Color vision
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/* Mathematics of color perception */ b(w)->l(w)
'''Color vision''' is the capacity of an organism or machine to distinguish objects based on the [[wavelength]]s (or [[frequency|frequencies]]) of the [[light]] they reflect or emit. The nervous system derives color by comparing the responses to light from the several types of [[Cone cell|cone photoreceptors]] in the eye. These cone photoreceptors are sensitive to different portions of the [[visible spectrum]]. For humans, the visible spectrum ranges approximately from 380 to 750 nm, and there are normally three types of cones. The visible range and number of cone types differ between species.
A 'red' apple does not emit red light. Rather, it simply absorbs all the [[frequency#Frequency of waves|frequencies]] of [[visible light]] shining on it except for a group of frequencies that is perceived as red, which are reflected. An apple is perceived to be red only because the [[human eye]] can distinguish between different wavelengths. Three things are needed to see [[color]]: a light source, a detector (e.g. the [[eye]]) and a sample to view.[[Image:psychophysical.jpg|right|]] The advantage of color, which is a quality constructed by the visual brain and not a property of objects as such, is the better discrimination of surfaces allowed by this aspect of visual processing.
==Physiology of color perception==
[[Image:Cones SMJ2 E.svg|right|frame|Normalized response spectra of human cones, S, M, and L types, to monochromatic spectral stimuli]]
[[Image:Spectrum locus 12.png|thumb|287px|The same figures as above represented here as a single curve in three (normalized cone response) dimensions]]
Perception of color is achieved in [[mammal]]s through color receptors containing pigments with different [[electromagnetic spectrum|spectral]] sensitivities. In most [[Catarrhini|primates closely related to humans]] there are three types of [[color receptors]] (known as [[cone cell]]s). This confers [[trichromatic color vision]], so these primates, like humans, are known as [[trichromat]]s. Many other primates and other mammals are [[dichromat]]s, and many mammals have little or no color vision.
In the human eye, the cones are maximally receptive to short, medium, and long wavelengths of light and are therefore usually called S-, M-, and L-cones. L-cones are often referred to as the [[red]] receptor, but while the perception of red depends on this receptor, microspectrophotometry has shown that its peak sensitivity is in the greenish-yellow region of the spectrum. Similarly, the S- and M-cones do not directly correspond to [[blue]] and [[green]], although they are often depicted as such (such as in the graph to the right). It is important to note that the [[RGB color model]] is merely a convenient means for representing color, and is not directly based on the types of cones in the human eye.
The peak response of human color receptors varies, even amongst individuals with 'normal' color vision;<ref>Neitz, Jay & Jacobs, Gerald H. (1986). [http://www.nature.com/nature/journal/v323/n6089/abs/323623a0.html "Polymorphism of the long-wavelength cone in normal human colour vision."] ''Nature''. '''323''', 623-625.</ref>
in non-human species this polymorphic variation is even greater, and it may well be adaptive.<ref>Jacobs, Gerald H. (1996). [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=40094 "Primate photopigments and primate color vision."] ''PNAS''. '''93''' (2), 577–581.</ref>
===Theories of color vision===
Two complementary theories of color vision are the [[trichromatic theory]] and the [[opponent process]] theory. The trichromatic theory, or [[Young–Helmholtz theory]], proposed in the 19th century by [[Thomas Young]] and [[Hermann von Helmholtz]], as mentioned above states that the retina's three types of cones are preferentially sensitive to blue, green, and red. [[Ewald Hering]] proposed the opponent process theory in 1872.<ref>{{cite journal|title=Zur Lehre vom Lichtsinne|journal=Sitzungsberichte der Mathematisch–Naturwissenschaftliche Classe der Kaiserlichen Akademie der Wissenschaften|issue=III Abtheilung|volume=LXVI. Band|first=Ewald|last=Hering|authorlink=Ewald Hering|year=1872| url=http://books.google.com/books?id=u5MCAAAAYAAJ&pg=PA5&lpg=PA5&dq=1872+hering+ewald+Zur+Lehre+vom+Lichtsinne.+Sitzungsberichte+der+kaiserlichen+Akademie+der+Wissenschaften.+Mathematisch%E2%80%93naturwissenschaftliche+Classe,&source=web&ots=fAdrz1yI8x&sig=99NSKb_P8-_QSDO1RTzt35QTRyk&hl=en}}</ref> It states that the visual system interprets color in an antagonistic way: red vs. green, blue vs. yellow, black vs. white. We now know both theories to be correct, describing different stages in visual physiology.
===Cone cells in the human eye===
{| class="wikitable"
!Cone type || Name || Range || Peak wavelength<ref name="Wyszecki">{{cite book
| first = Günther
| last = Wyszecki
| authorlink =
| coauthors = Stiles, W.S.
| year = 1982
| title = Color Science: Concepts and Methods, Quantitative Data and Formulae
| edition = 2nd ed.
| pages =
| publisher = Wiley Series in Pure and Applied Optics
| location = New York
| id = ISBN 0-471-02106-7
}}</ref><ref>{{cite book
| author = R. W. G. Hunt
| year = 2004
| title = The Reproduction of Colour
| edition = 6th ed.
| pages = 11–12
| publisher = Wiley–IS&T Series in Imaging Science and Technology
| location = Chichester UK
| id = ISBN 0-470-02425-9
}}</ref>
|-
|S || β || 400–500 [[Nanometre|nm]] || 420–440 nm
|-
|M || γ || 450–630 nm || 534–545 nm
|-
|L || ρ || 500–700 nm || 564–580 nm
|}
A range of wavelengths of light stimulates each of these receptor types to varying degrees. Yellowish-green light, for example, stimulates both L and M cones equally strongly, but only stimulates S-cones weakly. Red light, on the other hand, stimulates L cones much more than M cones, and S cones hardly at all; blue-green light stimulates M cones more than L cones, and S cones a bit more strongly, and is also the peak stimulant for rod cells;
and [[violet (color)|violet]] light stimulates almost exclusively S-cones. The brain combines the information from each type of receptor to give rise to different perceptions of different wavelengths of light.
The pigments present in the L and M cones are encoded on the X [[chromosome]]; defective encoding of these leads to the two most common forms of [[color blindness]]. The OPN1LW gene, which codes for the pigment that responds to yellowish light, is highly [[polymorphism (biology)|polymorphic]] (a recent study by Verrelli and Tishkoff found 85 variants in a sample of 236 men<ref>Verrelli, BC; Tishkoff, S (2004). [http://dx.doi.org/10.1086/423287 "Color vision molecular variation."] ''American Journal of Human Genetics''. '''75''' (3), 363-375</ref>), so up to ten percent of women<ref>[http://www.spie.org/x8849.xml?highlight=x2410 Biological color vision inspires artificial color processing]</ref> have an extra type of color receptor, and thus a degree of [[tetrachromat]]ic color vision.<ref>Roth, Mark (2006). [http://www.post-gazette.com/pg/06256/721190-114.stm "Some women may see 100 million colors, thanks to their genes"] ''Post-Gazette.com''</ref> Variations in OPN1MW, which codes for the bluish-green pigment, appear to be rare, and the observed variants have no effect on [[spectral sensitivity]].
===Color in the human brain===
Color processing begins at a very early level in the visual system (even within the retina) through initial color opponent mechanisms. Opponent mechanisms refer to the opposing color effect of red-green, blue-yellow, and light-dark. Visual information is then sent back via the [[optic nerve]] to the [[optic chiasm]]: a point where the two optic nerves meet and information from the temporal (contralateral) visual field crosses to the other side of the brain. After the optic chiasm the visual fiber tracts are referred to as the [[optic tract]]s, which enter the [[thalamus]] to synapse at the [[lateral geniculate nucleus]] (LGN). The LGN is segregated into six layers: two magnocellular (large cell) achromatic layers (M cells) and four parvocellular (small cell) chromatic layers (P cells). Within the LGN P-cell layers there are two chromatic opponent types: red vs. green and blue vs. green/red.
After [[Synapse|synapsing]] at the LGN, the visual tract continues on back toward the primary [[visual cortex]] (V1) located at the back of the brain within the [[occipital lobe]]. Within V1 there is a distinct band (striation). This is also referred to as "striate cortex", with other cortical visual regions referred to collectively as "extrastriate cortex".It is at this stage that color processing becomes much more complicated.
[[Image:Ventral-dorsal streams.svg|thumb|right|300px|Visual pathways in the human brain. The [[ventral stream]] (purple) is important in color recognition. The [[dorsal stream]] (green) is also shown. They originate from a common source in the [[visual cortex]].]]
In V1 the simple three-color segregation begins to break down. Many cells in V1 respond to some parts of the spectrum better than others, but this "color tuning" is often different depending on the adaptation state of the visual system. A given cell that might respond best to long wavelength light if the light is relatively bright might then become responsive to all wavelengths if the stimulus is relatively dim. Because the color tuning of these cells is not stable, some believe that a different, relatively small, population of neurons in V1 is responsible for color vision. These specialized "color cells" often have receptive fields that can compute local cone ratios. Such "double-opponent" cells were initially described in the goldfish retina by Nigel Daw;<ref>{{cite journal | doi = 10.1126/science.158.3803.942 | title = Goldfish Retina: Organization for Simultaneous Color Contrast | author = Nigel W. Daw | journal = Science | date = 17 November 1967 | volume = 158 | issue = 3803 | pages = 942–944 | pmid = 6054169 }}</ref><ref>{{cite book | title = Neural Mechanisms of Color Vision: Double-Opponent Cells in the Visual Cortex | author = Bevil R. Conway | url = http://books.google.com/books?id=pFodUlHfQmcC&pg=PR7&dq=goldfish+retina+by+Nigel-Daw&as_brr=3&ei=2AWqR764JI7-iAGh8vwE&sig=7vvLHGgrRP_QtPH6mjLuiqblglU | publisher = Springer | year = 2002 | isbn = 1402070926 }}</ref> their existence in primates was suggested by [[David H. Hubel]] and [[Torsten Wiesel]] and subsequently proven by Bevil Conway.<ref>Conway, Bevil R (2001). [http://www.jneurosci.org/cgi/content/full/21/8/2768 "Spatial structure of cone inputs to color cells in alert macaque primary visual cortex (V-1)"] ''Journal of Neuroscience''. '''21''' (8), 2768-2783.</ref> As Margaret Livingstone and David Hubel showed, double opponent cells are clustered within localized regions of V1 called blobs, and are thought to come in two flavors, red-green and blue-yellow.<ref>{{cite book | title = Neurons and Networks: An Introduction to Behavioral Neuroscience | author = John E. Dowling | publisher = Harvard University Press | year = 2001 | isbn = 0674004620 | url = http://books.google.com/books?id=adeUwgfwdKwC&pg=PA376&dq=Margaret+Livingstone+David+Hubel+double+opponent+blobs&as_brr=3&ei=YQaqR9-lAY6CiQHm1cmnCg&sig=D3znxI88shgNd8onK0RAWEMh6zY }}</ref> Red-green cells compare the relative amounts of red-green in one part of a scene with the amount of red-green in an adjacent part of the scene, responding best to local color contrast (red next to green). Modeling studies have shown that double-opponent cells are ideal candidates for the neural machinery of [[color constancy]] explained by [[Edwin H. Land]] in his [[retinex]] theory.<ref>McCann, M., ed. 1993. ''[[Edwin H. Land]]'s Essays.'' Springfield, Va.: Society for Imaging Science and Technology.</ref>
From the V1 blobs, color information is sent to cells in the second visual area, V2. The cells in V2 that are most strongly color tuned are clustered in the "thin stripes" that, like the blobs in V1, stain for the enzyme cytochrome oxidase (separating the thin stripes are interstripes and thick stripes, which seem to be concerned with other visual information like motion and high-resolution form). Neurons in V2 then synapse onto cells in area V4. Area V4 is a relatively large visual area, the largest by far cortical area outside V1, encompassing almost as much cortex as V1. Neurons in V4 were originally proposed by [[Semir Zeki]] to be exclusively dedicated to color, but this has since been shown not to be the case.<ref>John Allman and Steven W. Zucker, "On cytochrome oxidase blobs in visual cortex," in {{cite book | title = Spatial Vision in Humans and Robots: The Proceedings of the 1991 York Conference | author = Laurence Harris and Michael Jenkin, editors | date = 1993 | publisher = Cambridge University Press | isbn = 0521430712 | url = http://books.google.com/books?id=eWBiKaOCNIYC&pg=PA34&dq=v4+zeki+color&lr=&as_brr=3&ei=KBCqR7eGF4bQiwHpnZSoCg&sig=F_rbsAj3FD69wRMzWGhB1vK4RuQ }}</ref> Quantitative studies have argued that there is no higher concentration of color cells in V4 than in primary visual cortex, although this remains controversial. Independent of color sensitivity, V4 neurons have been shown to be very sensitive to the shape of stimuli, curvature, and stereo-scopic depth. V4 neurons have also been shown to be modulated by attention. The role of V4 neurons in color vision remains to be better characterized: indeed the vast majority of scientific papers examining the function of V4 do not concern color processing.
Anatomical studies have shown that neurons in V4 provide input to the inferior [[temporal lobe]] . "IT" cortex is thought to integrate color information with shape and form, although it has been difficult to define the appropriate criteria for this claim. Despite this murkiness, it has been useful to characterize this pathway (V1 > V2 > V4 > IT) as the [[ventral stream]] or the "what pathway", distinguished from the [[dorsal stream]] ("where pathway") that is thought to analyze motion, among many other features.
===In other animals===
Other animals, such as tropical [[fish]] and [[birds]], have more complex color vision systems than humans.<ref>Kelber, A., Osorio, D., Vorobyev, M. (2003) [http://www.blackwell-synergy.com/doi/abs/10.1017/S1464793102005985 "Animal colour vision--behavioural tests and physiological concepts."] Biol Rev Camb Philos Soc. 2003 Feb; 78(1):81-118. </ref> In the latter example, [[tetrachromacy]] is achieved through up to four cone types, depending on species. Brightly colored oil droplets inside the cones shift or narrow the spectral sensitivity of the cell. It has been suggested that it is likely that [[pigeon]]s are [[pentachromat]]s. Mammals other than primates generally have less effective two-receptor color perception systems, allowing only [[dichromat]]ic color vision; [[marine mammal]]s have only a single cone type and are thus [[monochromat]]s. Many invertebrates have color vision. [[Bees|Honey- and bumblebees]] have trichromatic color vision, which is insensitive to red but sensitive in ultraviolet to a color called ''bee purple''. ''Papilio'' butterflies apparently have tetrachromatic color vision despite possessing six photoreceptor types.<ref>Arikawa, K. (2003) [http://www.springerlink.com/content/whjepqnhpulyeevk/ "Spectral organization of the eye of a butterfly, Papilio"]. J. Comp. Phys. A 189, 791-800.</ref> The most complex color vision system in animal kingdom has been found in [[stomatopod]]s with up to 12 different spectral receptor types which are thought to work as multiple dichromatic units.<ref>Cronin T.W., Marshall, N.J. (1989) [http://www.nature.com/nature/journal/v339/n6220/abs/339137a0.html "A retina with at least ten spectral types of photoreceptors in a mantis shrimp"] Nature 339, 137 - 140.</ref>
==Evolution==
Color perception mechanisms are highly dependent on evolutionary factors, of which the most prominent is thought to be satisfactory recognition of food sources. In [[herbivorous]] primates, color perception is essential for finding proper (mature) leaves. In [[hummingbird]]s, particular flower types are often recognized by color as well. On the other hand, [[nocturnal]] mammals have less-developed color vision, since adequate light is needed for cones to function properly. There is evidence that [[ultraviolet]] light plays a part in color perception in many branches of the [[animal kingdom]], especially [[insect]]s.
The [[Evolution of color vision in primates|evolution of trichromatic color vision in primates]] occurred as the ancestors of modern monkeys, apes, and humans switched to [[Diurnal animal|diurnal]] (daytime) activity and began consuming fruits and leaves from flowering plants.<ref>[[Steven Pinker]]. ''[[How the Mind Works]]'', 1997. p. 191. ISBN 0-393-04535-8.</ref>
Some animals can distinguish colors in the ultraviolet spectrum. The UV spectrum falls below the human visible range. Birds, turtles, lizards, and fish have UV receptors in their retinas. These animals can see the UV patterns found on flowers and other wildlife that are otherwise invisible to the human eye. So far, there has not been enough evidence to show that any mammals are capable of UV vision.<ref>Timothy H. Goldsmith. "What Birds See", Scientific American, July 2006, Vol. 295, Issue 1.</ref>
UV and multi-dimensional vision is an especially important adaptation in birds. It allows birds to spot small prey from a distance, navigate, avoid predators, and forage while flying at high speeds. Birds also utilize their broad spectrum vision to recognize other birds, and in sexual selection.<ref>FJ Varela, AG Palacios, and TM Goldsmith. "Vision, Brain, and Behavior in Birds", 1993. p. 77-94.</ref><ref>IC Cuthill, JC Partridge, ATD Bennett, SC Church, NS Hart, and S Hunt. “Ultraviolet Vision in Birds”. Advances in the Study of Behavior. 2000. Vol. 29: 159-214.</ref>
==Mathematics of color perception==
A "physical color" is a combination of pure [[spectral color]]s (in the visible range). Since there are, in principle, infinitely many distinct spectral colors, the set of all physical colors may be thought of as an infinite-dimensional [[vector space]], in fact a [[Hilbert space]]. We call this space H<sub>color</sub>. More technically, the space of physical colors may be considered to be the (mathematical) [[cone (topology)|cone]] over the simplex whose vertices are the spectral colors.
An element C of H<sub>color</sub> is a function from the range of visible wavelengths—considered as an interval of real numbers [W<sub>min</sub>,W<sub>max</sub>]—to the real numbers, assigning to each wavelength w in [W<sub>min</sub>,W<sub>max</sub>] its intensity C(w).
A humanly perceived color may be modeled as three numbers: the extents to which each of the 3 types of cones is stimulated. Thus a humanly perceived color may be thought of as a point in 3-dimensional [[Euclidean space]]. We call this space R<sup>3</sup><sub>color</sub>.
Since each wavelength w stimulates each of the 3 types of cone cells to a known extent, these extents may be represented by 3 functions s(w), m(w), l(w) corresponding to the response of the S, M, and L cone cells, respectively.
Finally, since a beam of light can be composed of many different wavelengths, to determine the extent to which a physical color C in H<sub>color</sub> stimulates each cone cell, we must calculate the integral (with respect to w), over the interval [W<sub>min</sub>,W<sub>max</sub>], of C(w)*s(w), of C(w)*m(w), and of C(w)*l(w). The triple of resulting numbers associates to each physical color C (which is a region in H<sub>color</sub>) to a particular perceived color (which is a single point in R<sup>3</sup><sub>color</sub>). This association is easily seen to be linear. It may also easily be seen that many different regions in the "physical" space H<sub>color</sub> can all result in the same single perceived color in R<sup>3</sup><sub>color</sub>, so a perceived color is not unique to one physical color.
Thus human color perception is determined by a specific, non-unique linear mapping from the infinite-dimensional Hilbert space H<sub>color</sub> to the 3-dimensional Euclidean space R<sup>3</sup><sub>color</sub>.
Technically, the image of the (mathematical) cone over the simplex whose vertices are the spectral colors, by this linear mapping, is also a (mathematical) cone in R<sup>3</sup><sub>color</sub>. Moving directly away from the vertex of this cone represents maintaining the same [[chromaticity]] while increasing its intensity. Taking a cross-section of this cone yields a 2D chromaticity space. Both the 3D cone and its projection or cross-section are convex sets; that is, any mixture of spectral colors is also a color.
[[Image:CIExy1931.svg|thumb|right|300px|The CIE 1931 color space chromaticity diagram. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers. Note that the colors depicted depend on the color space of the device on which you are viewing the image, and therefore may not be a strictly accurate representation of the color at a particular position.]]
In practice, it would be quite difficult to measure an individual's cones' three responses to various physical color stimuli. So instead, three specific benchmark test lights are typically used; let us call them S, M, and L. In order to calibrate human perceptual space, scientists allowed human subjects to try to match any physical color by turning dials to create specific combinations of intensities (I<sub>S</sub>, I<sub>M</sub>, I<sub>L</sub>) for the S, M, and L lights, resp., until a match was found. This needed only to be done for physical colors that are spectral (since a linear combination of spectral colors will be matched by the same linear combination of their (I<sub>S</sub>, I<sub>M</sub>, I<sub>L</sub>) matches). Note that in practice, often at least one of S, M, L would have to be added with some intensity to the ''physical test color'', and that combination matched by a linear combination of the remaining 2 lights. Across different individuals (without color blindness), the matchings turned out to be nearly identical.
By considering all the resulting combinations of intensities (I<sub>S</sub>, I<sub>M</sub>, I<sub>L</sub>) as a subset of 3-space, a model for human perceptual color space is formed. (Note that when one of S, M, L had to be added to the test color, its intensity was counted as negative.) Again, this turns out to be a (mathematical) cone—not a quadric, but rather all rays through the origin in 3-space passing through a certain convex set. Again, this cone has the property that moving directly away from the origin corresponds to increasing the intensity of the S, M, L lights proportionately. Again, a cross-section of this cone is a planar shape that is (by definition) the space of "chromaticities" (informally: distinct colors); one particular such cross section, corresponding to constant X+Y+Z of the [[CIE 1931 color space]], gives the CIE chromaticity diagram.
It should be noted that this system implies that for any hue or non-spectral color, there are infinitely many distinct physical spectra that are all perceived as that hue or color. So, in general there is no such thing as ''the'' combination of spectral colors that we perceive as (say) yellow-green; instead there are infinitely many possibilities.
(The only exceptions to this rule are the perceptual colors corresponding to the ''boundary'' of the cone: in other words, those chromaticities on the simple closed curve that is the boundary of the 1931 C.I.E. diagram depicted in the figure. These comprise precisely all spectral colors plus the "line of purples" connecting the ends of the spectral colors: for each of these, there is only one physical color in H<sub>color</sub> that can create that perceived color.)
The CIE chromaticity diagram is horseshoe-shaped, with its curved edge corresponding to all spectral colors (the ''spectral [[locus (mathematics)|locus]]''), and the remaining straight edge corresponding to the most saturated [[purple]]s—mixtures of [[red]] and [[Violet (color)|violet]].
==Chromatic adaptation==
An object may be viewed under various conditions. For example, it may be illuminated by sunlight, the light of a fire, or a harsh electric light. In all of these situations, human vision perceives that the object has the same color: an apple always appears red, whether viewed at night or during the day. On the other hand, a camera with no adjustment for light may register the apple as having varying color. This feature of the visual system is called chromatic adaptation, or [[color constancy]]; when the correction occurs in a camera it is referred to as [[white balance]].
Chromatic adaptation is one aspect of vision that may fool someone into observing a color-based [[optical illusion]], such as the [[same color illusion]].
Though the human visual system generally does maintain constant perceived color under different lighting, there are situations where the relative brightness of two different stimuli will appear reversed at different [[illuminance]] levels. For example, the bright yellow petals of flowers will appear dark compared to the green leaves in dim light while the opposite is true during the day. This is known as the [[Purkinje effect]], and arises because the peak sensitivity of the human eye shifts toward the blue end of the spectrum at lower light levels.
{{splitsection}}
===Von Kries transform===
The von Kries chromatic adaptation method is a technique that is sometimes used in camera image processing. The method is to apply a gain to each of the human [[cone cell]] spectral sensitivity responses so as to keep the adapted appearance of the reference white constant. The application of [[Johannes von Kries]]'s idea of adaptive gains on the three [[cone cell]] types was first explicitly applied to the problem of color constancy by [[Herbert E. Ives]],<ref>Ives, H.E. (1912) "The relation between the color of the illuminant and the color of the illuminated object." ''Trans. Illuminat. Eng. Soc.'' 7, 62–72, (Reprinted in: ''Color Res. Appl.'' 20, 70–75.).</ref><ref>{{cite journal | title = Colour constancy in context: Roles for local adaptation and levels of reference | author = Hannah E. Smithson and Qasim Zaidi | journal = Journal of Vision | volume = 4 | issue = 9 | date = 2004 | url = http://www.journalofvision.org/4/9/3/article.aspx | pages = 693–710 | doi = 10.1167/4.9.3 }}</ref> and the method is sometimes referred to as the Ives transform<ref>{{cite journal | title = Review. Sensory, computational and cognitive components of human colour constancy | author = Hannah E. Smithson | journal = Philosophical Transactions of the Royal Society | volume = 360 | issue = 1458 | date = 2005 | url = http://journals.royalsociety.org/content/px26ma7w586vq2a7/ | pages = 1329–1346 | doi = 10.1098/rstb.2005.1633}}</ref> or the von Kries–Ives adaptation.<ref>{{cite book | title = Color Vision: From Genes to Perception | author = Karl R. Gegenfurtner, L. T. Sharpe | isbn = 052100439X | year = 1999 | publisher = Cambridge University Press | url = http://books.google.com/books?id=9R1ogJsPHi8C&pg=PA413&dq=von-kries+ives&ei=gYuSR--JOZ6ktgOAkPVE&ie=ISO-8859-1&sig=9fSl-f7sE95QZ2mfBQSauPMhvrc }}</ref>
The [[von Kries]] ''coefficient rule'' rests on the assumption that [[color constancy]] is achieved by individually adapting the gains of the three cone responses, the gains depending on the sensory context, that is, the color history and surround. Thus, the cone responses <math>c'</math> from two radiant spectra can be matched by appropriate choice of diagonal adaptation matrices <math>D_1</math> and <math>D_2</math><ref>{{cite book|author=Gaurav Sharma|publisher=[[CRC Press]]|title=Digital Color Imaging Handbook|year=2003}}</ref>:
:<math>c'=D_1\,S^T\,f_1 = D_2\,S^T\,f_2</math>
where <math>S</math> is the ''cone sensitivity matrix'' and <math>f</math> is the spectrum of the conditioning stimulus. This leads to the '''von Kries transform''' for chromatic adaptation in [[LMS color space]] (responses of long-, medium-, and short-wavelength cone response space):
:<math>D = D_1^{-1} D_2=\begin{bmatrix} L_2/L_1 & 0 & 0 \\ 0 & M_2/M_1 & 0 \\ 0 & 0 & S_2/S_1 \end{bmatrix}</math>
This diagonal matrix ''D'' maps cone responses, or colors, in one adaptation state to corresponding colors in another; when the adaptation state is presume to be determined by the illuminant, this matrix is useful as an illuminant adaptation transform. The elements of the diagonal matrix D are the ratios of the cone responses (Long, Medium, Short) for the illuminant's [[white point]].
The more complete von Kries transform, for colors represented in [[CIE 1931 color space|XYZ]] or [[RGB color space]], includes matrix transformations into and out of LMS space, with the diagonal transform D in the middle.<ref>{{cite book | title = High Dynamic Range Imaging: Acquisition, Display, and Image-Based Lighting | author = Erik Reinhard | isbn = 0125852630 | publisher = Morgan Kaufmann | year = 2006 | url = http://books.google.com/books?id=dH2lRxTg1UsC&pg=PA39&dq=von-kries-transform&ei=fIGSR6jlBoiGsgOK4qE9&sig=OjjbcXI1dbMkdqZWm3ojUvqV92Q#PPA36,M1 }}</ref>
==References==
{{reflist}}
==See also==
*[[Color theory]]
*[[Primary color]]
*[[Visual perception]]
==External links==
* [http://www.psycport.com/stories/ascribe_2004_07_14_eng-ascribe_eng-ascribe_014026_988726893508805748.xml.html "Evidence that men, women literally see the world differently: Study shows color vision may have been adaptive during evolution."]
* [http://www.rwc.uc.edu/koehler/biophys/6d.html Spectral Sensitivity of the Eye.]
* [http://www.4colorvision.com/files/tetrachromat.htm Vision may not be what we thought.]
* [http://www.diycalculator.com/sp-cvision.shtml Overview of color vision.]
* [http://survivor99.com/colorforum/ The decoding model: a symmetrical model of color vision.]
* [http://www.stareclips.com/ Working examples of Chromatic Adaptation.]
* [http://www.egopont.com/colorvision.php Egopont color vision test]
* [http://www.eyeforum.info/index.php?topic=4.msg4#msg4 What the eyes really see: brain image enhancement]
{{Color vision}}
[[Category:Color]]
[[Category:Image processing]]
[[Category:Visual perception]]
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