Complementary colors theory of color vision: Physiology, color mixture, color constancy and color perception

Complementary Colors Theory of ColorVision: Physiology, Color Mixture, ColorConstancy and Color Perception

Ralph W. Pridmore*Macquarie Center for Cognitive Science, Macquarie University, Sydney, Australia

Received 2 June 2009; revised 22 October 2009; accepted 25 November 2009

Abstract: I describe complementary colors’ physiologyand functional roles in color vision, in a three-stagetheory (receptor, opponent color, and complementarycolor stages). 40 specific roles include the complementarystructuring of: S and L cones, opponent single cells, car-dinal directions, hue cycle structure, hue constancy,trichromatic color mixture, additive/subtractive primaries,two unique hues, color mixture space, uniform huedifference, lightness-, saturation-, and wavelength/hue-discrimination, spectral sensitivity, chromatic adaptation,metamerism, chromatic induction, Helson-Judd effect, col-ored shadows, color rendering, warm-cool colors, bril-liance, color harmony, Aristotle’s flight of colors, white-black responsivity, Helmholtz-Kohlrausch effect, rain-bows/halos/glories, dichromatism, spectral-sharpening,and trimodality of functions (RGB peaks, CMY troughswhose complementarism adapts functions to illuminant).The 40 specific roles fall into 3 general roles: color mix-ture, color constancy, and color perception. Complemen-tarism evidently structures much of the visual process. Itsphysiology is evident in complementarism of cones, andopponent single cells in retina, LGN, and cortex. Geneticsshow our first cones were S and L, which are complemen-tary in daylight D65, giving a standard white to aid chro-matic adaptation. M cone later split from L to oppose thenonspectral (red and purple) hues mixed from SþL.Response curves and wavelength peaks of cones L, S, and(SþL), M, closely resemble, and lead to, those of oppo-nent-color chromatic responses y, b, and r, g, a bimodalsystem whose summation gives spectral-sharpened trimodalcomplementarism (RGB peaks, CMY troughs). Spectral

sharpening demands a post-receptoral, post-opponent-colorslocation, hence a third stage. � 2011 Wiley Periodicals, Inc. Col

Res Appl, 36, 394– 412, 2011; Published online 29 September 2011 in

Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/col.20611

Key words: color appearance; color constancy; colormixture; color vision; complementary colors

INTRODUCTION

Complementary colors have long been known to artists as

features of chromatic induction (e.g., after images),1 and

were initially defined as a color and its induced after

image. Goethe’s colleague Schopenhauer claimed the sum

of a color and its complementary after image equals unity

and the activity in the retina produces white.2 Today,

science defines complementary colors as a pair of color

stimuli of appropriate wavelengths and power ratio that

admix a given white.3,4

Little is known of the role of complementary colors in

vision despite 340 years of research from Newton,5,6

Helmholtz,7 and Maxwell8 to Cohen’s mathematical

study4 of complementary colors’. In a letter to the Royal

Society in 1673,5 Newton discusses the admixture of

white from pairs of lights, that is, complementary colors.

But in his major treatise,6 Newton later says, ‘‘For I could

never yet by mixing only two primary Colors produce a

perfect white.’’ Hence it remains controversial4 as to

whether Newton mixed white from two colors. However,

Newton’s well known circular diagram of color mixture6

(with white at center) clearly indicates that opposite pairs

mix white. This remains central to color mixture and col-

orimetry in theory and practice today.

In the 20th century complementary colors were defined

in wavelength and radiance for various CIE illuminants

over the spectrum9 and hue cycle.10 Multistage models of

color vision held that color appearance was governed by

*Correspondence to: Ralph W. Pridmore (e-mail: rpridmo@bigpond.

net.au).

VVC 2011 Wiley Periodicals, Inc.

394 COLOR research and application

opponent colors11 and that complementary colors were

limited to trichromatic (RGB) color mixture, unsoundly

assumed to occur in the receptor layer because of its so-

called RGB cones.12,13 (Its complete lack of neurons for

the complex color mixture task was overlooked.) This

contradicted the older role of complementarism in chro-

matic induction, which role was then adopted by oppo-

nent colors chromatic induction theory,14 and needs re-

evaluation.

A note on the similar terms color perception and colorappearance: the first is an act (or process) and the second is

a fact (or phenomenon). Color perception (or discrimina-

tion) is found from psychophysical experiments (e.g.,

wavelength discrimination) and implies color appearance

as perceived phenomena. For the sake of brevity, this arti-

cle sometimes uses color appearance terms, e.g. green (G),

to denote a physical stimulus.

The aim is primarily to describe specific functional roles

or features of complementary colors in vision from which

to deduce the general role(s). These specific roles may be in

structuring functions to enable or aid the operation of, for

example, color constancy. Secondly, the study describes

physiological evidence for complementarism in the cones,

retina, LGN, and cortex. Some of that evidence, in oppo-

nent response single cells, was mistakenly accepted in the

1950s and 60s as physiological support for opponent colors

theory. In sum, this article presents a comprehensive theory

of complementary colors, summarized as a three stage

theory of color vision.

The paper is developed in four main stages under the

following headings:

a. Previously known roles.

b. Newly found roles.

c. Specific roles grouped into three general roles (Table II).

d. Physiological basis of complementary colors (and

three-stage theory of color vision).

FUNCTIONAL ROLES IN COLOR VISION

AND PERCEPTION

Previously Known Roles

Fourteen specific (as distinct from general) roles of

complementary colors in color vision were previously

known or recently published. The earliest two roles to be

known are (additive) color mixture and color mixture

space,8 embedded since 1931 in CIE colorimetry includ-

ing Red Green Blue (RGB) color matching functions

(which complementarism helps establish) and trichromatic

color mixture diagrams. These two roles represent princi-

ples of applied science but imply similar principles in

human vision, particularly trichromacy.

In color mixture for a given illuminant, any two com-

plementary colors additively form white for that illumi-

nant. The sum of any two color mixture primaries is com-

plementary to the third, as Cohen showed.4 Interestingly,

the complementarism of color mixture extends even to

subtractive colorimetry, with the subtractive primaries

(CMY) exactly complementary to the additive (RGB).4

Cohen derived the curves for subtractive primaries from

the fundamentals of complementarism and showed

that the sum of R and B primaries gives the printer’s ma-

genta; the sum of G and R primaries gives printer’s

yellow; and the sum of B and G primaries gives printer’s

cyan.4 So a third role is the complementarism of additive

and subtractive color mixture primaries.

Additive color mixture relates to its innate color mix-

ture space, which has an illuminant or white point as its

center of gravity and complementary wavelength pairs as

opposites through the white point; this arrangement is the

basis of color mixture dating from Newton.6 Newton and

Maxwell8 after him focussed much attention on this

white-mixing color space and its origin. However, they

lacked the physiological data to find the basis of the

white-mixing feature, which so differs from the hearing

sense in which auditory stimuli (frequencies) do not

admix ‘‘white’’ (or any compound sound) but remain

heard in their original discrete frequencies, and in their

harmonic frequencies in higher octaves. In contrast, the

admixture of visible wavelengths to a compound color

(e.g., purple or white) leaves no sign of the original wave-

lengths or their harmonics, all completely expunged by

the admixture. (Another consequence is metamerism).

The physiological structure of such a white-centered color

space originates in the complementary pairing of S and L

cones in primates’ original dichromatic vision,15 as

detailed in the section Physiological Basis. The origin is

further discussed in the Appendix, Origin of the Single

Hue Cycle and White-centered Color Space.

The next 11 functional roles were found (or confirmed

in the case of chromatic induction) recently by the author

as described in Refs. 16–18 summarized as follows. The

first of these 11 roles, and fundamental to color mixture

and color mixture space, is hue cycle structure. The hue

cycle is symmetrically structured by complementary

wavelength relationships and scaled in a relative wave-length scale16 (the second role) designed to unite spectral

and nonspectral hues into one uniform psychophysical

scale presumably simulating the physiology; see Figs. 1

and 2. The hue cycle is isomorphic in varying illuminant

for ease of chromatic adaptation.16,17,18 The symmetrical

cycle structure is centered on the complementary wave-

length pair of minimum complementary interval (MCI)

found from CIE data; its mean wavelength gives the huecycle midpoint (e.g., 529 nm for illuminant D65; Fig. 1),

which shifts wavelength with illuminant (Fig. 2).18 The

relative wavelength scale’s usefulness is to extend known

spectral functions into nonspectral hues, by extending the

dominant wavelength uniform scale (of the colorimetri-

cally efficient spectrum) over the nonspectrum to com-

plete the hue cycle and thus (importantly) present the full

picture. The ‘‘efficient spectrum’’ is the range 442–613

nm, where monochromatic radiation represents optimal

aperture color stimuli10 (optimal in stimulating color and

in the efficiency of color mixture). Shorter or longer

Volume 36, Number 6, December 2011 395

wavelengths are less efficient (in radiant power, Watts) in

color mixture than optimal compound colors (nonspectral

hues) formed from 442 þ 613 nm; these hues lack a

physical wavelength so they have been given a nominal

wavelength scale called equivalent wavelength (e), as

shown in Fig. 1. Together, physical wavelengths and

equivalent wavelengths form the relative wavelengthscale, the only psychophysical scale to cover the hue

cycle. It is a ratio scale because it gives a wavelength

interval (240 nm/e, starting from zero nm) for the hue

cycle. This hue cycle scale helps present, but is not essen-

tial to, the present theory.16

Figure 2 shows a linear format of the hue cycle, between

hue cycle ends (labeled) in the plane of wavelength and re-

ciprocal illuminant color temperature (MK21).18,19 This

graph shows a mechanism of constant hue (another role)

notable for its symmetry. In this wavelength and MK21

plane, straight near-parallel complementary pairs of lines

at a certain angle were deduced from experimental data to

describe lines of constant hue and the complementary con-

stant hue. Figure 2 shows the global mechanism over the

whole hue cycle and practicable illuminant color tempera-

ture range. The x-axis utilizes the relative wavelength scale

in Fig. 1. In this plane, the hue cycle shifts wavelength

linearly with reciprocal illuminant color temperature. The

straight lines with data points ‘‘x’’ are complementary

pairs of lines from CIE data for respective illuminants,

deduced (from corresponding colors data) to represent

lines of complementary constant hues. Note those straight

lines align very closely (60.5 nm) with data points ‘‘þ’’

which represent octave ratios (or interharmonic ratios,

IH);19 this alignment allowed the use of IH lines to predict

exact angles of nonspectral constant hues in extending the

mechanism over the hue cycle. The wavelength ratio

between any pair of constant hue lines is near-invariant

over all illuminants, or exactly invariant for any pair of IH

lines.19

This remarkably accurate alignment between IH

ratios and complementary pairs of straight lines may

indicate merely a math convenience found serendipi-

tously by the author, but more importantly it may indi-

cate the physiology’s method of completing the hue

cycle, by extending (as does Ref. 19) the spectral sym-

metry of complementary wavelength pairs over the

nonspectral hues.

The relative wavelength scale is used to complete the

most basic functions of complementarism16,17 thought to

exist in the physiology: the ratio of complementary wave-

length intervals [see Fig. 3(A)] and the ratio of comple-

mentary radiant powers [see Fig. 4(A)], representing

another two roles. From these two basic functions, six

well-known visual functions with similar curve shapes

and RGB peaks have recently been modelled:17 wave-

length/hue discrimination, uniform hue difference, spectral

sensitivity, saturation discrimination (a general term also

indicating chroma, colorfulness, but not NCS chromatic-

ness), chromatic adaptation, and chromatic induction. All

except the latter are shown in Figs. 3 and 4 as follows.

Two of them (wavelength discrimination and uniform

FIG. 1. Hue circle in relative wavelength scale,16 for a240 nm/e cycle interval from 409 to 649 e relative wave-length for illuminant D65. HC denotes hue cycle.

FIG. 2. Global mechanism (spectral and nonspectral) ofhue constancy, in the plane of wavelength and reciprocalilluminant color temperature (MK21). The x-axis is physicalwavelength to represent octave wavelength scale andratios of octave [or interharmonic ratios (IH)], and isnumerically the same as relative wavelength scale (Fig. 1).Sloping black lines, data points ‘‘x,’’ are some of the infinitenumber of theoretical constant hues from Ref. 17; datapoints ‘‘þ’’ are wavelengths of IH ratios, labeled. Each linehas a complementary line whose wavelengths are comple-mentary to those on the first line for respective illuminantse.g., B, Y, and C, R. Midpoints are means of MCI (seemain text) wavelength pairs. Hue cycle extends betweenhue cycle ends (gray dashed lines). Gray dash-dot ordash-dot-dot lines represent two estimated MCI pairs forspectral-nonspectral complementary pairs.


hue) are shown in Figs. 3(B) and 3(C), modelled from

Fig. 3(A). Ref. 17 models three visual functions from the

inverse of Fig. 4(A), shown as Fig. 4(B): spectral sensitiv-

ity, saturation (the latter is modelled from the former),

and chromatic adaptation [specifically of the radiance

dimension of color constancy, in its two forms—Figs.

4(A) and 4(B)]. Figure 4(B) shows the adaptation over

three very different illuminants, A, D65, and D250. The

wavelength dimension of chromatic adaptation is shown

in Fig. 2. The third dimension of Fig. 2 is the radiance,

Watts, of the indicated wavelengths/constant hues and

their complementaries, or in other words the power ratios

FIG. 3. Complementary intervals ratio and examples of itsuse in modeling. (A) Solid curve (left y-axis): complemen-tary intervals (CI) ratio for illuminant D65. Solid diamonddata points are known from CIE data; open diamond pointsare estimates. RGB hues are high CI ratio, and CMY huesare low CI ratio. Dashed gray curve (right y-axis): wave-length nm per 5 degree hue angle in the CIE LUV dia-gram.The x-axis is in relative wavelength scale includingnonspectral hues. Note dashed vertical lines at 442 & 613nm, limits to optimal monochromatic stimuli. (B) Wave-length discrimination data. Black curves: data from fiveindicated studies,17 including the Judd curve which itself ismean of 7 studies for 20 observers. Heavy black line is thegrand mean of the five curves. Blue line: present model ofwavelength discrimination. Red line (displaced up 2.5 nmfor clarity): Hurvich and Jameson24 model for mid-lumi-nance, 30 cd/m2. The x-axis is same scale as Fig. A butfor comparison nonspectrals are shown by their comple-mentary wavelengths. (C) Distribution of wavelength perconstant 58 hue angle for 6 color order systems or UniformChromaticity Spaces (Munsell, DIN, OSA-UCS, Nickerson,CIE LUV, CIE LAB) plus a base model of uniform hue (grayline) and a final model (blue line).16

FIG. 4. (A) Radiant power of indicated wavelengthsrequired to neutralize 1 Watt of the complementaries, for il-luminant D65; also termed the relative powers of optimalcolor stimuli. The black curve is also a model of relativelightness (see main text). (B) Black solid curve shows theinverse power ratio, Watts, of the indicated wavelengthsrequired to neutralize 1 Watt of the complementary colorsfor illuminant D65. Dashed line: same for illuminant A. Dot-ted line: same for illuminant D250 (25,000 K color tempera-ture). The x-axis is as Fig. 1. Right ordinate is spectral sen-sitivity for illuminant D65, modelled as the black curve athalf the left-ordinate values. Note RGB peaks and comple-mentary CMY troughs. Gray line: Hurvich & Jamesonmodel of spectral sensitivity.24 The black solid curve is amodel of saturation discrimination for uniform radiance.The three illuminants D250, D65, and A, exemplify chro-matic adaptation of spectral sensitivity (and thus satura-tion). CMY troughs shift wavelength but RGB peaks arenear-constant, changing only amplitude with illuminant.


of complementary colors [Fig. 4(A)]. Together, Figs. 2

and 4(B) indicate the chromatic adaptation (in terms of

wavelength and radiance) of constant colors in illuminants

from 2800 to 25,000 K. This information has not previ-

ously been encapsulated in just two graphs.

The chromatic induction model has been shown20 to be

more accurate than opponent colors theory,14 whose major

(and easily demonstrated) error is to claim that unique

green induces a unique red after image (factually it is ma-

genta), or that unique red induces a unique green after

image (factually cyan).20 Chromatic induction is simulta-

neous or successive and sometimes termed color contrast.

The six modelled functions17 demonstrate that comple-

mentary colors have important functional roles in color

appearance. Together with hue cycle structure, relative

wavelength scale, constant hue, and ratios of complemen-

tary intervals and complementary powers, the number of

functional roles published to date is 11. With the three al-

ready-known roles, the total is 14.

Newly Found Roles

Twenty six new roles or features of complementarism

are described below. Two of them are modelled below.

First, the function of lightness discrimination can be mod-

elled in theory from the ratio of complementary powers

[Fig. 4(A)]. Pridmore’s model of relative lightness meas-

ured in luminance units (the usual convention) is shown

in Fig. 2 of Ref. 21 and Fig. 12 of recent Ref. 17. There,

the relative lightness curve (major peak in yellow, troughs

in violet and red) resembles data for perceived lightness

measured as relative luminance for equally bright mono-

chromatic lights,22 and represents the ratio of complemen-

tary CIE luminances Y,3,9,17 which, converted to radiance

Watts, becomes the CMY-peaked curve in Fig. 4(A)

above. Hence the latter represents relative lightness in

radiance units (and resembles the CMY peaks of value/

lightness of constant Munsell chroma at a given radiance

level; see Plate XI, Ref. 23). This model of relative light-

ness has been tested and corroborated; see below. Note

the reciprocity of Figs. 4(A) and 4(B) (where spectral sen-

sitivity represents saturation, as mentioned above) accords

with Helmholtz’s reciprocity of relative lightness and

saturation.7

The second role is a function here termed attributecontrast, first reported by Helmholtz7 and modelled by

Pridmore.21 This is the perception where, for high pu-

rity or zero-gray colors,23 the visual attributes contrast

as follows: (1) in a given color, the amount of satura-

tion appears reciprocal to the amount of lightness (mod-

elled as the ratio of complementary radiances), as in

Eqn (1); e.g., monochromatic blue has high saturation

but low lightness; and (2) given a color (e.g., blue) and

its attributes, the complementary color (e.g., yellow)

displays reciprocal amounts of the same attributes (e.g.,

low saturation, high lightness), as modelled in Eqns (1)

and (2).

wA ¼ 1=cA (1)

wC ¼ 1=wA (2)

where subscripts A and C denote a color A and its com-

plementary color C, w denotes lightness in terms of radi-

ance ratios Watts in Fig. 4(A), and c denotes chromatic-

ness [Fig. 4(B)]. The black curves in Figs. 4(A) and 4(B)

imply reciprocal lightness and chromaticness as in Eqns.

(1, 2). It’s uncertain which perception of chromaticness is

denoted by c but it is more likely to be colorfulness or

saturation than chroma (which falls to relatively low

levels for blue/violet hues). The advantage is color per-

ception from increased contrast: If a boundary color were

low in both saturation and lightness (e.g., yellow but

appearing brown), as an object color of decreasing satura-

tion and lightness it would increasingly resemble gray. It

would be less discriminable than colors whose attributes

contrast, so at least one attribute is relatively high. Eqns

(1, 2) mean a boundary color has contrasting high ([0.5)

and low (\0.5) attributes totalling unity (1.0) or it has

medium amounts of attributes (as in some green and

orange hues) again totalling unity. This reciprocity of

attributes between complementary colors probably con-

tributes to the perception of balance/harmony in comple-

mentary colors.

A third role is a form of chromatic induction known as

Helson-Judd effect where a surface lighter than the sur-

rounds appears the hue of the (chromatic) illuminant, and

one darker than the surrounds appears the illuminant’s

complementary.23,25 For example, in a yellow illuminant,

an illuminated object appears yellow and its shadow blue.

The ‘‘colored shadows effect’’ (a fourth role or feature)

throws two complementary shadows and may commonly

be seen in stage productions. Two light beams strike an

object from widely different angles. The first beam is col-

ored (e.g. magenta) and throws a complementary (green)

shadow; the second beam is white and it throws a ma-

genta shadow.23

A fifth complementary colors role is evident in dichro-matism (partial color blindness), in the complementariness

of neutral points and confusion points in protanopia, deu-

teranopia, and tritanopia (classes of dichromatism), and

also the complementariness of the two confused hues, and

of the two clearly discriminated hues, in each class.

Table I gives data from Ref. 26 (p.72) and Ref. 27

(p.464, Table 1). It is no surprise that complementarism

governs dichromatic vision systems as well as normal tri-

chromatic, since complementarism originated in early pri-

mate dichromatic vision (see below).

A sixth role is in color rendering. It has long been

known that power-efficient light sources, including fluo-

rescent and white phosphor LED, that give good color

rendering tend to have RGB peaks about 610, 540,

440 nm, and complementary CY troughs about 485,

580 nm.23,25,28,29

A seventh role is in brilliance as defined by

Evans.23,30,31 Colors diminish in grayness to zero (G0) as


the color’s luminance approaches that of its surround. The

zero-grayness/brilliance function has CMY peaks and

complementary RGB troughs in luminance, with maxi-

mum in yellow, but is clearer in radiance units where it

resembles Fig. 4(A). The inverse function is chromatic

strength.31

An eighth role is in white-black responsivity.32 The

function is measured as ratios of center-to-surround lumi-

nance, resembles the curve in Evan’s brilliance, and

relates to Natural Color System’s whiteness-blackness.

Maxima and minima are C(M)Y and complementary

RGB.

A ninth role is in color harmony, where complementary

colors provide a balance of opposites in hue and satura-

tion, as described by Chevreul and others.1,23,26

A tenth role is in metamerism,23,26,27 where metameric

spectral reflectance curves tend (for complex reasons) to

intersect, ‘‘approximately at the wavelengths of the peaks

of the Color Matching Functions of the given observer’’.27

(Note CMFs derive from spectral distribution functions in

the Maxwell method establishing not only RGB peaks but

complementary C(M)Y troughs.)

An eleventh role is in Helmholtz-Kohlrausch effect

(or Brightness:Luminance ratio).21,27 For equal purity, e.g.

monochromatic colors, higher saturated colors in RGB

appear brighter, and the less saturated (and complemen-

tary) in CMY appear dimmer. The function curve21

plotted for equal luminance resembles the inverse of bril-

liance (above), or Fig. 4(B) if plotted to equal radiance.

A twelfth role is in color emotion, where light-heavy

colors are reported as white-black or yellow-blue, and

warm-cool colors (ever since Goethe) as red versus blue,

green, or cyan.33

A 13th new role is in corresponding colors (over sev-

eral illuminants), whose complementaries for respective

illuminants are also a set of corresponding colors.34

A 14th role is the double helix structure of complemen-

tary colors in a graph of radiance and relative wavelength

versus wavelength. The two helices (separated by radi-

ance vertical to the plane) represent colors paired with

their complements. This arrangement (as in genetics) is

able to store large banks of data to aid chromatic adapta-

tion for a wide range of illuminants.35

Another six roles are described in the section Physiolog-

ical Basis: (1) complementary pairing of S and L cone

response peaks (�440 and 565 nm) in early primate di-

chromatic vision,15 to provide a white-centered color mix-

ture system, and (2) a standard white (from SþL) to aid

calculation of ambient light (chromatic adaptation); (3)

complementarism of single and double opponent response

cells of retina, LGN, cortex; (4) complementarism of chro-

matic cardinal directions of color space (axis ends are

complementary); and structuring opponent color chromatic

responses with one pair (y2b) complementary and the

other pair not, such that (5) summation of the two pairs

converts the bimodal system into trimodal complementar-

ism (functions with RGB peaks, complementary CMY

troughs), and (6) the null responses stimulate four unique

hues, two of them complementary.

A 21st role is trimodal structure. Most of the above

functions have RGB peaks with CMY troughs. The peaks

and their complementary troughs alter wavelength and

amplitude systematically with illuminant. Hence comple-

mentarism of these common trimodal functions enables

their chromatic adaptation.

A 22nd new role is spectral sharpening.36 Function

peaks increase from two (in opponent colors) to three thus

narrowing them; the longest wavelength peak is not 565

nm as in cone responses and opponent colors but 605 nm,

improving color perception and color constancy.25 Such

spectral sharpened RGB peaks are now commonly

designed into chromatic adaptation models.25

A 23rd role is in seeing daylight as white, a basis of

vision. Daylight’s spectral distribution27 is said to mix

white from RGB but every wavelength is actually com-

plemented; e.g. only longþshort wavelengths (RþB) neu-

tralize green 492–568 nm. So Gþ(RþB) gives white by

complementarism.

A 24th role is in color appearance spaces, e.g. Ostwald,

OSA-UCS, CIELAB, Munsell26,27 (but not NCS) where

hues perceived as opposites are mostly complementary;

e.g. red and cyan, not green, are opposites (see Munsell

and CIELAB in Figs. 1,2, Ref. 20).

A 25th role is in rainbows,23 halos and glories, out-

standing showpieces of complementarism in relative light-

ness and saturation, trimodal structure, attribute contrast,

brilliance, and color harmony.

A 26th role is the complementary switching (to/from

positive and negative) of after image colors23 sometimes

termed Aristotle’s ‘‘flight of colors’’ (see Conclusion).

In spectral sharpened functions, the constant-wave-

length RGB peaks are complemented by CMY troughs

TABLE I. Characteristics of the 3 classes of dichromatism (partial color blindness), showing dominantwavelengths (illum D65) of neutral points and confusion points, the latters’ CIE x, y, chromaticity coordinates(outside the boundary of real colors), hue names of confused hues, and hue names of clearly discriminatedhues (see references in main text). Note all pairs are complementary.

Dichromatismtype

Wavelength ofneutral point

Wavelengthand coords. of confusion point

Huesconfused

Hues clearlydiscriminated

Protanopia 490–495 nm 493 c, x 0.747, y 0.253 Red and bluish green Blue and yellowDeuteranopia 495–505 nm 499 c, x 1.08, y 20.08 Purplish red and green Blue and yellowTritanopia 568–570 nm 568 c, x 0.171, y 0.0 Greenish yellow and

purplish blueBluish green and red


which shift wavelength with illuminant [Fig. 4(B)]. Hence

a function’s complementarism enables chromatic adapta-

tion. Spectral sharpening necessitates a post-receptoral

location, meaning complementary colors are not restricted

to the receptoral layer as once assumed.12,13,27

Specific Roles Grouped into Three General Roles

From the above, there are 40 specific functional roles

for complementary colors. There may well be more on

further investigation. Some of these roles are not discrete

but overlapping, e.g., trichromatic color mixture overlaps

with color mixture space; and saturation overlaps with

spectral sensitivity. These 40 minor or specific roles rep-

resent much of the color vision process. They are listed in

Table II, tentatively divided into three general classes

described below.

Role nineteen (trimodal structure of functions) implies

a general role of complementary colors is color con-

stancy. Several other specific roles (e.g., constant hue and

spectral sensitivity) similarly indicate their common or

general role is chromatic adaptation for the purpose of

color constancy. On inspection, other specific roles fall

into a general role of color mixture (as a broad term) and

others (such as wavelength-discrimination) fall into a gen-

eral role of color perception.Some specific roles are arguably dual, falling into two

general roles. For example, role five (hue cycle structure)

may be argued to have a second general role in colorconstancy because hue cycle structure is (a) isomorphic

for ease of adaption to illuminant (see Fig. 2), and (b) sets

up the constant hue mechanism in Fig. 2. Role one (orig-

inal complementary cones S and L)15 may be listed under

color constancy or color mixture, since it provides (1) a

standard or default white to aid chromatic adaptation, and

(2) the origins of today’s white-centered color mixture

space (see Appendix).

The general role of color mixture especially depends

on (1) RGB color mixture functions; (2) associated color

mixture spaces (e.g., CIE spaces); (3) completion of the

hue cycle by admixing the nonspectral purples from short

and long wavelengths, thus complementing the central

spectrum (green hues); and (4) the color mixture space’s

underlying hue cycle structure, particularly its comple-

mentary wavelength organization16,17 which underlies all

color mixture space. The color mixture general role cov-

ers the rarely discussed fundamental structure of the

visual process (discussed in the Appendix) and includes

opponent colors role (role 2) in converting dichromatic

to trichromatic color mixture (see section Physiological

Basis).

Roles 16 and 18 (under color constancy) provide com-

plete chromatic adaptation in the wavelength and radiance

(or hue and lightness) dimensions of boundary colors [see

Figs. 2, 3(A), 4(A)]. Expanded to the purity dimension to

include object colors, a complementarism-based chromatic

adaptation theory (of constant hue, chroma, and lightness)

has been tested with experimental data and corrobo-

rated.37 Incidentally lightness, like radiance and lumi-

nance, cannot be an opponent process as claimed by

opponent colors theory38 since it has all positive and no

negative values. However white and black are comple-

mentary colors.

Roles 21 and 22 are dual roles suited to color percep-

tion besides color constancy, where their display of satu-

rated complementary hues helps observers discount the

chromatic light source.

Summary

Although only two or three roles were previously

accepted, complementary colors evidently have at least 40

varying roles (eight of which have been quantitatively

modelled) in vision, from which three general roles are

TABLE II. Specific roles of complementary colors in vision, tentatively grouped into three General Roles (colormixture/space, color constancy, color perception). Some roles may be dual (as indicated), having two generalroles: e.g., hue cycle structure (role 5) arguably serves both color mixture (primarily) and color constancy(secondarily).

Color mixture Color constancy Color perception

1. Complementary S & L cones 13. Standard white (from SþL cones) 25. Unique hues (50% complementary)2. Opponent color chromatic responses 14. Spectral sharpening 26. Wavelength/hue discrimination3. Trichromatic color mixture 15. Opponent single cells in retina/LGN/cortex) 27. Saturation discrimination4. Additive/subtractive mixture primaries 16. Constant hue mechanism 28. Lightness discrimination5. Hue cycle structure 17. Spectral sensitivity 29. Attribute contrast6. Color mixture spaces 18. Chromatic adaptation (of 10,17) 30. Chromatic induction7. Uniform hue difference 19. Trimodal structure of functions 31. Color rendering8. Relative wavelength scale 20. Cardinal directions of color space 32. Brilliance (zero-gray colors)9. Complementary intervals ratio 21. Helson-Judd effect 33. Color harmony10. Complementary powers ratio 22. Colored shadows effect 34. White-black responsivity11. Dichromatic systems (Table I) 23. Complementary corresponding colors 35. Warm-cool hues (color emotion)12. Metamerism (curve nodes) 24. Helical structure of complementary colors 36. Helmholtz-Kohlrausch effect

37. Seeing daylight as white38. Color appearance space39. Rainbows, halos, glories40. Aristotle’s flight of colors

Dual roles: 13, 18, 20 Dual roles: 1, 2, 5, 26, 27, 28, 30 Dual roles: 14, 16, 18, 21-23


concluded: color mixture, color constancy, and color

perception.

PHYSIOLOGICAL BASIS OF COMPLEMENTARY

COLORS

There are few physiological reports explicitly naming

complementary colors whereas the opponent colors

theory, first quantified in the 1950s,24,38 was soon sup-

ported by exciting (but later disputed) reports of so-called

opponent color single cells in the retina and lateral genic-

ulate nucleus (LGN).39,40 This section describes evidence

of the physiological basis of complementary colors in

cone absorption spectra and in spectrally opposed

responses of single cells in retina, LGN, and cortex. It

will be argued that cone responsivities convert directly to

opponent color chromatic responses and thence summate

to complementary color responses (RGB-peaked curves).

There is general agreement the cone spectral sensitivity

peaks (short, medium, and long wavelength, SML) are

about 440, 533, and 565 nm.15,41–46 Averaging the well

known fundamental spectral sensitivity curves estimated

by Smith and Pokorny (440, 540, 565 nm)45 and by Este-

vez (444, 526, 571 nm)46 produce mean peaks at 442,

533, 568 nm. Molecular genetics indicate the first two

cones to evolve were the S cone followed by the L cone

and finally the M cone,15 whose structure indicates it split

from the L cone relatively recently, after the New World

primates (who remain largely dichromatic) and their con-

tinent had separated from the Old World. So primate

vision was originally dichromatic, with S and L cones.

The wavelengths of the early dichromatic cones have

three important features. First, the S and L cone responsiv-

ity peaks at (or near) 442 and 568 nm45,46 are a comple-

mentary pair in daylight D65. That is, they admix daylight

white given the appropriate radiance ratio. It is significant

that S and L cones are complementary in not any daylight

but specifically D65, and that D65 is the CIE’s recom-

mended standard daylight. Second, this is a special pair of

wavelengths: In the context of chromatic adaptation of

spectral sensitivity [Fig. 4(B)], 445 nm is the B peak and

also the wavelength that shifts the least, while 568 nm is

the Y trough and also the wavelength that shifts the most,

with varying illuminant color temperature. So this pair is

central to the control of chromatic adaptation, from a con-

stant wavelength B peak (as stable base) and a widely

adaptive Y trough, e.g., varying from 561 to 580 nm

between illuminants D250 and A [Fig. 4(B)]. Third, the S

and L cone response peaks at (or near) 442 and 568 nm

are equidistant from 505 nm, the peak of rod responsivity

(about 507 nm),42,43 and the approximate wavelength of

unique Green (when it arises later).

Given that S and L cones are complementary in illumi-

nant D65, then the standard or default light source of

dichromatic vision was approximately D65; in other

words, vision was in equilibrium (or white balance) in

D65. Surprisingly, this standard and the complementarism

of the S and L cones is not mentioned in the literature.

The standard white may simplify chromatic adaptation,

even in human trichromatic vision, if the physiology cal-

culates the starndard white through the S and L cones. To

ensure white balance, the difference of another daylight

source from this standard may possibly be measured and

the system adapted to the ambient light.

On the M cone’s evolution, the three-cone system

would presumably have striven towards maintaining equi-

librium. It is proposed below that such equilibrium was

attained through the opponent colors system developing

into the trichromatic color mixture stage (with RGB color

matching functions); until that stage, the vision system

was certainly not spectral sharpened. Initially, the M cone

response would need an opposing or balancing response

to admix a white. So evolution of the M cone (and per-

ception of green hues) would have been simultaneous to

evolution of the opposing nonspectral hues from admix-

ture of S and L cone responses, in a post-receptoral level.

The admixed nonspectral response (say r) would have

completed the hue cycle. The two response systems, S-L

and M-r, or their equivalents in the immediately post-

receptoral level, closely resemble data on opponent color

chromatic responses b-y, g-r in Muller-Judd zone

theory12,13 or in Hurvich-Jameson theory24,38 (where they

represent hue-cancellation curves; this process cancels

the primary hue but not all hue unless, as in the case of

b-y, the response curves are complementary from peak

to null).

Typical mid-luminance b, y, g chromatic responses38,47

are shown in Fig. 5(A) together with the SML cone

response curves; the former evidently derive directly from

the cones, with their corresponding peaks at very similar

wavelengths (440–445, 530–535, 563–568 nm). Note the

L and y curves not only have the same wavelength peak

(563–568 nm) but are also broader than other curves.

Similarly, the S and b curves not only have the same

wavelength peak (440–445 nm) but are also narrower than

other curves. As the data show,38,47 the (largely nonspec-

tral) r curve forms from two spectral peaks near 440 and

615 nm. Hence, to follow the simplest route, it may be

concluded the b-y, g-r chromatic responses derive directly

from the SML cones. There are other options but their

modeling from the cones seems unnecessarily complex25

(see below).

Despite the obvious similarity between SML cone

peaks and b, g, y, chromatic responses, this article appears

to be the first to recognize and accept the similarity and

to derive the latter from the former. The original pro-

posal,24,38 updated as early data on cone pigments were

reported,48 was that y-b derives from (LþM)-S, with yderiving from LþM in about equal amounts. These

unnecessarily complex relationships were presumably

because in the mid-twentieth century the cones were cus-

tomarily (but misleadingly) termed RGB from early tri-

chromatic theory,7 and RþG was simplistically taken to

represent Yellow; this although R and G cone absorptions

were by 1967 known to peak near 567 and 530 nm,48

which certainly do not admix Yellow (about 575 nm in


illuminants C and D65). That the peak about 567 nm

closely represented Yellow (actually greenish yellow)

rather than Red was overlooked as an inconvenient

truth. With no need to change Hurvich and Jameson’s

original format since opponent color chromatic responses

(unlike complementary colors in CIE color matching

functions and color spaces) are not in regular or colori-

metric use, it has remained the unchallenged convention

until now. Also, Hurvich and Jameson lacked the data

available today on SML cone response peaks and b, g, ychromatic response peaks and their obvious coincidence

[Fig. 5(A)]. It is most unlikely such exact coincidence is

chance.

Whereas opponent color chromatic responses can be

derived directly from the cones, one cannot so derive

complementary colors, whose functions typically peak

about 445, 532, 605 nm. I propose the physiology derives

complementary color functions, specifically spectral sensi-

tivity (Fig. 4(B), by special summation of the opponent

color chromatic responses, as modelled in Eqn. (3) and

illustrated in Fig. 5(B). (Note the arbitrary convention of

b, g troughs are reversed to peaks in Fig. 5 so as to corre-

spond with the convention of RGB peaks for color match-

ing functions.)

Uðbþ gþ yþ rÞ ¼ C (3)

where C is the RGB-peaked curve typical of complemen-

tary color functions [see Fig. 4(B)], and where, in the

addition of bþgþyþr curves at every wavelength, symbol

F denotes an operator whereby the addition of two like

signs reverses the sign; e.g., (20.5 r) þ (20.3 y) ¼ 0.8.

This occurs only in the Cyan and Yellow regions [shaded

in Figs. 5(B) and 6] of overlapping curves bþg and

2y2r. The overlaps produce new curves R-C and the rcurve becomes M. Ref. 38 also used a similar special

summation to convert opponent color chromatic responses

to the RGB-peaked curve of spectral sensitivity, shown as

the gray curve in Fig. 4(B).

Figure 6 shows another perspective of the summation,

using response curves for the full hue cycle rather than

only the spectrum, over the relative wavelength scale.

This is particularly relevant to the r curve, since its two

spectral peaks near 440 and 615 nm admix to produce its

peak response in the nonspectral area. (The r peak is not

the 615 nm peak alone, as has been claimed, but both

peaks admixed.)38 The resulting nonspectral colors are

optimally efficient in additive color mixture because their

components are practically identical to the optimal com-

ponents 442 þ 613 nm,10 the colorimetrically computed

components. The 440 nm peak is probably the S cone but

what is the 615 nm peak? It may represent a secondary

peak to the L cone, or more likely the 613 nm limit to

optimal color stimuli as calculated by both colorimetry10

and physiology.

In Figs. 5(B) or 6, the R peak about 605 nm indicates

spectral sharpening, relative to the L cone response peak

at 565 nm, to improve color perception and constancy.25,36

This locates the initial formation of the RGB complemen-

tary color system at a necessarily post-receptoral level.

How does this fit with other evidence and with conven-

tion? There seems little doubt that opponent color

FIG. 5. (A) SML cone spectral sensitivity curves (black lines) from refs. 42–46 and b, g, y opponent color chromaticresponses adapted from Ref. 38 (gray lines, dashed or dotted) normalized at 1.0 response. (B) Opponent color chromaticresponses b-y, g-r (gray lines, dashed or dotted) summated per Eq. (3) to produce the black RGB-peaked curve (shownafter smoothing). The shaded areas show overlapping curves of the same sign, e.g., -y and -r, where special summationper Eq. (3) reverses the sign (to positive in this example). The x-axis is dominant wavelength nm. All functions are spectralas distinct from hue cycle functions in Fig. 6.


chromatic responses (a bimodal system of 2 peaks and 2

troughs) are formed directly from the cones and their

bimodal opponent system S-L, M-r described above. One

bimodal system easily develops into another. Stage

theories12,13 assumed complementary colors (a trimodal

system of 3 RGB peaks and 3 CMY troughs) were at the

receptoral level corresponding to trichromacy of cones.

But the latter are not a trimodal system as they total only

three peaks/troughs. The latter are sufficient (together with

data on the two spectral peaks forming the r curve) to pre-

dict a bimodal system such as opponent colors but not suf-

ficient to predict with any confidence a trimodal system. A

major problem is the R peak about 605 nm conflicts with

the L cone peak about 565 nm. However, complementary

colors are easily derived from the four opponent color

responses by summation (Eqn. 3), and this locates them

after the immediately-post-receptoral formation of oppo-

nent color responses, thus accounting for the spectral

sharpening of the RGB peaks.

Figure 7 (Top Inset) shows early primate dichromatic

vision with S and L cones, schematizing the two stages

involved in conversion of cone responses to complemen-

tary colors and color perception; the 2nd stage derives

directly from the 1st with no need for an intermediate

opponent colors stage. The cone response peaks about

442 and 568 nm imply a neutral point about the mean

wavelength, say 505–510 nm, in mid-spectrum. Admix-

ture of blue and yellow to form green could not occur

until an opponent hue, red, arose. Red, as largely non-

spectral SþL, arose later to oppose the newly evolved M

cone. This neutral point about 507 nm (also the approxi-

mate peak of the scotopic luminance curve) is the wave-

length that will later, in trichromatic vision, approximate

unique Green [see Fig. 6(A)]. Given this early dichro-

matic system was a complementary color system, the neu-

tral point about 507 nm would have required a comple-

mentary neutral point (507 c) in the nonspectral area, or a

potential neutral point for when the S and L cones later

admixed nonspectral compound colors representing the rchromatic response and its nonspectral peak about 507 c.

This scenario is offered as a tentative account for the

puzzling wavelength value of the r chromatic response

peak about 505–510 c in modern vision, calculated colori-

metrically from several graphs23,24,38,47 on the amplitudes

of spectral r peaks near 442 and 613 nm. The Inset’s 2nd

and final stage resembles deuteranopia in humans with a

neutral point about 495–505 nm and a fairly normal lumi-

nance curve peaking about 560 nm.26,27

Figure 7’s main figure is a three stage model of the

progress of cone responses to opponent colors to comple-

mentary colors/color perception. Color mixture and color

constancy probably start forming in retina/LGN and are

complete in cortex, as both involve complementarism and

manage constant changes of illuminant/reflectance to

deliver color perception. Color perception can only be in

cortex. Note peak wavelengths of SML cones carry

through all three stages: Starting with SML cone response

peaks about 442, 535, 568 nm,45,46 through the bgy peaks

to the final complementary color peaks BGY, all nine

peaks are 443, 533, 565 nm 63 nm. It would be difficult

to argue in logic or statistics that this close coincidence

between three peaks over three stages is accidental. This

FIG. 6. A different perspective of summation over the huecycle rather than spectrum. (A) Opponent color chromaticresponses b-y, g-r including nonspectral portions over thehue cycle (409–649 nm/e, or approx 530c–530c) in relativewavelength scale. The original two spectral r peaks [in Fig.5(B)] near 440 and 615 nm are calculated by CIE colorime-try to admix the indicated nonspectral peak �510 c (seealso Fig. 7, Stage 2), or �645 e in equivalent wavelength.Asterisks indicate unique hues bgyr. (B) Result of summa-tion of opponent color responses b-y, g-r per Eqn (3) toproduce RGB-peaked curve shown after smoothing. Noter peak at 510c in Fig. (A) has shifted to �530 c, peak ofMagenta (M) curve, through summation with the b curve(see also Stage 3, Fig. 7). Vertical dashed lines at 442 and613 nm show limits to optimal monochromatic stimuli.10


makes early convention’s tortuous origins of the chro-

matic response curves quite absurd, e.g. that y-b derive

from (LþM)-S,24,25,38 rather than directly from L-S. Why

would the physiology derive y (peak 565 nm) from

LþM, about 565þ535 nm, rather than directly from L

(565 nm)?

Trichromatic color mixture (e.g., CIE 1931 system) is

not fully in place until Stage 3. The trichromacy of color

mixture and color perception is the same spectral-sharpened

trichromacy, rather than the primitive trichromacy of the

cones. Retinal Stage 2 is bimodal, an intermediate stage

leading quickly to Stage 3 in cortex. Here trichromatic

FIG. 7. Schematic models of color vision. Top Inset: Early dichromatic primate; Stage 1 (complementary cones S and L)moves directly to Stage 2 (complementary colors B and Y) with no need for an opponent color stage. Main Figure: Threestage model of human vision showing relations between cone responses (Stage 1), opponent color chromatic responses(Stage 2), and complementary color functions with spectral sharpening (Stage 3). Lower case indicates peaks/troughs ofopponent color responses (asterisks ¼ unique hues); upper case indicates complementary color functions. Lines ‘‘0’’ shownull response. Circular diagrams: opponent pairing of cone outputs. Arrow A denotes Achromatic dimension, lightness.


color mixture combines wavelength and radiance to produce

potential hue, lightness, chroma, i.e. color appearance, with

progressive adaptations in subsequent interlinked cortical

areas. Another reason for Stage 2’s intermediacy if that its

opponent color chromatic responses are not fully balanced:

though the b-y mechanism is in balance (able to produce

white) because its opponency is actually complementary,

the g-r mechanism is not (i.e. the peaks about 535 nm and

507 c are not complementary). Hence the system in Stage 2

is unbalanced specifically to summate to the Stage 3 bal-

anced complementarism curves where trichromacy shifts to

a spectral sharpened longer wavelength range with a 606

nm peak.

Possibly Stage 2 took two steps to Stage 3: (1) M cone

and opposing r curve presumably evolved together in

complementary balance, so the chromatic response peaks

g-r were originally 535 nm, 535 c, in a balanced bimodal

system (corresponding to B-Y, G-M today), before

(2) shifting the r peak to 507 c and summating to adroitly

gain the extra R-C peak and trough in today’s spectral

sharpened B-Y, G-M, R-C complementary system.

Stage 2 response curves probably summate to Stage 3

in phases, through retina and LGN (see LGN opponent

cells below) to cortex for final phases of trichromatic

color mixture/complementarism. To account for unique

hue and hue-cancellation perceptions, a parallel channel

may carry Stage 2 signals (non-summated) direct to cor-

tex.

The third cone M (stimulating g chromatic response)

developed simultaneously with the admixture of SþL

cone outputs to admix red and nonspectral purple hues.

The M cone and its g chromatic response developed

from weak beginnings, in both saturation and luminance.

This may explain the rather odd colors of olive green(dark yellowish green) and brown (dark yellow or or-

ange), odd because they exist only at low luminance.

Both are based on the L cone (or y chromatic response)

and its overlap with either the newly arisen g chromatic

response to form olive green, or its overlap with the

newly arisen r response to form brown. No other colors

have a common hue name for their low luminance form.

Luminance and saturation grew as the M cone grew,

producing the green and orange hues we know. But the

olive green and brown sensations remain because they

add considerably to color perception.

The following sequence is proposed in Fig. 7: (1) In

early primate vision, a unimodal system (1 peak, 1

trough) of two cones S-L evolved to three SML cones

which lead to a bimodal opposed system S-L and M-r;(2) which leads to a bimodal system of four opponent

color response peaks and troughs b, g, and y, r; (3) whichsummate to a trimodal system of six complementary color

peaks and troughs RGB and CMY, respectively. Note the

simplicity of transfer between stages including the con-

stant wavelengths of three peaks over three stages. In con-

trast, opponent colors theory postulates illogically that

(non-spectral sharpened) opponent color chromatic

responses occur at a later stage than (spectral sharpened)

complementary colors. This difference between the two

theories is perhaps this article’s most contentious point

and easiest to resolve. Besides the spectral sharpening

issue and contradicting the accepted logic of evolving

from simple to complex systems,15 it is mathematically

and physiologically difficult (and unnecessary) to derive

the bimodal from the trimodal system, and to derive the

latter directly from the cones.

Complementarism structures the opponent colors sys-

tem (role 2) such that one pair (b, y) of chromatic

responses is complementary and the other is not, but so

formed that summation of the pairs produces a trimodal

function (Fig. 5B or 6). Its other role (25, Table II) is to

stimulate the unique hues. Itself a 50% complementary

system, the opponent color mechanism converts (with the

M cone’s aid) the unimodal complementarism (B-Y) of

early dichromacy to an improved, trimodal complementar-

ism (Stage 3), based on trichromatic color mixture. Oppo-

nent colors are necessarily a bimodal system to fit

between, and convert, the unimodal to the trimodal. Its band r chromatic responses mix nonspectrals from SþL

(about 440þ615 nm)38 to complete the hue cycle. Role 2

is dual, building color mixture and constancy. Early

dichromacy remains in the human S-L cone system and

(with the same wavelength peaks) the ancient B-Y system

that rarely fails, unlike the later failure-prone green-red

forms of dichromatism.26,27 The key logic in Fig. 7’s evo-

lutionary sequence is modality of color systems from

unimodal to trimodal, rather than the looser terms dichro-

macy and trichromacy (often indicating numbers of cones

rather than modality).

Single Cell Spectrally Opposed Responses

In the 1950s, Svaetichin found spectrally opposed sin-

gle cells in fish retina39 and De Valois et al.40 found sim-

ilar cells in primate LGN, which they called opponentcolor cells. Classed as Red-Green and Yellow-Blue types

(R-G, Y-B), they were initially seen as the biological

expression of Hering’s opponent colors theory. In fact the

‘‘Green’’ peaks are �485–495 nm, i.e. Cyan rather than

Green, making the opponent responses actually comple-

mentary Red-Cyan. These cells often remain described by

opponent color names R-G though without the ‘‘opponent

color’’ term. Figure 8 shows Svaetichin’s famous ‘‘R-G’’

cell and its ‘‘G’’ peak at 490 nm (Cyan in color-normal

human response).

Figure 9 shows some data from the De Valois experi-

ments and from Wiesel and Hubel’s work in the

1960s.49 Clearly, the ‘‘R-G’’ cells are actually Red-Cyan

(here labeled R-BG to better differentiate from R-G).

The ‘‘B-Y’’ cells approximate Blue and Yellow unique

hues (perceived about 470–480 and 570–580 nm), and

closely approximate complementary pairs also. The

opponent color system and complementary color system

are similar in the blue and yellow hue areas (see Figs. 6

and 7), since both relate closely to S and L cones.


Hence, unique hues Blue and Yellow are not only oppo-

nent colors but also complementary.

To date, the physiological literature has frequently

reported50–55 the opponent cells do not match Hering’s

opponent color unique hues R-G and Y-B. Such cells in

retina, LGN, and cortex V156,57 now tend to be termed

‘‘opponent’’, ‘‘opposed/opponent response’’ or ‘‘spectrally

opposed’’ or anything other than ‘‘opponent color.’’ De

Valois himself summed it up:54 ‘‘Although we...were most

impressed with finding opponent cells, in accord with

Hering’s suggestions,...the earliest recordings revealed a

discrepancy between the Hering...opponent perceptual

channels and the response characteristics of opponent

cells in macaque.’’

Today spectrally opponent cells are commonly treated

as complementary responses49–59 (role 15, Table II) even

if not so named, since physiologists know or care little

about colorimetry. However some physiologists refer to

opponent cells by complementary color terms Red-Cyan,

Green-Magenta, Blue-Yellow.56,57 Workers often graph

cell responses as opposites through the color space white

point, or opposed by 180 deg phase shifts (i.e., comple-

mentary pairs), as exemplified by the two cardinal axes of

color space in Fig. 10 (the third axis is luminance),

gained from primate LGN.58 The axes were determined

as the means of the experiment’s single cell opponent

responses, which clustered in two opponent groups

loosely called R-G (actually R-C) and Y-B. Because the

cardinal axes pass through the white point, their ends

are complementary pairs rather similar to protanopic

and tritanopic confusion pairs (see role 11, di-

chromatism). Note Fig. 10 also illustrates role 20

(cardinal directions).

Figure 11 shows detail of the azimuthal distribution for

some 240 opposed response cells,58,59 including those in

Fig. 10. All the opponent pairs are complementary.

FIG. 8. Opposed responses originally termed ‘‘Y-B’’ (top)and ‘‘R-G’’ (bottom) in fish horizontal cells, adapted fromSvaetichin & MacNichol (1958).39 In the supposedly R-Gresponse, note the 490 nm response peak (Cyan for humanobservers). Similar cells were found in primates (Fig. 9).

FIG. 9. Monkey LGN opposed-response cells. Solid lines(to left ordinate) are ON OFF cells after Wiesel & Hubel;49

labels refer to original figure numbers. Dashed lines (toright ordinate) are ON or OFF cells after De Valois.40 Huelabels (B-Y, R-BG, added by the author) indicate comple-mentary pairs.

FIG. 10. Cardinal directions in DKL color space (Ref. 58)in CIE 1931 diagram. Axes represent clustering of single cellopponent responses found in monkey LGN [see Fig. 11(A)].Axes intersect at the light source white point,hence opposite ends are complementary. 0–1808 axis re-sembles protanopic confusion line (cyan to red); 90–2708axis resembles tritanopic confusion line (violet to greenishyellow).


In summary, the evidence indicates single cell opponent

responses in the primate LGN (and thus the retina) are

better described as complementary colors than opponent

colors. There are also some reports of G-M opponent-

response cells in vertebrate retina (sometimes called

triphasic cells with three spectral peaks about 440, 530,

610 nm).60

There is limited evidence from primate cortex but rela-

tively recent work in striate cortex (or V1 area) indicates

most Double-Opponent cells have complementary pair

responses of three types:56,57 mainly R-C and B-Y as in

the LGN and a few G-M similar to triphasics in verte-

brate horizontal cells.

A number of early49 and recent physiological stud-

ies61,62 demonstrate that spectrally opponent cell

responses adapt to chromatic and achromatic lights, indi-

cating mechanisms of chromatic adaptation driven by

complementarism. Some physiologists reason that color

constancy requires cells with perfectly balanced oppo-

nency, spatially and chromatically,56,57,63,64,65,66 such as

Double-Opponent cells. For example, red light may excite

the center and inhibit the surround of a R-C cell, whereas

cyan light may inhibit the center and excite the surround.

The criterion of perfectly opposed chromatic balance is of

course complementary pairs, though these are rarely men-

tioned explicitly in the physiological literature.

Discussion

The physiological basis of complementary colors was

briefly described from cones to striate cortex. There is

wide agreement in the physiological literature that single

cell spectrally opponent responses do not align with

unique hue opponent colors, and that many such cells in

retina, LGN, and cortex V1 display complementary

responses. The difference between opponent color and

complementary color terms is more than semantic: it

may concern color constancy. Arguably, color constancy

would be assisted by cells with balanced chromatic

opponency, able to admix white or to calculate the aver-

age chromaticity (or neutral) of the scene, rather as in

Land’s retinex theory.67 Complementary pairs would

facilitate the calculation and thereby color constancy.

Given the above physiology, what does it do for color

vision? It is notoriously difficult to deduce the psycho-

physical purpose of many pieces of the visual physiol-

ogy,55,64 but the cones are the best understood. The pur-

pose of having complementary S and L cones is presum-

ably to (1) establish a white-centered color mixture space,

and also (2) establish a standard white from which to esti-

mate the ambient illuminant, so as to maintain color con-

stancy or ‘‘white balance’’ in terms of photography.

Human chromatic adaptation physiology is not known

in detail but a vast literature postulates possible operating

principles,25 some of which may be similar to the digital

camera. However, human vision may have some techni-

ques unavailable to cameras, such as the following four

examples.

1. The eye can scan a scene better than a camera to seek

achromatic or specular reflectances, from which to

directly calculate the illuminant. Further, the D65

white of the S and L cones gives the physiology a cen-

ter-of-range standard from which to estimate (from

several reflectances in the scene) whether the white is

warmer or cooler than the standard (D65) white, and

adjust iteratively.

2. Recall that the S and L cone responsivity peaks about

442 and 568 nm are the same wavelengths as the B

and Y peaks in chromatic adaptation of spectral sen-

sitivity [the RGB-peaked function, Fig. 4(B)]. Recall

the B peak is constant 445 nm in all illuminants and

only its complementary Y trough (568 nm in illumi-

nant D65) shifts with varying illuminant color tem-

perature. So this pair is central to the control of chro-

matic adaptation, from a constant wavelength B peak

(as stable base) and a widely adaptive Y trough,

FIG. 11. (A) Color tuning of some 60 cells in monkey LGNfrom Ref. 58: ‘‘R-G’’ (really Red-Cyan) opponent responsescluster at 0/3608 and 1808 (491 c and 491 nm), and Y-Bresponses cluster at 90 and 2708 (560 and 400 nm); seeaxes in Fig. 10. 1808 phase shifts means opponentresponses are opposites through the color space whitepoint, i.e. complementary pairs. (B) As Fig. (A) but fromRef. 59 showing color tuning of 177 cells in monkey LGNfor ‘‘R-G’’ (really Red-Cyan) opponent responses clusteredat 0 and 1808. 1808 phase shift represents complementarywavelength pairs.


varying from 561 to 580 nm between illuminants

D250 and A. Since the B peak is constant 445 nm,

only the Y trough and its difference from 568 nm

(the default Y trough) need be calculated by the vis-

ual system to find the ambient illuminant (or the

white balance).

3. Given the linear relationship of complementary wave-

lengths and reciprocal illuminant color temperature

MK21 (Fig. 2), and D65 as the standard illuminant,

the physiology may find the ambient illuminant by

estimating the difference from the standard in terms of

MK21. The latter linear measure represents a uniform

scale of illuminant ‘‘white’’ chromaticity (changing

from bluish to yellowish),68,69 commonly used by color

television colorimetrists. The fact the scale is perceptu-

ally uniform, in a physical measure (reciprocal Kelvin)

as distinct from a colorimetric or artifact measure, sug-

gests the scale has evolved for use by the physiology

rather than happened by chance.

4. Chromatic induction (e.g., after images) may possibly

be a means of chromatic adaptation. The effect of

simultaneous contrast is immediate, so it is cortical.

Successive contrast/after images are perceivable within

a few seconds and demonstrate adaptation to the illu-

minant. However, the potential after image is available

to the physiology within milli-seconds of scanning the

inducing image. A plausible method of such adaptation

may be as follows. Given that the after image is the

complementary color to an observed reflectance, the

observed reflectance is subtracted by the physiology

from the white (the standard white or the last calcu-

lated illuminant), leaving the complementary color as

the after image. The physiology may calculate if the

complementary and the observed reflectance admix a

white that matches the ambient white, and then itera-

tively re-estimate the white until satisfactorily

matched.

What is the purpose of spectrally opponent response

(complementary) single cells in retina, LGN, and cor-

tex? Many roles have been postulated in color discrimi-

nation, spatial color, color constancy and chromatic

induction. The average chromaticity of such a cell’s op-

ponent responses is white, and such cells indicate they

adapt automatically to illuminant.49,61,62 These abilities

enable such cells to play a role in color constancy,

though the actual mechanism is unknown.

CONCLUSION

Although only two or three roles were known before

Ref. 17 and the present study, complementarism was

shown to have some 40 widely varying roles, from hue

cycle structure to color perception functions. Eight roles

have been quantitatively modelled from complementary

colors. The 40 specific roles group into three general roles

of complementarism (Table II). These tend to overlap as

two general roles may share some specific roles. The first

general role was taken to be color mixture, including

structuring the hue cycle and color mixture space in the

three conventional dimensions (wavelength, radiance,

purity). This role corresponds to the Young-Helmholtz tri-

chromatic theory, and sets up the foundation of color

vision and its white-centered color mixture space. The

Appendix concludes that the latter and its single hue cycle

(principal features of color mixture) evolved to improve

visual acuity and avoid harmonic complications to color

mixture.

The second general role is color constancy. Its primary

mechanism is hue constancy; Fig. 2 (and its surprising

linear symmetry) implies a corresponding simplicity in

the physiology, possibly a simple cortical map of parallel

lines or even more simply an equivalent formula using

invariant wavelength ratios. The constant hue mechanism

is central to the present theory’s color constancy.37 The

secondary mechanism of color constancy is chromatic ad-

aptation (role 18) of the spectral sensitivity and radiance

dimensions. A complementary colors-based chromatic ad-

aptation model (with independent models of hue, lightness

and chroma)37 has been tested against experimental data

and shown to be as accurate as CIECAM02.

The third general role is color perception, particularly

saturation, lightness, and wavelength discrimination. Per-

ception of unique hues initially forms in retinal Stage 2

(opponent colors). A parallel channel possibly carries

Stage 2 signals (non-summated) direct to cortex for

perception.

There are similarities between the general roles of color

mixture and color constancy. Color constancy’s most evi-

dent feature is the trimodal structure of most visual func-

tions, deriving from trichromatic color mixture and hue

cycle structure. Hence some of the specific roles in color

mixture may well be shared with color constancy. The

two possibly evolved together in mutual support of their

common purpose, that is, color perception, which

improves an animal’s perception of environment.66 It’s

worth noting that chromatic induction (reportedly a

higher-order function)70 possibly serves both color per-

ception and color constancy. The general role of color

constancy seems to be a multi-stage process from recep-

toral level forward but mainly cortical.70,71,72

The three general roles of color complementarism are

arguably the principal functions of color vision. Given

that and the variety of the 40 specific roles, it may rea-

sonably be concluded complementarism is the principal

structural force driving the color vision process. No alter-

native force is apparent, particularly one that alone could

account for Table II functions. The table represents possi-

bly the majority of specific functional roles in color

vision. The physiology and neural location of the func-

tions remain scantily understood.55

The prevalence of RGB-peak functions in the 40 roles

is reflected in the maxima of Cohen’s matrix R and in

Thornton’s RGB ‘‘prime colors.’’4,28 These peaks are

commonly noted, e.g. in recent Ref. 73, to typify many

functions including wavelength or spectral sensitivity73


[agreeing with Fig. 4(B)], color rendering,28 Munsell

chroma, spectral sharpening, color mixture primaries,28

etc. These maxima have been noted with little account for

over a century.8 They are usually assumed to be spectral-

sharpened relative cone responses, with the L peak shifted

magically from 565 to 605 nm. Factually the 565 nm

peak remains as y and Y peaks in Stages 2 and 3, Fig. 7,

which also explains the 605 nm R peak. (This exemplifies

the explanatory power of the present three-stage theory.)

Note the maxima lie just within the 442–613 nm limits of

optimal monochromatic stimuli.10

In hindsight, the basis of the elegant constant hue

mechanism in Fig. 2 is that the complementaries (C) to a

set of corresponding colors (A) in a range of illuminants

are themselves a set of corresponding colors;34 i.e. C and

A are each (different) sets of corresponding colors. The

basic logic34 was later confirmed by further colorimetry.74

Hence, given A and C are represented in Fig. 2 by a pair

of parallel lines, other complementary sets of correspond-

ing colors will be similarly represented by parallel lines

(to infinity). That parallel straight lines represent constant

hues in the plane of Fig. 2 is inexplicable by mathematics

alone so seems to be physiological. The mechanism’s

symmetry is notable also for the agreement between lines

of constant hue and interharmonic ratios, implying the lat-

ter (as physical) establish the former (as psychological). It

cannot be the reverse.

In contrast to opponent colors theory, the present theory

of color complementarism covers most parts of the visual

process and seems to be the most broad-reaching theory

of color vision to date. It incorporates Young-Helmholtz

trichromatic theory and Hering’s opponent colors theory.

Opponent colors as a vision theory14,24,38 was always

limited to color appearance. Its success lies mainly

in defining the chromatic responses and the unique hues

perception.

Evidence was given that many opponent response sin-

gle cells in retina, LGN, and cortex V1 display comple-

mentary (rather than opponent color) responses. Although

the method is not yet clear, color constancy would

be assisted by such cells, able to admix white or to

calculate the average chromaticity (or neutral) of the

scene, similar to Land’s retinex theory and to the white

balance mechanism/algorithms in digital cameras.75,76

Mollon77 once wrote, ‘‘the four pure hues (are) perhaps

the chief unsolved mystery of color science.’’ A four-

color system enmeshed with two ‘‘trichromacies’’ (LMS

and RGB) is indeed eccentric. Fig. 7 offers a logical

three-step solution. No other sequence of steps suffices.

This paper includes four recent concepts in color sci-

ence: (1) relative wavelength, (2) constant hue mechanism

(Fig 2), (3) interharmonics, and (4) direct relations

between LMS cones, opponent color chromatic responses

ygb, and complementary color peaks/troughs YGB (all

three sets of peaks are 565, 533, 443 nm 63). Only the

fourth concept is essential to present theory.

In presenting a new perspective, this paper questions

several conventions. In perhaps the strangest, trichromatic

color mixture and its innate complementarism are buried

in the receptor layer without link to further visual process.

That is, the cones are assumed to (1) form, (2) spectral

sharpen and (3) operate the complex functions of color

mixture; e.g. admix wavelengths reflected from a surface

to give its (say pre-adaptation) color appearance—surely

a post-receptoral cortical process. This convention relates

to another: calculating cone spectral sensitivities from

color matching functions by matrix.25,27 That indicates

a linear relationship (as in present theory) but not the

claimed direct link.

The theory of color vision is supported by detail in

recent publications.16–20,37,78 It is similar to another recent

three-stage model (color complementarism as Stage 3) by

Wu,79 who concentrates more on the neurophysiology of

complementarism and color mixture, arguing their neural

substrate is layer 4c of cortex VI, than on functional

roles. Just two roles are analyzed: chromatic induction,

and the complementary switching in Aristotle’s flight of

colors (a late addition to Table II).80

APPENDIX: ORIGINS OF THE SINGLE HUE CYCLE

AND WHITE-CENTERED COLOR MIXTURE SPACE

One could argue that visual acuity would be better with

only one cone type. But accepting that color vision

gives a survival advantage,66 the need for visual acuity

necessitates a high density of cones in the fovea and a

very small number of cone types (typically 2–4),44 plus

a single hue cycle and color space. This type of color

vision evolved in most vertebrates in contrast to the

several octave cycles in hearing. This single hue cycle

has interesting features. It is worth noting the different

routes taken by vision and hearing. Perception of multi-

ple stimuli in color vision is more neurally structured

than in hearing, where frequency stimuli and their har-

monics occur without fully mixing and are useful in

music and voice recognition.

In the hearing sense, where two or three frequencies

are simultaneously heard, they do not completely mix to-

gether but retain their descrete frequencies, and also their

lower-energy harmonic frequencies in higher octaves. But

in vision two or three wavelengths reflected from an

object mix completely, such that the original hues may

admix a quite different hue or even white.

There is some evidence that vision treats not only the

quantum property of electromagnetic radiation but also

the wave property (e.g. harmonics). The latter is indicated

in (1) the wave-mode propagation of radiant energy

through cones’ inner segments, effectively as wave guides

or dielectric antenna81,82 (see also p. 97 of Ref. 27), and

(2) the remarkably close agreement in Fig. 2 between

lines of constant hue and interharmonic ratios (suggesting

the latter establish the former).

A number of questions arise. First, why are no har-

monic energies visible in the hue cycle or the physical

spectrum? After all, both sound and light are radiant


energies which produce harmonics at 2, 3, and 4 (etc)

times the fundamental frequency, as is evident in

music, and the visual spectrum, say 360–780 nm (as

distinct from the effective hue cycle), covers over an

octave. Second, why do the stimuli mix rather than

remain discretely perceptible? Third, why did vision not

evolve a hue cycle in which each hue is stimulated by

a single physical wavelength? Why have a hue cycle

consisting of both monochromatic hues and com-

pounded hues (e.g., nonspectrals)? Fourth, why did an

opponent type of color mixture evolve where every hue

has a complementary?

The answers to these questions all require a single hue

cycle of less-than octave range with a white-centered

color mixture space designed to avoid the generation of

harmonics. First, why are no harmonics visible? Over

the spectrum, luminance peaks near 555 nm and fades to

the spectrum extremes. Beyond 360 and 780 nm, near the

extremes, the luminance is so low (\0.01 lm/W) as to

effectively kill any harmonics generated. At less extreme

wavelengths, say 680 nm, luminance may be just high

enough to be visible in natural light but the harmonic at

340 nm is beyond the visible spectrum. So vision has

killed or damped harmonic energies from interfering with

color mixture.

Second, why do the stimuli admix compound colors

such as purple or white? This questions the very basis

of the hue cycle and color mixture. The strangest fea-

ture of hue cycle morphology is the formation of pur-

ple hues as compound rather than monochromatic stim-

uli. Why is it so, when it would be simpler for an

effective spectrum of physical wavelengths to cover the

whole hue cycle and thus obviate the compounds? One

problem would be that hue cycle ends must be the

same hue so as to complete the hue cycle seamlessly,

whereas hue cycle ends of different physical wave-

lengths would stimulate different hue sensations. A pos-

sible solution would be 1st and 2nd harmonics (e.g.,

360 and 720 nm) representing hue cycle ends, similar

to octave ends in hearing, and similarly producing

discriminably different wavelengths but the same note

or hue (since they are harmonics). But a problem with

that would be vision’s discriminating a short wave-

length purple and a long wavelength purple, complicat-

ing color mixture.

Another problem with a physical octave hue cycle

would be production of unwanted energies at harmonic

frequencies near the hue cycle ends interfering with

color mixture. Consider the admixture of white by a

color stimulus near hue cycle ends (say 360 and 720

nm) and its complementary wavelength (about 540 nm);

the 720 nm stimulus would produce a significant har-

monic energy in the 2nd harmonic (360 nm), to compli-

cate color mixture and color appearance (from extra

radiance).

So in real vision, admixing compound colors rather

than retaining perception of the discrete wavelengths,

successfully avoids harmonics and their interference

with color mixture. Another advantage of admixing

desaturated or achromatic colors would be formation of

a white-centered color mixture plane with simultaneous

formation of a useful new dimension, purity, as

discussed below.

Given the complications raised by harmonics in a hue

cycle whose hues are stimulated by discrete wavelengths,

and the need for visual acuity, it seems vision evolved a

single hue cycle of less-than octave range by omitting

extreme short and long wavelengths and substituting com-

pound stimuli formed from admixing short and long

wavelength pairs. These compounds filled the area inside

the hue circle, as a plane of relative wavelength16 and pu-

rity. Where component hue stimuli are similar hues, they

would admix a compound color of intermediate hue. As

the component pair become most different, the compo-

nents admix a maximally different hue. This hue, to avoid

duplication, cannot be the same as others hues around the

hue cycle. One option would be desaturation or white.

This would also resolve another factor: Compound colors

form another dimension (purity) to color space, allowing

a third color attribute, that is, saturation. The advantage

of a third color attribute is to hugely increase the varia-

tion of colors in color space. Purity varies from 100% to

nil or white, when component wavelengths are maximally

different, that is, complementary. Hence white as the cen-

ter of color mixture space represents two things: nil purity

and the admixture of complementary wavelengths.

White has yet another advantage. The planet’s sur-

face is flooded by daylight, allowing life to exploit the

free radiation to power color vision. But how to avoid

the radiation bombardment appearing an overpowering

monochromatic (say red) illumination? A solution

would be to mix the whole visible spectrum to appear

achromatic, i.e. to see daylight as white (Table II,

role 37). This allows objects to absorb (subtract) some

wavelengths of the white light and reflect the remain-

der to the eyes, to stimulate hues. Hence again a

white-centered color mixture space provides solutions

enabling color vision. All animals developing color

vision would have found this same problem and its

only solution: to see (any) daylight as white, by devel-

oping complementarism and its consequence, chromatic

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