Source code for colour.difference.delta_e

# -*- 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:`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
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.algebra import euclidean_distance
from colour.utilities import to_domain_100, tsplit

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - 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__ = [
    'delta_E_CIE1976', 'delta_E_CIE1994', 'delta_E_CIE2000', 'delta_E_CMC'
]


[docs]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
[docs]def delta_E_CIE1994(Lab_1, Lab_2, textiles=False): """ Returns the difference :math:`\\Delta E_{94}` between two given *CIE L\\*a\\*b\\** colourspace arrays using *CIE 1994* recommendation. Parameters ---------- Lab_1 : array_like *CIE L\\*a\\*b\\** colourspace array 1. Lab_2 : array_like *CIE L\\*a\\*b\\** colourspace array 2. textiles : bool, optional 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 ------- numeric or 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 d_E
[docs]def delta_E_CIE2000(Lab_1, Lab_2, textiles=False): """ Returns the difference :math:`\\Delta E_{00}` between two given *CIE L\\*a\\*b\\** colourspace arrays using *CIE 2000* recommendation. Parameters ---------- Lab_1 : array_like *CIE L\\*a\\*b\\** colourspace array 1. Lab_2 : array_like *CIE L\\*a\\*b\\** colourspace array 2. textiles : bool, optional 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 ------- numeric or 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] | +------------+-----------------------+-------------------+ - *CIE 2000* 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. - 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 d_E
[docs]def delta_E_CMC(Lab_1, Lab_2, l=2, c=1): # noqa """ Returns 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 : array_like *CIE L\\*a\\*b\\** colourspace array 1. Lab_2 : array_like *CIE L\\*a\\*b\\** colourspace array 2. l : numeric, optional Lightness weighting factor. c : numeric, optional Chroma weighting factor. Returns ------- numeric or 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 d_E