"""
RGB Colourspace Derivation
==========================
Defines the objects related to *RGB* colourspace derivation, essentially
calculating the normalised primary matrix for given *RGB* colourspace primaries
and whitepoint:
- :func:`colour.normalised_primary_matrix`
- :func:`colour.chromatically_adapted_primaries`
- :func:`colour.primaries_whitepoint`
- :func:`colour.RGB_luminance_equation`
- :func:`colour.RGB_luminance`
References
----------
- :cite:`SocietyofMotionPictureandTelevisionEngineers1993a` : Society of
Motion Picture and Television Engineers. (1993). RP 177:1993 - Derivation
of Basic Television Color Equations. In RP 177:1993: Vol. RP 177:199. The
Society of Motion Picture and Television Engineers.
doi:10.5594/S9781614821915
- :cite:`Trieu2015a` : Borer, T. (2017). Private Discussion with Mansencal,
T. and Shaw, N.
"""
from __future__ import annotations
import numpy as np
from colour.adaptation import chromatic_adaptation_VonKries
from colour.hints import (
ArrayLike,
LiteralChromaticAdaptationTransform,
NDArrayFloat,
Tuple,
)
from colour.models import XYZ_to_xy, XYZ_to_xyY, xy_to_XYZ
from colour.utilities import as_float, as_float_array, ones, tsplit
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"xy_to_z",
"normalised_primary_matrix",
"chromatically_adapted_primaries",
"primaries_whitepoint",
"RGB_luminance_equation",
"RGB_luminance",
]
def xy_to_z(xy: ArrayLike) -> float:
"""
Return the *z* coordinate using given :math:`xy` chromaticity coordinates.
Parameters
----------
xy
:math:`xy` chromaticity coordinates.
Returns
-------
:class:`float`
*z* coordinate.
Examples
--------
>>> xy_to_z(np.array([0.25, 0.25]))
0.5
"""
x, y = tsplit(xy)
z = 1 - x - y
return z
[docs]
def normalised_primary_matrix(
primaries: ArrayLike, whitepoint: ArrayLike
) -> NDArrayFloat:
"""
Compute the *Normalised Primary Matrix* (NPM) converting a *RGB*
colourspace array to *CIE XYZ* tristimulus values using given *primaries*
and *whitepoint* :math:`xy` chromaticity coordinates.
Parameters
----------
primaries
Primaries :math:`xy` chromaticity coordinates.
whitepoint
Illuminant / whitepoint :math:`xy` chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
*Normalised Primary Matrix* (NPM).
References
----------
:cite:`SocietyofMotionPictureandTelevisionEngineers1993a`
Examples
--------
>>> p = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> w = np.array([0.32168, 0.33767])
>>> normalised_primary_matrix(p, w) # doctest: +ELLIPSIS
array([[ 9.5255239...e-01, 0.0000000...e+00, 9.3678631...e-05],
[ 3.4396645...e-01, 7.2816609...e-01, -7.2132546...e-02],
[ 0.0000000...e+00, 0.0000000...e+00, 1.0088251...e+00]])
"""
primaries = np.reshape(primaries, (3, 2))
z = as_float_array(xy_to_z(primaries))[..., None]
primaries = np.transpose(np.hstack([primaries, z]))
whitepoint = xy_to_XYZ(whitepoint)
coefficients = np.dot(np.linalg.inv(primaries), whitepoint)
coefficients = np.diagflat(coefficients)
npm = np.dot(primaries, coefficients)
return npm
[docs]
def chromatically_adapted_primaries(
primaries: ArrayLike,
whitepoint_t: ArrayLike,
whitepoint_r: ArrayLike,
chromatic_adaptation_transform: LiteralChromaticAdaptationTransform
| str = "CAT02",
) -> NDArrayFloat:
"""
Chromatically adapt given *primaries* :math:`xy` chromaticity coordinates
from test ``whitepoint_t`` to reference ``whitepoint_r``.
Parameters
----------
primaries
Primaries :math:`xy` chromaticity coordinates.
whitepoint_t
Test illuminant / whitepoint :math:`xy` chromaticity coordinates.
whitepoint_r
Reference illuminant / whitepoint :math:`xy` chromaticity coordinates.
chromatic_adaptation_transform
*Chromatic adaptation* transform.
Returns
-------
:class:`numpy.ndarray`
Chromatically adapted primaries :math:`xy` chromaticity coordinates.
Examples
--------
>>> p = np.array([0.64, 0.33, 0.30, 0.60, 0.15, 0.06])
>>> w_t = np.array([0.31270, 0.32900])
>>> w_r = np.array([0.34570, 0.35850])
>>> chromatic_adaptation_transform = "Bradford"
>>> chromatically_adapted_primaries(
... p, w_t, w_r, chromatic_adaptation_transform
... )
... # doctest: +ELLIPSIS
array([[ 0.6484414..., 0.3308533...],
[ 0.3211951..., 0.5978443...],
[ 0.1558932..., 0.0660492...]])
"""
primaries = np.reshape(primaries, (3, 2))
XYZ_a = chromatic_adaptation_VonKries(
xy_to_XYZ(primaries),
xy_to_XYZ(whitepoint_t),
xy_to_XYZ(whitepoint_r),
chromatic_adaptation_transform,
)
P_a = XYZ_to_xyY(XYZ_a)[..., 0:2]
return P_a
[docs]
def primaries_whitepoint(npm: ArrayLike) -> Tuple[NDArrayFloat, NDArrayFloat]:
"""
Compute the *primaries* and *whitepoint* :math:`xy` chromaticity
coordinates using given *Normalised Primary Matrix* (NPM).
Parameters
----------
npm
*Normalised Primary Matrix*.
Returns
-------
:class:`tuple`
*Primaries* and *whitepoint* :math:`xy` chromaticity coordinates.
References
----------
:cite:`Trieu2015a`
Examples
--------
>>> npm = np.array(
... [
... [9.52552396e-01, 0.00000000e00, 9.36786317e-05],
... [3.43966450e-01, 7.28166097e-01, -7.21325464e-02],
... [0.00000000e00, 0.00000000e00, 1.00882518e00],
... ]
... )
>>> p, w = primaries_whitepoint(npm)
>>> p # doctest: +ELLIPSIS
array([[ 7.3470000...e-01, 2.6530000...e-01],
[ 0.0000000...e+00, 1.0000000...e+00],
[ 1.0000000...e-04, -7.7000000...e-02]])
>>> w # doctest: +ELLIPSIS
array([ 0.32168, 0.33767])
"""
npm = np.reshape(npm, (3, 3))
primaries = XYZ_to_xy(np.transpose(np.dot(npm, np.identity(3))))
whitepoint = np.squeeze(XYZ_to_xy(np.transpose(np.dot(npm, ones((3, 1))))))
# TODO: Investigate if we return an ndarray here with primaries and
# whitepoint stacked together.
return primaries, whitepoint
[docs]
def RGB_luminance_equation(primaries: ArrayLike, whitepoint: ArrayLike) -> str:
"""
Return the *luminance equation* from given *primaries* and *whitepoint*.
Parameters
----------
primaries
Primaries chromaticity coordinates.
whitepoint
Illuminant / whitepoint chromaticity coordinates.
Returns
-------
:class:`str`
*Luminance* equation.
Examples
--------
>>> p = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = np.array([0.32168, 0.33767])
>>> RGB_luminance_equation(p, whitepoint) # doctest: +ELLIPSIS
'Y = 0.3439664...(R) + 0.7281660...(G) + -0.0721325...(B)'
"""
return "Y = {}(R) + {}(G) + {}(B)".format(
*np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6]
)
[docs]
def RGB_luminance(
RGB: ArrayLike, primaries: ArrayLike, whitepoint: ArrayLike
) -> NDArrayFloat:
"""
Return the *luminance* :math:`Y` of given *RGB* components from given
*primaries* and *whitepoint*.
Parameters
----------
RGB
*RGB* chromaticity coordinate matrix.
primaries
Primaries chromaticity coordinate matrix.
whitepoint
Illuminant / whitepoint chromaticity coordinates.
Returns
-------
:class:`numpy.ndarray`
*Luminance* :math:`Y`.
Examples
--------
>>> RGB = np.array([0.21959402, 0.06986677, 0.04703877])
>>> p = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = np.array([0.32168, 0.33767])
>>> RGB_luminance(RGB, p, whitepoint) # doctest: +ELLIPSIS
0.1230145...
"""
Y = np.sum(
normalised_primary_matrix(primaries, whitepoint)[1] * RGB, axis=-1
)
return as_float(Y)