# -*- coding: utf-8 -*-
"""
Optical Society of America Uniform Colour Scales (OSA UCS)
==========================================================
Defines the *OSA UCS* colourspace:
- :func:`colour.XYZ_to_OSA_UCS`
- :func:`colour.OSA_UCS_to_XYZ`
References
----------
- :cite:`Cao2013` : Cao, R., Trussell, H. J., & Shamey, R. (2013). Comparison
of the performance of inverse transformation methods from OSA-UCS to
CIEXYZ. Journal of the Optical Society of America A, 30(8), 1508.
doi:10.1364/JOSAA.30.001508
- :cite:`Moroney2003` : Moroney, N. (2003). A Radial Sampling of the OSA
Uniform Color Scales. Color and Imaging Conference, 2003(1), 175-180.
ISSN:2166-9635
"""
from __future__ import division, unicode_literals
import numpy as np
from scipy.optimize import fmin
from colour.algebra import spow
from colour.models import XYZ_to_xyY
from colour.utilities import (as_float_array, domain_range_scale, vector_dot,
from_range_100, to_domain_100, tsplit, tstack)
from colour.utilities.deprecation import handle_arguments_deprecation
__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__ = ['XYZ_to_OSA_UCS', 'OSA_UCS_to_XYZ']
MATRIX_XYZ_TO_RGB_OSA_UCS = np.array([
[0.799, 0.4194, -0.1648],
[-0.4493, 1.3265, 0.0927],
[-0.1149, 0.3394, 0.717],
])
"""
*OSA UCS* matrix converting from *CIE XYZ* tristimulus values to *RGB*
colourspace.
MATRIX_XYZ_TO_RGB_OSA_UCS : array_like, (3, 3)
"""
[docs]def XYZ_to_OSA_UCS(XYZ):
"""
Converts from *CIE XYZ* tristimulus values under the
*CIE 1964 10 Degree Standard Observer* to *OSA UCS* colourspace.
The lightness axis, *L* is usually in range [-9, 5] and centered around
middle gray (Munsell N/6). The yellow-blue axis, *j* is usually in range
[-15, 15]. The red-green axis, *g* is usually in range [-20, 15].
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values under the
*CIE 1964 10 Degree Standard Observer*.
Returns
-------
ndarray
*OSA UCS* :math:`Ljg` lightness, jaune (yellowness), and greenness.
Notes
-----
+------------+-----------------------+--------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+====================+
| ``XYZ`` | [0, 100] | [0, 1] |
+------------+-----------------------+--------------------+
+------------+-----------------------+--------------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+====================+
| ``Ljg`` | ``L`` : [-100, 100] | ``L`` : [-1, 1] |
| | | |
| | ``j`` : [-100, 100] | ``j`` : [-1, 1] |
| | | |
| | ``g`` : [-100, 100] | ``g`` : [-1, 1] |
+------------+-----------------------+--------------------+
- *OSA UCS* uses the *CIE 1964 10 Degree Standard Observer*.
References
----------
:cite:`Cao2013`, :cite:`Moroney2003`
Examples
--------
>>> import numpy as np
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) * 100
>>> XYZ_to_OSA_UCS(XYZ) # doctest: +ELLIPSIS
array([-3.0049979..., 2.9971369..., -9.6678423...])
"""
XYZ = to_domain_100(XYZ)
x, y, Y = tsplit(XYZ_to_xyY(XYZ))
Y_0 = Y * (4.4934 * x ** 2 + 4.3034 * y ** 2 - 4.276 * x * y - 1.3744 * x -
2.5643 * y + 1.8103)
o_3 = 1 / 3
Y_0_es = spow(Y_0, o_3) - 2 / 3
# Gracefully handles Y_0 < 30.
Y_0_s = Y_0 - 30
Lambda = 5.9 * (Y_0_es + 0.042 * spow(Y_0_s, o_3))
RGB = vector_dot(MATRIX_XYZ_TO_RGB_OSA_UCS, XYZ)
RGB_3 = spow(RGB, 1 / 3)
C = Lambda / (5.9 * Y_0_es)
L = (Lambda - 14.4) / spow(2, 1 / 2)
j = C * np.dot(RGB_3, np.array([1.7, 8, -9.7]))
g = C * np.dot(RGB_3, np.array([-13.7, 17.7, -4]))
Ljg = tstack([L, j, g])
return from_range_100(Ljg)
[docs]def OSA_UCS_to_XYZ(Ljg, optimisation_kwargs=None, **kwargs):
"""
Converts from *OSA UCS* colourspace to *CIE XYZ* tristimulus values under
the *CIE 1964 10 Degree Standard Observer*.
Parameters
----------
Ljg : array_like
*OSA UCS* :math:`Ljg` lightness, jaune (yellowness), and greenness.
optimisation_kwargs : dict_like, optional
Parameters for :func:`scipy.optimize.fmin` definition.
Other Parameters
----------------
\\**kwargs : dict, optional
Keywords arguments for deprecation management.
Returns
-------
ndarray
*CIE XYZ* tristimulus values under the
*CIE 1964 10 Degree Standard Observer*.
Warnings
--------
There is no analytical inverse transformation from *OSA UCS* to :math:`Ljg`
lightness, jaune (yellowness), and greenness to *CIE XYZ* tristimulus
values, the current implementation relies on optimization using
:func:`scipy.optimize.fmin` definition and thus has reduced precision and
poor performance.
Notes
-----
+------------+-----------------------+--------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+====================+
| ``Ljg`` | ``L`` : [-100, 100] | ``L`` : [-1, 1] |
| | | |
| | ``j`` : [-100, 100] | ``j`` : [-1, 1] |
| | | |
| | ``g`` : [-100, 100] | ``g`` : [-1, 1] |
+------------+-----------------------+--------------------+
+------------+-----------------------+--------------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+====================+
| ``XYZ`` | [0, 100] | [0, 1] |
+------------+-----------------------+--------------------+
- *OSA UCS* uses the *CIE 1964 10 Degree Standard Observer*.
References
----------
:cite:`Cao2013`, :cite:`Moroney2003`
Examples
--------
>>> import numpy as np
>>> Ljg = np.array([-3.00499790, 2.99713697, -9.66784231])
>>> OSA_UCS_to_XYZ(Ljg) # doctest: +ELLIPSIS
array([ 20.6540240..., 12.1972369..., 5.1369372...])
"""
optimisation_kwargs = handle_arguments_deprecation({
'ArgumentRenamed': [['optimisation_parameters', 'optimisation_kwargs']
],
}, **kwargs).get('optimisation_kwargs', optimisation_kwargs)
Ljg = to_domain_100(Ljg)
shape = Ljg.shape
Ljg = np.atleast_1d(Ljg.reshape([-1, 3]))
optimisation_settings = {'disp': False}
if optimisation_kwargs is not None:
optimisation_settings.update(optimisation_kwargs)
def error_function(XYZ, Ljg):
"""
Error function.
"""
# Error must be computed in "reference" domain and range.
with domain_range_scale('ignore'):
error = np.linalg.norm(XYZ_to_OSA_UCS(XYZ) - Ljg)
return error
x_0 = np.array([30, 30, 30])
XYZ = as_float_array([
fmin(error_function, x_0, (Ljg_i, ), **optimisation_settings)
for Ljg_i in Ljg
])
return from_range_100(XYZ.reshape(shape))