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https://github.com/pdlporters/pdl-transform-color


https://github.com/pdlporters/pdl-transform-color

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README 

        
=head1 OVERVIEW



This module provides transformations for manipulating color.  This repository 

stores the history for the PDL::Transform::Color module on CPAN. 



=cut



=encoding utf8



=head1 NAME



PDL::Transform::Color - Useful color system conversions for PDL



=head1 SYNOPSIS



     ### Shrink an RGB image with proper linear interpolation:

     ### DEcode the sRGB image values, then interpolate, then ENcode sRGB

     $im = rpic("big_colorimage.jpg");

     $im2 = $im->invert(t_srgb())->match([500,500],{m=>'g'})->apply(t_srgb());



=head1 DESCRIPTION



PDL::Transform::Color includes a variety of useful color conversion

transformations.  It can be used for simple hacks on machine-native

color representations (RGB <-> HSV, etc.), for simple

encoding/decoding of machine-native color representations such as

sRGB, or for more sophisticated manipulation of absolute color

standards including large-gamut or perceptual systems.



The color transforms in this module can be used for converting between

proper color systems, for gamma-converting pixel values, or for

generating pseudocolor from one or two input parameters.  In addition

to transforming color data between different representations, Several

named "color maps" (also called "color tables") are provided.



The module uses linearized sRGB (lsRGB) as a fundamental color basis.

sRGB is the standard color system used by most consumer- to mid-grade

computer equipment, so casual users can use this color representation

without much regard for gamuts, colorimetric standards, etc.



Most of the transform generators convert from lsRGB to various

other systems.  Notable simple ones are HSV (Hue, Saturation, Value),

HSL (Hue, Saturation, Lightness), and CMYK (Cyan, Magenta, Yellow,

blacK).



If you aren't familiar with PDL::Transform, you should read that POD

now, as this is a subclass of PDL::Transform.  Transforms represent

and encapsulate vector transformations -- one- or two-way vector

functions that may be applied, composed, or (if possible) inverted.

They are created through constructor methods that often allow

parametric adjustment at creation time.



If you just want to "manipulate some RGB images" and not learn about

the esoterica of color representations, you can treat all the routines

as working "from RGB" on the interval [0,1], and use C to

import/export color images from/to "24-bit color" that your computer

probably expects.  If you care about the esoterica, read on.



The output transfer function for sRGB is nonlinear -- the luminance of

a pixel on-screen varies somewhat faster than the square of the input

value -- which is inconvenient for blending, merging, and manipulating

color.  Many common operations work best with a linear photometric

representation.  PDL::Transform::Color works with an internal model

that is a floating-point linear system representing pixels as

3-vectors whose components are proportional to photometric brightness

in the sRGB primary colors.  This system is called "lsRGB" within the

module.



Note that, in general, RGB representations are limited to a particular

narrow gamut of physically accessible values.  While the human eye has

three dominant colorimetric input channels and hence color can be

represented as a 3-vector, the human eye does not cleanly separate the

spectra responsible for red, green, and blue stimuli.  As a result, no

trio of physical primary colors (which must have positive-definite

spectra and positive-definite overall intensities) can represent every

perceivable color -- even though they form a basis of color space.



But in digital representation, there is no hard limit on the values

of the RGB vectors -- they can be negative or arbitrarily large.  This

permits representation of out-of-gamut values using negative or

over-unity intensities.  So floating-point lsRGB allows you to

represent literally any color value that the human eye can perceive,

and many that it can't.  This is useful even though many such colors

can't be rendered on a monitor.  For example, you can change between

several color representations and not be limited by the formal gamut

of each representation -- only by the final export standard.



Three major output formats are supported: sRGB (standard "24-bit

color" with the industry standard transfer function); bRGB (bytescaled

RGB with a controllable gamma function (default 2.2, matching the

average gamma value of most CRTs and calibrated flat monitors); or

CMYK (direct linear inversion of the RGB values, with byte

scaling). These are created by applying the transforms C,

C, and C, respectively, to an lsRGB color triplet.



The C export routine will translate represented colors in

floating-point lsRGB to byte-encoded sRGB (or, if inverted, vice

versa), using the correct (slightly more complicated than gamma

functions) nonlinear scaling.  In general, you can use C to

import existing images you may have found lying around the net;

manipulate their hue, etc.; and re-export with C.



If you prefer to work with direct gamma functions or straight

scaling, you can import/export from/to byte values with C

instead.  For example, to export a color in the CIE RGB system

(different primaries than sRGB), use C.



There are also some pseudocolor transformations, which convert a

single data value to normalized RGB.  These transformations are

C for photometric (typical scientific) values and C for

perceptual (typical consumer camera) values.  They are described

below, along with a collection of named pseudocolor maps that are

supplied with the module.



=head1 OVERVIEW OF COLOR THEORY



Because of the biophysics of the human eye, color is well represented

as a 3-vector of red, green, and blue brightness values representing

brightness in the long, middle, and short portions of the visible

spectrum.  However, the absorption/sensitivity bands overlap

significantly, therefore no physical light (of any wavelength) can

form a proper "primary color" (orthonormal basis element) of this

space.  While any vector in color space can be represented as a linear

sum of three indepenent basis vectors ("primary colors"), there is no

such thing as a negative intensity and therefore any tricolor

representation of the color space is limited to a "gamut" that can be

formed by I linear combinations of the selected primary colors.



Some professional color representations (e.g. 5- and 7-color dye

processes) expand this gamut to better match the overall spectral

response of the human eye, at the cost of over-determining color

values in what is fundamentally a 3-space.



RGB color representations require the specification of particular

primary colors that represent particular spectral profiles.  The

choice of primaries depends on the technical solution being used for

I/O.  The most universal "standard" representation is the CIE RGB

standard developed in 1931 by the Commission Internationale de

l'Eclairage (CIE; International Commission on Illumination).  The 1931

CIE RGB system is also called simply CIERGB by many sources.  It uses

primary wavelengths of 700nm (red), 546.1 nm (green), and 435.8 nm

(blue).



The most universal "computer" representation is the sRGB standard

defined by Anderson et al.  (1996), which uses on slightly different

primary colors than does the 1931 CIE RGB standard.  This is because

sRGB is based on the colorimetric output of color television phosphors

in CRTs, while CIE RGB was developed based on easily lab-reproducible

spectra.



The C transformations are all relative to the

sRGB color basis.  Negative values are permitted, allowing

representation of all colors -- possible or impossible.



CIE defined several other important color systems: first, an XYZ

system based on nonphysical primaries X, Y, and Z that correspond to

red, green, and blue, respectively. The XYZ system can represent all

colors detectable to the human eye with positive-definite intensities

of the "primaries": the necessary negative intensities are hidden in

the formal spectrum of each of the primaries.  The Y primary of this

system corresponds closely to green, and is used by CIE as a proxy for

overall luminance.



The CIE also separated "chrominance" and "luminance" signals, in a

separate system called "xyY", which represents color as sum-normalized

vectors "x=X/(X+Y+Z), "y=Y/(X+Y+Z)", and "z=Z/(X+Y+Z)".  By construction,

x+y+z=1, so "x" and "y" alone describe the color range of the system, and

"Y" stands in for overall luminance.



A linear RGB system is specified exactly by the chrominance (CIE XYZ

or xyY) coordinates of the three primaries, and a white point

chrominance.  The white point chrominance sets the relative scaling

between the brightnesses of the primaries to achieve a color-free

("white") luminance.  Different systems with the same R, G, B primary

vectors can have different gains between those colors, yielding a

slightly different shade of color at the R=G=B line.  This "white"

reference chrominance varies across systems, with the most common

"white" standard being CIE's D65 spectrum based on a 6500K black body

-- but CIE, in particular, specifies a large number of white

standards, and some systems use none of those but instead specify CIE

XYZ values for the white point.



Similarly, real RGB systems typically use dynamic range compression

via a nonlinear transfer function which is most typically a "gamma

function".  A built-in database tracks about 15 standard named

systems, so you can convert color values between them.  Or you can

specify your own system with a standard hash format (see C).



Provision exists for converting between different RGB systems with

different primaries and different white points, by linearizing and

then scaling.  The most straightforward way to use this module to

convert between two RGB systems (neither of which is lsRGB) is to

inverse-transform one to lsRGB, then transform forward to the other.

This is accomplished with the C transform.



Many other representations than RGB exist to separate chromatic

value from brightness.  In general, these can be divided into polar

coordinates that represent hue as a single value divorced from the rgb

basis, and those that represent it as a combination of two values like

the 'x' and 'y' of the CIE xyY space.  These are all based on the

Munsell and Ostwald color systems, which were worked out at about the

same time as the CIE system.  Both Ostwald and Munsell worked around

the start of the 20th century pioneered colorimetric classification.



Ostwald worked with quasi-linear representations of chromaticity as a

2-vector independent of brightness; these representations relate to

CIERGB, CIEXYZ, and related systems via simple geometric projection;

the CIE xyY space is an example.  The most commonly used variant of

xyY is CIELAB, a perceptual color space that separates color into a

perceived lightness parameter L, and separate chromaticities 'a' and

'b'.  CIELAB is commonly used by graphic artists and related

professions, because it is an absolute space like XYZ (so that each

LAB value corresponds to a particular perceivable color), and because

the Cartesian norm between vectors in LAB space is approximately

proportional to perceived difference between the corresponding colors.

The system is thus useful for communicating color values precisely

across different groups or for developing perceptually-uniform display

maps for generated data.  The L, A, and B coordinates are highly

nonlinear to approximately match the typical human visual system.



Other related systems include YUV, YPbPr, and YCbCr -- which are used

for representing color for digital cinema and for video transmission.



Munsell developed a color system based on separating the "hue" of a

color into a single value separate from both its brightness and

saturation level.  This system is closely related to cylindrical polar

coordinates in an RGB space, with the center of the cylinder on top of

the line of values corresponding to neutral shades from "black"

through "grey" to "white".



Two simple Munsell-like representations that work within the gamut of

a particular RGB basis are HSL and HSV.  Both of these systems are

loose representations that are best defined relative to a particular

RGB system. They are both designed specifically to represent an entire

RGB gamut with a quasi-polar coordinate system, and are based on

hexagonal angle -- i.e. they are not exactly polar in nature.



HSL separates "Hue" and "Saturation" from "Lightness".  Hue represents

the spectral shade of the color as a direction from the central white

reference line through RGB space: the R=G=B line.  Saturation is a

normalized chromaticity measuring fraction of the distance from the

white locus to the nearest edge of the RGB gamut at a particular hue

and lightness.  Lightness is an approximately hue- independent measure

of total intensity.  Deeply objectively "saturated" colors are only

accessible at L=0.5; the L=0.5 surface includes all the additive and

subtractive primary colors of the RGB system.  Darker colors are

less-saturated shades, while brighter colors fade to pastels.



HSV is similar to HSL, but tracks only the brightest component among

the RGB triplet as "Value" rather than the derived "Lightness".  As a

result, highly saturated HSV values have lower overall luminance than

unsaturated HSV values with the same V, and the V=1 surface includes

all the primary and secondary colors of the parent RGB system.  This system takes

advantage of the of the "Helmholtz-Kolhrausch effect" that

I brightness increases with saturation, so V better

approximates perceived brightness at a given hue and saturation, than

does L.



Modern display devices generally produce physical brightnesses that

are proportional not to their input signal, but to a nonlinear

function of the input signal.  The most common nonlinear function is a

simple power law ("gamma function"): output is approximately

proportional to the "gamma" power of the input.  Raising a signal

value to the power "1/gamma" is C it, and raising it

to the power "gamma" is C it.



The sRGB 24-bit color standard specifies a slightly more complicated

transfer curve, that consists of a linear segment spliced onto a

horizontally-offset power law with gamma=2.4.  This reduces

quantization noise for very dark pxels, but approximates an overall

power law with gamma=2.2.  Hence, C (which supports general

power law transfer functions) defaults to an output gamma of 2.2, but

C yields a more accurate export transfer in typical use.  The

gamma value of 2.2 was selected in the early days of the television

era, to approximately match the perceptual response of the human eye,

and for nearly 50 years cathode-ray-tube (CRT) displays were

specifically designed for a transfer gamma of 2.2 between applied

voltage at the electron gun input stage and luminance (luminous energy

flux) at the display screen.



Incidentally, some now-obsolete display systems (early MacOS systems

and Silcon Graphics displays) operated with a gamma factor of 1.8,

slightly less nonlinear than the standard.  This derives from early

use of checkerboard (and similar) pixelwise dithering to achieve a

higher-bit-depth color palette than was otherwise possible, with early

equipment.  The display gamma of 2.2 interacted with direct dithering

of digital values in the nonlinear space, to produce an effective gamma

closer to 1.8 than 2.2.



=head1 STANDARD OPTIONS



=over 3



=item gamma



This is a gamma correction exponent used to get physical luminance

values from the represented RGB values in the source RGB space.  Most

color manipulation is performed in linear (gamma=1) representation --

i.e. if you specify a gamma to a conversion transform, the normalized

RGB values are B to linear physical values before processing

in the forward direction, or B after processing in the

reverse direction.



For example, to square the normalized floating-point lsRGB values

before conversion to bRGB, use C2)>.  The "gamma"

option specifies that the desired brightness of the output device

varies as the square of the pixel value in the stored data.



Since lsRGB is the default working space for most transforms, you

don't normally need to specify C -- the default value of 1.0

is correct.



Contrariwise, the C export transform has a C option

that specifies the gamma function for the output bytes.  Therefore,

C<< t_brgb(display_gamma=>2) >> square-roots the data before export (so that

squaring them would yield numbers proportional to the desired luminance

of a display device).



The C option is kept for completeness, but unless you know it's

what you really want, you probably don't actually want it: instead,

you should consider working in a linear space and decoding/encoding

the gamma of your import/export color space only as you read in or write

out values.  For example, generic images found on the internet are

typically in the sRGB system, and can be imported to lsRGB via the

C transform or exported with C -- or other

gamma-corrected 24-bit color systems can be handled directly with

C and its C option.



=back



=head1 FUNCTIONS



=cut

=head2 t_gamma



=for usage



    $t = t_gamma($gamma);



=for ref



This is an internal generator that is used to implement the standard

C 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, C applies/decodes the gamma correction

indicated -- e.g. if the C<$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.



=cut

=head2 t_brgb



=for usage



    $t = t_brgb();



=for ref



Convert lsRGB (normalized to [0,1]) to byte-scaled RGB ( [0,255] ).

By default, C 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 C and

C in this usage is that C uses the actual

spliced-curve approximation specified in the sRGB standard, while

C uses a simple gamma law for export.



C accepts the following options, all of which may be abbreviated:



=over 3



=item gamma (default 1)



If set, this is a gamma-encoding value for the original lsRGB, which

is decoded before the transform.



=item 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 C.



=item clip (default 1)



If set, the output is clipped to [0,256) in the forward direction and

to [0,1] in the reverse direction.



=item 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.)



=back



=cut

=head2 t_srgb



=for ref



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 C instead.



C accepts the following options, all of which may be abbreviated:



=over 3



=item gamma (default 1)



If set, this is a gamma-encoding value for the original lsRGB, which

is decoded before the transform.



=item 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.)



=item clip (default 0)



If set, this causes output to be clipped to the range [0,255] even if the

C option is not set.



=back



=cut

=head2 t_pc and t_pcp



=for ref



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.



C 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.



C 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 C and C generate transforms based on a collection

of named transformations stored in an internal database (the global

hash ref C<$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 C vs C -- for example, C

will yield the same transform as C.



Some of the color transformations are "split" and intended for display of signed

data -- for example, the C transformation fades red-to-white-to-blue and

is intended for display of Doppler or similar signals.



NOTE: C and C 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 C or C will

list a collection of named pseudocolor transformations that work, on

the standard output.



Options accepted are:



=over 3



=item gamma (default 1) - presumed encoding gamma of the input



The input is *decoded* from this gamma value.  1 treats it as linear

in luminance.



=item lsRGB (default 0) - produce lsRGB output instead of sRGB.



(this may be abbreviated "l" for "linear")



=item domain - domain of the input; synonym for irange.



=item 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. C[0,undef]> causes the color map

to be scaled from 0 to the maximum value of the input.  For full

autoscaling, use C[]>.



=item 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

C<-Cn> to the (possibly abbreviated) name of the table.  (Replace

the 'n' with a number).



For example, if you specify the color table C or C you'll

get the sepiatone color table.  If you specify C you'll get

almost the exact same color table as C.



=back



You can abbreviate color table names with unique abbreviations.

Tables currently accepted, and their intended uses are:



=over 3



=item QUASI-PHOTOMETRIC PSEUDOCOLOR MAPS FOR NORMAL USE



=over 3



=item  grey, gray, or mono (photometric)



Simple monochrome.



=item sepia, blepia, grepia, vepia, ryg - sepiatone and variants



These use color scaling to enhance contrast in a simple luminance

transfer.  C 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.



=item heat



This black-red-yellow-white is reminiscent of blackbody curves

(but does not match them rigorously).



=item 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.



=item ocean



deep green through blue to white



=item 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.



=back



=item SPLIT PSEUDOCOLOR MAPS FOR SIGNED QUANTITIES



=over 3



=item dop, dop1, dop2, dop3



These are various presentations of signed information, originally

intended to display Doppler shift.  They are all quasi-photometric

and split.



=item vbg



This is a violet-black-green signed fade useful for non-Doppler

signed quantities.  Quasi-photometric and split.



=back



=item NON-PHOTOMETRIC PSEUDOCOLOR MAPS



=over 3



=item rainbow



Colors of the rainbow, red through "violet" (magenta)



=item wheel



The full "color wheel", including the controversial magenta-to-red segment



=back



=back



=cut

=head2 t_cieXYZ, t_xyz



=for ref



The C transform (also C, 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)



C accepts the following options:



=over 3



=item 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.



=item 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 C.  If none is specified, then

the standard linearized sRGB used by the rest of the module is assumed.



=item use_system_gamma (default 0)



If this flag is set, and C 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.



=back



=cut

=head2 t_rgi



=for ref



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.



=cut

=head2 t_xyy and t_xyY



=for ref



Convert from sRGB to CIE xyY.  The C 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.



=cut

=head2 t_cielab or t_lab



=for usage



    $t = t_cielab();



=for ref



Convert RGB to CIE Lab colors.  C 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 C constructor

returns a compound transform of C and C.



=head2 t_xyz2lab



=for usage



    $t = t_xyz2lab();



=for ref



Converts CIE XYZ to CIE Lab.



=cut

=head2 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:



=over 3



=item gamma (default 1)



The standard gamma affecting the RGB cube



=item htgamma (default 1)



A "halftone gamma" that is suitable for non-wash output processes

such as halftoning. it acts on the CMYK values themselves.



=item byte (default 0)



If present, the CMYK side is scaled to 0-255 and converted to a byte type.



=back



=cut

=head2 t_hsl and t_hsv



=for usage



    $rgb = $hsl->invert($t_hsl());



=for ref



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 I brightness is less S-dependent: V follows

total I 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:



=over 3



=item gamma (default 1)



Treat the base RGB as gamma-encoded (default 1 is linear)



=item lgamma (default 1)



Treat the L coordinate as gamma-encoded (default 1 is linear).



=item 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.



=item 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.



=back



=cut

=head2 t_shift_illuminant



=for ref



C 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,

C<< gamma=>2 >>, then the RGB values are squared, then transformed, then

square-rooted.



Options are:



=over 3



=item gamma (default=1)



If present, this is the gamma coefficient for the representation of

both the source and destination RGB spaces.



=item 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).



=item 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.



=item method (default="Bradford")



This can be "Bradford", "Von Kries", "XYZ", or a 3x3 matrix Ma (see

C)



=back



=cut

=head2 t_shift_rgb



=for usage



  $t = t_shift_rgb("NTSC",{from=>"sRGB"});



=for ref



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

C.  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 C.



C takes several options.



=over 3



=item gamma (default 1)



The input triplets are assumed to be encoded with this gamma function.

The default assumes linear representation.



=item ogamma (default gamma)



The output triplets are assumed to need encoding with this gamma function.



=item use_system_gammas (default 0)



This overrides the settings of "gamma" and "ogamma", and

encodes/decodes according to the original system.



=item wp_method (default undef)



This is the whitepoint shift method used to change illuminant value between

systems with different whitepoints.  See C for an

explanation.



=item 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).



=back



=cut

=head2 PDL::Transform::Color::xyy_from_D



=for usage



     $xyy = PDL::Transform::Color::xyy_from_D($D_value)



=for ref



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 C, which handles most

of the CIE-recognized standard illuminant sources including the D's.



See C for a description of the CIE xyY absolute colorimetric system.



C accepts the following options:



=over 3



=item Y - the Y value of the output xyY coordinate



=back



=cut

=head2 PDL::Transform::Color::xyy_from_illuminant



=for usage



     $xyy = PDL::Transform::Color::xyy_from_illuminant($name)



=for ref



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 I, 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:



=over 3



=item * a 3-PDL in CIE xyY coordinates



=item * a CIE standard name



=back



The CIE names are:



=over 3



=item A - a gas-filled tungsten filament lamp at 2856K



=item B - not supported (deprecated by CIE)



=item C - early daylight simulant, replaced by the D[n] sources



=item D[n] - Blackbody radiation at 100[n] Kelvin (e.g. D65)



=item F[n] - Fluorescent lights of various types (n=1-12 or 3.1-3.15)



=item HP[n] - High Pressure discharge lamps (n=1-5)



=item L[n] - LED lighting (not yet supported)



=back



=cut

=head2 PDL::Transform::Color::get_rgb



=for usage



    my $rgb_hash = get_rgb( $name );



=for ref



C 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:



=over 3



=item gamma - the specified gamma of that RGB system (or 2.2, for sRGB)



=item w_name - the name of the illuminant / white-point for that system



=item w - the xyY value of the illuminant / white-point for that system



=item r - the xyY value of the red primary color at unit intensity



=item g - the xyY value of the green primary color at unit intensity



=item b - the xyY value of the blue primary color at unit intensity



=back



As of 1.007, because this module now uses L

for some calculations, the hash ref will also include fields used by

that module.



Recognized RGB system names are:



=over 3



=item Adobe - Adobe's 1998 RGB, intended to encompass nearly all of the CMYK gamut (gamma=2.2, white=D65)



=item Apple - Apple's display standard from c. 1990 - c. 2010 (gamma=1.8, white=D65)



=item Best - Wide-gamut RGB developed by Don Hutcheson (L) (gamma=2.2, white=D50)



=item Beta - Bruce Lindbloom's optimized ultra-wide-gamut RGB (gamma=2.2, white=D50)



=item Bruce - Bruce Fraser's conservative-gamut RGB space for 8-bit editing (gamma=2.2, white=D65)



=item BT 601 - ITU-R standard BT.601 (used for MPEG & SDTV) (gamma=2.2, white=D65)



=item BT 709 - ITU-R standard BT.709 (used for HDTV) (gamma=2.2, white=D65)



=item CIE - CIE 1931 calibrated color space (based on physical emission lines) (gamma=2.2, white=E)



=item ColorMatch - quasi-standard from c.1990 -- matches Radius Pressview CRT monitors.  (gamma=1.8, white=D50)



=item Don 4 - wide-gamut D50 working space gets the Ektachrome color gamut (gamma=2.2, white=D50)



=item ECI v2 - RGB standard from the European Color Initiative (gamma=1, white=D50)



=item Ekta PS5 - developed by Joseph Holms (L) for scanned Ektachrome slides (gamma=2.2, white=D50)



=item NTSC - National Television System Committee (U.S. analog TV standard) (gamma=2.2, white=C)



=item PAL - Phase Alternating Line (U.K. analog TV standard) (gamma = 2.2, white=D65)



=item ProPhoto - Wide gamut from Kodak, designed for photo output. (gamma=1.8, white=D60)



=item ROMM - Synonym for ProPhoto (gamma=1.8, white=D60)



=item SECAM - Séquentiel de Couleur À Mémoire (French analog TV standard) (gamma=2.2, white=D65)



=item SMPTE-C - Soc. Motion Pict. & TV Engineers (current U.S. TV standard) (gamma=2.2, white=D65)



=item sRGB - Standard for consumer computer monitors (gamma~2.2, white=D65)



=item wgRGB - Wide Gamut RGB (gamma=2.2, white=D50)



=back



=cut

=head1 AUTHOR



Copyright 2017, Craig DeForest ([email protected]).  This

module may be modified and distributed under the same terms as PDL

itself.  The module comes with NO WARRANTY.



=cut