#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
CIE 1994 Chromatic Adaptation Model
===================================
Defines CIE 1994 chromatic adaptation model objects:
- :func:`chromatic_adaptation_CIE1994`
See Also
--------
`CIE 1994 Chromatic Adaptation Model IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/adaptation/cie1994.ipynb>`_ # noqa
References
----------
.. [1] CIE TC 1-32. (1994). CIE 109-1994 A Method of Predicting Corresponding
Colours under Different Chromatic and Illuminance Adaptations
(pp. 1–18). ISBN:978-3-900734-51-0
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.adaptation import VON_KRIES_CAT
from colour.utilities import warning
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['CIE1994_XYZ_TO_RGB_MATRIX',
'CIE1994_RGB_TO_XYZ_MATRIX',
'chromatic_adaptation_CIE1994',
'XYZ_to_RGB_cie1994',
'RGB_to_XYZ_cie1994',
'intermediate_values',
'effective_adapting_responses',
'beta_1',
'beta_2',
'exponential_factors',
'K_coefficient',
'corresponding_colour']
CIE1994_XYZ_TO_RGB_MATRIX = VON_KRIES_CAT
"""
CIE 1994 colour appearance model *CIE XYZ* colourspace to cone
responses matrix.
CIE1994_XYZ_TO_RGB_MATRIX : array_like, (3, 3)
"""
CIE1994_RGB_TO_XYZ_MATRIX = np.linalg.inv(CIE1994_XYZ_TO_RGB_MATRIX)
"""
CIE 1994 colour appearance model cone responses to *CIE XYZ* colourspace
matrix.
CIE1994_RGB_TO_XYZ_MATRIX : array_like, (3, 3)
"""
[docs]def chromatic_adaptation_CIE1994(XYZ_1,
xy_o1,
xy_o2,
Y_o,
E_o1,
E_o2,
n=1):
"""
Adapts given *CIE XYZ_1* colourspace stimulus from test viewing conditions
to reference viewing conditions using CIE 1994 chromatic adaptation
model.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix of test sample / stimulus in domain
[0, 100].
xy_o1 : array_like, (2,)
Chromaticity coordinates :math:`x_{o1}` and :math:`y_{o1}` of test
illuminant and background.
xy_o2 : array_like, (2,)
Chromaticity coordinates :math:`x_{o2}` and :math:`y_{o2}` of reference
illuminant and background.
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage in
domain [18, 100].
E_o1 : numeric
Test illuminance :math:`E_{o1}` in :math:`cd/m^2`.
E_o2 : numeric
Reference illuminance :math:`E_{o2}` in :math:`cd/m^2`.
n : numeric, optional
Noise component in fundamental primary system.
Returns
-------
ndarray, (3,)
Adapted *CIE XYZ_2* colourspace test stimulus.
Warning
-------
The input domain of that definition is non standard!
Notes
-----
- Input *CIE XYZ_1* colourspace matrix is in domain [0, 100].
- Output *CIE XYZ_2* colourspace matrix is in domain [0, 100].
Examples
--------
>>> XYZ_1 = np.array([28.0, 21.26, 5.27])
>>> xy_o1 = (0.4476, 0.4074)
>>> xy_o2 = (0.3127, 0.3290)
>>> Y_o = 20
>>> E_o1 = 1000
>>> E_o2 = 1000
>>> chromatic_adaptation_CIE1994(XYZ_1, xy_o1, xy_o2, Y_o, E_o1, E_o2) # noqa # doctest: +ELLIPSIS
array([ 24.0337952..., 21.1562121..., 17.6430119...])
"""
if not 18 <= Y_o <= 100:
warning(('"Y_o" luminance factor must be in [18, 100] domain, '
'unpredictable results may occur!'))
XYZ_1 = np.ravel(XYZ_1)
RGB_1 = XYZ_to_RGB_cie1994(XYZ_1)
xez_1 = intermediate_values(xy_o1)
xez_2 = intermediate_values(xy_o2)
RGB_o1 = effective_adapting_responses(Y_o, E_o1, xez_1)
RGB_o2 = effective_adapting_responses(Y_o, E_o2, xez_2)
bRGB_o1 = exponential_factors(RGB_o1)
bRGB_o2 = exponential_factors(RGB_o2)
K = K_coefficient(Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2, n)
RGB_2 = corresponding_colour(
RGB_1, Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2, K, n)
XYZ_2 = RGB_to_XYZ_cie1994(RGB_2)
return XYZ_2
[docs]def XYZ_to_RGB_cie1994(XYZ):
"""
Converts from *CIE XYZ* colourspace to cone responses.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix.
Returns
-------
ndarray, (3,)
Cone responses.
Examples
--------
>>> XYZ = np.array([28.0, 21.26, 5.27])
>>> XYZ_to_RGB_cie1994(XYZ) # doctest: +ELLIPSIS
array([ 25.8244273..., 18.6791422..., 4.8390194...])
"""
return np.dot(CIE1994_XYZ_TO_RGB_MATRIX, XYZ)
[docs]def RGB_to_XYZ_cie1994(RGB):
"""
Converts from cone responses to *CIE XYZ* colourspace.
Parameters
----------
RGB : array_like, (3,)
Cone responses.
Returns
-------
ndarray, (3,)
*CIE XYZ* colourspace matrix.
Examples
--------
>>> RGB = np.array([25.8244273, 18.6791422, 4.8390194])
>>> RGB_to_XYZ_cie1994(RGB) # doctest: +ELLIPSIS
array([ 28. , 21.26, 5.27])
"""
return np.dot(CIE1994_RGB_TO_XYZ_MATRIX, RGB)
[docs]def effective_adapting_responses(Y_o, E_o, xez):
"""
Derives the effective adapting responses in the fundamental primary system
of the test or reference field.
Parameters
----------
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage in
domain [18, 100].
E_o : numeric
Test or reference illuminance :math:`E_{o}` in lux.
xez: ndarray, (3,)
Intermediate values :math:`\\xi`, :math:`\eta`, :math:`\zeta`.
Returns
-------
ndarray, (3,)
Effective adapting responses.
Examples
--------
>>> Y_o = 20
>>> E_o = 1000
>>> xez = np.array([1.11857195, 0.9329553, 0.32680879])
>>> effective_adapting_responses(Y_o, E_o, xez) # doctest: +ELLIPSIS
array([ 71.2105020..., 59.3937790..., 20.8052937...])
"""
RGB_o = ((Y_o * E_o) / (100 * np.pi)) * xez
return RGB_o
[docs]def beta_1(x):
"""
Computes the exponent :math:`\\beta_1` for the middle and long-wavelength
sensitive cones.
Parameters
----------
x: numeric
Middle and long-wavelength sensitive cone response.
Returns
-------
numeric
Exponent :math:`\\beta_1`.
Examples
--------
>>> beta_1(318.323316315) # doctest: +ELLIPSIS
4.6106222...
"""
return (6.469 + 6.362 * (x ** 0.4495)) / (6.469 + (x ** 0.4495))
[docs]def beta_2(x):
"""
Computes the exponent :math:`\\beta_2` for the short-wavelength sensitive
cones.
Parameters
----------
x: numeric
Short-wavelength sensitive cone response.
Returns
-------
numeric
Exponent :math:`\\beta_2`.
Examples
--------
>>> beta_2(318.323316315) # doctest: +ELLIPSIS
4.6522416...
"""
return 0.7844 * (8.414 + 8.091 * (x ** 0.5128)) / (8.414 + (x ** 0.5128))
[docs]def exponential_factors(RGB_o):
"""
Returns the chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
:math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)` of given cone responses.
Parameters
----------
RGB_o: ndarray, (3,)
Cone responses.
Returns
-------
ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_o)`,
:math:`\\beta_1(G_o)` and :math:`\\beta_2(B_o)`.
Examples
--------
>>> RGB_o = np.array([318.32331631, 318.30352317, 318.23283482])
>>> exponential_factors(RGB_o) # doctest: +ELLIPSIS
array([ 4.6106222..., 4.6105892..., 4.6520698...])
"""
R_o, G_o, B_o = np.ravel(RGB_o)
bR_o = beta_1(R_o)
bG_o = beta_1(G_o)
bB_o = beta_2(B_o)
return np.array([bR_o, bG_o, bB_o])
[docs]def K_coefficient(Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2, n=1):
"""
Computes the coefficient :math:`K` for correcting the difference between
the test and references illuminances.
Parameters
----------
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage in
domain [18, 100].
xez_1: ndarray, (3,)
Intermediate values :math:`\\xi_1`, :math:`\eta_1`, :math:`\zeta_1` for
the test illuminant and background.
xez_2: ndarray, (3,)
Intermediate values :math:`\\xi_2`, :math:`\eta_2`, :math:`\zeta_2` for
the reference illuminant and background.
bRGB_o1: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o1})`,
:math:`\\beta_1(G_{o1})` and :math:`\\beta_2(B_{o1})` of test sample.
bRGB_o2: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o2})`,
:math:`\\beta_1(G_{o2})` and :math:`\\beta_2(B_{o2})` of reference
sample.
n : numeric, optional
Noise component in fundamental primary system.
Returns
-------
numeric
Coefficient :math:`K`.
Examples
--------
>>> Y_o = 20
>>> xez_1 = np.array([1.11857195, 0.9329553, 0.32680879])
>>> xez_2 = np.array([1.00000372, 1.00000176, 0.99999461])
>>> bRGB_o1 = np.array([3.74852518, 3.63920879, 2.78924811])
>>> bRGB_o2 = np.array([3.68102374, 3.68102256, 3.56557351])
>>> K_coefficient(Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2)
1.0
"""
xi_1, eta_1, zeta_1 = xez_1
xi_2, eta_2, zeta_2 = xez_2
bR_o1, bG_o1, bB_o1 = bRGB_o1
bR_o2, bG_o2, bB_o2 = bRGB_o2
K = (((Y_o * xi_1 + n) / (20 * xi_1 + n)) ** ((2 / 3) * bR_o1) /
((Y_o * xi_2 + n) / (20 * xi_2 + n)) ** ((2 / 3) * bR_o2))
K *= (((Y_o * eta_1 + n) / (20 * eta_1 + n)) ** ((1 / 3) * bG_o1) /
((Y_o * eta_2 + n) / (20 * eta_2 + n)) ** ((1 / 3) * bG_o2))
return K
[docs]def corresponding_colour(RGB_1, Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2, K, n=1):
"""
Computes the corresponding colour cone responses of given test sample cone
responses :math:`RGB_1`.
Parameters
----------
RGB_1: ndarray, (3,)
Test sample cone responses :math:`RGB_1`.
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage in
domain [18, 100].
xez_1: ndarray, (3,)
Intermediate values :math:`\\xi_1`, :math:`\eta_1`, :math:`\zeta_1` for
the test illuminant and background.
xez_2: ndarray, (3,)
Intermediate values :math:`\\xi_2`, :math:`\eta_2`, :math:`\zeta_2` for
the reference illuminant and background.
bRGB_o1: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o1})`,
:math:`\\beta_1(G_{o1})` and :math:`\\beta_2(B_{o1})` of test sample.
bRGB_o2: ndarray, (3,)
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o2})`,
:math:`\\beta_1(G_{o2})` and :math:`\\beta_2(B_{o2})` of reference
sample.
K : numeric
Coefficient :math:`K`.
n : numeric, optional
Noise component in fundamental primary system.
Returns
-------
ndarray, (3,)
Corresponding colour cone responses of given test sample cone
responses.
Examples
--------
>>> RGB_1 = np.array([25.8244273, 18.6791422, 4.8390194])
>>> Y_o = 20
>>> xez_1 = np.array([1.11857195, 0.9329553, 0.32680879])
>>> xez_2 = np.array([1.00000372, 1.00000176, 0.99999461])
>>> bRGB_o1 = np.array([3.74852518, 3.63920879, 2.78924811])
>>> bRGB_o2 = np.array([3.68102374, 3.68102256, 3.56557351])
>>> K = 1.0
>>> corresponding_colour(RGB_1, Y_o, xez_1, xez_2, bRGB_o1, bRGB_o2, K) # noqa # doctest: +ELLIPSIS
array([ 23.1636901..., 20.0211948..., 16.2001664...])
"""
R_1, G_1, B_1 = RGB_1
xi_1, eta_1, zeta_1 = xez_1
xi_2, eta_2, zeta_2 = xez_2
bR_o1, bG_o1, bB_o1 = bRGB_o1
bR_o2, bG_o2, bB_o2 = bRGB_o2
RGBc = lambda x1, x2, y1, y2, z: (
(Y_o * x2 + n) * K ** (1 / y2) *
((z + n) / (Y_o * x1 + n)) ** (y1 / y2) - n)
R_2 = RGBc(xi_1, xi_2, bR_o1, bR_o2, R_1)
G_2 = RGBc(eta_1, eta_2, bG_o1, bG_o2, G_1)
B_2 = RGBc(zeta_1, zeta_2, bB_o1, bB_o2, B_1)
return np.array([R_2, G_2, B_2])
Colour 0.3