"""
:math:`\\Delta E^*_{ab}` - Delta E Colour Difference
====================================================
Defines 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`
References
----------
- :cite:`Lindbloom2003c` : Lindbloom, B. (2003). Delta E (CIE 1976).
Retrieved February 24, 2014, from
http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
- :cite:`Lindbloom2009e` : Lindbloom, B. (2009). Delta E (CIE 2000).
Retrieved February 24, 2014, from
http://brucelindbloom.com/Eqn_DeltaE_CIE2000.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:`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, Boolean, Floating, FloatingOrNDArray
from colour.utilities import as_float, to_domain_100, tsplit
from colour.utilities.documentation import (
DocstringFloat,
is_documentation_building,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 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__ = [
"JND_CIE1976",
"delta_E_CIE1976",
"delta_E_CIE1994",
"delta_E_CIE2000",
"delta_E_CMC",
]
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) -> FloatingOrNDArray:
"""
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.floating` or :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: Boolean = False
) -> FloatingOrNDArray:
"""
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.floating` or :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
delta_H = np.sqrt(delta_A**2 + delta_B**2 - delta_C**2)
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: Boolean = False
) -> FloatingOrNDArray:
"""
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.floating` or :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:`Lindbloom2009e`, :cite:`Melgosa2013b`
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
l_bar_prime = 0.5 * (L_1 + L_2)
c_1 = np.hypot(a_1, b_1)
c_2 = np.hypot(a_2, b_2)
c_bar = 0.5 * (c_1 + c_2)
c_bar7 = c_bar**7
g = 0.5 * (1 - np.sqrt(c_bar7 / (c_bar7 + 25**7)))
a_1_prime = a_1 * (1 + g)
a_2_prime = a_2 * (1 + g)
c_1_prime = np.hypot(a_1_prime, b_1)
c_2_prime = np.hypot(a_2_prime, b_2)
c_bar_prime = 0.5 * (c_1_prime + c_2_prime)
h_1_prime = np.degrees(np.arctan2(b_1, a_1_prime)) % 360
h_2_prime = np.degrees(np.arctan2(b_2, a_2_prime)) % 360
h_bar_prime = np.where(
np.fabs(h_1_prime - h_2_prime) <= 180,
0.5 * (h_1_prime + h_2_prime),
(0.5 * (h_1_prime + h_2_prime + 360)),
)
t = (
1
- 0.17 * np.cos(np.deg2rad(h_bar_prime - 30))
+ 0.24 * np.cos(np.deg2rad(2 * h_bar_prime))
+ 0.32 * np.cos(np.deg2rad(3 * h_bar_prime + 6))
- 0.20 * np.cos(np.deg2rad(4 * h_bar_prime - 63))
)
h = h_2_prime - h_1_prime
delta_h_prime = np.where(h_2_prime <= h_1_prime, h - 360, h + 360)
delta_h_prime = np.where(np.fabs(h) <= 180, h, delta_h_prime)
delta_L_prime = L_2 - L_1
delta_C_prime = c_2_prime - c_1_prime
delta_H_prime = (
2
* np.sqrt(c_1_prime * c_2_prime)
* np.sin(np.deg2rad(0.5 * delta_h_prime))
)
s_L = 1 + (
(0.015 * (l_bar_prime - 50) * (l_bar_prime - 50))
/ np.sqrt(20 + (l_bar_prime - 50) * (l_bar_prime - 50))
)
s_C = 1 + 0.045 * c_bar_prime
s_H = 1 + 0.015 * c_bar_prime * t
delta_theta = 30 * np.exp(
-((h_bar_prime - 275) / 25) * ((h_bar_prime - 275) / 25)
)
c_bar_prime7 = c_bar_prime**7
r_C = np.sqrt(c_bar_prime7 / (c_bar_prime7 + 25**7))
r_T = -2 * r_C * np.sin(np.deg2rad(2 * delta_theta))
d_E = np.sqrt(
(delta_L_prime / (k_L * s_L)) ** 2
+ (delta_C_prime / (k_C * s_C)) ** 2
+ (delta_H_prime / (k_H * s_H)) ** 2
+ (delta_C_prime / (k_C * s_C)) * (delta_H_prime / (k_H * s_H)) * r_T
)
return as_float(d_E)
[docs]def delta_E_CMC(
Lab_1: ArrayLike,
Lab_2: ArrayLike,
l: Floating = 2, # noqa
c: Floating = 1,
) -> FloatingOrNDArray:
"""
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.floating` or :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)