# -*- coding: utf-8 -*-
"""
CIE 1994 Chromatic Adaptation Model
===================================
Defines *CIE 1994* chromatic adaptation model objects:
- :func:`colour.adaptation.chromatic_adaptation_CIE1994`
See Also
--------
`CIE 1994 Chromatic Adaptation Model Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/adaptation/cie1994.ipynb>`_
References
----------
- :cite:`CIETC1-321994b` : CIE TC 1-32. (1994). CIE 109-1994 A Method of
Predicting Corresponding Colours under Different Chromatic and Illuminance
Adaptations. ISBN:978-3-900734-51-0
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import spow
from colour.adaptation import VON_KRIES_CAT
from colour.utilities import (as_float_array, dot_vector, from_range_100,
to_domain_100, tsplit, tstack, usage_warning)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - https://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* tristimulus values 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* tristimulus
values 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 stimulus *CIE XYZ_1* tristimulus values from test viewing
conditions to reference viewing conditions using *CIE 1994* chromatic
adaptation model.
Parameters
----------
XYZ_1 : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
xy_o1 : array_like
Chromaticity coordinates :math:`x_{o1}` and :math:`y_{o1}` of test
illuminant and background.
xy_o2 : array_like
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
normalised to domain [18, 100] in **'Reference'** domain-range scale.
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
Adapted *CIE XYZ_2* tristimulus values of test stimulus.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ_1`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
| ``Y_o`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ_2`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`CIETC1-321994b`
Examples
--------
>>> XYZ_1 = np.array([28.00, 21.26, 5.27])
>>> xy_o1 = np.array([0.4476, 0.4074])
>>> xy_o2 = np.array([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)
... # doctest: +ELLIPSIS
array([ 24.0337952..., 21.1562121..., 17.6430119...])
"""
XYZ_1 = to_domain_100(XYZ_1)
Y_o = to_domain_100(Y_o)
E_o1 = as_float_array(E_o1)
E_o2 = as_float_array(E_o2)
if np.any(Y_o < 18) or np.any(Y_o > 100):
usage_warning(('"Y_o" luminance factor must be in [18, 100] domain, '
'unpredictable results may occur!'))
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(xez_1, Y_o, E_o1)
RGB_o2 = effective_adapting_responses(xez_2, Y_o, E_o2)
bRGB_o1 = exponential_factors(RGB_o1)
bRGB_o2 = exponential_factors(RGB_o2)
K = K_coefficient(xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o, n)
RGB_2 = corresponding_colour(RGB_1, xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o, K,
n)
XYZ_2 = RGB_to_XYZ_CIE1994(RGB_2)
return from_range_100(XYZ_2)
def XYZ_to_RGB_CIE1994(XYZ):
"""
Converts from *CIE XYZ* tristimulus values to cone responses.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Returns
-------
ndarray
Cone responses.
Examples
--------
>>> XYZ = np.array([28.00, 21.26, 5.27])
>>> XYZ_to_RGB_CIE1994(XYZ) # doctest: +ELLIPSIS
array([ 25.8244273..., 18.6791422..., 4.8390194...])
"""
return dot_vector(CIE1994_XYZ_TO_RGB_MATRIX, XYZ)
def RGB_to_XYZ_CIE1994(RGB):
"""
Converts from cone responses to *CIE XYZ* tristimulus values.
Parameters
----------
RGB : array_like
Cone responses.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Examples
--------
>>> RGB = np.array([25.82442730, 18.67914220, 4.83901940])
>>> RGB_to_XYZ_CIE1994(RGB) # doctest: +ELLIPSIS
array([ 28. , 21.26, 5.27])
"""
return dot_vector(CIE1994_RGB_TO_XYZ_MATRIX, RGB)
def intermediate_values(xy_o):
"""
Returns the intermediate values :math:`\\xi`, :math:`\\eta`,
:math:`\\zeta`.
Parameters
----------
xy_o : array_like
Chromaticity coordinates :math:`x_o` and :math:`y_o` of whitepoint.
Returns
-------
ndarray
Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`.
Examples
--------
>>> xy_o = np.array([0.4476, 0.4074])
>>> intermediate_values(xy_o) # doctest: +ELLIPSIS
array([ 1.1185719..., 0.9329553..., 0.3268087...])
"""
x_o, y_o = tsplit(xy_o)
# Computing :math:`\\xi` :math:`\\eta`, :math:`\\zeta` values.
xi = (0.48105 * x_o + 0.78841 * y_o - 0.08081) / y_o
eta = (-0.27200 * x_o + 1.11962 * y_o + 0.04570) / y_o
zeta = (0.91822 * (1 - x_o - y_o)) / y_o
xez = tstack([xi, eta, zeta])
return xez
def effective_adapting_responses(xez, Y_o, E_o):
"""
Derives the effective adapting responses in the fundamental primary system
of the test or reference field.
Parameters
----------
xez: ndarray
Intermediate values :math:`\\xi`, :math:`\\eta`, :math:`\\zeta`.
E_o : numeric
Test or reference illuminance :math:`E_{o}` in lux.
Y_o : numeric
Luminance factor :math:`Y_o` of achromatic background as percentage
normalised to domain [18, 100] in **'Reference'** domain-range scale.
Returns
-------
ndarray
Effective adapting responses.
Examples
--------
>>> xez = np.array([1.11857195, 0.93295530, 0.32680879])
>>> E_o = 1000
>>> Y_o = 20
>>> effective_adapting_responses(xez, Y_o, E_o) # doctest: +ELLIPSIS
array([ 71.2105020..., 59.3937790..., 20.8052937...])
"""
xez = as_float_array(xez)
Y_o = as_float_array(Y_o)
E_o = as_float_array(E_o)
RGB_o = ((
(Y_o[..., np.newaxis] * E_o[..., np.newaxis]) / (100 * np.pi)) * xez)
return RGB_o
def beta_1(x):
"""
Computes the exponent :math:`\\beta_1` for the middle and long-wavelength
sensitive cones.
Parameters
----------
x: numeric or array_like
Middle and long-wavelength sensitive cone response.
Returns
-------
numeric or array_like
Exponent :math:`\\beta_1`.
Examples
--------
>>> beta_1(318.323316315) # doctest: +ELLIPSIS
4.6106222...
"""
return (6.469 + 6.362 * spow(x, 0.4495)) / (6.469 + spow(x, 0.4495))
def beta_2(x):
"""
Computes the exponent :math:`\\beta_2` for the short-wavelength sensitive
cones.
Parameters
----------
x: numeric or array_like
Short-wavelength sensitive cone response.
Returns
-------
numeric or array_like
Exponent :math:`\\beta_2`.
Examples
--------
>>> beta_2(318.323316315) # doctest: +ELLIPSIS
4.6522416...
"""
return 0.7844 * (8.414 + 8.091 * spow(x, 0.5128)) / (
8.414 + spow(x, 0.5128))
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: array_like
Cone responses.
Returns
-------
ndarray
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 = tsplit(RGB_o)
bR_o = beta_1(R_o)
bG_o = beta_1(G_o)
bB_o = beta_2(B_o)
bRGB_o = tstack([bR_o, bG_o, bB_o])
return bRGB_o
def K_coefficient(xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o, n=1):
"""
Computes the coefficient :math:`K` for correcting the difference between
the test and references illuminances.
Parameters
----------
xez_1: array_like
Intermediate values :math:`\\xi_1`, :math:`\\eta_1`, :math:`\\zeta_1`
for the test illuminant and background.
xez_2: array_like
Intermediate values :math:`\\xi_2`, :math:`\\eta_2`, :math:`\\zeta_2`
for the reference illuminant and background.
bRGB_o1: array_like
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: array_like
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o2})`,
:math:`\\beta_1(G_{o2})` and :math:`\\beta_2(B_{o2})` of reference
sample.
Y_o : numeric or array_like
Luminance factor :math:`Y_o` of achromatic background as percentage
normalised to domain [18, 100] in **'Reference'** domain-range scale.
n : numeric or array_like, optional
Noise component in fundamental primary system.
Returns
-------
numeric or array_like
Coefficient :math:`K`.
Examples
--------
>>> xez_1 = np.array([1.11857195, 0.93295530, 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])
>>> Y_o = 20
>>> K_coefficient(xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o)
1.0
"""
xi_1, eta_1, _zeta_1 = tsplit(xez_1)
xi_2, eta_2, _zeta_2 = tsplit(xez_2)
bR_o1, bG_o1, _bB_o1 = tsplit(bRGB_o1)
bR_o2, bG_o2, _bB_o2 = tsplit(bRGB_o2)
Y_o = as_float_array(Y_o)
K = (spow((Y_o * xi_1 + n) / (20 * xi_1 + n), (2 / 3) * bR_o1) / spow(
(Y_o * xi_2 + n) / (20 * xi_2 + n), (2 / 3) * bR_o2))
K *= (spow((Y_o * eta_1 + n) / (20 * eta_1 + n), (1 / 3) * bG_o1) / spow(
(Y_o * eta_2 + n) / (20 * eta_2 + n), (1 / 3) * bG_o2))
return K
def corresponding_colour(RGB_1, xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o, K, n=1):
"""
Computes the corresponding colour cone responses of given test sample cone
responses :math:`RGB_1`.
Parameters
----------
RGB_1: array_like
Test sample cone responses :math:`RGB_1`.
xez_1: array_like
Intermediate values :math:`\\xi_1`, :math:`\\eta_1`, :math:`\\zeta_1`
for the test illuminant and background.
xez_2: array_like
Intermediate values :math:`\\xi_2`, :math:`\\eta_2`, :math:`\\zeta_2`
for the reference illuminant and background.
bRGB_o1: array_like
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: array_like
Chromatic adaptation exponential factors :math:`\\beta_1(R_{o2})`,
:math:`\\beta_1(G_{o2})` and :math:`\\beta_2(B_{o2})` of reference
sample.
Y_o : numeric or array_like
Luminance factor :math:`Y_o` of achromatic background as percentage
normalised to domain [18, 100] in **'Reference'** domain-range scale.
K : numeric or array_like
Coefficient :math:`K`.
n : numeric or array_like, optional
Noise component in fundamental primary system.
Returns
-------
ndarray
Corresponding colour cone responses of given test sample cone
responses.
Examples
--------
>>> RGB_1 = np.array([25.82442730, 18.67914220, 4.83901940])
>>> xez_1 = np.array([1.11857195, 0.93295530, 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])
>>> Y_o = 20
>>> K = 1.0
>>> corresponding_colour(RGB_1, xez_1, xez_2, bRGB_o1, bRGB_o2, Y_o, K)
... # doctest: +ELLIPSIS
array([ 23.1636901..., 20.0211948..., 16.2001664...])
"""
R_1, G_1, B_1 = tsplit(RGB_1)
xi_1, eta_1, zeta_1 = tsplit(xez_1)
xi_2, eta_2, zeta_2 = tsplit(xez_2)
bR_o1, bG_o1, bB_o1 = tsplit(bRGB_o1)
bR_o2, bG_o2, bB_o2 = tsplit(bRGB_o2)
Y_o = as_float_array(Y_o)
K = as_float_array(K)
def RGB_c(x_1, x_2, y_1, y_2, z):
"""
Computes the corresponding colour cone responses component.
"""
return ((Y_o * x_2 + n) * spow(K, 1 / y_2) * spow(
(z + n) / (Y_o * x_1 + n), y_1 / y_2) - n)
R_2 = RGB_c(xi_1, xi_2, bR_o1, bR_o2, R_1)
G_2 = RGB_c(eta_1, eta_2, bG_o1, bG_o2, G_1)
B_2 = RGB_c(zeta_1, zeta_2, bB_o1, bB_o2, B_1)
RGB_2 = tstack([R_2, G_2, B_2])
return RGB_2