Title: | CIE XYZ and some of Its Derived Color Spaces |
---|---|
Description: | Functions for converting among CIE XYZ, xyY, Lab, and Luv. Calculate Correlated Color Temperature (CCT) and the Planckian and daylight loci. The XYZs of some standard illuminants and some standard linear chromatic adaptation transforms (CATs) are included. Three standard color difference metrics are included. |
Authors: | Glenn Davis [aut,cre] |
Maintainer: | Glenn Davis <[email protected]> |
License: | GPL (>= 3) |
Version: | 1.3-0 |
Built: | 2024-11-18 06:42:51 UTC |
Source: | CRAN |
This package covers the basic CIE 1931 space, and derived spaces CIE xyY, Lab, and Luv. The equations are taken from Bruce Lindbloom's CIE Color Calculator. Color areas that are *not* covered are:
spectral color data
device color spaces, e.g. RGB and CMYK
color order systems, e.g. Munsell, DIN, NCS, Ostwald, ...
The API is small. There are functions to
convert between CIE XYZ and other CIE spaces
create and perform some standard chromatic adaptation transforms (CATs)
compute 3 standard color difference E metrics
retrieve XYZ and xy of some standard illuminants
Package colorscience is a superset of this one.
Package colorspace has similar functionality, and is much faster because it in compiled C.
Package grDevices also has similar functionality
(in the function convertColor()
),
but is missing chromaticities xy, uv, and u'v'.
Glenn Davis <[email protected]>
Lindbloom, Bruce. CIE Color Calculator. http://brucelindbloom.com/index.html?ColorCalculator.html
Lindbloom, Bruce. Color Difference Calculator. http://brucelindbloom.com/index.html?ColorDifferenceCalc.html
Adapt XYZ, xyY, Lab, or Luv from a source viewing enviroment with a given illuminant, to a target viewing environment with a different illuminant.
## S3 method for class 'CAT' adaptXYZ( x, XYZ.src ) ## S3 method for class 'CAT' adaptxyY( x, xyY.src ) ## S3 method for class 'CAT' adaptLab( x, Lab.src ) ## S3 method for class 'CAT' adaptLuv( x, Luv.src )
## S3 method for class 'CAT' adaptXYZ( x, XYZ.src ) ## S3 method for class 'CAT' adaptxyY( x, xyY.src ) ## S3 method for class 'CAT' adaptLab( x, Lab.src ) ## S3 method for class 'CAT' adaptLuv( x, Luv.src )
x |
a CAT object as returned from |
XYZ.src |
an Nx3 matrix, or a vector that can be converted to such a matrix, by rows. Each row has an XYZ in the source viewing environment. |
xyY.src |
an Nx3 matrix, or a vector that can be converted to such a matrix, by rows. Each row has an xyY in the source viewing environment. |
Lab.src |
an Nx3 matrix, or a vector that can be converted to such a matrix, by rows. Each row has an Lab in the source viewing environment. |
Luv.src |
an Nx3 matrix, or a vector that can be converted to such a matrix, by rows. Each row has an Luv in the source viewing environment. |
adaptXYZ()
is the most fundamental of the group;
it simply multiplies each of the input XYZs by x$M
.
adaptxyY()
converts xyY.src to XYZ,
calls adaptXYZ()
,
and then converts back to xyY.tgt.
And it does an additional check:
if the xy of xyY.src is equal to the xy of x$source.xyY
,
then the xy of the returned xyY.tgt is set to be the xy of x$target.xyY
.
adaptLab()
and adaptLuv()
work in a similar way.
When Lab.src
is transformed to XYZ, the whitepoint is set to x$source.XYZ
.
And when the adapted XYZ is transformed to adapted Lab, the whitepoint is set to target.XYZ
.
adaptXYZ()
returns an Nx3 matrix with adapted XYZ.
Each row has an XYZ in the target viewing environment.
adaptxyY()
returns an Nx3 matrix with adapted xyY.
Each row has an xyY in the target viewing environment.
adaptLab()
and adaptLuv()
return adapted Lab and Luv respectively.
Hunt, R. W. G. The Reproduction of Colour. 6th Edition. John Wiley & Sons. 2004.
International Color Consortium. ICC.1:2001-04. File Format for Color Profiles. 2001.
Lindbloom, Bruce. Chromatic Adaptation. http://brucelindbloom.com/Eqn_ChromAdapt.html
Wikipedia. CIECAM02. https://en.wikipedia.org/wiki/CIECAM02
CAT()
,
standardXYZ()
# try the Bradford method bCAT = CAT( 'D50', 'D65', method='bradford' ) adaptXYZ( bCAT, c(1,1,0.5) ) ## X Y Z ## [1,] 0.9641191 0.9921559 0.6567701 adaptLab( bCAT, c(50,20,-10) ) ## L a b ## [1,] 49.97396 20.84287 -10.19661 # as expected, there is a change adaptLab( bCAT, c(40,0,0) ) ## L a b ## [1,] 40 0 0 # but adaptLab() always preserves neutrals adaptLuv( bCAT, c(40,0,0) ) ## L u v ## [1,] 40 0 0 # and adaptLuv() also preserves neutrals # try the scaling method - now XYZ are scaled independently sCAT = CAT( 'D50', 'D65', method='scaling' ) adaptLab( sCAT, c(50,20,-10) ) ## L a b ## [1,] 50 20 -10 with sCAT, adaptLab() is now the identity for *all* colors adaptLuv( sCAT, c(50,-20,10) ) ## L u v ## [1,] 50 -18.32244 11.29946 but adaptLuv() is NOT the identity for all colors
# try the Bradford method bCAT = CAT( 'D50', 'D65', method='bradford' ) adaptXYZ( bCAT, c(1,1,0.5) ) ## X Y Z ## [1,] 0.9641191 0.9921559 0.6567701 adaptLab( bCAT, c(50,20,-10) ) ## L a b ## [1,] 49.97396 20.84287 -10.19661 # as expected, there is a change adaptLab( bCAT, c(40,0,0) ) ## L a b ## [1,] 40 0 0 # but adaptLab() always preserves neutrals adaptLuv( bCAT, c(40,0,0) ) ## L u v ## [1,] 40 0 0 # and adaptLuv() also preserves neutrals # try the scaling method - now XYZ are scaled independently sCAT = CAT( 'D50', 'D65', method='scaling' ) adaptLab( sCAT, c(50,20,-10) ) ## L a b ## [1,] 50 20 -10 with sCAT, adaptLab() is now the identity for *all* colors adaptLuv( sCAT, c(50,-20,10) ) ## L u v ## [1,] 50 -18.32244 11.29946 but adaptLuv() is NOT the identity for all colors
Construct transforms from a source viewing enviroment with a given illuminant, to a target viewing environment with a different illuminant. Some standard linear von-Kries-based CAT methods are available.
CAT( source.XYZ, target.XYZ, method="Bradford" )
CAT( source.XYZ, target.XYZ, method="Bradford" )
source.XYZ |
the XYZ of the illuminant in the source viewing environment.
|
target.XYZ |
the XYZ of the illuminant in the target viewing environment.
|
method |
the method used for the chromatic adaptation. Available methods are:
|
CAT()
returns an object with S3 class CAT, which can be passed to
adaptXYZ()
,
adaptxyY()
,
adaptLab()
, or
adaptLuv()
.
An object with S3 class CAT is a list with the following items:
full name of the adaptation method, as in Arguments.
If argument method
is a 3x3 matrix, then this method
is NA
.
3x3 cone response matrix for the method, as defined in Lindbloom
XYZ of the illuminant in the source viewing environment
xyY of the illuminant in the source viewing environment
XYZ of the illuminant in the target viewing environment
xyY of the illuminant in the target viewing environment
3x3 matrix defining the CAT. The matrix is written on the left and the source XYZ is written as a column vector on the right. This matrix depends continuously on source.XYZ and target.XYZ, and when these are equal, M is the identity. Therefore, when source.XYZ and target.XYZ are close, M is close to the identity. Compare with Lindbloom.
Chromatic adaptation can be viewed as an Aristotelian Analogy of Proportions. For more about this, see the vignette Chromatic Adaptation.
Bianco, Simone and Raimondo Schettini. Two new von Kries based chromatic adaptation transforms found by numerical optimization. Color Research & Application. v. 35. i. 3. Jan 2010.
Hunt, R. W. G. The Reproduction of Colour. 6th Edition. John Wiley & Sons. 2004.
International Color Consortium. ICC.1:2001-04. File Format for Color Profiles. 2001.
Lindbloom, Bruce. Chromatic Adaptation. http://brucelindbloom.com/Eqn_ChromAdapt.html
Pascale, Danny. A Review of RGB Color Spaces ...from xyY to R'G'B'. https://babelcolor.com/index_htm_files/A%20review%20of%20RGB%20color%20spaces.pdf 2003.
Wikipedia. CIECAM02. https://en.wikipedia.org/wiki/CIECAM02
standardXYZ()
,
adaptXYZ()
,
adaptxyY()
,
adaptLab()
,
adaptLuv()
D65toC = CAT( 'D65', 'C' ) D65toC ## $method ## [1] "Bradford" ## ## $Ma ## X Y Z ## L 0.8951 0.2664 -0.1614 ## M -0.7502 1.7135 0.0367 ## S 0.0389 -0.0685 1.0296 ## ## $source.XYZ ## X Y Z ## D65 0.95047 1 1.08883 ## ## $source.xyY ## x y Y ## D65 0.3127266 0.3290231 1 ## ## $target.XYZ ## X Y Z ## C 0.98074 1 1.18232 ## ## $target.xyY ## x y Y ## C 0.3100605 0.3161496 1 ## ## $M ## X Y Z ## X 1.009778519 0.007041913 0.012797129 ## Y 0.012311347 0.984709398 0.003296232 ## Z 0.003828375 -0.007233061 1.089163878 ## ## attr(,"class") ## [1] "CAT" "list" adaptXYZ( D65toC, c(1,1,0.5) ) ## X Y Z ## [1,] 1.023219 0.9986689 0.5411773
D65toC = CAT( 'D65', 'C' ) D65toC ## $method ## [1] "Bradford" ## ## $Ma ## X Y Z ## L 0.8951 0.2664 -0.1614 ## M -0.7502 1.7135 0.0367 ## S 0.0389 -0.0685 1.0296 ## ## $source.XYZ ## X Y Z ## D65 0.95047 1 1.08883 ## ## $source.xyY ## x y Y ## D65 0.3127266 0.3290231 1 ## ## $target.XYZ ## X Y Z ## C 0.98074 1 1.18232 ## ## $target.xyY ## x y Y ## C 0.3100605 0.3161496 1 ## ## $M ## X Y Z ## X 1.009778519 0.007041913 0.012797129 ## Y 0.012311347 0.984709398 0.003296232 ## Z 0.003828375 -0.007233061 1.089163878 ## ## attr(,"class") ## [1] "CAT" "list" adaptXYZ( D65toC, c(1,1,0.5) ) ## X Y Z ## [1,] 1.023219 0.9986689 0.5411773
Compute the CCT in Kelvin, of XYZ, xy, and uv, by multiple methods. And compute points on the Planckian locus.
The reference Planckian locus is defined spectrally - from
the famous equation for the Planckian radiator
(with )
and from the tabulated CIE 1931 standard observer color matching functions,
from 360 to 830nm in 1nm steps.
The reference locus is a
curve, parameterized by temperature,
in a 2D chromaticity space,
usually either xy (1931) or uv (1960).
Computing uv values (and derivatives) is lengthy because there are 471 wavelengths.
An approximation to the reference locus is desirable.
The default locus approximation is a spline
(using stats::splinefun()
with method="fmm"
)
through the 31 uv locus points in Robertson and Wyszecki & Stiles.
This spline does not appear in Robertson, but I think he would approve of it.
It has continuity and good agreement with the reference locus.
The maximum RMS error in the uv-plane is about
over the valid temperature interval [1667,
] K.
A similar piecewise-linear interpolating path has a maximum RMS error about 10 times larger.
The 31 uv values in the table are accurate to the given 5 decimal places
(but see Note), and the rounding to 5 places is a big limitation in accuracy.
The locus is parameterized directly by reciprocal color temperature (
),
and therefore indirectly by
.
We call either of these the native pameterization of the locus.
See Planckian Loci.
The lines that are perpendicular to the locus are called the native isotherms.
The second available locus is a quintic spline through 65 points (knots),
that were computed and saved with full precision.
The maximum RMS error in the uv-plane is about
over the valid temperature interval [1000,
] K.
For this one the 1st and 2nd derivatives were also computed,
so the normal vectors at the knots are accurate,
and the curve is also
.
See Planckian Loci.
The lines that are perpendicular to the locus are also called the native isotherms.
Two more families of isotherms are available.
The Robertson isotherms are tabulated just like the points on the locus,
and a special linear interpolation is used for intermediate temperatures.
The McCamy isotherms are defined by a single cubic rational function in xy,
and no interpolation is necessary.
Each isotherm family induces a slightly different parameterization of the locus -
the temperature at a locus point is the temperature of the isotherm
passing through that point.
The Robertson parameterization is only continuous of class ,
but the geometric continuity class is
.
The McCamy parameterization is as smooth as the locus itself, which is
.
For the Robertson parameterization the
valid temperature interval is [1667,] K.
For the McCamy parameterization the valid temperature interval
is at most [1621,34530] K, and may be smaller depending on the locus.
CCTfromXYZ( XYZ, isotherms='robertson', locus='robertson', strict=FALSE ) CCTfromxy( xy, isotherms='robertson', locus='robertson', strict=FALSE ) CCTfromuv( uv, isotherms='robertson', locus='robertson', strict=FALSE ) planckLocus( temperature, locus='robertson', param='robertson', delta=0, space=1960 )
CCTfromXYZ( XYZ, isotherms='robertson', locus='robertson', strict=FALSE ) CCTfromxy( xy, isotherms='robertson', locus='robertson', strict=FALSE ) CCTfromuv( uv, isotherms='robertson', locus='robertson', strict=FALSE ) planckLocus( temperature, locus='robertson', param='robertson', delta=0, space=1960 )
XYZ |
a numeric Mx3 matrix with XYZ tristimulus values (CIE 1931) in the rows, or a numeric vector that can be converted to such a matrix, by row. |
xy |
a numeric Mx2 matrix with xy chromaticity values (CIE 1931) in the rows, or a numeric vector that can be converted to such a matrix, by row. |
uv |
a numeric Mx2 matrix with uv chromaticity values (CIE UCS 1960) in the rows, or a numeric vector that can be converted to such a matrix, by row. |
isotherms |
A character vector whose elements match one
of the available isotherm families:
|
locus |
valid values are |
strict |
The CIE considers the CCT of a chromaticity |
temperature |
a M-vector of temperatures (in K) at which to compute points on the
Planckian locus, either for |
param |
the desired parameterization of the locus.
It can be either |
delta |
a vector of offset distances in |
space |
the year of the chromaticity space to return.
Valid values are 1960 (the default |
Each of the isotherm families correspond to a parameterization of the locus. All this is designed so a round trip: temperature → uv → CCT (with the same choice of isotherm/parameterization) has neglible error.
When isotherms='native'
the tangent line at a point on the locus is computed using the deriv=1
argument to
stats::splinefun()
and the normal line - the isotherm at the point - is then easily computed from the tangent line.
When isotherms='robertson'
or isotherms='mccamy'
the locus curve
has no effect on the computed CCT.
The locus is only used when computing the distance from the given uv point to the locus
(along the corresponding isotherm),
and therefore only affects the decision whether the CCT is meaningful
when strict=TRUE
.
CCTfromXYZ()
, CCTfromxy()
, and CCTfromuv()
return a numeric vector of length M, or an MxN matrix.
It returns a matrix iff length(isotherms) = N
2,
and the column names are set to the isotherm family names.
The names or rownames are set to the rownames of the input.
In case of error, the element of the vector or matrix is set to
NA_real_
.
In case there is an error in the arguments, the functions return NULL
.
In these functions, the locus is not used unless
isotherms='native'
or strict=TRUE
.
planckLocus()
returns an Mx2 matrix with chromaticies in the rows.
The column names are set appropriately for the value of space
.
The row names are set from temperature
.
In case of a single error, both entries in the row are set to NA_real_
.
In case there is an error in the arguments, the functions return NULL
.
The lookup table on page 228 in Wyszecki & Stiles contains an error at 325 mired, which was corrected by Bruce Lindbloom (see Source).
http://www.brucelindbloom.com/index.html?Eqn_XYZ_to_T.html
McCamy, C. S. Correlated color temperature as an explicit function of chromaticity coordinates. Color Research & Application. Volume 17. Issue 2. pages 142-144. April 1992.
Robertson, A. R. Computation of correlated color temperature and distribution temperature. Journal of the Optical Society of America. 58. pp. 1528-1535 (1968).
Wyszecki, Günther and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition. John Wiley & Sons, 1982. Table 1(3.11). pp. 227-228.
stats::splinefun()
,
colorSpec::computeCCT()
,
RobertsonLocus
,
PrecisionLocus
,
the vignette Correlated Color Temperature Isotherms
# do a round trip and then compare temperature = c(5003,6504) uv = planckLocus( temperature, delta=0.05 ) CCTfromuv( uv ) - temperature ## 2.772227e-05 5.094369e-05 # find some points on the daylight locus, and then their CCT temperature = seq( 2000, 10000, by=1000 ) xy = daylightLocus( temperature ) cbind( xy, CCT=CCTfromxy(xy,iso='mccamy') ) ## x y CCT ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 0.3823436 0.3837663 4005.717 ## D5000 0.3457410 0.3586662 4999.998 ## D6000 0.3216915 0.3377984 5999.437 ## D7000 0.3053570 0.3216459 6997.542 ## D8000 0.2937719 0.3092195 7985.318 ## D9000 0.2852645 0.2995816 8948.809 ## D10000 0.2787996 0.2919672 9881.115 # compare all 3 different isotherms CCTfromxy( xy, isotherms=c('robertson',NA,'mccamy') ) ## Robertson native McCamy ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 4000.096 4000.062 4005.717 ## D5000 4999.749 4999.608 4999.998 ## D6000 5998.015 5999.242 5999.437 ## D7000 6997.858 6998.258 6997.542 ## D8000 7997.599 7996.985 7985.318 ## D9000 8999.301 8993.811 8948.809 ## D10000 9991.920 9992.672 9881.115 cbind( default=CCTfromxy(xy), prec.native=CCTfromxy(xy,locus='prec',iso=NA) ) ## default prec.native ## 2000K NA NA ## 3000K NA NA ## 4000K 4000.096 4000.052 ## 5000K 4999.749 4999.767 ## 6000K 5998.015 5999.097 ## 7000K 6997.858 6997.857 ## 8000K 7997.599 7997.951 ## 9000K 8999.301 8995.835 ## 10000K 9991.920 9992.839
# do a round trip and then compare temperature = c(5003,6504) uv = planckLocus( temperature, delta=0.05 ) CCTfromuv( uv ) - temperature ## 2.772227e-05 5.094369e-05 # find some points on the daylight locus, and then their CCT temperature = seq( 2000, 10000, by=1000 ) xy = daylightLocus( temperature ) cbind( xy, CCT=CCTfromxy(xy,iso='mccamy') ) ## x y CCT ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 0.3823436 0.3837663 4005.717 ## D5000 0.3457410 0.3586662 4999.998 ## D6000 0.3216915 0.3377984 5999.437 ## D7000 0.3053570 0.3216459 6997.542 ## D8000 0.2937719 0.3092195 7985.318 ## D9000 0.2852645 0.2995816 8948.809 ## D10000 0.2787996 0.2919672 9881.115 # compare all 3 different isotherms CCTfromxy( xy, isotherms=c('robertson',NA,'mccamy') ) ## Robertson native McCamy ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 4000.096 4000.062 4005.717 ## D5000 4999.749 4999.608 4999.998 ## D6000 5998.015 5999.242 5999.437 ## D7000 6997.858 6998.258 6997.542 ## D8000 7997.599 7996.985 7985.318 ## D9000 8999.301 8993.811 8948.809 ## D10000 9991.920 9992.672 9881.115 cbind( default=CCTfromxy(xy), prec.native=CCTfromxy(xy,locus='prec',iso=NA) ) ## default prec.native ## 2000K NA NA ## 3000K NA NA ## 4000K 4000.096 4000.052 ## 5000K 4999.749 4999.767 ## 6000K 5998.015 5999.097 ## 7000K 6997.858 6997.857 ## 8000K 7997.599 7997.951 ## 9000K 8999.301 8995.835 ## 10000K 9991.920 9992.839
Compute points on the daylight locus, in multiple chromaticity spaces
daylightLocus( temperature, space=1931 )
daylightLocus( temperature, space=1931 )
temperature |
an M-vector of temperatures (in K) at which to compute points on the
daylight locus.
The valid temperatures range is 4000K to 25000K;
outside this range the output is set to |
space |
the year of the output chromaticity space desired - valid values are
1931, 1976 and 1960.
The 1931 is the original and denoted by xy; the others are derived from it.
The 1960 coordinates are usually denoted by uv,
and the 1976 coordinates by u'v'.
The only difference is that |
a numeric Mx2 matrix with xy, uv, or u'v' coordinates in the rows. The colnames of the output are set appropriately.
The names of the temperature are copied to the rownames of the output,
unless these names are NULL
when the temperatures followed by 'K' are used.
If the input is invalid, the function returns NULL
.
Wyszecki, Günther and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition. John Wiley & Sons, 1982. pp. 145-146.
uvfromxy()
# find some points on the daylight locus, and then their CCT temp = seq( 2000, 10000, by=1000 ) xy = daylightLocus( temp ) cbind( xy, CCT=CCTfromxy(xy) ) ## x y CCT ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 0.3823436 0.3837663 4000.096 ## D5000 0.3457410 0.3586662 4999.749 ## D6000 0.3216915 0.3377984 5998.015 ## D7000 0.3053570 0.3216459 6997.858 ## D8000 0.2937719 0.3092195 7997.599 ## D9000 0.2852645 0.2995816 8999.301 ## D10000 0.2787996 0.2919672 9991.920
# find some points on the daylight locus, and then their CCT temp = seq( 2000, 10000, by=1000 ) xy = daylightLocus( temp ) cbind( xy, CCT=CCTfromxy(xy) ) ## x y CCT ## D2000 NA NA NA ## D3000 NA NA NA ## D4000 0.3823436 0.3837663 4000.096 ## D5000 0.3457410 0.3586662 4999.749 ## D6000 0.3216915 0.3377984 5998.015 ## D7000 0.3053570 0.3216459 6997.858 ## D8000 0.2937719 0.3092195 7997.599 ## D9000 0.2852645 0.2995816 8999.301 ## D10000 0.2787996 0.2919672 9991.920
Calculate Standard CIE Color Differences between two Colors
DeltaE( Lab1, Lab2, metric=1976 )
DeltaE( Lab1, Lab2, metric=1976 )
Lab1 |
a numeric Nx3 matrix with Lab values in the rows, or a vector that can be converted to such a matrix, by row.
|
Lab2 |
a numeric Nx3 matrix with Lab values in the rows, or a vector that can be converted to such a matrix, by row.
|
metric |
a vector of color metric specifiers.
Valid values are |
DeltaE()
returns a numeric vector of length N, or an NxM matrix.
It returns a matrix iff length(metric)=
M 2;
the column names are set to the metric names.
The elements of the output are the pairwise differences,
i.e. between row i of
Lab1
and row i of Lab2
.
The names or rownames are set to the rownames of one of the input matrices.
For metric=1976
the distance is simply the Euclidean distance between the two points in Lab, see Hunt p. 111.
For metric=1994
the symmetric variant is used, see Hunt p. 670.
There is an asymmetric variant which is not available in this package.
The weighting coefficients are for graphic arts (not for textiles).
For metric=2000
the distance is insanely complicated, see Hunt p. 671.
All these metrics are symmetric,
which means that swapping Lab1
and Lab2
does not change the result.
Hunt, R. W. G. The Reproduction of Colour. 6th Edition. John Wiley & Sons. 2004.
DeltaE( c(50,0,0), c(51,2,2, 52,10,11, 46,-13,16) ) ## [1] 3 15 21 path = system.file( "extdata/ciede2000testdata.txt", package='spacesXYZ' ) df = read.table( path, sep='\t', quote='', head=TRUE ) Lab1 = as.matrix( df[ , 1:3 ] ) Lab2 = as.matrix( df[ , 4:6 ] ) cbind( Lab1, Lab2, DeltaE( Lab1, Lab2, metric=c(1976,2000) ) )[ 1:10, ] ## LAB_L_REF LAB_A_REF LAB_B_REF LAB_L_SAM LAB_A_SAM LAB_B_SAM DeltaE.1976 DeltaE.2000 ## [1,] 50.0000 2.6772 -79.7751 50.0000 0.0000 -82.7485 4.0010633 2.0424597 ## [2,] 50.0000 3.1571 -77.2803 50.0000 0.0000 -82.7485 6.3141501 2.8615102 ## [3,] 50.0000 2.8361 -74.0200 50.0000 0.0000 -82.7485 9.1776999 3.4411906 ## [4,] 50.0000 -1.3802 -84.2814 50.0000 0.0000 -82.7485 2.0627008 0.9999989 ## [5,] 50.0000 -1.1848 -84.8006 50.0000 0.0000 -82.7485 2.3695707 1.0000047 ## [6,] 50.0000 -0.9009 -85.5211 50.0000 0.0000 -82.7485 2.9152927 1.0000130 ## [7,] 50.0000 0.0000 0.0000 50.0000 -1.0000 2.0000 2.2360680 2.3668588 ## [8,] 50.0000 -1.0000 2.0000 50.0000 0.0000 0.0000 2.2360680 2.3668588 ## [9,] 50.0000 2.4900 -0.0010 50.0000 -2.4900 0.0009 4.9800004 7.1791720 ## [10,] 50.0000 2.4900 -0.0010 50.0000 -2.4900 0.0010 4.9800004 7.1791626
DeltaE( c(50,0,0), c(51,2,2, 52,10,11, 46,-13,16) ) ## [1] 3 15 21 path = system.file( "extdata/ciede2000testdata.txt", package='spacesXYZ' ) df = read.table( path, sep='\t', quote='', head=TRUE ) Lab1 = as.matrix( df[ , 1:3 ] ) Lab2 = as.matrix( df[ , 4:6 ] ) cbind( Lab1, Lab2, DeltaE( Lab1, Lab2, metric=c(1976,2000) ) )[ 1:10, ] ## LAB_L_REF LAB_A_REF LAB_B_REF LAB_L_SAM LAB_A_SAM LAB_B_SAM DeltaE.1976 DeltaE.2000 ## [1,] 50.0000 2.6772 -79.7751 50.0000 0.0000 -82.7485 4.0010633 2.0424597 ## [2,] 50.0000 3.1571 -77.2803 50.0000 0.0000 -82.7485 6.3141501 2.8615102 ## [3,] 50.0000 2.8361 -74.0200 50.0000 0.0000 -82.7485 9.1776999 3.4411906 ## [4,] 50.0000 -1.3802 -84.2814 50.0000 0.0000 -82.7485 2.0627008 0.9999989 ## [5,] 50.0000 -1.1848 -84.8006 50.0000 0.0000 -82.7485 2.3695707 1.0000047 ## [6,] 50.0000 -0.9009 -85.5211 50.0000 0.0000 -82.7485 2.9152927 1.0000130 ## [7,] 50.0000 0.0000 0.0000 50.0000 -1.0000 2.0000 2.2360680 2.3668588 ## [8,] 50.0000 -1.0000 2.0000 50.0000 0.0000 0.0000 2.2360680 2.3668588 ## [9,] 50.0000 2.4900 -0.0010 50.0000 -2.4900 0.0009 4.9800004 7.1791720 ## [10,] 50.0000 2.4900 -0.0010 50.0000 -2.4900 0.0010 4.9800004 7.1791626
Convert the Polar Form of CIE Lab and Luv to Rectangular Form
LabfromLCHab( LCHab ) LuvfromLCHuv( LCHuv )
LabfromLCHab( LCHab ) LuvfromLCHuv( LCHuv )
LCHab |
a numeric Nx3 matrix with CIE LCHab coordinates in the rows, or a vector that can be converted to such a matrix, by row. The hue angle H must be in degrees. |
LCHuv |
a numeric Nx3 matrix with CIE LCHuv coordinates in the rows, or a vector that can be converted to such a matrix, by row. The hue angle H must be in degrees. |
LabfromLCHab() |
returns a numeric Nx3 matrix with CIE Lab coordinates in the rows. |
LuvfromLCHuv() |
returns a numeric Nx3 matrix with CIE Luv coordinates in the rows. |
In both cases, the rownames are copied from input to output.
If the input is invalid, the functions return NULL
.
Wikipedia. CIE 1931 color space. https://en.wikipedia.org/wiki/CIE_1931_color_space
LCHabfromLab()
,
LCHuvfromLuv()
LabfromLCHab( c(50,10,45) ) ## L a b ## [1,] 50 7.071068 7.071068 # on line with slope 1
LabfromLCHab( c(50,10,45) ) ## L a b ## [1,] 50 7.071068 7.071068 # on line with slope 1
Convert from XYZ to other Color Spaces
xyYfromXYZ( XYZ ) LabfromXYZ( XYZ, white ) LuvfromXYZ( XYZ, white )
xyYfromXYZ( XYZ ) LabfromXYZ( XYZ, white ) LuvfromXYZ( XYZ, white )
XYZ |
a numeric Nx3 matrix with CIE XYZ coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
white |
a numeric 3-vector giving the XYZ of reference white; all 3 numbers must be positive.
|
xyYfromXYZ() |
returns a numeric Nx3 matrix with CIE xyY coordinates in the rows.
If the sum |
LabfromXYZ() |
returns a numeric Nx3 matrix with CIE Lab coordinates in the rows |
LuvfromXYZ() |
returns a numeric Nx3 matrix with CIE Luv coordinates in the rows |
In all cases, the rownames are copied from input to output.
If the input is invalid, the functions return NULL
.
Wikipedia. CIE 1931 color space. https://en.wikipedia.org/wiki/CIE_1931_color_space
D65 = standardXYZ( 'D65' ) xyYfromXYZ( D65 ) ## x y Y ## D65 0.3127266 0.3290231 1 # probably not familiar round( xyYfromXYZ(D65), 4 ) ## x y Y ## D65 0.3127 0.329 1 # probably more familiar LabfromXYZ( 0.18*D65, D65 ) # 18% gray card ## L a b ## D65 49.49611 0 0 # exactly neutral, and L is about 50 D50 = standardXYZ( 'D50' ) LabfromXYZ( D50, D65 ) ## L a b ## D50 100 2.399554 17.65321 # D50 is far from neutral (yellowish) in D65 viewing environment
D65 = standardXYZ( 'D65' ) xyYfromXYZ( D65 ) ## x y Y ## D65 0.3127266 0.3290231 1 # probably not familiar round( xyYfromXYZ(D65), 4 ) ## x y Y ## D65 0.3127 0.329 1 # probably more familiar LabfromXYZ( 0.18*D65, D65 ) # 18% gray card ## L a b ## D65 49.49611 0 0 # exactly neutral, and L is about 50 D50 = standardXYZ( 'D50' ) LabfromXYZ( D50, D65 ) ## L a b ## D50 100 2.399554 17.65321 # D50 is far from neutral (yellowish) in D65 viewing environment
RobertsonLocus |
the table from Robertson, with 31 points from 0 to 600 mired |
PrecisionLocus |
a precomputed table, with 65 points from 0 to 1000 mired |
Both objects are data.frame
s with these columns
mired |
the reciprocal temperature |
u |
the u chromaticity, in 1960 CIE |
v |
the v chromaticity, in 1960 CIE |
The PrecisionLocus
data.frame
has these additional columns:
up |
the 1st derivative of u with respect to mired |
vp |
the 1st derivative of v with respect to mired |
upp |
the 2nd derivative of u with respect to mired |
vpp |
the 2nd derivative of v with respect to mired |
For RobertsonLocus
, the values are taken from
Wyszecki & Stiles.
The lookup table on page 228
contains an error at 325 mired,
which was corrected by Bruce Lindbloom (see Source).
For PrecisionLocus
, the chromaticity values u
and v
are computed from first principles,
from the famous equation for the Planckian radiator
(with )
and from the tabulated CIE 1931 standard observer color matching functions,
by summing from 360 to 830nm.
Let
denote the reciprocal temperature
.
We think of
u
as a function .
The column
up
is , and
upp
is .
And similarly for
v
.
The derivatives are computed from first principles, by summing the derivatives
of the Planckian formula from 360 to 830nm.
This includes the limiting case .
When this package is loaded (during .onLoad()
),
cubic splines are computed from RobertsonLocus
,
using stats::splinefun()
with method="fmm"
).
And quintic splines are computed from PrecisionLocus
.
Both splines are continuous.
http://www.brucelindbloom.com/index.html?Eqn_XYZ_to_T.html
Robertson, A. R. Computation of correlated color temperature and distribution temperature. Journal of the Optical Society of America. 58. pp. 1528-1535. 1968.
Wyszecki, Günther and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition. John Wiley & Sons, 1982. Table 1(3.11). pp. 227-228.
CCTfromuv()
,
planckLocus()
RobertsonLocus[ 1:10, ] ## mired u v ## 1 0 0.18006 0.26352 ## 2 10 0.18066 0.26589 ## 3 20 0.18133 0.26846 ## 4 30 0.18208 0.27119 ## 5 40 0.18293 0.27407 ## 6 50 0.18388 0.27709 ## 7 60 0.18494 0.28021 ## 8 70 0.18611 0.28342 ## 9 80 0.18740 0.28668 ## 10 90 0.18880 0.28997 PrecisionLocus[ 1:10, ] ## mired u v up vp upp vpp ## 1 0 0.1800644 0.2635212 5.540710e-05 0.0002276279 7.115677e-07 1.977793e-06 ## 2 10 0.1806553 0.2658948 6.291429e-05 0.0002469232 7.900243e-07 1.873208e-06 ## 3 20 0.1813253 0.2684554 7.120586e-05 0.0002649377 8.679532e-07 1.722425e-06 ## 4 30 0.1820820 0.2711879 8.026143e-05 0.0002812384 9.423039e-07 1.531723e-06 ## 5 40 0.1829329 0.2740733 9.002982e-05 0.0002954676 1.010028e-06 1.309700e-06 ## 6 50 0.1838847 0.2770894 1.004307e-04 0.0003073613 1.068393e-06 1.066350e-06 ## 7 60 0.1849432 0.2802122 1.113592e-04 0.0003167582 1.115240e-06 8.120582e-07 ## 8 70 0.1861132 0.2834161 1.226923e-04 0.0003235990 1.149155e-06 5.566812e-07 ## 9 80 0.1873980 0.2866757 1.342971e-04 0.0003279171 1.169532e-06 3.088345e-07 ## 10 90 0.1887996 0.2899664 1.460383e-04 0.0003298241 1.176525e-06 7.543963e-08
RobertsonLocus[ 1:10, ] ## mired u v ## 1 0 0.18006 0.26352 ## 2 10 0.18066 0.26589 ## 3 20 0.18133 0.26846 ## 4 30 0.18208 0.27119 ## 5 40 0.18293 0.27407 ## 6 50 0.18388 0.27709 ## 7 60 0.18494 0.28021 ## 8 70 0.18611 0.28342 ## 9 80 0.18740 0.28668 ## 10 90 0.18880 0.28997 PrecisionLocus[ 1:10, ] ## mired u v up vp upp vpp ## 1 0 0.1800644 0.2635212 5.540710e-05 0.0002276279 7.115677e-07 1.977793e-06 ## 2 10 0.1806553 0.2658948 6.291429e-05 0.0002469232 7.900243e-07 1.873208e-06 ## 3 20 0.1813253 0.2684554 7.120586e-05 0.0002649377 8.679532e-07 1.722425e-06 ## 4 30 0.1820820 0.2711879 8.026143e-05 0.0002812384 9.423039e-07 1.531723e-06 ## 5 40 0.1829329 0.2740733 9.002982e-05 0.0002954676 1.010028e-06 1.309700e-06 ## 6 50 0.1838847 0.2770894 1.004307e-04 0.0003073613 1.068393e-06 1.066350e-06 ## 7 60 0.1849432 0.2802122 1.113592e-04 0.0003167582 1.115240e-06 8.120582e-07 ## 8 70 0.1861132 0.2834161 1.226923e-04 0.0003235990 1.149155e-06 5.566812e-07 ## 9 80 0.1873980 0.2866757 1.342971e-04 0.0003279171 1.169532e-06 3.088345e-07 ## 10 90 0.1887996 0.2899664 1.460383e-04 0.0003298241 1.176525e-06 7.543963e-08
In careful calcuations with standard illuminants and whitepoints, it is often helpful to have the 'official' values of XYZ and xy, i.e. with the right number of decimal places.
standardXYZ( name ) standardxy( name )
standardXYZ( name ) standardxy( name )
name |
a subvector of
|
All XYZ values are taken from the ASTM publication in References,
except B
which is taken from Wyszecki & Stiles
and D50.ICC
which is taken from ICC publications.
xy values were taken from CIE, BT.709, SMPTE EG 432-1, and TB-2018-001. For D65 the values in CIE and BT.709 disagree; the former has 5 digits and the latter has 4. We have selected the value in BT.709 (page 3) since is far more commonly used. Three of the Illuminant C variants are rarely used and obsolete.
standardXYZ()
returns
an Mx3 matrix where M is the length of name
.
But if name
is NULL
or '*'
, M is the number of records available.
Each row filled with the official XYZ, but if the illuminant name is not recognized
or if there is no data, the row is all NA
s.
The output XYZ is normalized so that Y=1
.
The matrix rownames
are set to the full illuminant names, and colnames
to c('X','Y','Z')
.
Similarly, standardxy()
returns an Mx2 matrix
with colnames
set to c('x','y')
.
The returned XYZs are normalized so that Y=1. In other color domains, it is common to normalize so that Y=100; in these cases be sure to multiply by 100.
Some illuminants have no standard XYZ available and some have no standard xy. In these cases, the rows are filled with NAs.
ASTM E 308 - 01. Standard Practice for Computing the Colors of Objects by Using the CIE System. 2001.
BT.709. Parameter values for the HDTV standards for production and international programme exchange. June 2015.
CIE 015:2004 - Colorimetry, 3rd edition. International Commission on Illumination (CIE). Vienna Austria. Technical Report. 2004.
Günther Wyszecki and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition. John Wiley & Sons, 1982. Table I(3.3.8) p. 769.
TB-2018-001. Derivation of the ACES White Point CIE Chromaticity Coordinates. The Academy of Motion Picture Arts and Sciences. Science and Technology Council. Academy Color Encoding System (ACES) Project. June 15, 2018.
SMPTE RP 431-2. D-Cinema Quality - Reference Projector and Environment for the Display of DCDM in Review Rooms and Theaters. 2011.
standardXYZ( c('a','d50','D50.ICC','D65') ) # X Y Z # A 1.0985000 1 0.3558500 # D50 0.9642200 1 0.8252100 # D50.ICC 0.9642029 1 0.8249054 # D65 0.9504700 1 1.0888300 standardxy( c('a','D65','D60','D60.ACES','E','F2') ) # x y # A 0.44758 0.40745 # D65 0.31270 0.32900 # D60 0.32163 0.33774 # D60.ACES 0.32168 0.33767 # E 0.33333 0.33333 # F2 NA NA
standardXYZ( c('a','d50','D50.ICC','D65') ) # X Y Z # A 1.0985000 1 0.3558500 # D50 0.9642200 1 0.8252100 # D50.ICC 0.9642029 1 0.8249054 # D65 0.9504700 1 1.0888300 standardxy( c('a','D65','D60','D60.ACES','E','F2') ) # x y # A 0.44758 0.40745 # D65 0.31270 0.32900 # D60 0.32163 0.33774 # D60.ACES 0.32168 0.33767 # E 0.33333 0.33333 # F2 NA NA
Convert the Rectangular Form of CIE Lab and Luv to Polar Form
LCHabfromLab( Lab ) LCHuvfromLuv( Luv )
LCHabfromLab( Lab ) LCHuvfromLuv( Luv )
Lab |
a numeric Nx3 matrix with CIE Lab coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
Luv |
a numeric Nx3 matrix with CIE Luv coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
a numeric Nx3 matrix with LCH coordinates in the rows. The lightness L is simply copied from input to output. The chroma C corresponds to radius in polar coordinates, and the hue H corresponds to theta. H is in degrees, not radians. The rownames are copied from input to output.
Wikipedia. CIE 1931 color space. https://en.wikipedia.org/wiki/CIE_1931_color_space
LabfromLCHab()
,
LuvfromLCHuv()
LCHabfromLab( c(50,0,0) ) # a neutral gray ## L Cab Hab ## [1,] 50 0 0 # Hue is undefined, but set to 0 LCHabfromLab( c(50,0,20) ) ## L Cab Hab ## [1,] 50 20 90 # 90 degrees, on yellow axis LCHabfromLab( c(50,0,-20) ) ## L Cab Hab ## [1,] 50 20 270 # 270 degrees, on blue axis
LCHabfromLab( c(50,0,0) ) # a neutral gray ## L Cab Hab ## [1,] 50 0 0 # Hue is undefined, but set to 0 LCHabfromLab( c(50,0,20) ) ## L Cab Hab ## [1,] 50 20 90 # 90 degrees, on yellow axis LCHabfromLab( c(50,0,-20) ) ## L Cab Hab ## [1,] 50 20 270 # 270 degrees, on blue axis
Convert other Color Spaces to XYZ
XYZfromxyY( xyY ) XYZfromLab( Lab, white ) XYZfromLuv( Luv, white )
XYZfromxyY( xyY ) XYZfromLab( Lab, white ) XYZfromLuv( Luv, white )
xyY |
a numeric Nx3 matrix with CIE xyY coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
Lab |
a numeric Nx3 matrix with CIE Lab coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
Luv |
a numeric Nx3 matrix with CIE Luv coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
white |
a numeric 3-vector giving the XYZ of reference white.
|
a numeric Nx3 matrix with XYZ coordinates in the rows.
The rownames are copied from input to output.
In XYZfromxyY()
if y==0
then X
and Z
are set to NA
.
Exception: Y==0
is treated as a special case (pure black);
x
and y
are ignored, and XYZ
are all set to 0.
Wikipedia. CIE 1931 color space. https://en.wikipedia.org/wiki/CIE_1931_color_space
XYZfromxyY(c(0.310897, 0.306510, 74.613450)) ## X Y Z ## [1,] 75.68137 74.61345 93.13427 XYZfromLab( c(50,2,-3), 'D50' ) ## X Y Z ## [1,] 0.1813684 0.1841865 0.1643335
XYZfromxyY(c(0.310897, 0.306510, 74.613450)) ## X Y Z ## [1,] 75.68137 74.61345 93.13427 XYZfromLab( c(50,2,-3), 'D50' ) ## X Y Z ## [1,] 0.1813684 0.1841865 0.1643335
Convert from XYZ or xy to Uniform Chromaticity Spaces
uvfromXYZ( XYZ, space=1976 ) uvfromxy( xy, space=1976 )
uvfromXYZ( XYZ, space=1976 ) uvfromxy( xy, space=1976 )
XYZ |
a numeric Nx3 matrix with CIE XYZ coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
xy |
a numeric Nx2 matrix with CIE xy coordinates in the rows, or a vector that can be converted to such a matrix, by row. |
space |
the year of the space of output uv desired - valid spaces are 1976 and 1960.
The default |
a numeric Nx2 matrix with u'v' (or uv) coordinates in the rows.
For uvfromXYZ()
,
if , uv are set to
NA
.
For uvfromxy()
,
if , uv are set to
NA
.
The rownames are copied from input to output.
If the input is invalid, the function returns NULL
.
Wikipedia. CIE 1931 color space. https://en.wikipedia.org/wiki/CIE_1931_color_space
Wikipedia. CIE 1960 color space. https://en.wikipedia.org/wiki/CIE_1960_color_space
LuvfromXYZ()
,
standardXYZ()
# locate some standard illuminants on the 1976 UCS diagram uvfromXYZ( standardXYZ( c('C','D50','D65','E') ) ) ## u' v' ## C 0.2008921 0.4608838 ## D50 0.2091601 0.4880734 ## D65 0.1978398 0.4683363 ## E 0.2105263 0.4736842
# locate some standard illuminants on the 1976 UCS diagram uvfromXYZ( standardXYZ( c('C','D50','D65','E') ) ) ## u' v' ## C 0.2008921 0.4608838 ## D50 0.2091601 0.4880734 ## D65 0.1978398 0.4683363 ## E 0.2105263 0.4736842