"""
:math:`\\Delta E^*_{ab}` - Delta E Colour Difference
====================================================
Define the :math:`\\Delta E^*_{ab}` colour difference computation objects:
The following attributes and methods are available:
- :attr:`colour.difference.JND_CIE1976`
- :func:`colour.difference.delta_E_CIE1976`
- :func:`colour.difference.delta_E_CIE1994`
- :func:`colour.difference.delta_E_CIE2000`
- :func:`colour.difference.delta_E_CMC`
- :func:`colour.difference.delta_E_ITP`
References
----------
- :cite:`InternationalTelecommunicationUnion2019` : International
Telecommunication Union. (2019). Recommendation ITU-R BT.2124-0 -
Objective metric for the assessment of the potential visibility of colour
differences in television (pp. 1-36). http://www.itu.int/dms_pubrec/itu-r/\
rec/bt/R-REC-BT.470-6-199811-S!!PDF-E.pdf
- :cite:`Lindbloom2003c` : Lindbloom, B. (2003). Delta E (CIE 1976).
Retrieved February 24, 2014, from
http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
- :cite:`Lindbloom2009f` : Lindbloom, B. (2009). Delta E (CMC). Retrieved
February 24, 2014, from http://brucelindbloom.com/Eqn_DeltaE_CMC.html
- :cite:`Lindbloom2011a` : Lindbloom, B. (2011). Delta E (CIE 1994).
Retrieved February 24, 2014, from
http://brucelindbloom.com/Eqn_DeltaE_CIE94.html
- :cite:`Melgosa2013b` : Melgosa, M. (2013). CIE / ISO new standard:
CIEDE2000. http://www.color.org/events/colorimetry/\
Melgosa_CIEDE2000_Workshop-July4.pdf
- :cite:`Sharma2005b` : Sharma, G., Wu, W., & Dalal, E. N. (2005). The
CIEDE2000 color-difference formula: Implementation notes, supplementary
test data, and mathematical observations. Color Research & Application,
30(1), 21-30. doi:10.1002/col.20070
- :cite:`Mokrzycki2011` : Mokrzycki, W., & Tatol, M. (2011). Color difference
Delta E - A survey. Machine Graphics and Vision, 20, 383-411.
"""
from __future__ import annotations
import numpy as np
from colour.algebra import euclidean_distance
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float, to_domain_100, tsplit, zeros
from colour.utilities.documentation import (
DocstringFloat,
is_documentation_building,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"JND_CIE1976",
"delta_E_CIE1976",
"delta_E_CIE1994",
"delta_E_CIE2000",
"delta_E_CMC",
"delta_E_ITP",
]
JND_CIE1976 = 2.3
if is_documentation_building(): # pragma: no cover
JND_CIE1976 = DocstringFloat(JND_CIE1976)
JND_CIE1976.__doc__ = """
Just Noticeable Difference (JND) according to *CIE 1976* colour difference
formula, i.e., Euclidean distance in *CIE L\\*a\\*b\\** colourspace.
Notes
-----
A standard observer sees the difference in colour as follows:
- 0 < :math:`\\Delta E^*_{ab}` < 1 : Observer does not notice the difference.
- 1 < :math:`\\Delta E^*_{ab}` < 2 : Only experienced observer can notice the
difference.
- 2 < :math:`\\Delta E^*_{ab}` < 3:5 : Unexperienced observer also notices
the difference.
- 3:5 < :math:`\\Delta E^*_{ab}` < 5 : Clear difference in colour is noticed.
- 5 < :math:`\\Delta E^*_{ab}` : Observer notices two different colours.
References
----------
:cite:`Mokrzycki2011`
"""
[docs]
def delta_E_CIE1976(Lab_1: ArrayLike, Lab_2: ArrayLike) -> NDArrayFloat:
"""
Return the difference :math:`\\Delta E_{76}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *CIE 1976* recommendation.
Parameters
----------
Lab_1
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2
*CIE L\\*a\\*b\\** colourspace array 2.
Returns
-------
:class:`numpy.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
[docs]
def delta_E_CIE1994(
Lab_1: ArrayLike, Lab_2: ArrayLike, textiles: bool = False
) -> NDArrayFloat:
"""
Return the difference :math:`\\Delta E_{94}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *CIE 1994* recommendation.
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_L=2,\\ k_C=k_H=1,\\ k_1=0.048,\\ k_2=0.014` weights are used
instead of :math:`k_L=k_C=k_H=1,\\ k_1=0.045,\\ k_2=0.015`.
Returns
-------
:class:`numpy.ndarray`
Colour difference :math:`\\Delta E_{94}`.
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] |
+------------+-----------------------+-------------------+
- *CIE 1994* colour differences are not symmetrical: difference between
``Lab_1`` and ``Lab_2`` may not be the same as difference between
``Lab_2`` and ``Lab_1`` thus one colour must be understood to be the
reference against which a sample colour is compared.
References
----------
:cite:`Lindbloom2011a`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1994(Lab_1, Lab_2) # doctest: +ELLIPSIS
83.7792255...
>>> delta_E_CIE1994(Lab_1, Lab_2, textiles=True) # doctest: +ELLIPSIS
88.3355530...
"""
L_1, a_1, b_1 = tsplit(to_domain_100(Lab_1))
L_2, a_2, b_2 = tsplit(to_domain_100(Lab_2))
k_1 = 0.048 if textiles else 0.045
k_2 = 0.014 if textiles else 0.015
k_L = 2 if textiles else 1
k_C = 1
k_H = 1
C_1 = np.hypot(a_1, b_1)
C_2 = np.hypot(a_2, b_2)
s_L = 1
s_C = 1 + k_1 * C_1
s_H = 1 + k_2 * C_1
delta_L = L_1 - L_2
delta_C = C_1 - C_2
delta_A = a_1 - a_2
delta_B = b_1 - b_2
radical = delta_A**2 + delta_B**2 - delta_C**2
delta_H = zeros(radical.shape)
delta_H[radical > 0] = np.sqrt(radical[radical > 0])
L = (delta_L / (k_L * s_L)) ** 2
C = (delta_C / (k_C * s_C)) ** 2
H = (delta_H / (k_H * s_H)) ** 2
d_E = np.sqrt(L + C + H)
return as_float(d_E)
[docs]
def delta_E_CIE2000(
Lab_1: ArrayLike, Lab_2: ArrayLike, textiles: bool = False
) -> NDArrayFloat:
"""
Return the difference :math:`\\Delta E_{00}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *CIE 2000* recommendation.
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_L=2,\\ k_C=k_H=1` weights are used instead of
:math:`k_L=k_C=k_H=1`.
Returns
-------
:class:`numpy.ndarray`
Colour difference :math:`\\Delta E_{00}`.
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] |
+------------+-----------------------+-------------------+
- Parametric factors :math:`k_L=k_C=k_H=1` weights under
*reference conditions*:
- Illumination: D65 source
- Illuminance: 1000 lx
- Observer: Normal colour vision
- Background field: Uniform, neutral gray with :math:`L^*=50`
- Viewing mode: Object
- Sample size: Greater than 4 degrees
- Sample separation: Direct edge contact
- Sample colour-difference magnitude: Lower than 5.0
:math:`\\Delta E_{00}`
- Sample structure: Homogeneous (without texture)
References
----------
:cite:`Melgosa2013b`, :cite:`Sharma2005b`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE2000(Lab_1, Lab_2) # doctest: +ELLIPSIS
94.0356490...
>>> Lab_2 = np.array([50.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE2000(Lab_1, Lab_2) # doctest: +ELLIPSIS
100.8779470...
>>> delta_E_CIE2000(Lab_1, Lab_2, textiles=True) # doctest: +ELLIPSIS
95.7920535...
"""
L_1, a_1, b_1 = tsplit(to_domain_100(Lab_1))
L_2, a_2, b_2 = tsplit(to_domain_100(Lab_2))
k_L = 2 if textiles else 1
k_C = 1
k_H = 1
C_1_ab = np.hypot(a_1, b_1)
C_2_ab = np.hypot(a_2, b_2)
C_bar_ab = (C_1_ab + C_2_ab) / 2
C_bar_ab_7 = C_bar_ab**7
G = 0.5 * (1 - np.sqrt(C_bar_ab_7 / (C_bar_ab_7 + 25**7)))
a_p_1 = (1 + G) * a_1
a_p_2 = (1 + G) * a_2
C_p_1 = np.hypot(a_p_1, b_1)
C_p_2 = np.hypot(a_p_2, b_2)
h_p_1 = np.where(
np.logical_and(b_1 == 0, a_p_1 == 0),
0,
np.degrees(np.arctan2(b_1, a_p_1)) % 360,
)
h_p_2 = np.where(
np.logical_and(b_2 == 0, a_p_2 == 0),
0,
np.degrees(np.arctan2(b_2, a_p_2)) % 360,
)
delta_L_p = L_2 - L_1
delta_C_p = C_p_2 - C_p_1
h_p_2_s_1 = h_p_2 - h_p_1
C_p_1_m_2 = C_p_1 * C_p_2
delta_h_p = np.select(
[
C_p_1_m_2 == 0,
np.fabs(h_p_2_s_1) <= 180,
h_p_2_s_1 > 180,
h_p_2_s_1 < -180,
],
[
0,
h_p_2_s_1,
h_p_2_s_1 - 360,
h_p_2_s_1 + 360,
],
)
delta_H_p = 2 * np.sqrt(C_p_1_m_2) * np.sin(np.deg2rad(delta_h_p / 2))
L_bar_p = (L_1 + L_2) / 2
C_bar_p = (C_p_1 + C_p_2) / 2
a_h_p_1_s_2 = np.fabs(h_p_1 - h_p_2)
h_p_1_a_2 = h_p_1 + h_p_2
h_bar_p = np.select(
[
C_p_1_m_2 == 0,
a_h_p_1_s_2 <= 180,
np.logical_and(a_h_p_1_s_2 > 180, h_p_1_a_2 < 360),
np.logical_and(a_h_p_1_s_2 > 180, h_p_1_a_2 >= 360),
],
[
h_p_1_a_2,
h_p_1_a_2 / 2,
(h_p_1_a_2 + 360) / 2,
(h_p_1_a_2 - 360) / 2,
],
)
T = (
1
- 0.17 * np.cos(np.deg2rad(h_bar_p - 30))
+ 0.24 * np.cos(np.deg2rad(2 * h_bar_p))
+ 0.32 * np.cos(np.deg2rad(3 * h_bar_p + 6))
- 0.20 * np.cos(np.deg2rad(4 * h_bar_p - 63))
)
delta_theta = 30 * np.exp(-(((h_bar_p - 275) / 25) ** 2))
C_bar_p_7 = C_bar_p**7
R_C = 2 * np.sqrt(C_bar_p_7 / (C_bar_p_7 + 25**7))
L_bar_p_2 = (L_bar_p - 50) ** 2
S_L = 1 + ((0.015 * L_bar_p_2) / np.sqrt(20 + L_bar_p_2))
S_C = 1 + 0.045 * C_bar_p
S_H = 1 + 0.015 * C_bar_p * T
R_T = -np.sin(np.deg2rad(2 * delta_theta)) * R_C
d_E = np.sqrt(
(delta_L_p / (k_L * S_L)) ** 2
+ (delta_C_p / (k_C * S_C)) ** 2
+ (delta_H_p / (k_H * S_H)) ** 2
+ R_T * (delta_C_p / (k_C * S_C)) * (delta_H_p / (k_H * S_H))
)
return as_float(d_E)
[docs]
def delta_E_CMC(
Lab_1: ArrayLike,
Lab_2: ArrayLike,
l: float = 2, # noqa: E741
c: float = 1,
) -> NDArrayFloat:
"""
Return the difference :math:`\\Delta E_{CMC}` between two given
*CIE L\\*a\\*b\\** colourspace arrays using *Colour Measurement Committee*
recommendation.
The quasimetric has two parameters: *Lightness* (l) and *chroma* (c),
allowing the users to weight the difference based on the ratio of l:c.
Commonly used values are 2:1 for acceptability and 1:1 for the threshold of
imperceptibility.
Parameters
----------
Lab_1
*CIE L\\*a\\*b\\** colourspace array 1.
Lab_2
*CIE L\\*a\\*b\\** colourspace array 2.
l
Lightness weighting factor.
c
Chroma weighting factor.
Returns
-------
:class:`numpy.ndarray`
Colour difference :math:`\\Delta E_{CMC}`.
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:`Lindbloom2009f`
Examples
--------
>>> Lab_1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab_2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CMC(Lab_1, Lab_2) # doctest: +ELLIPSIS
172.7047712...
"""
L_1, a_1, b_1 = tsplit(to_domain_100(Lab_1))
L_2, a_2, b_2 = tsplit(to_domain_100(Lab_2))
C_1 = np.hypot(a_1, b_1)
C_2 = np.hypot(a_2, b_2)
s_L = np.where(L_1 < 16, 0.511, (0.040975 * L_1) / (1 + 0.01765 * L_1))
s_C = 0.0638 * C_1 / (1 + 0.0131 * C_1) + 0.638
h_1 = np.degrees(np.arctan2(b_1, a_1)) % 360
t = np.where(
np.logical_and(h_1 >= 164, h_1 <= 345),
0.56 + np.fabs(0.2 * np.cos(np.deg2rad(h_1 + 168))),
0.36 + np.fabs(0.4 * np.cos(np.deg2rad(h_1 + 35))),
)
C_4 = C_1 * C_1 * C_1 * C_1
f = np.sqrt(C_4 / (C_4 + 1900))
s_h = s_C * (f * t + 1 - f)
delta_L = L_1 - L_2
delta_C = C_1 - C_2
delta_A = a_1 - a_2
delta_B = b_1 - b_2
delta_H2 = delta_A**2 + delta_B**2 - delta_C**2
v_1 = delta_L / (l * s_L)
v_2 = delta_C / (c * s_C)
v_3 = s_h
d_E = np.sqrt(v_1**2 + v_2**2 + (delta_H2 / (v_3 * v_3)))
return as_float(d_E)
[docs]
def delta_E_ITP(ICtCp_1: ArrayLike, ICtCp_2: ArrayLike) -> NDArrayFloat:
"""
Return the difference :math:`\\Delta E_{ITP}` between two given
:math:`IC_TC_P` colour encoding arrays using
*Recommendation ITU-R BT.2124*.
Parameters
----------
ICtCp_1
:math:`IC_TC_P` colour encoding array 1.
ICtCp_2
:math:`IC_TC_P` colour encoding array 2.
Returns
-------
:class:`numpy.ndarray`
Colour difference :math:`\\Delta E_{ITP}`.
Notes
-----
- A value of 1 is equivalent to a just noticeable difference when viewed
in the most critical adaptation state.
References
----------
:cite:`InternationalTelecommunicationUnion2019`
Examples
--------
>>> ICtCp_1 = np.array([0.4885468072, -0.04739350675, 0.07475401302])
>>> ICtCp_2 = np.array([0.4899203231, -0.04567508203, 0.07361341775])
>>> delta_E_ITP(ICtCp_1, ICtCp_2) # doctest: +ELLIPSIS
1.42657228...
"""
I_1, T_1, P_1 = tsplit(ICtCp_1)
T_1 *= 0.5
I_2, T_2, P_2 = tsplit(ICtCp_2)
T_2 *= 0.5
d_E_ITP = 720 * np.sqrt(
((I_2 - I_1) ** 2) + ((T_2 - T_1) ** 2) + ((P_2 - P_1) ** 2)
)
return as_float(d_E_ITP)
