Source code for colour.models.rgb.derivation

# -*- coding: utf-8 -*-
"""
RGB Colourspace Derivation
==========================

Defines 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 division, unicode_literals

import numpy as np

from colour.adaptation import chromatic_adaptation_VonKries
from colour.models import XYZ_to_xy, XYZ_to_xyY, xy_to_XYZ
from colour.utilities import as_numeric, ones, tsplit

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - Colour Developers'
__license__ = 'New BSD License - 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):
    """
    Returns the *z* coordinate using given :math:`xy` chromaticity coordinates.

    Parameters
    ----------
    xy : array_like
        :math:`xy` chromaticity coordinates.

    Returns
    -------
    numeric
        *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, whitepoint): """ Returns the *normalised primary matrix* using given *primaries* and *whitepoint* :math:`xy` chromaticity coordinates. Parameters ---------- primaries : array_like, (3, 2) Primaries :math:`xy` chromaticity coordinates. whitepoint : array_like Illuminant / whitepoint :math:`xy` chromaticity coordinates. Returns ------- ndarray, (3, 3) *Normalised primary matrix*. 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 = xy_to_z(primaries)[..., np.newaxis] 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, whitepoint_t, whitepoint_r, chromatic_adaptation_transform='CAT02'): """ Chromatically adapts given *primaries* :math:`xy` chromaticity coordinates from test ``whitepoint_t`` to reference ``whitepoint_r``. Parameters ---------- primaries : array_like, (3, 2) Primaries :math:`xy` chromaticity coordinates. whitepoint_t : array_like Test illuminant / whitepoint :math:`xy` chromaticity coordinates. whitepoint_r : array_like Reference illuminant / whitepoint :math:`xy` chromaticity coordinates. chromatic_adaptation_transform : unicode, optional **{'CAT02', 'XYZ Scaling', 'Von Kries', 'Bradford', 'Sharp', 'Fairchild', 'CMCCAT97', 'CMCCAT2000', 'CAT02_BRILL_CAT', 'Bianco', 'Bianco PC'}**, *Chromatic adaptation* transform. Returns ------- 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): """ Returns the *primaries* and *whitepoint* :math:`xy` chromaticity coordinates using given *normalised primary matrix*. Parameters ---------- npm : array_like, (3, 3) *Normalised primary matrix*. Returns ------- tuple *Primaries* and *whitepoint* :math:`xy` chromaticity coordinates. References ---------- :cite:`Trieu2015a` Examples -------- >>> npm = np.array([[9.52552396e-01, 0.00000000e+00, 9.36786317e-05], ... [3.43966450e-01, 7.28166097e-01, -7.21325464e-02], ... [0.00000000e+00, 0.00000000e+00, 1.00882518e+00]]) >>> 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 = npm.reshape([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, whitepoint): """ Returns the *luminance equation* from given *primaries* and *whitepoint*. Parameters ---------- primaries : array_like, (3, 2) Primaries chromaticity coordinates. whitepoint : array_like Illuminant / whitepoint chromaticity coordinates. Returns ------- unicode *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]) >>> # Doctests skip for Python 2.x compatibility. >>> RGB_luminance_equation(p, whitepoint) # doctest: +SKIP 'Y = 0.3439664...(R) + 0.7281660...(G) + -0.0721325...(B)' """ return 'Y = {0}(R) + {1}(G) + {2}(B)'.format( *np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6])
[docs]def RGB_luminance(RGB, primaries, whitepoint): """ Returns the *luminance* :math:`Y` of given *RGB* components from given *primaries* and *whitepoint*. Parameters ---------- RGB : array_like *RGB* chromaticity coordinate matrix. primaries : array_like, (3, 2) Primaries chromaticity coordinate matrix. whitepoint : array_like Illuminant / whitepoint chromaticity coordinates. Returns ------- numeric or 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_numeric(Y)