#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
:math:`\Delta E_{ab}` - Delta E Colour Difference
=================================================
Defines :math:`\Delta E_{ab}` colour difference computation objects:
The following methods are available:
- :func:`delta_E_CIE1976`
- :func:`delta_E_CIE1994`
- :func:`delta_E_CIE2000`
- :func:`delta_E_CMC`
See Also
--------
`Delta E - Colour Difference IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/difference/delta_e.ipynb>`_ # noqa
References
----------
.. [1] Wikipedia. (n.d.). Color difference. Retrieved August 29, 2014, from
http://en.wikipedia.org/wiki/Color_difference
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.utilities import CaseInsensitiveMapping, tsplit
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['delta_E_CIE1976',
'delta_E_CIE1994',
'delta_E_CIE2000',
'delta_E_CMC',
'DELTA_E_METHODS',
'delta_E']
[docs]def delta_E_CIE1976(Lab1, Lab2, **kwargs):
"""
Returns the difference :math:`\Delta E_{ab}` between two given
*CIE Lab* colourspace arrays using CIE 1976 recommendation.
Parameters
----------
Lab1 : array_like
*CIE Lab* colourspace array 1.
Lab2 : array_like
*CIE Lab* colourspace array 2.
\*\*kwargs : \*\*, optional
Unused parameter provided for signature compatibility with other
:math:`\Delta E_{ab}` computation objects.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
References
----------
.. [2] Lindbloom, B. (2003). Delta E (CIE 1976). Retrieved February 24,
2014, from http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
Examples
--------
>>> Lab1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1976(Lab1, Lab2) # doctest: +ELLIPSIS
451.7133019...
"""
delta_E = np.linalg.norm(np.asarray(Lab1) - np.asarray(Lab2), axis=-1)
return delta_E
[docs]def delta_E_CIE1994(Lab1, Lab2, textiles=True, **kwargs):
"""
Returns the difference :math:`\Delta E_{ab}` between two given *CIE Lab*
colourspace arrays using CIE 1994 recommendation.
Parameters
----------
Lab1 : array_like
*CIE Lab* colourspace array 1.
Lab2 : array_like
*CIE Lab* colourspace array 2.
textiles : bool, optional
Application specific weights.
\*\*kwargs : \*\*, optional
Unused parameter provided for signature compatibility with other
:math:`\Delta E_{ab}` computation objects.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
References
----------
.. [3] Lindbloom, B. (2011). Delta E (CIE 1994). Retrieved February 24,
2014, from http://brucelindbloom.com/Eqn_DeltaE_CIE94.html
Examples
--------
>>> Lab1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE1994(Lab1, Lab2) # doctest: +ELLIPSIS
88.3355530...
>>> delta_E_CIE1994(Lab1, Lab2, textiles=False) # doctest: +ELLIPSIS
83.7792255...
"""
k1 = 0.048 if textiles else 0.045
k2 = 0.014 if textiles else 0.015
kL = 2 if textiles else 1
kC = 1
kH = 1
L1, a1, b1 = tsplit(Lab1)
L2, a2, b2 = tsplit(Lab2)
C1 = np.sqrt(a1 ** 2 + b1 ** 2)
C2 = np.sqrt(a2 ** 2 + b2 ** 2)
sL = 1
sC = 1 + k1 * C1
sH = 1 + k2 * C1
delta_L = L1 - L2
delta_C = C1 - C2
delta_A = a1 - a2
delta_B = b1 - b2
delta_H = np.sqrt(delta_A ** 2 + delta_B ** 2 - delta_C ** 2)
L = (delta_L / (kL * sL)) ** 2
C = (delta_C / (kC * sC)) ** 2
H = (delta_H / (kH * sH)) ** 2
delta_E = np.sqrt(L + C + H)
return delta_E
[docs]def delta_E_CIE2000(Lab1, Lab2, **kwargs):
"""
Returns the difference :math:`\Delta E_{ab}` between two given *CIE Lab*
colourspace arrays using CIE 2000 recommendation.
Parameters
----------
Lab1 : array_like
*CIE Lab* colourspace array 1.
Lab2 : array_like
*CIE Lab* colourspace array 2.
\*\*kwargs : \*\*, optional
Unused parameter provided for signature compatibility with other
:math:`\Delta E_{ab}` computation objects.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
References
----------
.. [4] Lindbloom, B. (2009). Delta E (CIE 2000). Retrieved February 24,
2014, from http://brucelindbloom.com/Eqn_DeltaE_CIE2000.html
Examples
--------
>>> Lab1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CIE2000(Lab1, Lab2) # doctest: +ELLIPSIS
94.0356490...
"""
kL = 1
kC = 1
kH = 1
L1, a1, b1 = tsplit(Lab1)
L2, a2, b2 = tsplit(Lab2)
l_bar_prime = 0.5 * (L1 + L2)
c1 = np.sqrt(a1 * a1 + b1 * b1)
c2 = np.sqrt(a2 * a2 + b2 * b2)
c_bar = 0.5 * (c1 + c2)
c_bar7 = np.power(c_bar, 7)
g = 0.5 * (1 - np.sqrt(c_bar7 / (c_bar7 + 25 ** 7)))
a1_prime = a1 * (1 + g)
a2_prime = a2 * (1 + g)
c1_prime = np.sqrt(a1_prime * a1_prime + b1 * b1)
c2_prime = np.sqrt(a2_prime * a2_prime + b2 * b2)
c_bar_prime = 0.5 * (c1_prime + c2_prime)
h1_prime = np.asarray(np.rad2deg(np.arctan2(b1, a1_prime)))
h1_prime[np.asarray(h1_prime < 0.0)] += 360
h2_prime = np.asarray(np.rad2deg(np.arctan2(b2, a2_prime)))
h2_prime[np.asarray(h2_prime < 0.0)] += 360
h_bar_prime = np.where(np.fabs(h1_prime - h2_prime) <= 180,
0.5 * (h1_prime + h2_prime),
(0.5 * (h1_prime + h2_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 = h2_prime - h1_prime
delta_h_prime = np.where(h2_prime <= h1_prime, h - 360, h + 360)
delta_h_prime = np.where(np.fabs(h) <= 180, h, delta_h_prime)
delta_L_prime = L2 - L1
delta_C_prime = c2_prime - c1_prime
delta_H_prime = (2 * np.sqrt(c1_prime * c2_prime) *
np.sin(np.deg2rad(0.5 * delta_h_prime)))
sL = 1 + ((0.015 * (l_bar_prime - 50) * (l_bar_prime - 50)) /
np.sqrt(20 + (l_bar_prime - 50) * (l_bar_prime - 50)))
sC = 1 + 0.045 * c_bar_prime
sH = 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
rC = np.sqrt(c_bar_prime7 / (c_bar_prime7 + 25 ** 7))
rT = -2 * rC * np.sin(np.deg2rad(2 * delta_theta))
delta_E = np.sqrt(
(delta_L_prime / (kL * sL)) * (delta_L_prime / (kL * sL)) +
(delta_C_prime / (kC * sC)) * (delta_C_prime / (kC * sC)) +
(delta_H_prime / (kH * sH)) * (delta_H_prime / (kH * sH)) +
(delta_C_prime / (kC * sC)) * (delta_H_prime / (kH * sH)) * rT)
return delta_E
[docs]def delta_E_CMC(Lab1, Lab2, l=2, c=1):
"""
Returns the difference :math:`\Delta E_{ab}` between two given *CIE Lab*
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
----------
Lab1 : array_like
*CIE Lab* colourspace array 1.
Lab2 : array_like
*CIE Lab* colourspace array 2.
l : numeric, optional
Lightness weighting factor.
c : numeric, optional
Chroma weighting factor.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
References
----------
.. [5] Lindbloom, B. (2009). Delta E (CMC). Retrieved February 24, 2014,
from http://brucelindbloom.com/Eqn_DeltaE_CMC.html
Examples
--------
>>> Lab1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E_CMC(Lab1, Lab2) # doctest: +ELLIPSIS
172.7047712...
"""
L1, a1, b1 = tsplit(Lab1)
L2, a2, b2 = tsplit(Lab2)
c1 = np.sqrt(a1 * a1 + b1 * b1)
c2 = np.sqrt(a2 * a2 + b2 * b2)
sl = np.where(L1 < 16, 0.511, (0.040975 * L1) / (1 + 0.01765 * L1))
sc = 0.0638 * c1 / (1 + 0.0131 * c1) + 0.638
h1 = np.where(c1 < 0.000001, 0, np.rad2deg(np.arctan2(b1, a1)))
while np.any(h1 < 0):
h1[np.asarray(h1 < 0)] += 360
while np.any(h1 >= 360):
h1[np.asarray(h1 >= 360)] -= 360
t = np.where(np.logical_and(h1 >= 164, h1 <= 345),
0.56 + np.fabs(0.2 * np.cos(np.deg2rad(h1 + 168))),
0.36 + np.fabs(0.4 * np.cos(np.deg2rad(h1 + 35))))
c4 = c1 * c1 * c1 * c1
f = np.sqrt(c4 / (c4 + 1900))
sh = sc * (f * t + 1 - f)
delta_L = L1 - L2
delta_C = c1 - c2
delta_A = a1 - a2
delta_B = b1 - b2
delta_H2 = delta_A * delta_A + delta_B * delta_B - delta_C * delta_C
v1 = delta_L / (l * sl)
v2 = delta_C / (c * sc)
v3 = sh
delta_E = np.sqrt(v1 * v1 + v2 * v2 + (delta_H2 / (v3 * v3)))
return delta_E
DELTA_E_METHODS = CaseInsensitiveMapping(
{'CIE 1976': delta_E_CIE1976,
'CIE 1994': delta_E_CIE1994,
'CIE 2000': delta_E_CIE2000,
'CMC': delta_E_CMC})
"""
Supported *Delta E* computations methods.
DELTA_E_METHODS : CaseInsensitiveMapping
{'CIE 1976', 'CIE 1994', 'CIE 2000', 'CMC'}
Aliases:
- 'cie1976': 'CIE 1976'
- 'cie1994': 'CIE 1994'
- 'cie2000': 'CIE 2000'
"""
DELTA_E_METHODS['cie1976'] = DELTA_E_METHODS['CIE 1976']
DELTA_E_METHODS['cie1994'] = DELTA_E_METHODS['CIE 1994']
DELTA_E_METHODS['cie2000'] = DELTA_E_METHODS['CIE 2000']
[docs]def delta_E(Lab1, Lab2, method='CMC', **kwargs):
"""
Returns the *Lightness* :math:`L^*` using given method.
Parameters
----------
Lab1 : array_like
*CIE Lab* colourspace array 1.
Lab2 : array_like
*CIE Lab* colourspace array 2.
method : unicode, optional
{'CMC', 'CIE 1976', 'CIE 1994', 'CIE 2000'}
Computation method.
\*\*kwargs : \*\*
Keywords arguments.
Returns
-------
numeric or ndarray
Colour difference :math:`\Delta E_{ab}`.
Examples
--------
>>> Lab1 = np.array([100.00000000, 21.57210357, 272.22819350])
>>> Lab2 = np.array([100.00000000, 426.67945353, 72.39590835])
>>> delta_E(Lab1, Lab2) # doctest: +ELLIPSIS
172.7047712...
>>> delta_E(Lab1, Lab2, method='CIE 1976') # doctest: +ELLIPSIS
451.7133019...
>>> delta_E(Lab1, Lab2, method='CIE 1994') # doctest: +ELLIPSIS
88.3355530...
>>> delta_E(Lab1, Lab2, method='CIE 1994', textiles=False) # noqa # doctest: +ELLIPSIS
83.7792255...
>>> delta_E(Lab1, Lab2, method='CIE 2000') # doctest: +ELLIPSIS
94.0356490...
"""
return DELTA_E_METHODS.get(method)(Lab1, Lab2, **kwargs)
Colour 0.3