def excitation_purity(xy,
xy_n,
cmfs=CMFS['CIE 1931 2 Degree Standard Observer']):
"""
Returns the *excitation purity* :math:`P_e` for given colour stimulus
:math:`xy`.
Parameters
----------
xy : array_like
Colour stimulus *xy* chromaticity coordinates.
xy_n : array_like
Achromatic stimulus *xy* chromaticity coordinates.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
Returns
-------
numeric or array_like
*Excitation purity* :math:`P_e`.
Examples
--------
>>> xy = np.array([0.28350, 0.68700])
>>> xy_n = np.array([0.31270, 0.32900])
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> excitation_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS
0.9386035...
"""
wl, xy_wl, xy_cwl = dominant_wavelength(xy, xy_n, cmfs)
P_e = euclidean_distance(xy_n, xy) / euclidean_distance(xy_n, xy_wl)
return P_e
def test_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition.
"""
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 426.67945353, 72.39590835])),
451.71330197,
places=7)
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 74.05216981, 276.45318193])),
52.64986116,
places=7)
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 8.32281957, -73.58297716])),
346.06489172,
places=7)
def test_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition.
"""
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 426.67945353, 72.39590835])),
451.71330197,
places=7)
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 74.05216981, 276.45318193])),
52.64986116,
places=7)
self.assertAlmostEqual(
euclidean_distance(
np.array([100.00000000, 21.57210357, 272.22819350]),
np.array([100.00000000, 8.32281957, -73.58297716])),
346.06489172,
places=7)
def test_n_dimensional_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition
n-dimensional arrays support.
"""
a = np.array([100.00000000, 21.57210357, 272.22819350])
b = np.array([100.00000000, 426.67945353, 72.39590835])
distance = 451.71330197
np.testing.assert_almost_equal(
euclidean_distance(a, b),
distance,
decimal=7)
a = np.tile(a, (6, 1))
b = np.tile(b, (6, 1))
distance = np.tile(distance, 6)
np.testing.assert_almost_equal(
euclidean_distance(a, b),
distance,
decimal=7)
a = np.reshape(a, (2, 3, 3))
b = np.reshape(b, (2, 3, 3))
distance = np.reshape(distance, (2, 3))
np.testing.assert_almost_equal(
euclidean_distance(a, b),
distance,
decimal=7)
def test_n_dimensional_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition
n-dimensional arrays support.
"""
a = np.array([100.00000000, 21.57210357, 272.22819350])
b = np.array([100.00000000, 426.67945353, 72.39590835])
distance = 451.71330197
np.testing.assert_almost_equal(euclidean_distance(a, b),
distance,
decimal=7)
a = np.tile(a, (6, 1))
b = np.tile(b, (6, 1))
distance = np.tile(distance, 6)
np.testing.assert_almost_equal(euclidean_distance(a, b),
distance,
decimal=7)
a = np.reshape(a, (2, 3, 3))
b = np.reshape(b, (2, 3, 3))
distance = np.reshape(distance, (2, 3))
np.testing.assert_almost_equal(euclidean_distance(a, b),
distance,
decimal=7)
def test_nan_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition nan
support.
"""
cases = [-1.0, 0.0, 1.0, -np.inf, np.inf, np.nan]
cases = set(permutations(cases * 3, r=3))
for case in cases:
a = np.array(case)
b = np.array(case)
euclidean_distance(a, b)
def test_nan_euclidean_distance(self):
"""
Tests :func:`colour.algebra.geometry.euclidean_distance` definition nan
support.
"""
cases = [-1.0, 0.0, 1.0, -np.inf, np.inf, np.nan]
cases = set(permutations(cases * 3, r=3))
for case in cases:
a = np.array(case)
b = np.array(case)
euclidean_distance(a, b)
def colour_quality_scales(test_data, reference_data, CCT_f):
"""
Returns the *VS test colour samples* rendering scales.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
CCT_f : numeric
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
dict
*VS Test colour samples* colour rendering scales.
"""
Q_as = {}
for i, _ in enumerate(test_data):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = euclidean_distance(test_data[i].Lab, reference_data[i].Lab)
if D_C_ab > 0:
D_Ep_ab = np.sqrt(D_E_ab**2 - D_C_ab**2)
else:
D_Ep_ab = D_E_ab
Q_a = scale_conversion(D_Ep_ab, CCT_f)
Q_as[i + 1] = VS_ColourQualityScaleData(test_data[i].name, Q_a, D_C_ab,
D_E_ab, D_Ep_ab)
return Q_as
def delta_E_CIE1976(Lab_1, Lab_2):
"""
Returns the difference :math:`\Delta E_{ab}` between two given
*CIE L\*a\*b\** colourspace arrays using *CIE 1976* recommendation.
Parameters
----------
Lab_1 : array_like
*CIE L\*a\*b\** colourspace array 1.
Lab_2 : array_like
*CIE L\*a\*b\** colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
References
----------
- :cite:`Lindbloom2003c`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab_1, Lab_2) # doctest: +ELLIPSIS
451.7133019...
"""
d_E = euclidean_distance(Lab_1, Lab_2)
return d_E
def colour_rendering_indexes(
test_data: Tuple[TCS_ColorimetryData, ...],
reference_data: Tuple[TCS_ColorimetryData, ...],
) -> Dict[Integer, TCS_ColourQualityScaleData]:
"""
Return the *test colour samples* rendering indexes :math:`Q_a`.
Parameters
----------
test_data
Test data.
reference_data
Reference data.
Returns
-------
:class:`dict`
*Test colour samples* *Colour Rendering Index* (CRI).
"""
Q_as = {}
for i in range(len(test_data)):
Q_as[i + 1] = TCS_ColourQualityScaleData(
test_data[i].name,
100
- 4.6
* as_float_scalar(
euclidean_distance(reference_data[i].UVW, test_data[i].UVW)
),
)
return Q_as
def delta_E_DIN99(Lab_1, Lab_2, textiles=False):
"""
Returns the difference :math:`\\Delta E_{DIN99}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *DIN99* formula.
Parameters
----------
Lab_1 : array_like
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2 : array_like
*CIE L\\*a\\*b\\** colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\\Delta E_{DIN99}`.
Notes
-----
+------------+-----------------------+-------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===================+
| ``Lab_1`` | ``L_1`` : [0, 100] | ``L_1`` : [0, 1] |
| | | |
| | ``a_1`` : [-100, 100] | ``a_1`` : [-1, 1] |
| | | |
| | ``b_1`` : [-100, 100] | ``b_1`` : [-1, 1] |
+------------+-----------------------+-------------------+
| ``Lab_2`` | ``L_2`` : [0, 100] | ``L_2`` : [0, 1] |
| | | |
| | ``a_2`` : [-100, 100] | ``a_2`` : [-1, 1] |
| | | |
| | ``b_2`` : [-100, 100] | ``b_2`` : [-1, 1] |
+------------+-----------------------+-------------------+
References
----------
:cite:`ASTMInternational2007`
Examples
--------
>>> import numpy as np
>>> Lab_1 = np.array([60.2574, -34.0099, 36.2677])
>>> Lab_2 = np.array([60.4626, -34.1751, 39.4387])
>>> delta_E_DIN99(Lab_1, Lab_2) # doctest: +ELLIPSIS
1.1772166...
"""
k_E = 2 if textiles else 1
k_CH = 0.5 if textiles else 1
factor = 100 if get_domain_range_scale() == '1' else 1
d_E = euclidean_distance(
Lab_to_DIN99(Lab_1, k_E, k_CH) * factor,
Lab_to_DIN99(Lab_2, k_E, k_CH) * factor)
return d_E
def delta_E_DIN99(Lab_1, Lab_2, textiles=False):
"""
Returns the difference :math:`\\Delta E_{DIN99}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *DIN99* formula.
Parameters
----------
Lab_1 : array_like
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2 : array_like
*CIE L\\*a\\*b\\** colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\\Delta E_{DIN99}`.
Notes
-----
+------------+-----------------------+-------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===================+
| ``Lab_1`` | ``L_1`` : [0, 100] | ``L_1`` : [0, 1] |
| | | |
| | ``a_1`` : [-100, 100] | ``a_1`` : [-1, 1] |
| | | |
| | ``b_1`` : [-100, 100] | ``b_1`` : [-1, 1] |
+------------+-----------------------+-------------------+
| ``Lab_2`` | ``L_2`` : [0, 100] | ``L_2`` : [0, 1] |
| | | |
| | ``a_2`` : [-100, 100] | ``a_2`` : [-1, 1] |
| | | |
| | ``b_2`` : [-100, 100] | ``b_2`` : [-1, 1] |
+------------+-----------------------+-------------------+
References
----------
:cite:`ASTMInternational2007`
Examples
--------
>>> import numpy as np
>>> Lab_1 = np.array([60.2574, -34.0099, 36.2677])
>>> Lab_2 = np.array([60.4626, -34.1751, 39.4387])
>>> delta_E_DIN99(Lab_1, Lab_2) # doctest: +ELLIPSIS
1.1772166...
"""
k_E = 2 if textiles else 1
k_CH = 0.5 if textiles else 1
factor = 100 if get_domain_range_scale() == '1' else 1
d_E = euclidean_distance(
Lab_to_DIN99(Lab_1, k_E, k_CH) * factor,
Lab_to_DIN99(Lab_2, k_E, k_CH) * factor)
return d_E
def excitation_purity(
xy: ArrayLike,
xy_n: ArrayLike,
cmfs: Optional[MultiSpectralDistributions] = None,
) -> FloatingOrNDArray:
"""
Return the *excitation purity* :math:`P_e` for given colour stimulus
:math:`xy`.
Parameters
----------
xy
Colour stimulus *CIE xy* chromaticity coordinates.
xy_n
Achromatic stimulus *CIE xy* chromaticity coordinates.
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
Returns
-------
:class:`np.floating` or :class:`numpy.ndarray`
*Excitation purity* :math:`P_e`.
References
----------
:cite:`CIETC1-482004o`, :cite:`Erdogana`
Examples
--------
>>> from colour.colorimetry import MSDS_CMFS
>>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> xy = np.array([0.54369557, 0.32107944])
>>> xy_n = np.array([0.31270000, 0.32900000])
>>> excitation_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS
0.6228856...
"""
_wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs)
P_e = euclidean_distance(xy_n, xy) / euclidean_distance(xy_n, xy_wl)
return P_e
def objective_function(M: ArrayLike, RGB: ArrayLike,
Jab: ArrayLike) -> FloatingOrNDArray:
""":math:`J_za_zb_z` colourspace based objective function."""
M = np.reshape(M, [3, 3])
XYZ_t = vector_dot(RGB_COLOURSPACE_ACES2065_1.matrix_RGB_to_XYZ,
vector_dot(M, RGB))
Jab_t = XYZ_to_Jzazbz(XYZ_t)
return np.sum(euclidean_distance(Jab, Jab_t))
def objective_function(M, RGB, Jab):
"""
:math:`J_zA_zB_z` colourspace based objective function.
"""
M = np.reshape(M, [3, 3])
XYZ_t = vector_dot(RGB_COLOURSPACE_ACES2065_1.matrix_RGB_to_XYZ,
vector_dot(M, RGB))
Jab_t = XYZ_to_JzAzBz(XYZ_t)
return np.sum(euclidean_distance(Jab, Jab_t))
def test_delta_E_CIE1976(self):
"""
Tests :func:`colour.difference.delta_e.delta_E_CIE1976` definition.
"""
Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
Lab_1 = np.tile(Lab_1, (6, 1)).reshape((2, 3, 3))
Lab_2 = np.tile(Lab_2, (6, 1)).reshape((2, 3, 3))
np.testing.assert_almost_equal(delta_E_CIE1976(Lab_1, Lab_2),
euclidean_distance(Lab_1, Lab_2),
decimal=7)
def excitation_purity(xy,
xy_n,
cmfs=CMFS['CIE 1931 2 Degree Standard Observer']):
"""
Returns the *excitation purity* :math:`P_e` for given colour stimulus
:math:`xy`.
Parameters
----------
xy : array_like
Colour stimulus *CIE xy* chromaticity coordinates.
xy_n : array_like
Achromatic stimulus *CIE xy* chromaticity coordinates.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
Returns
-------
numeric or array_like
*Excitation purity* :math:`P_e`.
References
----------
:cite:`CIETC1-482004o`, :cite:`Erdogana`
Examples
--------
>>> xy = np.array([0.54369557, 0.32107944])
>>> xy_n = np.array([0.31270000, 0.32900000])
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> excitation_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS
0.6228856...
"""
_wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs)
P_e = euclidean_distance(xy_n, xy) / euclidean_distance(xy_n, xy_wl)
return P_e
def delta_E_CIE1976(Lab_1, Lab_2):
"""
Returns the difference :math:`\\Delta E_{76}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *CIE 1976* recommendation.
Parameters
----------
Lab_1 : array_like
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2 : array_like
*CIE L\\*a\\*b\\** colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\\Delta E_{76}`.
Notes
-----
+------------+-----------------------+-------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===================+
| ``Lab_1`` | ``L_1`` : [0, 100] | ``L_1`` : [0, 1] |
| | | |
| | ``a_1`` : [-100, 100] | ``a_1`` : [-1, 1] |
| | | |
| | ``b_1`` : [-100, 100] | ``b_1`` : [-1, 1] |
+------------+-----------------------+-------------------+
| ``Lab_2`` | ``L_2`` : [0, 100] | ``L_2`` : [0, 1] |
| | | |
| | ``a_2`` : [-100, 100] | ``a_2`` : [-1, 1] |
| | | |
| | ``b_2`` : [-100, 100] | ``b_2`` : [-1, 1] |
+------------+-----------------------+-------------------+
References
----------
:cite:`Lindbloom2003c`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab_1, Lab_2) # doctest: +ELLIPSIS
451.7133019...
"""
d_E = euclidean_distance(to_domain_100(Lab_1), to_domain_100(Lab_2))
return d_E
def delta_E_CIE1976(Lab_1, Lab_2):
"""
Returns the difference :math:`\\Delta E_{76}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *CIE 1976* recommendation.
Parameters
----------
Lab_1 : array_like
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2 : array_like
*CIE L\\*a\\*b\\** colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\\Delta E_{76}`.
Notes
-----
+------------+-----------------------+-------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===================+
| ``Lab_1`` | ``L_1`` : [0, 100] | ``L_1`` : [0, 1] |
| | | |
| | ``a_1`` : [-100, 100] | ``a_1`` : [-1, 1] |
| | | |
| | ``b_1`` : [-100, 100] | ``b_1`` : [-1, 1] |
+------------+-----------------------+-------------------+
| ``Lab_2`` | ``L_2`` : [0, 100] | ``L_2`` : [0, 1] |
| | | |
| | ``a_2`` : [-100, 100] | ``a_2`` : [-1, 1] |
| | | |
| | ``b_2`` : [-100, 100] | ``b_2`` : [-1, 1] |
+------------+-----------------------+-------------------+
References
----------
:cite:`Lindbloom2003c`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab_1, Lab_2) # doctest: +ELLIPSIS
451.7133019...
"""
d_E = euclidean_distance(to_domain_100(Lab_1), to_domain_100(Lab_2))
return d_E
def test_delta_E_CIE1976(self):
"""
Tests :func:`colour.difference.delta_e.delta_E_CIE1976` definition.
"""
Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
Lab_1 = np.tile(Lab_1, (6, 1)).reshape([2, 3, 3])
Lab_2 = np.tile(Lab_2, (6, 1)).reshape([2, 3, 3])
np.testing.assert_almost_equal(
delta_E_CIE1976(Lab_1, Lab_2),
euclidean_distance(Lab_1, Lab_2),
decimal=7)
def test_domain_range_scale_delta_E_CIE1976(self):
"""
Tests :func:`colour.difference.delta_e.delta_E_CIE1976` definition
domain and range scale support.
"""
Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
d_r = (('reference', 1), (1, 0.01), (100, 1))
for scale, factor in d_r:
with domain_range_scale(scale):
np.testing.assert_almost_equal(
delta_E_CIE1976(Lab_1 * factor, Lab_2 * factor),
euclidean_distance(Lab_1, Lab_2),
decimal=7)
def test_domain_range_scale_delta_E_CIE1976(self):
"""
Tests :func:`colour.difference.delta_e.delta_E_CIE1976` definition
domain and range scale support.
"""
Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
d_r = (('reference', 1), (1, 0.01), (100, 1))
for scale, factor in d_r:
with domain_range_scale(scale):
np.testing.assert_almost_equal(
delta_E_CIE1976(Lab_1 * factor, Lab_2 * factor),
euclidean_distance(Lab_1, Lab_2),
decimal=7)
def colour_quality_scales(test_data, reference_data, CCT_f):
Q_as = {}
from colour.algebra import euclidean_distance
for i, _ in enumerate(test_data):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = euclidean_distance(test_data[i].Lab, reference_data[i].Lab)
if D_C_ab > 0:
D_Ep_ab = np.sqrt(D_E_ab**2 - D_C_ab**2)
else:
D_Ep_ab = D_E_ab
Q_a = scale_conversion(D_Ep_ab, CCT_f)
Q_as[i + 1] = VS_ColourQualityScaleData(test_data[i].name, Q_a, D_C_ab,
D_E_ab, D_Ep_ab)
return Q_as
def colour_quality_scales(
test_data: Tuple[VS_ColorimetryData, ...],
reference_data: Tuple[VS_ColorimetryData, ...],
scaling_f: Floating,
CCT_f: Floating,
) -> Dict[Integer, VS_ColourQualityScaleData]:
"""
Return the *VS test colour samples* rendering scales.
Parameters
----------
test_data
Test data.
reference_data
Reference data.
scaling_f
Scaling factor constant.
CCT_f
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
:class:`dict`
*VS Test colour samples* colour rendering scales.
"""
Q_as = {}
for i in range(len(test_data)):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = as_float_scalar(
euclidean_distance(test_data[i].Lab, reference_data[i].Lab))
if D_C_ab > 0:
D_Ep_ab = np.sqrt(D_E_ab**2 - D_C_ab**2)
else:
D_Ep_ab = D_E_ab
Q_a = scale_conversion(D_Ep_ab, CCT_f, scaling_f)
Q_as[i + 1] = VS_ColourQualityScaleData(test_data[i].name, Q_a, D_C_ab,
D_E_ab, D_Ep_ab)
return Q_as
def colour_rendering_indexes(test_data, reference_data):
"""
Returns the *test colour samples* rendering indexes :math:`Q_a`.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
Returns
-------
dict
*Test colour samples* *Colour Rendering Index* (CRI).
"""
Q_as = {}
for i, _ in enumerate(test_data):
Q_as[i + 1] = TCS_ColourQualityScaleData(
test_data[i].name, 100 -
4.6 * euclidean_distance(reference_data[i].UVW, test_data[i].UVW))
return Q_as
def colour_rendering_indexes(test_data, reference_data):
"""
Returns the *test colour samples* rendering indexes :math:`Q_a`.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
Returns
-------
dict
*Test colour samples* *Colour Rendering Index* (CRI).
"""
Q_as = {}
for i, _ in enumerate(test_data):
Q_as[i + 1] = TCS_ColourQualityScaleData(
test_data[i].name, 100 -
4.6 * euclidean_distance(reference_data[i].UVW, test_data[i].UVW))
return Q_as
def delta_E_CIE1976(Lab_1, Lab_2):
"""
Returns the difference :math:`\Delta E_{ab}` between two given
*CIE Lab* colourspace arrays using CIE 1976 recommendation.
Parameters
----------
Lab_1 : array_like
*CIE Lab* colourspace array 1.
Lab_2 : array_like
*CIE Lab* colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
See Also
--------
colour.euclidean_distance
References
----------
.. [2] Lindbloom, B. (2003). Delta E (CIE 1976). Retrieved February 24,
2014, from http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab_1, Lab_2) # doctest: +ELLIPSIS
451.7133019...
"""
d_E = euclidean_distance(Lab_1, Lab_2)
return d_E
def delta_E_CIE1976(Lab_1, Lab_2):
"""
Returns the difference :math:`\Delta E_{ab}` between two given
*CIE Lab* colourspace arrays using CIE 1976 recommendation.
Parameters
----------
Lab_1 : array_like
*CIE Lab* colourspace array 1.
Lab_2 : array_like
*CIE Lab* colourspace array 2.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
See Also
--------
colour.euclidean_distance
References
----------
.. [2] Lindbloom, B. (2003). Delta E (CIE 1976). Retrieved February 24,
2014, from http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab_1, Lab_2) # doctest: +ELLIPSIS
451.7133019...
"""
d_E = euclidean_distance(Lab_1, Lab_2)
return d_E
def colour_quality_scales(test_data, reference_data, scaling_f, CCT_f):
"""
Returns the *VS test colour samples* rendering scales.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
scaling_f : numeric, optional
Scaling factor constant.
CCT_f : numeric
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
dict
*VS Test colour samples* colour rendering scales.
"""
Q_as = {}
for i, _ in enumerate(test_data):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = euclidean_distance(test_data[i].Lab, reference_data[i].Lab)
if D_C_ab > 0:
D_Ep_ab = np.sqrt(D_E_ab ** 2 - D_C_ab ** 2)
else:
D_Ep_ab = D_E_ab
Q_a = scale_conversion(D_Ep_ab, scaling_f, CCT_f)
Q_as[i + 1] = VS_ColourQualityScaleData(test_data[i].name, Q_a, D_C_ab,
D_E_ab, D_Ep_ab)
return Q_as
def delta_E_DIN99(Lab_1: ArrayLike,
Lab_2: ArrayLike,
textiles: Boolean = False) -> FloatingOrNDArray:
"""
Return the difference :math:`\\Delta E_{DIN99}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *DIN99* formula.
Parameters
----------
Lab_1
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2
*CIE L\\*a\\*b\\** colourspace array 2.
textiles
Textiles application specific parametric factors,
:math:`k_E=2,\\ k_{CH}=0.5` weights are used instead of
:math:`k_E=1,\\ k_{CH}=1`.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Colour difference :math:`\\Delta E_{DIN99}`.
Notes
-----
+------------+-----------------------+-------------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===================+
| ``Lab_1`` | ``L_1`` : [0, 100] | ``L_1`` : [0, 1] |
| | | |
| | ``a_1`` : [-100, 100] | ``a_1`` : [-1, 1] |
| | | |
| | ``b_1`` : [-100, 100] | ``b_1`` : [-1, 1] |
+------------+-----------------------+-------------------+
| ``Lab_2`` | ``L_2`` : [0, 100] | ``L_2`` : [0, 1] |
| | | |
| | ``a_2`` : [-100, 100] | ``a_2`` : [-1, 1] |
| | | |
| | ``b_2`` : [-100, 100] | ``b_2`` : [-1, 1] |
+------------+-----------------------+-------------------+
References
----------
:cite:`ASTMInternational2007`
Examples
--------
>>> import numpy as np
>>> Lab_1 = np.array([60.2574, -34.0099, 36.2677])
>>> Lab_2 = np.array([60.4626, -34.1751, 39.4387])
>>> delta_E_DIN99(Lab_1, Lab_2) # doctest: +ELLIPSIS
1.1772166...
"""
k_E = 2 if textiles else 1
k_CH = 0.5 if textiles else 1
factor = 100 if get_domain_range_scale() == "1" else 1
d_E = euclidean_distance(
Lab_to_DIN99(Lab_1, k_E, k_CH) * factor,
Lab_to_DIN99(Lab_2, k_E, k_CH) * factor,
)
return d_E
def colour_fidelity_index_CIE2017(sd_test, additional_data=False):
"""
Returns the *CIE 2017 Colour Fidelity Index* (CFI) :math:`R_f` of given
spectral distribution.
Parameters
----------
sd_test : SpectralDistribution
Test spectral distribution.
additional_data : bool, optional
Whether to output additional data.
Returns
-------
numeric or ColourRendering_Specification_CIE2017
*CIE 2017 Colour Fidelity Index* (CFI) :math:`R_f`.
References
----------
:cite:`CIETC1-902017`
Examples
--------
>>> from colour.colorimetry import SDS_ILLUMINANTS
>>> sd = SDS_ILLUMINANTS['FL2']
>>> colour_fidelity_index_CIE2017(sd) # doctest: +ELLIPSIS
70.1208254...
"""
if sd_test.shape.start > 380 or sd_test.shape.end < 780:
usage_warning('Test spectral distribution shape does not span the'
'recommended 380-780nm range, missing values will be'
'filled with zeros!')
# NOTE: "CIE 2017 Colour Fidelity Index" standard recommends filling
# missing values with zeros.
sd_test = sd_test.copy()
sd_test.extrapolator = Extrapolator
sd_test.extrapolator_kwargs = {
'method': 'constant',
'left': 0,
'right': 0
}
if sd_test.shape.interval > 5:
raise ValueError('Test spectral distribution interval is greater than'
'5nm which is the maximum recommended value '
'for computing the "CIE 2017 Colour Fidelity Index"!')
shape = SpectralShape(SPECTRAL_SHAPE_CIE2017.start,
SPECTRAL_SHAPE_CIE2017.end, sd_test.shape.interval)
CCT, D_uv = CCT_reference_illuminant(sd_test)
sd_reference = sd_reference_illuminant(CCT, shape)
# NOTE: All computations except CCT calculation use the
# "CIE 1964 10 Degree Standard Observer".
cmfs_10 = MSDS_CMFS['CIE 1964 10 Degree Standard Observer'].copy().align(
shape)
sds_tcs = load_TCS_CIE2017(shape).align(shape)
test_tcs_colorimetry_data = tcs_colorimetry_data(sd_test, sds_tcs, cmfs_10)
reference_tcs_colorimetry_data = tcs_colorimetry_data(
sd_reference, sds_tcs, cmfs_10)
delta_E_s = np.empty(len(sds_tcs.labels))
for i, _delta_E in enumerate(delta_E_s):
delta_E_s[i] = euclidean_distance(
test_tcs_colorimetry_data[i].Jpapbp,
reference_tcs_colorimetry_data[i].Jpapbp)
R_s = delta_E_to_R_f(delta_E_s)
R_f = delta_E_to_R_f(np.average(delta_E_s))
if additional_data:
return ColourRendering_Specification_CIE2017(
sd_test.name, sd_reference, R_f, R_s, CCT, D_uv,
(test_tcs_colorimetry_data, reference_tcs_colorimetry_data),
delta_E_s)
else:
return R_f
def colour_fidelity_index_CIE2017(
sd_test: SpectralDistribution,
additional_data: Boolean = False
) -> Union[Floating, ColourRendering_Specification_CIE2017]:
"""
Return the *CIE 2017 Colour Fidelity Index* (CFI) :math:`R_f` of given
spectral distribution.
Parameters
----------
sd_test
Test spectral distribution.
additional_data
Whether to output additional data.
Returns
-------
:class:`numpy.floating` or \
:class:`colour.quality.ColourRendering_Specification_CIE2017`
*CIE 2017 Colour Fidelity Index* (CFI) :math:`R_f`.
References
----------
:cite:`CIETC1-902017`
Examples
--------
>>> from colour.colorimetry import SDS_ILLUMINANTS
>>> sd = SDS_ILLUMINANTS['FL2']
>>> colour_fidelity_index_CIE2017(sd) # doctest: +ELLIPSIS
70.1208254...
"""
if sd_test.shape.start > 380 or sd_test.shape.end < 780:
usage_warning("Test spectral distribution shape does not span the"
"recommended 380-780nm range, missing values will be"
"filled with zeros!")
# NOTE: "CIE 2017 Colour Fidelity Index" standard recommends filling
# missing values with zeros.
sd_test = cast(SpectralDistribution, sd_test.copy())
sd_test.extrapolator = Extrapolator
sd_test.extrapolator_kwargs = {
"method": "constant",
"left": 0,
"right": 0,
}
if sd_test.shape.interval > 5:
raise ValueError("Test spectral distribution interval is greater than"
"5nm which is the maximum recommended value "
'for computing the "CIE 2017 Colour Fidelity Index"!')
shape = SpectralShape(
SPECTRAL_SHAPE_CIE2017.start,
SPECTRAL_SHAPE_CIE2017.end,
sd_test.shape.interval,
)
CCT, D_uv = tsplit(CCT_reference_illuminant(sd_test))
sd_reference = sd_reference_illuminant(CCT, shape)
# NOTE: All computations except CCT calculation use the
# "CIE 1964 10 Degree Standard Observer".
# pylint: disable=E1102
cmfs_10 = reshape_msds(MSDS_CMFS["CIE 1964 10 Degree Standard Observer"],
shape)
# pylint: disable=E1102
sds_tcs = reshape_msds(load_TCS_CIE2017(shape), shape)
test_tcs_colorimetry_data = tcs_colorimetry_data(sd_test, sds_tcs, cmfs_10)
reference_tcs_colorimetry_data = tcs_colorimetry_data(
sd_reference, sds_tcs, cmfs_10)
delta_E_s = np.empty(len(sds_tcs.labels))
for i, _delta_E in enumerate(delta_E_s):
delta_E_s[i] = euclidean_distance(
test_tcs_colorimetry_data[i].Jpapbp,
reference_tcs_colorimetry_data[i].Jpapbp,
)
R_s = as_float_array(delta_E_to_R_f(delta_E_s))
R_f = as_float_scalar(delta_E_to_R_f(np.average(delta_E_s)))
if additional_data:
return ColourRendering_Specification_CIE2017(
sd_test.name,
sd_reference,
R_f,
R_s,
CCT,
D_uv,
(test_tcs_colorimetry_data, reference_tcs_colorimetry_data),
delta_E_s,
)
else:
return R_f
