# Source code for colour.difference.delta_e

#!/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_CIE_1976
-   :func:delta_E_CIE_1994
-   :func:delta_E_CIE_2000
-   :func:delta_E_CMC

--------
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]  http://en.wikipedia.org/wiki/Color_difference
(Last accessed 29 August 2014)
"""

from __future__ import division, unicode_literals

import math
import numpy as np

__author__ = 'Colour Developers'
__maintainer__ = 'Colour Developers'
__status__ = 'Production'

__all__ = ['delta_E_CIE_1976',
'delta_E_CIE_1994',
'delta_E_CIE_2000',
'delta_E_CMC',
'DELTA_E_METHODS',
'delta_E']

[docs]def delta_E_CIE_1976(lab1, lab2, **kwargs):
"""
Returns the difference :math:\Delta E_{ab} between two given
*CIE Lab* *array_like* colours using *CIE 1976* recommendation.

Parameters
----------
lab1 : array_like, (3,)
*CIE Lab* *array_like* colour 1.
lab2 : array_like, (3,)
*CIE Lab* *array_like* colour 2.
\*\*kwargs : \*\*, optional
Unused parameter provided for signature compatibility with other
:math:\Delta E_{ab} computation objects.

Returns
-------
numeric
Colour difference :math:\Delta E_{ab}.

References
----------
.. [2]  http://brucelindbloom.com/Eqn_DeltaE_CIE76.html
(Last accessed 24 February 2014)

Examples
--------
>>> lab1 = np.array([100, 21.57210357, 272.2281935])
>>> lab2 = np.array([100, 426.67945353, 72.39590835])
>>> delta_E_CIE_1976(lab1, lab2)  # doctest: +ELLIPSIS
451.7133019...
"""
return np.linalg.norm(np.array(lab1) - np.array(lab2))

[docs]def delta_E_CIE_1994(lab1, lab2, textiles=True, **kwargs):
"""
Returns the difference :math:\Delta E_{ab} between two given *CIE Lab*
*array_like* colours using *CIE 1994* recommendation.

Parameters
----------
lab1 : array_like, (3,)
*CIE Lab* *array_like* colour 1.
lab2 : array_like, (3,)
*CIE Lab* *array_like* colour 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
Colour difference :math:\Delta E_{ab}.

References
----------
.. [3]  http://brucelindbloom.com/Eqn_DeltaE_CIE94.html
(Last accessed 24 February 2014)

Examples
--------
>>> lab1 = np.array([100, 21.57210357, 272.2281935])
>>> lab2 = np.array([100, 426.67945353, 72.39590835])
>>> delta_E_CIE_1994(lab1, lab2)  # doctest: +ELLIPSIS
88.3355530...
>>> delta_E_CIE_1994(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 = np.ravel(lab1)
L2, a2, b2 = np.ravel(lab2)

C1 = math.sqrt(a1 ** 2 + b1 ** 2)
C2 = math.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

try:
delta_H = math.sqrt(delta_A ** 2 + delta_B ** 2 - delta_C ** 2)
except ValueError:
delta_H = 0.0

L = (delta_L / (kL * sL)) ** 2
C = (delta_C / (kC * sC)) ** 2
H = (delta_H / (kH * sH)) ** 2

return math.sqrt(L + C + H)

[docs]def delta_E_CIE_2000(lab1, lab2, **kwargs):
"""
Returns the difference :math:\Delta E_{ab} between two given *CIE Lab*
*array_like* colours using *CIE 2000* recommendation.

Parameters
----------
lab1 : array_like, (3,)
*CIE Lab* *array_like* colour 1.
lab2 : array_like, (3,)
*CIE Lab* *array_like* colour 2.
\*\*kwargs : \*\*, optional
Unused parameter provided for signature compatibility with other
:math:\Delta E_{ab} computation objects.

Returns
-------
numeric
Colour difference :math:\Delta E_{ab}.

References
----------

.. [4]  http://brucelindbloom.com/Eqn_DeltaE_CIE2000.html
(Last accessed 24 February 2014)

Examples
--------
>>> lab1 = np.array([100, 21.57210357, 272.2281935])
>>> lab2 = np.array([100, 426.67945353, 72.39590835])
>>> delta_E_CIE_2000(lab1, lab2)  # doctest: +ELLIPSIS
94.0356490...
"""

L1, a1, b1 = np.ravel(lab1)
L2, a2, b2 = np.ravel(lab2)

kL = 1
kC = 1
kH = 1

l_bar_prime = 0.5 * (L1 + L2)

c1 = math.sqrt(a1 * a1 + b1 * b1)
c2 = math.sqrt(a2 * a2 + b2 * b2)

c_bar = 0.5 * (c1 + c2)
c_bar7 = math.pow(c_bar, 7)

g = 0.5 * (1 - math.sqrt(c_bar7 / (c_bar7 + 25 ** 7)))

a1_prime = a1 * (1 + g)
a2_prime = a2 * (1 + g)
c1_prime = math.sqrt(a1_prime * a1_prime + b1 * b1)
c2_prime = math.sqrt(a2_prime * a2_prime + b2 * b2)
c_bar_prime = 0.5 * (c1_prime + c2_prime)

h1_prime = (math.atan2(b1, a1_prime) * 180) / math.pi
if h1_prime < 0:
h1_prime += 360

h2_prime = (math.atan2(b2, a2_prime) * 180) / math.pi
if h2_prime < 0.0:
h2_prime += 360

h_bar_prime = (0.5 * (h1_prime + h2_prime + 360)
if math.fabs(h1_prime - h2_prime) > 180 else
0.5 * (h1_prime + h2_prime))

t = (1 - 0.17 * math.cos(math.pi * (h_bar_prime - 30) / 180) +
0.24 * math.cos(math.pi * (2 * h_bar_prime) / 180) +
0.32 * math.cos(math.pi * (3 * h_bar_prime + 6) / 180) -
0.20 * math.cos(math.pi * (4 * h_bar_prime - 63) / 180))

if math.fabs(h2_prime - h1_prime) <= 180:
delta_h_prime = h2_prime - h1_prime
else:
delta_h_prime = (h2_prime - h1_prime + 360
if h2_prime <= h1_prime else
h2_prime - h1_prime - 360)

delta_L_prime = L2 - L1
delta_C_prime = c2_prime - c1_prime
delta_H_prime = (2 * math.sqrt(c1_prime * c2_prime) *
math.sin(math.pi * (0.5 * delta_h_prime) / 180))

sL = 1 + ((0.015 * (l_bar_prime - 50) * (l_bar_prime - 50)) /
math.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 * math.exp(-((h_bar_prime - 275) / 25) *
((h_bar_prime - 275) / 25)))

c_bar_prime7 = c_bar_prime ** 7

rC = math.sqrt(c_bar_prime7 / (c_bar_prime7 + 25 ** 7))
rT = -2 * rC * math.sin(math.pi * (2 * delta_theta) / 180)

return math.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)

[docs]def delta_E_CMC(lab1, lab2, l=2, c=1):
"""
Returns the difference :math:\Delta E_{ab} between two given *CIE Lab*
*array_like* colours 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, (3,)
*CIE Lab* *array_like* colour 1.
lab2 : array_like, (3,)
*CIE Lab* *array_like* colour 2.
l : numeric, optional
Lightness weighting factor.
c : numeric, optional
Chroma weighting factor.

Returns
-------
numeric
Colour difference :math:\Delta E_{ab}.

References
----------
.. [5]  http://brucelindbloom.com/Eqn_DeltaE_CMC.html
(Last accessed 24 February 2014)

Examples
--------
>>> lab1 = np.array([100, 21.57210357, 272.2281935])
>>> lab2 = np.array([100, 426.67945353, 72.39590835])
>>> delta_E_CMC(lab1, lab2)  # doctest: +ELLIPSIS
172.7047712...
"""

L1, a1, b1 = np.ravel(lab1)
L2, a2, b2 = np.ravel(lab2)

c1 = math.sqrt(a1 * a1 + b1 * b1)
c2 = math.sqrt(a2 * a2 + b2 * b2)
sl = 0.511 if L1 < 16 else (0.040975 * L1) / (1 + 0.01765 * L1)
sc = 0.0638 * c1 / (1 + 0.0131 * c1) + 0.638
h1 = 0 if c1 < 0.000001 else (math.atan2(b1, a1) * 180) / math.pi

while h1 < 0:
h1 += 360

while h1 >= 360:
h1 -= 360

t = (0.56 + math.fabs(0.2 * math.cos((math.pi * (h1 + 168)) / 180))
if 164 <= h1 <= 345 else
0.36 + math.fabs(0.4 * math.cos((math.pi * (h1 + 35)) / 180)))
c4 = c1 * c1 * c1 * c1
f = math.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

return math.sqrt(v1 * v1 + v2 * v2 + (delta_H2 / (v3 * v3)))

DELTA_E_METHODS = {
'CIE 1976': delta_E_CIE_1976,
'CIE 1994': delta_E_CIE_1994,
'CIE 2000': delta_E_CIE_2000,
'CMC': delta_E_CMC,
}
"""
Supported *Delta E* computations methods.

DELTA_E_METHODS : dict
('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, (3,)
*CIE Lab* *array_like* colour 1.
lab2 : array_like, (3,)
*CIE Lab* *array_like* colour 2.
method : unicode, optional
('CIE 1976', 'CIE 1994', 'CIE 2000', 'CMC')
Computation method.
\*\*kwargs : \*\*
Keywords arguments.

Returns
-------
numeric
Colour difference :math:\Delta E_{ab}.

Examples
--------
>>> lab1 = np.array([100, 21.57210357, 272.2281935])
>>> lab2 = np.array([100, 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)