Editing Chromatic adaptation (section)

== 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>{{Cite journal|author=Ives HE |title=The relation between the color of the illuminant and the color of the illuminated object |journal=Trans. Illuminat. Eng. Soc. |volume=7 |pages=62–72 |year=1912}} (Reprinted in: {{Cite journal|journal=Color Research & Application |volume=20 |pages=70–5 |doi=10.1002/col.5080200112 |title=The relation between the color of the illuminant and the color of the illuminated object |year=1995 |author=Brill, Michael H. }})</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 | year = 2004 | pages = 693–710 | doi = 10.1167/4.9.3 | pmid = 15493964 | doi-access = free }}</ref> and the method is sometimes referred to as the Ives transform<ref>{{Cite journal| title = Review. Sensory, computational and cognitive components of human color constancy | author = Hannah E. Smithson | journal = Philosophical Transactions of the Royal Society | volume = 360 | issue = 1458 | year = 2005 | pages = 1329–46 | doi = 10.1098/rstb.2005.1633 | pmid = 16147525 | pmc = 1609194}}</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 = 0-521-00439-X | year = 1999 | publisher = Cambridge University Press | url = https://books.google.com/books?id=9R1ogJsPHi8C&dq=von-kries+ives&pg=PA413 }}</ref>

The [[von Kries Coefficient Law|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 ''D''<sub>1</sub> and ''D''<sub>2</sub>:<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 presumed 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 Color Space|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 = 0-12-585263-0 | publisher = Morgan Kaufmann | year = 2006 | url = https://books.google.com/books?id=dH2lRxTg1UsC&dq=von-kries-transform&pg=PA39 }}</ref>