t_gamma
$t = t_gamma($gamma);
This is an internal generator that is used to implement the standard "gamma" parameter for all color
transforms. It is exported as well because many casual users just want to apply a gamma curve to
existing data rather than doing anything more rigorous.
In the forward direction, "t_gamma" applies/decodes the gamma correction indicated -- e.g. if the $gamma
parameter at generation time is 2, then the forward direction squares its input, and the inverse
direction takes the square root (encodes the gamma correction).
Gamma correction is implemented using a sign-tolerant approach: all values have their magnitude scaled
with the power law, regardless of the sign of the value.
t_brgb
$t = t_brgb();
Convert lsRGB (normalized to [0,1]) to byte-scaled RGB ( [0,255] ). By default, "t_brgb" prepares byte
values tuned for a display gamma of 2.2, which approximates sRGB (the standard output color coding for
most computer displays). The difference between "t_brgb" and "t_srgb" in this usage is that "t_srgb"
uses the actual spliced-curve approximation specified in the sRGB standard, while "t_brgb" uses a simple
gamma law for export.
"t_brgb" accepts the following options, all of which may be abbreviated:
gamma (default 1)
If set, this is a gamma-encoding value for the original lsRGB, which is decoded before the transform.
display_gamma (default 2.2)
If set, this is the gamma of the display for which the output is intended. The default compresses the
brightness vector before output (taking approximately the square root). This matches the "standard
gamma" applied by MacOS and Microsoft Windows displays, and approximates the sRGB standard. See also
"t_srgb".
clip (default 1)
If set, the output is clipped to [0,256) in the forward direction and to [0,1] in the reverse
direction.
byte (default 1)
If set, the output is converted to byte type in the forward direction. This is a non-reversible
operation, because precision is lost in the conversion to bytes. (The reverse transform always creates
a floating point value, since lsRGB exists on the interval [0,1] and an integer type would be
useless.)
t_srgb
Converts lsRGB (the internal floating-point base representation) to sRGB - the typical RGB encoding used
by most computing devices. Since most computer terminals use sRGB, the representation's gamut is well
matched to most computer monitors.
sRGB is a spliced standard, rather than having a direct gamma correction. Hence there is no way to
adjust the output gamma. If you want to do that, use "t_brgb" instead.
"t_srgb" accepts the following options, all of which may be abbreviated:
gamma (default 1)
If set, this is a gamma-encoding value for the original lsRGB, which is decoded before the transform.
byte (default 1)
If set, this causes the output to be clipped to the range [0,255] and rounded to a byte type PDL
("24-bit color"). (The reverse transform always creates a floating point value, since lsRGB exists on
the interval [0,1] and an integer type would be useless.)
clip (default 0)
If set, this causes output to be clipped to the range [0,255] even if the "byte" option is not set.
t_pcandt_pcp
These two transforms implement a general purpose pseudocolor transformation. You input a monochromatic
value (zero active dims) and get out an RGB value (one active dim, size 3). Because the most common use
case is to generate sRGB values, the default output is sRGB -- you have to set a flag for lsRGB output,
for example if you want to produce output in some other system by composing t_pc with a color
transformation.
"t_pc" generates pseudocolor transforms ("color maps") with a photometric interpretation of the input:
the input data are considered to be proportional to some kind of measured luminance or similar physical
parameter. This produces "correct" renderings of scenes captured by scientific cameras and similar
instrumentation.
"t_pcp" generates pseudocolor transforms ("color maps") with a perceptual interpretation of the input:
the input data are considered to be proportional to the *perceptual* variation desired across the
display. This produces "correct" renderings of many non-luminant types of data, such as temperature,
Doppler shift, frequency plots, etc.
Both "t_pc" and "t_pcp" generate transforms based on a collection of named transformations stored in an
internal database (the global hash ref $PDL::Transform::Color::pc_tab). The transformations come in two
basic sorts: quasi-photometric transformations, which use luminance as the dominant varying parameter;
and non- photometric transformations, which use hue or saturation as the dominant varying parameter.
Only the photometric transformations get modified by "t_pc" vs "t_pcp" -- for example, t_pcp('rainbow')
will yield the same transform as t_pc('rainbow').
Some of the color transformations are "split" and intended for display of signed data -- for example, the
"dop" transformation fades red-to-white-to-blue and is intended for display of Doppler or similar
signals.
NOTE: "t_pc" and "t_pcp" work BACKWARDS from most of the transformations in this package: they convert
FROM a data value TO sRGB or lsRGB.
There are options to adjust input gamma and the domain of the transformation (e.g. if your input data are
on [0,1000] instead of [0,1]).
If you feed in no arguments at all, either "t_pc" or "t_pcp" will list a collection of named pseudocolor
transformations that work, on the standard output.
Options accepted are:
gamma (default 1) - presumed encoding gamma of the input
The input is *decoded* from this gamma value. 1 treats it as linear in luminance.
lsRGB (default 0) - produce lsRGB output instead of sRGB.
(this may be abbreviated "l" for "linear")
domain - domain of the input; synonym for irange.
irange (default [0,1]) - input range of the data
Input data are by default clipped to [0,1] before application of the color map. Specifying an
undefined value causes the color map to be autoscaled to the input data, e.g. "ir="[0,undef]> causes
the color map to be scaled from 0 to the maximum value of the input. For full autoscaling, use
"ir="[]>.
combination (default 0) - recombine r,g,b post facto
This option allows you to perturb maps you like by mixing up r, g, and b after all the other
calculations are done. You feed in a number from 0 to 5. If it's nonzero, you get a different
combination of the three primaries. You can mock this up more compactly by appending "-Cn" to the
(possibly abbreviated) name of the table. (Replace the 'n' with a number).
For example, if you specify the color table "sepia" or "sepia-c0" you'll get the sepiatone color
table. If you specify "sepia-c5" you'll get almost the exact same color table as "grepia".
You can abbreviate color table names with unique abbreviations. Tables currently accepted, and their
intended uses are:
QUASI-PHOTOMETRIC PSEUDOCOLOR MAPS FOR NORMAL USE
grey, gray, or mono (photometric)
Simple monochrome.
sepia, blepia, grepia, vepia, ryg - sepiatone and variants
These use color scaling to enhance contrast in a simple luminance transfer. "sepia" is a black-
brown-white curve reminiscent of sepia ink. The others are similar, but emphasize different
primary colors. The 'ryg' duplicates sepiatone, but with green highlights to increase contrast in
near-saturated parts of an image.
heat
This black-red-yellow-white is reminiscent of blackbody curves (but does not match them
rigorously).
pm3d, voy
"pm3d" is the default color table for Gnuplot. It's a colorblind-friendly, highly saturated table
with horrible aesthetics but good contrast throughout. "voy" is violet-orange-yellow. It's a more
aesthetically pleasing colorblind- friendly map with a ton of contrast throughout the range.
ocean
deep green through blue to white
spring, summer, autumn, winter
These are reminiscent of the "seasonal" colors provided by MatLab. The "spring" is horrendous but
may be useful for certain aesthetic presentations. Summer and Winter are similar to the sepia-like
tables, but with different color paths. Autumn is similar to heat, but less garish.
SPLIT PSEUDOCOLOR MAPS FOR SIGNED QUANTITIES
dop, dop1, dop2, dop3
These are various presentations of signed information, originally intended to display Doppler
shift. They are all quasi-photometric and split.
vbg
This is a violet-black-green signed fade useful for non-Doppler signed quantities. Quasi-
photometric and split.
NON-PHOTOMETRIC PSEUDOCOLOR MAPS
rainbow
Colors of the rainbow, red through "violet" (magenta)
wheel
The full "color wheel", including the controversial magenta-to-red segment
t_cieXYZ,t_xyz
The "t_cieXYZ" transform (also "t_xyz", which is a synonym) converts the module-native lsRGB to the CIE
XYZ representation. CIE XYZ is a nonphysical RGB-style system that minimally represents every physical
color it is possible for humans to perceive in steady illumination. It is related to sRGB by a linear
transformation (i.e. matrix multiplication) and forms the basis of many other color systems (such as CIE
xyY).
CIE XYZ values are defined in such a way that they are positive definite for all human-perceptible
colors, at the cost that the primaries are nonphysical (they correspond to no possible spectral color)
"t_ciexyz" accepts the following options:
gamma (default 1)
This is taken to be a coded gamma value in the original lsRGB, which is decoded before conversion to
the CIE XYZ system.
rgb_system (default undef)
If present, this must be either the name of an RGB system or an RGB system descriptor hash as
described in "t_shift_rgb". If none is specified, then the standard linearized sRGB used by the rest
of the module is assumed.
use_system_gamma (default 0)
If this flag is set, and "rgb_system" is set also, then the RGB side of the transform is taken to be
gamma-encoded with the default value for that RGB system. Unless you explicitly specify an RGB system
(with a name or a hash), this flag is ignored.
t_rgi
Convert RGB to RG chroma with a separate intensity channel.
Note that intensity is just the average of the R, G, and B values. If you want perceptible luminance,
use t_rgl or t_ycbcr instead.
t_xyyandt_xyY
Convert from sRGB to CIE xyY. The "xyY" system is part of the CIE 1931 color specification. Luminance
is in the 2 coordinate, and chrominance x and y are in the 0 and 1 coordinates.
This is the coordinate system in which "chromaticity diagrams" are plotted. It is capable of
representing every illuminant color that can be perceived by the typical human eye, and also many that
can't, with positive-definite coordinates.
Most of the domain space (which runs over [0-1] in all three dimensions) is inaccessible to most
displays, because RGB gamuts are generally smaller than the actual visual gamut, which in turn is a
subset of the actual xyY data space.
t_cielabort_lab
$t = t_cielab();
Convert RGB to CIE Lab colors. "Lab" stands for Lightness, "a", and "b", representing the overall
luminance detection and two opponent systems (a: red/green, and b:yellow/blue) in the human eye. Lab
colors are approximately perceptually uniform: they're mapped using a nonlinear transformation involving
cube roots. Lab has the property that Euclidean distances of equal size in the space yield approximately
equal perceptual shifts in the represented color.
Lightness runs 0-100, and the a and b opponent systems run -100 to +100.
The Lab space includes the entire CIE XYZ gamut and many "impossible colors". that cannot be represented
directly with physical light. Many of these "impossible colors" (also "chimeric colors") can be
experienced directly using visual fatigue effects, and can be classified using Lab.
Lab is easiest to convert directly from XYZ space, so the "t_lab" constructor returns a compound
transform of "t_xyz2lab" and "t_xyz".
t_xyz2lab
$t = t_xyz2lab();
Converts CIE XYZ to CIE Lab.
t_cmyk
converts rgb to cmyk in the most straightforward way (by subtracting RGB values from unity).
CMYK and other process spaces are very complicated; this transform presents only a relatively simple
conversion that does not take into account ink gamut variation or many other effects.
There *is* a provision for halftone gamma correction: "htgamma", which works exactly like the rgb gamma
correction but is applied to the CMYK output.
Options:
gamma (default 1)
The standard gamma affecting the RGB cube
htgamma (default 1)
A "halftone gamma" that is suitable for non-wash output processes such as halftoning. it acts on the
CMYK values themselves.
byte (default 0)
If present, the CMYK side is scaled to 0-255 and converted to a byte type.
t_hslandt_hsv
$rgb = $hsl->invert($t_hsl());
HSL stands for Hue, Saturation, Lightness. It's not an absolute color space, simply derived from each
RGB (by default, linearized sRGB). it has the same gamut as the host RGB system. The coordinates are
hexagonal on the (RYGCBM) hexagon, following the nearest face of the (diagonally sliced) RGB cube.
HSL is a double-cone system, so iso-L surfaces are close to the plane perpendicular to the double-
diagonal white/illuminant line R=G=B. This has the effect of reducing saturation at high lightness
levels, but maintains luminosity independent of saturation. Maximum saturation occurs when S=1 and
L=0.5; at higher values of L, colors grow less saturated and more pastel, so that L follows total
luminosity of the output.
HSV is a stacked-cone system: iso-V surfaces are parallel to the bright faces of the RGB cube, so maximal
bright saturation occurs when S=1 and V=1. This means that output luminosity drops with saturation, but
due to Helmholtz-Kolrausch effect (linking saturation to apparent brightness) the perceived brightness is
less S-dependent: V follows total apparentbrightness of the output, though output luminosity drops with
S.
You can represent out-of-gamut values in either system, by using S values greater than unity, or
"illegal" V or L values.
Hue, Saturation, and (Lightness or Value) each run from 0 to 1.
By default, the hue value follows a sin**4 scaling along each side of the RYGCBM hexagon. This softens
the boundaries near the edges of the RGB cube, giving a better peceptual "color-wheel" transition between
hues. There is a flag to switch to the linear behavior described in, e.g., the Wikipedia article on the
HSV system.
You can encode the Lightness or Value with a gamma value ("lgamma") if desired.
Options:
gamma (default 1)
Treat the base RGB as gamma-encoded (default 1 is linear)
lgamma (default 1)
Treat the L coordinate as gamma-encoded (default 1 is linear).
hsv (default 0 if called as "t_hsl", 1 if called as "t_hsv")
Sets which of the HSL/HSV transform is to be used.
hue_linear (default 0)
This flag determines how the hue ("angle") is calculated. By default, a sin**4 scaling is used along
each branch of the RYGCBM hexagon, to soften the perceptual effects at the corners. If you set this
flag, then the calculated "hue" is linear along each branch of the hexagon, to match (e.g.) the
Wikipedia definition.
t_shift_illuminant
"t_new_illuminant" shifts a color from an old RGB system to a new one with a different white point. It
accepts either a PDL containing a CIE xyY representation of the new illuminant, or a name of the new
illuminant, and some options.
Because this is shifting RGB to RGB in the same representation, gamma transformations get re-encoded
afterward: if you use, for example, "gamma=>2", then the RGB values are squared, then transformed, then
square-rooted.
Options are:
gamma (default=1)
If present, this is the gamma coefficient for the representation of both the source and destination
RGB spaces.
from (default="D65")
If present, this is the xyY or name of the OLD illuminant. The default is D65, the illuminant for
sRGB (and therefore lsRGB as well).
basis (default="sRGB")
If present, this needs to be either "sRGB" or "XYZ" (case insensitive). If it's sRGB, the input and
output are treated as standard lsRGB coordinates. If it's XYZ, then the input and output are in CIE
XYZ coordinates.
method (default="Bradford")
This can be "Bradford", "Von Kries", "XYZ", or a 3x3 matrix Ma (see
"http://www.brucelindbloom.com/index.html?WorkingSpaceInfo.html")
t_shift_rgb
$t = t_shift_rgb("NTSC",{from=>"sRGB"});
Shifts the primary color basis of the lsrgb TO the destination system. Most named RGB systems have an
associated preferred gamma, but that is ignored by default: the RGB values are treated as if they are all
linear representations. You can specify EITHER the name of the system OR the specific RGB parameters for
that system.
The RGB parameters, if you specify them, need to be in the form of a hash ref. The hash keys should be
the same as would be returned by "PDL::Transform::Color::get_rgb". All the keys must be present, except
for gamma (which is ignored).
Alternatively, you can use the name of a known system. These are listed in the documentation for
"PDL::Transform::Color::get_rgb".
"t_shift_rgb" takes several options.
gamma (default 1)
The input triplets are assumed to be encoded with this gamma function. The default assumes linear
representation.
ogamma (default gamma)
The output triplets are assumed to need encoding with this gamma function.
use_system_gammas (default 0)
This overrides the settings of "gamma" and "ogamma", and encodes/decodes according to the original
system.
wp_method (default undef)
This is the whitepoint shift method used to change illuminant value between systems with different
whitepoints. See "t_shift_illuminant" for an explanation.
from (default "sRGB")
This is the RGB system to convert from, in the same format as the system to convert to (names or a
hash ref as described).
PDL::Transform::Color::xyy_from_D
$xyy = PDL::Transform::Color::xyy_from_D($D_value)
This utility routine generates CIE xyY system colorimetric values for standard CIE D-class illuminants
(e.g., D50 or D65). The illuminants are calculated from a standard formula and correspond to black body
temperatures between 4,000K and 250,000K. The D value is the temperature in K divided by 100, e.g. broad
daylight is D65, corresponding to 6500 Kelvin.
This is used for calculating standard reference illuminants, to convert RGB values between illuminants.
For example, sRGB uses a D65 illuminant, but many other color standards refer to a D50 illuminant.
The colorimetric values are xy only; the Y coordinate can be specified via an option, or defaults to 0.5.
This routine is mainly used by "xyy_from_illuminant", which handles most of the CIE-recognized standard
illuminant sources including the D's.
See "t_xyy" for a description of the CIE xyY absolute colorimetric system.
"xyy_from_D" accepts the following options:
Y - the Y value of the output xyY coordinate
PDL::Transform::Color::xyy_from_illuminant
$xyy = PDL::Transform::Color::xyy_from_illuminant($name)
This utility routine generates CIE xyY system colorimetric values for all of the standard CIE
illuminants. The illuminants are looked up in a table populated from the CIE publication Colorimetry,
3rd edition.
The illuminant of a system is equivalent to its white point -- it is the location in xyY absolute
colorimetric space that corresponds to "white".
CIE recognizes many standard illuminants, and (as of 2017) is in the process of creating a new set -- the
"L" series illuminants -- that is meant to represent LED lighting.
Proper treatment of an illuminant requires a full spectral representation, which the CIE specifies for
each illuminant. Analysis of that spectrum is a major part of what CIE calls "Color rendering index
(CRI)" for a particular light source. PDL::Transform::Color is a strictly tri-coordinate system and does
not handle the nuances of spectral effects on CRI. In effect, all illuminants are treated as having a
CRI of unity (perfect).
Illuminants that are understood are:
• a 3-PDL in CIE xyY coordinates
• a CIE standard name
The CIE names are:
A - a gas-filled tungsten filament lamp at 2856K
B - not supported (deprecated by CIE)
C - early daylight simulant, replaced by the D[n] sources
D[n] - Blackbody radiation at 100[n] Kelvin (e.g. D65)
F[n] - Fluorescent lights of various types (n=1-12 or 3.1-3.15)
HP[n] - High Pressure discharge lamps (n=1-5)
L[n] - LED lighting (not yet supported)
PDL::Transform::Color::get_rgb
my $rgb_hash = get_rgb( $name );
"PDL::Transform::Color::get_rgb" is an internal routine that retrieves a set of RGB primary colors from
an internal database. There are several named RGB systems, with different primary colors for each. The
primary colors are represented as CIE xyY values in a returned hash ref.
The return value is a hash ref with the following fields:
gamma - the specified gamma of that RGB system (or 2.2, for sRGB)
w_name - the name of the illuminant / white-point for that system
w - the xyY value of the illuminant / white-point for that system
r - the xyY value of the red primary color at unit intensity
g - the xyY value of the green primary color at unit intensity
b - the xyY value of the blue primary color at unit intensity
As of 1.007, because this module now uses PDL::Graphics::ColorSpace for some calculations, the hash ref
will also include fields used by that module.
Recognized RGB system names are:
Adobe - Adobe's 1998 RGB, intended to encompass nearly all of the CMYK gamut (gamma=2.2, white=D65)
Apple - Apple's display standard from c. 1990 - c. 2010 (gamma=1.8, white=D65)
Best - Wide-gamut RGB developed by Don Hutcheson (www.hutchcolor.com) (gamma=2.2, white=D50)
Beta - Bruce Lindbloom's optimized ultra-wide-gamut RGB (gamma=2.2, white=D50)
Bruce - Bruce Fraser's conservative-gamut RGB space for 8-bit editing (gamma=2.2, white=D65)
BT 601 - ITU-R standard BT.601 (used for MPEG & SDTV) (gamma=2.2, white=D65)
BT 709 - ITU-R standard BT.709 (used for HDTV) (gamma=2.2, white=D65)
CIE - CIE 1931 calibrated color space (based on physical emission lines) (gamma=2.2, white=E)
ColorMatch - quasi-standard from c.1990 -- matches Radius Pressview CRT monitors. (gamma=1.8, white=D50)
Don 4 - wide-gamut D50 working space gets the Ektachrome color gamut (gamma=2.2, white=D50)
ECI v2 - RGB standard from the European Color Initiative (gamma=1, white=D50)
Ekta PS5 - developed by Joseph Holms (www.josephholmes.com) for scanned Ektachrome slides (gamma=2.2,
white=D50)
NTSC - National Television System Committee (U.S. analog TV standard) (gamma=2.2, white=C)
PAL - Phase Alternating Line (U.K. analog TV standard) (gamma = 2.2, white=D65)
ProPhoto - Wide gamut from Kodak, designed for photo output. (gamma=1.8, white=D60)
ROMM - Synonym for ProPhoto (gamma=1.8, white=D60)
SECAM - Séquentiel de Couleur À Mémoire (French analog TV standard) (gamma=2.2, white=D65)
SMPTE-C - Soc. Motion Pict. & TV Engineers (current U.S. TV standard) (gamma=2.2, white=D65)
sRGB - Standard for consumer computer monitors (gamma~2.2, white=D65)
wgRGB - Wide Gamut RGB (gamma=2.2, white=D50)
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