et al, 1994b). In addition,
units in V1/V2 receive voltage-dependent connections from V4
corresponding to the backward connections observed in visual cortex
(Felleman and Van Essen, 1991; Rocklandef al, 1994). The patchy nature
common to forward connections and intra-areal connections is not seen
in backward connections (for a review see Salin and Bullier, 1995). To
reflect this, all backward connections were such that each V4 unit
projects back with equal strength to all units from which it received
connections. This results in a more diffuse pattern of connectivity than is
the case with the forward and intrinsic connections.
In the present paper, a potential functional role of IT in color vision is
proposed, namely to provide a representation in neural space of the
constructed color. This is obtained by remapping the activity of each of
the four mapped sets of V4 cells onto space within IT. Briefly, each IT
unit receives 16 connections from the center part of each V4 map. The
strengths of these connections follow four gradients: the gradients from
the red and green V4 units run in opposite directions to each other and
orthogonal to the gradients from the blue and yellow units, which
themselves run in opposite directions. Full details of this mapping is
given in Appendix A. Although this designated area is labeled IT, it is in
no way meant to model the complete functionality of the inferior
temporal cortex.
The major features of the model are summarized here; further details
of the exact parameters used are given in Appendix A. Among the most
important features of the model are the following.
1. Hierarchical organization: as in the visual system, the model was
constructed in a hierarchical manner such that, in the progression from
lower to higher areas, the receptive fields became larger and their tuning
properties changed. For example, in the progression from the LGN to
V1/V2 the units changed from being tuned to respond to differences in
cone signals to being tuned to the axes of perceptual color space.
2. Topographic mapping: each modeled area, except IT, was
topographically mapped with respect to the input image. As observed in
the visual cortex, this topography became less strict as the progression to
higher areas was made.
3. Inter-areal connections: forward connections were organized in
such a way as to determine classical receptive field properties, such as
chromatic tuning, of units in the higher area. In general, this means that a
large region of a lower area projected to a smaller region of a higher area
resulting in a progressive increase in classical receptive field size when
going from lower to higher areas. Specificity of the forward connections
resulted in a change in chromatic tuning properties from lower to higher
areas. In accord with the observed anatomy, the backward connections
had much less chromatic specificity than either forward or intra-areal
connections.
4. Local circuitry: the modeled cortical areas (V1/V2 and V4) consisted
of four types of excitatory and inhibitory units tuned to respond
maximally to red, yellow, green and blue, the axes of the perceptual color
space. The local patterning of excitatory and inhibitory connections
between units tuned to the same spectral region determined the dynamic
operating range for these units.
5. Intra-areal connections: areas V1/V2 and V4 had an extensive
pattern of long-range horizontal connections that provided the
anatomical basis of the observed influences beyond the classical
receptive field (Schein and Desimone, 1990). The connections were such
Cerebral Cortex Sep/On 1996, V6N 5 703
Pd-Pv
Pv
RJ
(b)
Figure 2. Quantification of color constancy and color induction, (a) Color circles produced in a hypothetical color constancy experiment. The three circles represent the model's
response to the 10 standard stimuli in three conditions: (i) under white light (circle 1); (ii) under colored light with no contextual background (circle 2); and (iii) under colored light with
a contextual background (circle 3). Movement from circle 2 to circle 3 when a contextual background is added indicates a degree of color constancy. Perfect constancy would be indi
cated by the overlaying of circles 1 and 3. (6) Two hypothetical population vectors produced by a yellow stimulus in a void (r>) and by the same stimulus with a red inducing surround
(pd). The rotation of the population vector in the green (G) direction indicates induction by the red surround. In both figures the marked vectors illustrate those used in calculating the
measure of constancy or induction that is described in the text. In both graphs Y = yellow, B = blue. R = red and G = Green.
as to mediate isochromatic inhibition and opponent facilitation following
the observed functional connectivity. Since not all units were connected
to all units, the connections formed a patchy mosaic of terminal arbors as
is known to occur in the cerebral cortex (Yoshioka et aL, 1992; Lund et
aL, 1993; Levitt et aL, 1994b).
6. Voltage-dependent connections: both the back connections from V4
to V1/V2 and the long-range intrinsic connections are modeled to be
voltage-dependent. This reflects the view (Tononi etaL, 1992) that these
connections are more likely to modulate rather than drive the firing of
their target cells. Although no direct evidence exists to support the
voltage dependence of V2 and V4 intrinsic connections, a study on similar
connections in area 17 of the cat highlights their voltage dependence
(Hirsch and Gilbert, 1991). In addition, the distribution of
voltage-dependent receptor types shows a preference for the
supragranular layers of the cortex (Fox et aL, 1989; Huntley et aL, 1994)
which form the major termination site of both intrinsic and back
connections but not of forward connections; this suggests that intrinsic
and back connections may be preferentially voltage-dependent.
7. Population response: the response of the model was judged by
observing the firing pattern in area IT which consisted of a population of
units that responded to all hues evenly spread around the hue circle. As
proposed, /T provides a representation in neural space of the constructed
color.
8. Anatomical constraints: in an attempt to model accurately the
anatomical characteristics of the relevant areas of visual cortex, the
relative convergence and divergence of forward connections, the spread
of intra-areal connections and the extent of backward connections were
all determined by reported quantitative data (see Appendix A) obtained
from single cell reconstruction experiments.
Population Response of IT
In order to characterize particular firing patterns within 77" and quantify
the model's response to different stimuli, an approach similar to the
population vector method of Georgopoulos et aL (1983) was utilized.
This method provides a way of representing the activity pattern of a
population of neurons as a vector. In short, each unit in the population
under consideration is tuned to a particular preferred stimulus parameter
[movement direction in the case of Georgopoulos etaL (1983), hue in our
case] and, at each point in time, that unit contributes to the resultant
vector in the direction of its preferred stimulus with a length proportional
to its activity at that time. The resultant population vector characterizes
the activity pattern of the complete population and enables comparisons
to be made between the model's responses to different stimuli. A similar
procedure has been utilized in analyzing the response of IT cells to the
presentation of faces (Young and Yamane, 1992).
The majority of the results in the next section will be presented as
population vector representations of the activity pattern within IT. These
are obtained by summing all vectors calculated by taking the value of the
average response of each unit over the last 10 cycles from the 40 cycles
used for each stimulus presentation and multiplying that value by a unit
vector in the preferred direction of that unit. The space chosen in which
to represent the results is the so-called perceptual space as defined by the
opponent axes of green-red and yellow-blue [cf. the uniform appearance
diagram of Abramov et al. (1990)]. Details of the calculation of the
preferred directions of 77" units within this space are given in Appendix B.
The angle of the population vector represents the constructed hue
and the length of the vector represents saturation. Note that this length is
not a function of activity level but rather is dependent upon the pattern
of activity within IT. Saturation reflects how far a stimulus is from
achromatic. This has a direct correspondence to the representation of
saturation within the model. An achromatic stimulus does not produce a
null response within IT but rather a symmetric response pattern around
the center position with a vector sum of approximately zero. As a stimulus
becomes more saturated, this activity pattern becomes less symmetric
and skews in the direction of the constructed hue. The more saturated the
color, the larger the skewness of the activity pattern and the longer the
population vector. In this manner, saturation is represented directly by
the length of the vector.
The maximum theoretical length of a resultant population vector was
used to normalize the axes used to represent the results. To calculate this
value, we assumed that the position of a unit within the 1 6 * 1 6 matrix of
units making up IT defines the preferred direction of that unit and thus a
maximum vector length would be produced if all the units in one half of
IT were fully active (si = 1) and all the units in the other half of IT were
silent (si = 0). Since we are assuming an idealized spatial positioning of
preferred directions, the response pattern so produced would be
symmetrical in the half that is active and produce a resultant vector that is
at right angles to the line dividing the active and silent halves of IT. The
length of this vector is given by
M = 2 1 1 cos(tan-1 (y/x)) = 84.8
l l
704 CorticaBy Based Model of Color Vision • Wray and Eddman
where Nx = Ny = 8 inasmuch as ITis modeled as a 16 * 16 array of units and
one-quarter of IT contains 8*8 units. In all the results presented in terms
of population vectors, the resultant vectors are normalized by dividing by
this value. Data points then represent the fraction of this theoretical
maximum that the model produces.
To calculate the population vector for a particular stimulus, we used
the average activity of a unit over 10 simulation cycles. In their study of
cells in motor cortex, Georgopoulos et al. (1988) used a variety of
averaging methods to calculate each cell's contribution to the resultant
vector. They found that all such methods gave reasonable results, with
some clearly better than others. We replicated such a comparison with
our model and found that the averaging method used had only minor
effects on the results.
Measures of Constancy and Induction
In order to compare the model's results to psychophysical data and to
compare the results of different models, for example after simulated
lesions, quantitative measures of color constancy and color induction
produced by the model are needed. The vectors used in obtaining these
measures are illustrated in Figure 2. Figure 2a illustrates a hypothetical
constancy diagram, with circles produced by the model's response to 10
stimuli under white light, under colored light with non-contextual
background and under colored light with a contextual background. The
diagram is of the same form asfiguresused later in the paper to document
the model's response in color constancy experiments. Figure 2fc
illustrates hypothetical population vectors produced by the model in
response to a yellow stimulus both in a void and when surrounded by a
homogeneous red background.
The measure of constancy used is
calculated from the response of IT are used to characterize the
results. An example of an average activity pattern in IT and the
corresponding population vector is shown in Figure 3b.
Local Properties
We perceive color as a continuum. To test the ability of the
model to produce firing patterns consistent with this perceptual
ability, it was tested with the standard 10 Munsell papers
(Munsell 10R 6/6-10RP 6/6), having a constant chroma and
value and differing only in hue, as well as with Munsell papers
having constant hue and value but differing in chroma. [The
Munsell system uses a three part code to specify the reflectance
properties of a colored object. For example, the notation 10R 4/6
describes an object with Munsell hue 10R, Munsell value 4/ and
Munsell chroma /6, which roughly corresponds to saturation.
For a full description of the Munsell color notation refer to
Wyszecki and Stiles (1982).] The model was presented with
stimuli consisting of a colored square on a black background
viewed under white light. The response of the model to these
stimuli is shown in Figure 4.
The results in Figure 4 show how the response varies in a
constant manner as the stimuli are varied in hue only, producing
the hue circle around the origin and as they are varied in chroma
only, producing the various saturation lines radiating away from
the origin.
Contextually Influenced
K, = 100x
(\
Properties
• — v •)• (v • — v
|(v ri -vj| 2
where vm/ and v^ are the population vectors produced by the model
when presented with stimuli i in the Mondrian and void conditions
respectively. Vrt is the population vector produced by the model with
stimulus i in the reference condition (white light and contextual
background). Thus, the value Ki represents the size of the shift towards
constancy expressed as a percentage of the amount required for perfect
constancy.
The measure of color induction used is given by
where pv and pa are the population vectors produced by the model for
the stimulus with no surround and the stimulus with a surround of radius
d respectively. In the basic experiments testing induction, an achromatic
(Munsell N6) center stimulus is utilized. In this case pB is almost zero and
the measure of induction used is simply the length of the population
vector produced.
Results
Chromatic Tuning within IT
The pattern of forward connectivity into IT provided units with
an even spread of preferred directions throughout the hue circle.
Figure 3« shows the distribution of preferred directions of units
in IT. The pinwheel pattern centered at the origin illustrates that
the distribution of preferred directions is relatively even. Note
that in addition to producing a population of units with an even
spread of preferred hues, the pattern of forward connectivity
also produces a 'chromatopic' map within IT: units close to each
other respond maximally to similar hues.
As discussed in the previous section, population vectors
Color Constancy
In order to test the hypothesis that long-range intra-cortical
connections in V4 and V1/V2 and cortico-cortical connections
between V4 and V1/V2 can mediate contextual integration,
experiments were conducted using stimuli similar to those used
to test color constancy. Physiological experiments on monkeys
using a color constancy paradigm showed that cells in area V4
responded in accord with the color observed by the
experimenter whereas cells in area VI responded to the major
wavelength component of light in the cell's receptivefield(Zeki,
1983b). To illustrate that units in the model exhibit similar
properties, the response of two unit types in both VI/V2 and V4
were recorded while being presented a stimulus under white
light and colored light both with and without a contextual
surround. In all of the experiments discussed in this section, the
Mondrian-like contextual surround consisted of a 5 * 5
checkerboard made up of squares of with equal Munsell values
but varying chromas. Figure 5 shows the average response of red
and green units when presented with a stimulus of Munsell 10R
6/6 under white light and illuminant 122 (fern green).
The data reveal a clear difference in the responses of units in
V1/V2 and V4. Under white light, red units in both V1/V2 and
V4 respond strongly and green units show a weak response.
When the illuminant is changed to fern green and the stimulus is
viewed in the void condition, the response of the red units drops
and the response of the green units rises in both cortical regions.
Under this condition, all units show firing which is purely
dependent on the wavelength distribution of light in their
receptive fields. When a contextual surround is added, a clear
difference between the response properties of V1/V2 and V4
units is seen. Units in V1/V2 show very little alteration in their
firing levels when a contextual surround is added; they continue
to fire in correlation with the local properties of the visual scene.
Units in V4, however, change their firing levels when a
contextual surround is added. Red units increase their firing
Cerebral Cortex Sep/Oct 1996, V 6 N 5 705
2 %
-1 —
R
Figure 3. Characterization of region IT. In both figures color is used as a heuristic indicator of value, not to represent actual or perceived color, (a) Distribution of preferred direction of
units. The position in the diagram represents the position within IT and the color represents the preferred direction of that unit. The angles refer to angles in the space defined in
Appendix B, with 0 corresponding to the V (yellow) axis. Note that black squares refer to units with a regression curve giving i2 < 0.85; these units are not used when calculating
subsequent population vectors. (/)) Example of an average activity pattern and resultant (unnormalized) population vector for a stimulus of 10Y 6/6 on a black background under white
light. The individual vectors contributed by each IT unit are shown in green and the resultant population vector in red. Note that the axes are shortened to show the individual vectors
in more detail and therefore the population vector is not shown at its full length.
0.5
0.5
G
G
0.3
0.3
10C
10BG
-0.1
D
10GY
0.1
B
J
/
-»10B
V
Q
10PB
1 3RP
-0.3
0.1
10Y
•f
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Y
-0.1
6/10
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(J
J"
6/2 C
B
-0.5
-0.3
-0.1
j
6/2
6/8
=>-©
Y
10R
-0.3
6/10
R
R
-0.5
-
6/1 I
0.1
0.3
0.5
-0.5
-0.5
-0.3
-0.1
0.1
0.3
0.5
Figure 4. Responses of the model to various stimuli of constant chroma (Munsell 6) but varying hue (Munsell 10R, 10YR throughiORP) and constant hue (Munsell 10R, 10Y 10G and
10B) but varying chroma (Munsell 2. 4, 6.8 and 10 for 10R. 10G and 10B. and 2.4,6 and 8 for 10Y). The points shown represent the end points of the normalized population vectors
calculated from the response of IT.
706 Cortically Based Model of Color Vision
• Wray and Edelman
Mondrian, white light
Void, green light
Mondrian, green light
V1/V2
0
10 20 30
cycles
40
50
0
10
20 30
cycles
40
50
0
10
20 30
cycles
40
50
0
10
40
50
0
10
20 30
cycles
40
50
0
10 20 30
cycles
40
50
V4
20 30
cycles
Figure 5. Response of red (solid lines) and green (dotted lines) units in V1/V2 (top) and V4 (bottom) under white light (left) and under fern green light in both the void condition
(center) and with a Mondrian-like surround (right). The lines give the average activation of 64 V1/V2 units and 16 V4 units at the center of the topographic maps when presented with
a stimulus of Munsell 10R 6/6. Thex-axis represents cycles of the simulation.
Illuminant 122 (l-ern Green)
Illuminant 110 (Middle rose)
0.7
0.7
G
O.b
-
Mondrian, white light
Void, colored light
Mondrian, colored light
Grey background, colored light
0.3
o.i
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0.1
-0.1
-0.3
-0.3
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Illuminant 134 (Golden amber)
Illuminant 136 (Pale lavender)
G
0.3
0.5
;
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R
Illuminant 202 (Half CT blue)
0.5
0.1
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-0.1
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-0.3
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-0.5
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i
0.7
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-0.7
-0.7-0.5-0.3-0.1 0.1 0.3 0.5 0.7
0.1 0.3 0.5 0.7
0.7
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R
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-0.7-0.5-0.3-0.1 0.1 0.3 0.5 0.7
B * T ^ | ^ ;
-0.5
R
-0.7
-0.7-0.5-0.3-0.1 0.1 0.3 0.5 0.7
Figure 6. Results of color constancy experiments for five different illuminants. In each case the black line shows the results for the non-void condition under white light' the green
line shows the void condition under colored light; the red line shows the non-void condition with a Mondrian-like background under colored light and the orange line shows the
non-void condition with a background of Munsell N6. The points shown represent the end points of the normalized population vectors. The difference between the black and green
circles represents the color shift that occurs as the result of changing the color of the illuminant For perfect color constancy the red or orange circle should overlay the black circle.
The deviation from this situation represents the deviation from ideal color constancy.
Cerebral Cortex Sep/Oct 1996, V 6 N 5 707
Table 1
Quantification of color constancy
Source of data
Mean constancy ± 1 SD (%)
Uicassen and Walraven 119931"
valberg and Lange-Malecki (1990)*
Arend and Reeves (1986)c
Arend etal. (19911*
Current model
72
69
19
15
38
±20
±15
±20
±23
±23
60
8
30
40
50
The table lists the mean and SD of constancy observed in the various studies expressed as a percentage of perfect constancy. All experimental values quoted are calculated using values obtained from
measurements taken from the original papers. The value of n is the number of measurements used in calculating the average constancy value. All experiments compared a void condition to a condition with
a Mondrian surround.
'Measurements taken from their figure 6.
'Measurements are taken from therr figure 2.
'Measurements taken from the 'paper match' data given in the left column of their figure 3.
''Measurements taken from the 'paper match' data given in the left column of their figure 4.
while green units decrease their activation levels and fire more in
accordance with what is seen under white light than would be
predicted from the local cues in the visual scene. These
properties of the model agree with the observed physiology
(Zeki, 1983b).
To characterize the model's color constancy behavior more
fully, experiments were conducted imitating psychophysical
investigations on color constancy (Arend and Reeves, 1986;
Valberg and Lange-Malecki, 1990; Arend et al, 1991; Lucassen
and Walraven, 1993). Each experiment consisted of presenting
the 10 standard stimuli to the model under three different
viewing conditions: (i) with a Mondrian-like background
(non-void viewing condition) under white light; (ii) with a black
background under colored light; and (iii) with a Mondrian-like
background under colored light.
Figure 6 shows the results of five experiments with five
different illuminants that produce color shifts towards different
parts of the perceptual color space. The model shows
qualitatively similar results to those seen psychophysically. In
particular: (i) when the illuminant color is changed and the
stimuli viewed in a void, the constructed color changes; (ii)
when a background context is added, the color circles shift back
from those produced in the void condition towards those
produced with white light. In the psychophysical data, when a
contextual background is added, the color matches move from
those obtained in the void condition towards those obtained
under white light; (iii) the shift that is observed when a context
is added does not produce ideal constancy in any situation; (iv)
the shape of the color circle produced in die void condition can
change when the illuminant is colored; and (v) when context is
added, the shape of the color circle is not altered dramatically
from that seen in the void condition but its center point is
shifted. These last two points are also seen in the psychophysical
data of Lucassen and Walraven (1993).
In order to compare our results quantitatively with data on
human psychophysics, the amount of constancy achieved by the
model was quantified using the measure, Ki, described in
Materials and Methods. The data in a number of quantitative
psychophysical studies of color constancy were analyzed using
the same measure. A comparison between the average constancy
values achieved by the model and those observed
psychophysically is given in Table 1. The model of Courtney et
al (1995), which investigates the possible role in color
constancy of interactions between retinal and cortical
mechanisms, shows an average degree of constancy of 20%.
The degree of constancy varies with the stimulus used, the
708 Cortically Based Model of Color Vision • Wray and Edebnan
particular illuminant and the observer. The quantitative
psychophysical data show considerable variance in the values of
color constancy, from zero or even negative values (Arend and
Reeves, 1986; Arend et al, 1991), to values approaching 80% of
perfect constancy (Valberg and Lange-Malecki, 1990; Lucassen
and Walraven, 1993). As shown in Table 1, the results in the
present study gave values in the mid-range of those reported by
various authors. It is important to note that our model only
attempted to model cortically mediated aspects of color
constancy. Non-central mechanisms, such as retinal adaptation
or the interaction of the color stream with the rest of the brain,
could change the degree of constancy observed.
The psychophysical data from the study of Lucassen and
Walraven (1993) showed effects not seen in the results presented
so far. With one particular illuminant (cyan) their results show a
flattening of the color circle due to the use of stimuli which
approached the physical limit of the monitor used to produce
them. Since we use actual pieces of Munsell paper rather than
simulated images, this cannot occur. However, if our
illumination level or model parameters were changed to produce
saturation in either the camera input or unit responses, then a
similar effect of a flattening of the color circle was seen (data not
shown). More importantly, when context was added to such
saturated stimuli, the resultant model response produced a
flattened color circle that was shifted with respect to the void
condition towards the circle seen under white light (data not
shown). This agrees, qualitatively, with the psychophysical data
of Lucassen and Walraven for the cyan illuminant.
In addition to Mondrian-like backgrounds, recent psychophysical experiments have shown that a uniform achromatic
background can also produce color constancy effects (Arend and
Reeves, 1986; Valberg and Lange-Malecki, 1990; Arend et al,
1991). Figure 6 shows the results from a similar experiment
conducted with the model. This experiment was identical to the
color constancy experiments described above except the
Mondrian surround was replaced by a uniform achromatic
surround (Munsell N6). The results agree with the psychophysical findings in that a similar degree of constancy occurs
with either a Mondrian or a uniform achromatic surround.
Color Induction
Anodier major contextual effect of color vision is color induction
or simultaneous color contrast (Jameson and Hurvich, 1959;
Kinney, 1962) in which an object appears to be of the opposing
color to an inducing surround. To test the model's ability to
produce this basic property of the color vision system, an
0.15
G
0.10
10R 6/6
0.05
0.00
10Y 6/6
1OP 6/6
\
s^
/
10B6/6
—n
Y
B
-0.05
1OG6/6
-0.10
R
-0.15
-0.15 -0.10 -0.05 0.00
0.05
0.10
0.15
(a)
— • 10R 6/6
- »10Y6/6
- •» 10G 6/6
—O10B6/6
-D10P6/6
0.15
0.12
c
o
^
0.10
0.08 ,
"" 0.05
0.03
0.00
0.0
4.0
8.0
12.0 16.0 20.0 24.0
r, (pixels)
(b)
0.00
0.0
4.0
8.0
12.0 16.0 20.0 24.0
r2 (pixels)
(c)
Figure 7. Results from the color induction experiments, (a) Response of the model to a basic color induction paradigm. The lines represent the normalized population vectors
produced by the model when presented with an achromatic stimulus (Munsell N6) surrounded by a uniform field of a given Munsell color. The color of this inducing surround is
indicated at the end of the vector. (6) Graph of induction, measured as the normalized length of the population vector, as a function of surround radius, t\. (c) Graph of induction as a
function of test-to-surround gap. In all experiments the inducing surround was one of five colors and the test-to-surround gap was Munsell N6. The inserts illustrate the spatial
arrangement of the stimuli in both experiments. The legends given between (6) and (c) apply to both graphs.
experiment was conducted replicating a basic color induction
paradigm. The stimuli presented to the model consisted of an
achromatic square (Munsell N6) surrounded by a field of one
color (the inducing color) viewed under white light. The results
of this experiment are shown in Figure la. The figure shows
induction effects in that an achromatic stimulus produces
responses consistent with the color opposing the inducing
surround.
A number of studies have also been conducted investigating
the effects of more complex inducing surrounds on the level of
induction and we replicate one of those here. The experiment
conducted was to investigate the effect on induction of surround
radius and distance to surround.
The experiment consisted of two parts. In the first part the
distance to the surround (r£) was fixed at zero (i.e. no
test-to-surround gap) and the surround radius (n) was varied. In
the second part the surround radius was fixed at full field width
and the distance to the surround, and therefore the size of the
gray ring separating the stimulus and the inducing surround was
varied. The results, shown in Figure 7, agree with the
psychophysical observations (Kinney, 1962; Walraven, 1973;
Tiplitz Blackwell and Buchsbaum, 1988; Wesner and Shevell,
1992; Singer and D'Zmura, 1994) in that increasing the size of
the surround increases the induction effect, while increasing the
stimulus to surround distance decreases the induction effect.
Role of Reentry
The results presented in the previous sections show how the
model produces responses consistent with the phenomena of
color constancy and simultaneous color contrast. The model
consists of three reentrant pathways mediated by the long-range
intrinsic connections within V1/V2 and within V4, and the
backward connections from V4 to V1/V2. In order to assess the
role of these different circuits in affecting the model's response,
selective lesion experiments were performed in which the
connections underlying one reentrant circuit were perturbed
and the effect on color constancy and color inductions observed.
Figure 8a shows the effect on constancy of cutting each of the
three different sets of connections for the standard stimuli under
- fern green light (no. 122). Figure 86 summarizes the effect on
constancy of the different lesions as measured with 50 different
stimuli, made up of the 10 standard stimuli under five different
illuminants. Note that in order to avoid any potential artifacts
due to uneven distribution of hues in the contextual surround a
Cerebral CortexSep/Oct 1996, V6N 5 709
100.0
5?
80.0
60.0
&
_
I
75.0
73
I
40.0
<D
Q.
20.0
nn
•
V . T . ^9- • « - •
1 2 3 4 5 6 7 8 9 10
stimulus (i)
"L
S
CD
s
3
g
100.0
O)
l_
|
c
X
50.0
-
*
25.0
age
w
G
o full model
B
a no intrinsic V1A/2, o- - •© no intrinsic V4
\ A A no V4->V1/V2
"*
T
0.0
V4
V1/V2
T
V4->VI/V2
-25.0
(b)
(a)
Figure 8. Effect of selective lesions on color constancy produced by the model, (a) Ki. the degree of constancy observed as a percentage of the ideal value, for 10 different stimuli (*
= 1 refers to 10R 6/6, x = 2 to 10YR 6/6 etc.) and an illuminant of fern green (no. 122). These graphs are typical of those seen with all illuminants.tf>)Effect on constancy averaged
over the 10 standard stimuli and five different illuminants. Bars represent the mean effect of the specific lesions by plotting the reduction in constancy as a percentage of the value
observed with the unlesioned model. Error bars are 1 SD around the mean.
homogeneous surround of Munsell N6 was used in these
experiments.
Figure 9 shows the effect of lesions on induction with a
background of 10R 6/6 surrounding a stimulus of 10Y 6/6. In
each case the amount of induction measured as a percentage of
that shown by the intact model is plotted against surround
radius. In this manner, the graph illustrates the effect of the
particular lesions as a function of surround size.
A number of conclusions can be drawn from the data: (i)
long-range intrinsic connections within V4 have the greatest
effect on both constancy and induction; (ii) long-range intrinsic
connections within V1/V2 have a smaller but significant effect
on constancy. Changes shown in Figure 8a are significant at P <
0.01 (n = 10) in the Wilcoxon signed-rank test. The changes
underlying the average effect shown in Figure 86 are significant
at P < 0.01 (n = 50) in the Wilcoxon signed-rank test. The V1/V2
intrinsic connections have an effect on induction that depends
on the size of the stimulus surround. With small surrounds, the
V1/V2 intrinsic connections can have as much effect on
induction as the V4 intrinsic connections; and (iii) backward
connections from V4 to V1/V2 do not affect constancy in a
significant manner. These connections have a small but
measurable effect on induction. This effect is also surround size
dependent, although to a smaller degree than with V4 and V1/V2
intrinsic connections. The differences in the shape of the curves
in Figure 9 can be related directly to the modeled anatomy and
are discussed below.
These selective lesion experiments demonstrate that both
color constancy and color induction are mediated by the system
as a whole and not by one specific circuit. Constancy or
induction cannot be removed by the lesioning of just one
pathway. The differential contributions of V4 and V1/V2
intrinsic connections to constancy and induction can be
explained by considering the relative spread of connections
within V4 as compared to within V2 (8 mm compared with 5
mm; see Table 5) and the -2:1 ratio of cortical magnification
factors between V2 and V4 (Van Essen and Zeki, 1978; Gattass et
aL, 1988). V4 intrinsic connections cover almost four times the
visual angle as do similar connections within V2 and so V4
intrinsic connections have more potential to affect contextual
integration than V2 intrinsic connections. Similarly, the back
710 Cortically Based Model of Color Vision
• Wray and Edclman
100.0
80.0
•5
•§
60.0
o
o
o no intrinsic V4
Q no intrinsic V1/V2
o- - © no V4 - > V1/V2
40.0
20.0
0.0
0.0
5.0
10.0 15.0 20.0 25.0
surround radius (pixels)
30.0
Figure 9. Graphs of the change in induction as the result of selective model lesions.
Each graph shows the change in induction, measured as a percentage of that observed
with the full model, against the size of the inducing surround.
connections from V4 to V1/V2 cover only a small visual angle
within the V1/V2 topographic map and so have less potential to
affect contextual integration than the V4 intrinsic connections.
The color induction stimuli further demonstrate the causal role
of this difference in visual angle coverage. The curves in Figure 9
can be viewed as illustrating the relative effectiveness on
induction of the different pathways in the intact model. A low
value indicates a large effectiveness. Consider the curves relating
to the intrinsic connections within both V1/V2 and V4. Both
curves show an initial increase of effectiveness as size of the
inducing surround is increased. This increase is due to an
increase in the number of connections within both regions being
activated. Thus both pathways become more effective at
producing induction. At a certain surround size, the relative
effectiveness of the V1/V2 intrinsic connections starts to
decrease, producing the U shaped curve shown. This reversal
occurs because, at a certain size of inducing surround, all the
intrinsic connections within V1/V2 are active. Increasing the
size of the stimulus further activates more V4 connections but
not more V1/V2 connections. Thus the relative effectiveness of
the V1/V2 connections decreases. Eventually the effectiveness of
the V4 connections reaches an asymptote when the stimulus size
is big enough to activate them all.
A similar effect is seen with the backward connections except
no initial increase in effectiveness is seen. This is because, with
the smallest stimulus used, all of the back connections afferent to
V1/V2 units at positions in the retinotopic map corresponding to
the position of the center stimulus are active. Thus, increasing
the surround size does not recruit any more back connections
and their relative effectiveness decreases.
Unlike the long-range intrinsic connections within VJ/V2 and
V4, the detailed functional connectivity of the backward
connections is not constrained by available data, other than the
fact that they are less specific in their terminations. If the
modeled connectivity of the backward connections is an
accurate reflection of the real anatomical arrangement then the
results presented above suggest that their role in contextual
integration is small but also not detrimental.
Discussion
The simulations described here are concerned with the effects of
context on color perception, as revealed by a dynamic, neurally
based model capturing known anatomical details of the primate
visual system. Since the demonstrations of contextual aspects of
color vision by Land (1964), the effects of context on color
perception have been studied by a number of different authors
from many different perspectives, including physiology and
psychophysics (McCann et al, 1976; Zeki, 1983a, b; Arend and
Reeves, 1986; Valberg and Lange-Malecki, 1990). What, is
lacking, however, are theories that incorporate the essential
features for color perception of cortical anatomy, dynamics and
physiology in accord with the reported data. To instantiate such
a theory, we constructed a model based on known anatomical
and physiological properties of the visual cortex, in particular
areas VI, V2, V4 and IT, and analyzed its behavior with stimuli
obtained from signals from a video camera. Tests of the model
were based on stimuli used in psychophysical experiments
designed to investigate color constancy and color induction.
In the remaining parts of this discussion, the salient results of
the study and links to the known physiology are considered in
greater detail. The proposed role of IT in color vision is also
discussed in more detail. Finally, the relationships to previous
models and theories of color vision are examined.
Contextual Effects
A major result of the tests of the model is that the reentrant
interactions within and between V4 and V1/V2 can give rise to
firing patterns compatible with the psychological phenomena of
color constancy and color induction. Specifically, the model
demonstrates that both phenomena can be mediated by the same
anatomical arrangement and that the effects can be nonlocal, e.g.
the dependence of induction on the distance to surround
parameter. The long-range intrinsic connections within V1/V2
and V4 and the backward connections between V4 and V1/V2
serve to mediate reentrant interactions that can span noncontiguous regions of the visual field, thus producing these
non-local effects.
A simulated selective lesion study of the model illustrated how
the phenomena of color constancy and color induction are the
result of system-wide interactions; neither phenomenon can be
destroyed by the lesion of one circuit alone. In addition, the
testing of the lesioned model with different stimuli illustrated
how the role of specific pathways is dependent on the stimulus
configuration used. For example, the backward connections
made no significant contributions to color constancy but had an
influence on color induction. This occurs because the
contextual background in the color induction experiments
consists of one hue, compared with a mixture of many hues in
the color constancy experiments, and so only a subset of all the
backward connections are active, producing a differential
influence on units within V1/V2. The relative contribution to
induction of all three sets of connections was shown to be
dependent on the size of the inducing surround. This effect is a
direct result of the relative spread of these connections over the
cortical maps. The changes seen in the neural equivalent of the
psychological phenomena of color induction are directly
dependent on changes made to the underlying anatomy.
Role of IT in Color Vision
In this paper we suggest that a functional role of area IT in color
vision may be to provide a spatially organized map which
explicitly represents a given color. This was obtained by
remapping the activity levels of four sets of cells within V4 onto
neural space within IT. The remapping constitutes a change
from an implicit representation of hue and saturation, where
color is represented as the ratio between the firing levels of four
populations of cells, to an explicit relationship, in which color is
represented by specific firing patterns within one population of
cells. Our proposal is consistent with evidence in the literature
concerned with the role of IT in color vision. Lesion data
(Heywood et al., 1995) comparing monkeys with lesions to V4
and lesions to IT suggest that IT but not V4 is necessary for color
vision. The data reveal that the IT lesioned animals show
performance degradation on color related tasks that is similar to
that shown by humans with cerebral achromatopsia, suggesting
that IT corresponds to a brain region that is needed for conscious
experience of color. In addition to the lesion data, cooling
experiments (Horel, 1994) have shown IT to be involved with
color and anatomical studies have shown IT to be a major
recipient of V4 projections (Felleman and Van Essen, 1991).
Moreover, electrophysiological recordings have shown
chromatic specificity of cells within IT (Komatsu etaL,l992).
In the model, the pattern of connections from V4 to IT
produces a 'chromatopic' map within IT: units spatially close to
each other respond to similar colors. Although this spatial
mapping is not used in the results presented here, the existence
of such a topography is an interesting possibility. Some evidence
exits as to the existence of columns within IT (Fujita, 1993) in
which neurons with similar response properties are grouped
together. However, it is not known whether such columns are
organized in any systematic manner, and the existence or
absence of a chromatopic organization within IT remains a
question open to experimentation.
Traditionally, IT has been associated with higher level aspects
of vision (see e.g. Tanaka, 1992; Miyashita, 1993; Desimone and
Duncan, 1995) such as size and spatial invariance, memory and
attention. The proposed role of IT in color vision obviously does
not exclude involvement of this area in other aspects of vision.
Indeed, the response of IT can be viewed as producing a spatially
invariant representation of the constructed color which is a
direct parallel of a proposed role of IT in form vision (e.g.
Lueschowef a£, 1994; Itoet al, 1995).
Other Models of Color Vision
Computational approaches have been employed to characterize
color vision and may be considered complementary to those
used in the present work, hi such a computational approach,
Cerebral Cortex Sep/Oct 1996, V 6 N 5 711
color constancy is expressed as the problem of discounting the
illuminant or the recovery of reflectance (Hurlbert, 1986). These
approaches, however, produce a system of under-determined
equations and additional assumptions must be made about the
properties of the visual scene, the illuminant or both (for a
review see Lennie and D'Zmura, 1988).
In addition to purely computational approaches, a number of
neural network-based methods have been utilized to study color
constancy. Hurlbert and Poggio (1988) showed how multi-layer
perceptrons and radial basis function networks could be trained
to recover reflectance. Although this approach utilizes neural
networks, it says little about the actual underlying neural
mechanisms involved in color vision. Dufort and Lumsden
(1991) constructed a network model based on double-opponent
cells that was able to show color constancy and color
categorization behavior. However, the existence of
double-opponent cells in the visual cortex has recently been
questioned (Lennie and D'Zmura, 1988; Ts'o and Gilbert, 1988)
and the model of Dufort and Lumsden does not attempt to
address the role of cortical circuitry in color vision.
In a recent simulation study (Courtney et aL, 1995) the
relative contribution of retinal and cortical mechanisms to color
constancy was studied; a comparison between the two models is
useful. Our goal in the present study was to construct a model
based on the anatomical details of the visual cortex in order to
investigate the cortical bases of color vision. As such, the model
presented here differs in a number of ways from that of Courtney
et aL: (i) our model simulates multiple cortical areas
corresponding to V1/V2, V4 and IT; (ii) it has a large collection
of both intra- and inter-areal reciprocal connections. The
convergence-divergence of the forward connections and the
lateral extent of the intra-areal and backward connections are
constrained by quantitative neuroanatomical data; (iii) changes
in the responses of our model are documented by observing the
changes in firing patterns in a non-retinotopically mapped
population of neuronal units; (iv) our model does not require the
proposal of a cell type that has not been observed in V4 or of a
very specific 'push-pull' circuitry to produce a response
consistent with color constancy and color induction; and (v) the
model of Courtney et al. had the virtue of showing how both
retinal and cortical stages can play a role in color constancy and
color induction. Our model does not simulate retinal adaptation
and the contribution of this mechanism to color perception after
incorporating it into the model has not yet been studied.
Limitations and Experimental Tests
The units in region V1/V2 of our model are chromatically tuned
to respond maximally along the perceptual color axes following
the proposal of De Valois and De Valois (1993). Their model
shows how, by combining the output of the different cell types
in ratios of their relative abundance, the S+ and S- cells can be
utilized to provide a rotation of the cardinal axes (seen at the
LGN) to the perceptual axes. The areas of visual cortex involved
in this rotation are not known but evidence suggests that cells in
the CO-rich blobs of VI (Livingstone and Hubel, 1984; Ts'o and
Gilbert, 1988; Hubel and Livingstone, 1990) and thin stripes of
V2 (DeYoe and Van Essen, 1985; Hubel and Livingstone, 1987;
Levitt et aL, 1994a) are tuned to the perceptual axes.
Controversy still exists, however, as to the existence of such
tuning (Lennie et aL, 1990).
Within our model, V4 units were also tuned, locally, to the
perceptual color axes. The study of Schein and Desimone (1990)
shows three definite peaks in the relative abundance of V4 cells
712 Cortically Based Model of Color Vision • Wray and Edelman
tuned to different wavelengths, with the peaks occurring at
approximately the wavelengths of red, yellow and blue light. A
fourth peak at green, while not as definite, does suggest itself in
their data. The model presented here is dependent on the
existence of such chromatic tuning at stages V1/V2 and V4. If
this turns out not to occur in the primate visual system, the
fundamental assumptions of the model will have to be altered.
The long-range intrinsic connections in both V1/V2 and V4
are defined according to the functional connectivity of V4 cells
highlighted by the study of Schein and Desimone (1990). This
assumption seems reasonable since analogous functional
connectivity (Allman et aL, 1985; Desimone et aL, 1985;
Knierim and Van Essen, 1992) is seen in other visual areas,
suggesting the possibility that this functional connectivity is a
fundamental property of visual cortical areas. If the actual
functional connectivity in VI or V2 is radically different from
that in V4 then this aspect of the model will have to be changed.
Although there is considerable evidence for the separation of
function within the visual cortex, a fact that allows us to consider
the color stream in isolation, there is also evidence of
interactions between visual submodalities. For example, recent
psychophysical studies (Wesner and Shevell, 1992; Zaidi et al.,
1992; Bauml, 1994; Jenness and Shevell, 1995) have shown how
color perception can be altered by the spatial organization of the
visual scene. An extension of the current model to study the
interactions of different anatomical pathways may shed light on
how the perception of color is affected by shape or motion.
The present results concerning context dependent effects
could be tested with a number of different neurophysiological
experiments. The selective lesion experiments suggest that, with
small stimuli, V2 may have as much influence on contextual
integration as V4. This could be tested directly by recording from
V2 while a monkey is viewing stimuli designed to test color
constancy or color induction. With large stimuli, the expected
result would be that the firing of V2 neurons would be correlated
with the local wavelength distribution of light reflected from the
stimulus, whereas with small stimuli, V2 neurons would have
firing rate correlated more •with the perceived color. Other
experiments that suggest themselves, but are not yet technically
feasible, involve the selective deactivation of one or more of the
reentrant pathways modeled in this study. Such experiments
would directly confirm or contradict the results of the selective
lesion experiments presented here.
The proposal concerning the role of IT in color vision could be
tested experimentally by recording the response of a population
of IT neurons to chromatic stimuli. A population vector could
then be constructed along the lines outlined in Materials and
Methods. Comparison of such a vector with the actual object
color would provide a test of this hypothesis.
Analogous Effects in Other Submodalities
Phenomena analogous to color induction exist in other visual
submodalities, such as in .motion and form vision. Within motion
vision there exists an analog of brightness induction (very similar
to color induction) in which the perceived velocity of moving
dots is altered by the velocity of surrounding dots (Loomis and
Nakayama, 1973). The induced motion is in the direction
opposite to the inducing motion field. In the form domain the tilt
illusion forms an analogous perceptual phenomenon to color
induction. In this illusion the perceived angle of a bar can be
made to change when a surround of angled bars is introduced.
The shift in perception is away from the angle of the inducing
bars. Neurophysiological studies of motion sensitive cells in MT
(Altaian et al., 1985), of form-sensitive cells in V4 (Desimone et
aL, 1985) and of cells in VI (Knierim and Van Essen, 1992) have
shown analogous results to the V4 chromatic study of Schein and
Desimone (1990). The modeling study of Gilbert and Wiesel
(1990) suggests that such long-range interactions could explain
the tilt illusion. However, in area 17 of the cat, they found that
the majority of cells did not possess appropriate receptive field
properties. A similar study in monkey (Knierim and Van Essen,
1992) did, nevertheless, find cells with the appropriate response
properties. These results suggest that mechanisms similar to
those described in the present paper may apply more generally
to other systems. The regular pattern of long-range patchy
connections seen throughout the cortex may serve to integrate
context into visual percepts for various submodalities. This
generalization could be tested relatively easily by changing the
modal properties of units within a model similar to the one we
have presented here.
Table 2
Specific parameters used to construct the receptive field properties of the LGN units
Center connections (1 off)
Surround connections (8 off)
Cell type
Source image
Strength
Strength (S]I
Strength (M)
Strength (L)
L+
M+
S+
L
M
S
L
M
S
40.32
40.32
8.064
-40.32
-40.32
-8.064
-0.315
-0.315
-0.063
0.315
0.315
0.063
-1.575
-1.575
-3.15
-3.15
-0.63
3.15
3.15
0.63
LMS-
-0.315
1.575
1.575
0.315
In all units the size of the center is one pixel and the surround is 3 x 3 pixels with no connection
to the center pixel (i.e. a total of eight connections from each input image defines the surround).
Note that the connections to the S + and S- units are scaled down by a factor of 5. This is to
ensure a reasonable dynamic operating range for these cells; this scale factor is corrected for in
the subsequent forward connections from LGN to V1/V2.
Conclusion
The major goal of this work was to construct an anatomically and
physiologically based model of the color stream of the visual
cortex in order to investigate the neural bases of color
perception. The model investigates the role of several cortical
areas in color vision. The main results illustrate how a system of
lateral and backward connections within and between cortical
regions can mediate the integration of contextual cues into the
color percept. Selective lesion experiments demonstrate the
dependence of color constancy and color induction on all three
reentrant pathways. These experiments also indicate that the
relative contribution of the different pathways to contextual
integration can vary depending on the stimulus properties.
Table 31
Values of the scale factor Igi) for the connections from LGN to VI/V2
R
L+
M+
S+
LM~
S-
1.2
1.2
0.6
-
Ri
Y
0.27
1.2
0.6
1.2
0.27
0.135
-
Yi
G
Gi
B
Bi
0.27
_
0.6
1.2
_
1.2
_
_
_
0.135
0.6
1.2
1.2
_
-
0.135
0.27
0.27
_
0.135
0.27
0.27
_
0.27
_
-
R refers to an excitatory unit tuned to red and Ri to an inhibitory unit tuned to red. The notation
extends to Y, G and B for yellow, green and blue tuning. The relative strengths of these connection
scale factors are in accordance with the model of De Valois and De Valois (1993). which specifies
a ratio of connection strengths of L:M:S::10:5:2. Note that the connections from S + and S- are
scaled up by a factor of 5 to account for the scaling down of connections into LGN.
Appendix A: Model Specifics
The general architecture of the model and the observations
forming the basis of its construction were described in the main
text. This appendix describes each area in more detail, outlining
all the parameters used. Although units in each modeled region
had specific parameters, a number of model parameters apply to
many or all areas and will be described first. Several of these
parameters are generally not constrained by experimental data
and values were chosen to ensure that the model operated
within reasonable dynamic bounds (e.g. so that no units are
continuously saturated).
All units within the model had the same persistence
parameter co = 0.3, and at each time step units in LGN had noise
added to their activation levels. This noise value was drawn from
a Gaussian distribution with a mean of 0.01 and an SD of 0.005.
All voltage-dependent connections had the same sigmoidal
function defined by TI = 0.038. All c//s, except those defining the
receptive field properties of the LGN cells and those connections
from V4 to IT, were random values drawn from a Gaussian
distribution with a mean of 0.5 and an SD of 0.1. Specificities of
connection strengths between different unit types were defined
by the scale factor, gi and these values are described later.
LGN
The receptive field properties of the LGN cells were constructed
using the forward connections from the input image sampled
from the camera. The scheme of De Valois and De Valois (1993)
was used to construct the chromatic specificity of the LGN units
and the V1/V2 units. Following the data of Derrington et al.
(1984), the overall strengths of connections to the center and
Table 4
Values of the scale factor igi) for connections from V1IV2 to V4
W2R
V1IV2Y
W/V7G
W/V2B
V4R
V4 Ri
V4Y
V4Yi
0.15
0.035
0.05
0.0115
-
-
0.035
0.15
0.035
0.0115
0.05
0.0115
0.035
0.0115
-
-
V4 G
0.035
0.15
0.035
V4 Gi
V4 B
V4Bi
_
0.035
0.0115
0.0115
0.05
0.0115
0.035
0.15
0.0115
0.05
Note that all units receive 10 connections from a 4 x 4 area on each V1/V2 map that projects to
that particular unit type.
surround were equal. Table 2 lays out the specific parameters
used in constructing the receptive field properties of these cells.
V1/V2 and V4
The scale factors used for the forward connections between the
LGN and V1/V2 and between V1/V2 and V4 are given in Tables
3 and 4 respectively.
hi addition to the forward connections units in V1/V2 and V4
have four major connection types.
1. Local excitatory: Excitatory units within VI/V2 and V4
receive four voltage-dependent connections from units of the
same chromatic specificity within a 2 x 2 area centered at each
unit. Within both regions, the scale factor is g/=0.15. Inhibitory
units within V1/V2 and V4 also receive four voltage-dependent
connections from excitatory units of the same chromatic
Cerebral Cortex Sep/Oct 1996, V 6 N 5 713
specificity. Again the connections are from a 2 * 2 area centered
on the topographic position of the receiving cell and with gi =
0.035.
2. Local inhibitory: Excitatory units within V1/V2 and V4
receive three sets of connections from inhibitory units tuned to
the same chromatic region and the two neighboring regions (e.g.
a yellow unit receives connections from yellow, red and green
inhibitory units). Each set of projections consists of four
connections from a 2 x 2 region centered on the topographic
position of the receiving unit. The scale factors for connections
within V1/V2 were gi = 0.34 from units tuned to the same
chromatic region and gi = 0.1 from cells tuned to the neighboring
region. Within V4, the scale factors were gi = 0.27 and gi = 0.05Inhibitory units received four connections from inhibitory units
of the same chromatic specificity, again in a topographic
manner, with gi = 0.023 in both V1/V2 and V4.
3- Long range excitatory: Both excitatory and inhibitory units
received long-range voltage-dependent, excitatory connections.
These connections were arranged so that the probability for any
unit to receive a connection from another unit [p(connect)] fell
off exponentially with distance between the cells. This fall-off
was approximated by a square wave starting value of p(connect)
= 0.7 at a distance defined by an area of 3 x 3 units centered on
the topographic location of the receiving unit and falling to a
value of p(connect) = 0.1 at a distance defined by the maximum
spread of intrinsic connections. Each step width was two units
wide in each direction. Within V1/V2, the area covered by the
connections was 17x17 units and the scale factor wasg/ = 0.005.
Within V4, the area covered by the connections was 27 x 27
units and gi = 0.002. hi both areas the chromatic specificity was
such that excitatory units received connections from units of the
opposing chromatic tuning and inhibitory units from units of the
same chromatic tuning.
4. Backward excitatory. Units in V1/V2, both excitatory and
inhibitory, received excitatory voltage-dependent connections
from V4. Each unit received three sets of 21 connections each
from a 7 x 7 area arranged topographically. The chromatic
specificity was such that a V1/V2 unit received connections
from units of the same chromatic specificity •within V4 to which
it projects with a scale factor of gi = 0.005- The strength of the
long-range excitatory connections in both V1/V2 and V4 and the
backward excitatory connections were adjusted so that all
connection types had an equal average effect on the
post-synaptic unit.
To model the anatomy of visual cortex accurately up to V4, an
attempt was made to quantify as much of the connectivity as
possible. As a basis for the quantification, it was decided that
four modeled units should correspond to an area of one
experimentally observed patch of axonal arbors, -340 um in
diameter in both V2 and V4 (Lund et al, 1993). In both of these
areas the average observed inter-patch interval was -650 m. In
addition, anatomical data from V2 was used to define the
connectivity to, within and from V1/V2. These assumptions
allowed V1/V2 to be modeled as an array of 64 x 64 units and V4
as an array of size 32 x 32, which, from empirical observation,
provided enough spatial resolution for the model's purpose. The
2:1 reduction in size between V1/V2 and V4 corresponds to the
approximate 2:1 reduction in cortical magnification factor
between V2 and V4 (Van Essen and Zeki, 1978; Gattass et al,
1988). Using these assumptions as a basis, various anatomical
714 Corticauy Based Model of Color Vision
• Wray and Edclman
Table 5
Summary of the anatomical data used to establish various model parameters
Parameter
Anatomical data
V1/V2 -»V4
convergence and
divergence
a cell in V2 projects, on Rockland (1992)
average, to 2.5 patches
in V4 spaced 1-2
inter-patch distances
apart
References
Extent of V1/V2 intrinsic upper bound - 5 mm
patchy connections
Lund eta/. (1993);
Levitt eta/. (1994b)
Extent of V4 intrinsic
patchy connections
Yoshiokaefa/. (1992);
Lund era/. (1993)
upper bound - 8 mm
V4 - » V1/V2 divergence 1 V4 cell projects over Rockland et al. (1994)
3-5 mm of V2
Model specifics
on average, a VIA/2
unit wSI project to 2.5
V4 units over an area of
2 x 2 inter-patch
intervals. This is
implemented by having
each V4 unit receive 10
connections from a 4 x
4 grid of V1IV2 units
- 5 mm is equivalent to
7.7 inter-patch intervals
and so t o - 1 7 W/V?
units
8 mm is equivalent to
12.3 inter-patch
intervals and so to -27
W units
4 mm is equivalent to
6.2 inter-patch intervals
and so to 14 V1/V2
units. Since V4 is half
the size of V1/V2. one
VI/V2 cell receives
from a 7 x 7 V4 grid
measurements can be translated into model parameters and these
are summarized in Table 5.
IT
The chromatic tuning of units in IT was constructed to reflect
those actually observed in IT: a population of cells with broad
chromatic tuning, a non-null response to white stimuli and a
uniform distribution of preferred hues (Komatsu et al, 1992). In
all the experiments conducted with the model, the stimulus, as
opposed to the contextual surround, was in the center of the
visual field. Thus to ensure that the firing patterns within FT
depended on the constructed color of the stimulus, the activity
levels of the central 4*4 units of V4 were remapped onto space
in IT. This produced activity patterns within IT that depend on
the relationship between the activity of the different units within
V4. Each /Tunit received 16 connections from each of the four
V4 unit types. The strength of all connections (.aj) was random
and was drawn from a Gaussian distribution with an SD of 0.15.
The mean of the distribution was determined by a gradient
defined by the position of the receiving unit in IT. The gradients
were defined to ensure an approximately even distribution of
preferred directions (hue that excites a unit maximally) around
the color circle. Mathematically the gradient used was defined
by:
where x and y are the relative positions in the half of IT being
considered. The Cxy values define the corner points of the
gradient and are given by 0.5 for the maximum, 0.25 at the top
left and right, -0.2 at the bottom center and -0.1 at the bottom
left and right. The distribution of preferred directions is obtained
by having the maximum strength connections at different
positions in IT depending upon the chromatic specificity of the
V4 units sending the projections. For example, for V4 red units
the maximum point was at the bottom, for green units it was at
the top, for yellow units on the right and for V4 blue units it was
on the left.
Appendix B: Calculation of IT Preferred Directions
In order to calculate the preferred directions of units within IT,
we presented the model with 10 different square stimuli on
black backgrounds under white light. The stimuli were defined
in terms of their Munsell notation and were chosen to cover the
entire color circle at approximately equal intervals. Figure 4
gives the full Munsell notation of the stimuli used. For each
stimulus, the activity of each unit in IT was recorded for a total of
40 simulation cycles, and the average activity level, over the last
10 cycles, scaled by the total mean activity of IT over the same
cycles, was calculated for each unit. Using these 10 average
values, a sinusoidal regression curve of the form,
a(9) = bo +b[ cos(9) + &2 sin(e)
was calculated for each unit using least-squares regression. The
maximum of the sinusoid was then obtained. This maximum
was then taken as the preferred direction of that particular unit.
If the r2 statistic for a particular regression curve was <0.85 (i.e.
the regression explained <85% of the data being fitted) then that
unit was not used in subsequent calculations of population
vectors (this means, in effect, that the particular unit in question
was not tuned to a particular hue). No transformation exists
between the Munsell color space (in which our stimuli are
defined) and perceptual space, and so the formula given by De
Valois and De Valois (1993) for the response of the perceptual
axis in terms of the response of the three cones was used to
define the axes. These are given by
YB=13OL-95M-25S
GR = -90L+ll5M-25S
where L, M and S are the response of the longwave,
mediumwave and shortwave cones respectively. Practically, the
average pixel value of each of the three gray images obtained
•when viewing a square of a particular stimulus color under white
light was obtained and then used to calculate the positions in
perceptual color space. Using these 10 basic stimuli, the
preferred directions of the units in IT were calculated as
described above.
Notes
This work was carried out as part of the theoretical neurobiology
program at The Neurosciences Institute, which is supported by the
Neurosciences Research Foundation. The Foundation receives major
support for this program from the J.D. and C.T. MacArthur Foundation,
the W.M. Keck Foundation, the van Ameringen Foundation and Sandoz
Pharmaceutical Corporation.
Correspondence should be addressed to Dr Jonathan Wray, The
Neurosciences Institute, 10640 John Jay Hopkins Drive, San Diego, CA
92121, USA.
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