# -*- coding: utf-8 -*-
"""
Colour Quality Scale
====================
Defines *Colour Quality Scale* (CQS) computation objects:
- :class:`colour.quality.CQS_Specification`
- :func:`colour.colour_quality_scale`
See Also
--------
`Colour Quality Scale Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/quality/cqs.ipynb>`_
References
----------
- :cite:`Davis2010a` : Davis, W., & Ohno, Y. (2010). Color quality scale.
Optical Engineering, 49(3), 33602. doi:10.1117/1.3360335
- :cite:`Ohno2008a` : Ohno, Y., & Davis, W. (2008). NIST CQS simulation 7.4.
Retrieved from https://drive.google.com/file/d/\
1PsuU6QjUJjCX6tQyCud6ul2Tbs8rYWW9/view?usp=sharing
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.algebra import euclidean_distance
from colour.colorimetry import (
ASTME30815_PRACTISE_SHAPE, D_illuminant_relative_spd, ILLUMINANTS,
STANDARD_OBSERVERS_CMFS, blackbody_spd, spectral_to_XYZ)
from colour.quality.dataset.vs import VS_INDEXES_TO_NAMES, VS_SPDS
from colour.models import (Lab_to_LCHab, UCS_to_uv, XYZ_to_Lab, XYZ_to_UCS,
XYZ_to_xy, xy_to_XYZ)
from colour.temperature import CCT_to_xy_CIE_D, uv_to_CCT_Ohno2013
from colour.adaptation import chromatic_adaptation_VonKries
from colour.utilities import tsplit
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2018 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'D65_GAMUT_AREA', 'VS_ColorimetryData', 'VS_ColourQualityScaleData',
'CQS_Specification', 'colour_quality_scale', 'gamut_area',
'vs_colorimetry_data', 'CCT_factor', 'scale_conversion', 'delta_E_RMS',
'colour_quality_scales'
]
D65_GAMUT_AREA = 8210
class VS_ColorimetryData(
namedtuple('VS_ColorimetryData', ('name', 'XYZ', 'Lab', 'C'))):
"""
Defines the the class storing *VS test colour samples* colorimetry data.
"""
class VS_ColourQualityScaleData(
namedtuple('VS_ColourQualityScaleData', ('name', 'Q_a', 'D_C_ab',
'D_E_ab', 'D_Ep_ab'))):
"""
Defines the the class storing *VS test colour samples* colour quality
scale data.
"""
[docs]class CQS_Specification(
namedtuple('CQS_Specification', ('name', 'Q_a', 'Q_f', 'Q_p', 'Q_g',
'Q_d', 'Q_as', 'colorimetry_data'))):
"""
Defines the *Colour Quality Scale* (CQS) colour quality specification.
Parameters
----------
name : unicode
Name of the test spectral power distribution.
Q_a : numeric
Colour quality scale :math:`Q_a`.
Q_f : numeric
Colour fidelity scale :math:`Q_f` intended to evaluate the fidelity
of object colour appearances (compared to the reference illuminant of
the same correlated colour temperature and illuminance).
Q_p : numeric
Colour preference scale :math:`Q_p` similar to colour quality scale
:math:`Q_a` but placing additional weight on preference of object
colour appearance. This metric is based on the notion that increases
in chroma are generally preferred and should be rewarded.
Q_g : numeric
Gamut area scale :math:`Q_g` representing the relative gamut formed
by the (:math:`a^*`, :math:`b^*`) coordinates of the 15 samples
illuminated by the test light source in the *CIE L\*a\*b\** object
colourspace.
Q_d : numeric
Relative gamut area scale :math:`Q_d`.
Q_as : dict
Individual *Colour Quality Scale* (CQS) data for each sample.
colorimetry_data : tuple
Colorimetry data for the test and reference computations.
References
----------
- :cite:`Davis2010a`
- :cite:`Ohno2008a`
"""
[docs]def colour_quality_scale(spd_test, additional_data=False):
"""
Returns the *Colour Quality Scale* (CQS) of given spectral power
distribution.
Parameters
----------
spd_test : SpectralPowerDistribution
Test spectral power distribution.
additional_data : bool, optional
Output additional data.
Returns
-------
numeric or CQS_Specification
Color quality scale.
References
----------
- :cite:`Davis2010a`
- :cite:`Ohno2008a`
Examples
--------
>>> from colour import ILLUMINANTS_RELATIVE_SPDS
>>> spd = ILLUMINANTS_RELATIVE_SPDS['F2']
>>> colour_quality_scale(spd) # doctest: +ELLIPSIS
64.6863391...
"""
cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer'].copy(
).trim(ASTME30815_PRACTISE_SHAPE)
shape = cmfs.shape
spd_test = spd_test.copy().align(shape)
vs_spds = {spd.name: spd.copy().align(shape) for spd in VS_SPDS.values()}
XYZ = spectral_to_XYZ(spd_test, cmfs)
uv = UCS_to_uv(XYZ_to_UCS(XYZ))
CCT, _D_uv = uv_to_CCT_Ohno2013(uv)
if CCT < 5000:
spd_reference = blackbody_spd(CCT, shape)
else:
xy = CCT_to_xy_CIE_D(CCT)
spd_reference = D_illuminant_relative_spd(xy)
spd_reference.align(shape)
test_vs_colorimetry_data = vs_colorimetry_data(
spd_test, spd_reference, vs_spds, cmfs, chromatic_adaptation=True)
reference_vs_colorimetry_data = vs_colorimetry_data(
spd_reference, spd_reference, vs_spds, cmfs)
XYZ_r = spectral_to_XYZ(spd_reference, cmfs)
XYZ_r /= XYZ_r[1]
CCT_f = CCT_factor(reference_vs_colorimetry_data, XYZ_r)
Q_as = colour_quality_scales(test_vs_colorimetry_data,
reference_vs_colorimetry_data, CCT_f)
D_E_RMS = delta_E_RMS(Q_as, 'D_E_ab')
D_Ep_RMS = delta_E_RMS(Q_as, 'D_Ep_ab')
Q_a = scale_conversion(D_Ep_RMS, CCT_f)
Q_f = scale_conversion(D_E_RMS, CCT_f, 2.928)
p_delta_C = np.average(
[sample_data.D_C_ab if sample_data.D_C_ab > 0 else 0
for sample_data in Q_as.values()]) # yapf: disable
Q_p = 100 - 3.6 * (D_Ep_RMS - p_delta_C)
G_t = gamut_area(
[vs_CQS_data.Lab for vs_CQS_data in test_vs_colorimetry_data])
G_r = gamut_area(
[vs_CQS_data.Lab for vs_CQS_data in reference_vs_colorimetry_data])
Q_g = G_t / D65_GAMUT_AREA * 100
Q_d = G_t / G_r * CCT_f * 100
if additional_data:
return CQS_Specification(spd_test.name, Q_a, Q_f, Q_p, Q_g, Q_d, Q_as,
(test_vs_colorimetry_data,
reference_vs_colorimetry_data))
else:
return Q_a
def gamut_area(Lab):
"""
Returns the gamut area :math:`G` covered by given *CIE L\*a\*b\** matrices.
Parameters
----------
Lab : array_like
*CIE L\*a\*b\** colourspace matrices.
Returns
-------
numeric
Gamut area :math:`G`.
Examples
--------
>>> Lab = [
... np.array([39.94996006, 34.59018231, -19.86046321]),
... np.array([38.88395498, 21.44348519, -34.87805301]),
... np.array([36.60576301, 7.06742454, -43.21461177]),
... np.array([46.60142558, -15.90481586, -34.64616865]),
... np.array([56.50196523, -29.54655550, -20.50177194]),
... np.array([55.73912101, -43.39520959, -5.08956953]),
... np.array([56.20776870, -53.68997662, 20.21134410]),
... np.array([66.16683122, -38.64600327, 42.77396631]),
... np.array([76.72952110, -23.92148210, 61.04740432]),
... np.array([82.85370708, -3.98679065, 75.43320144]),
... np.array([69.26458861, 13.11066359, 68.83858372]),
... np.array([69.63154351, 28.24532497, 59.45609803]),
... np.array([61.26281449, 40.87950839, 44.97606172]),
... np.array([41.62567821, 57.34129516, 27.46718170]),
... np.array([40.52565174, 48.87449192, 3.45121680])
... ]
>>> gamut_area(Lab) # doctest: +ELLIPSIS
8335.9482018...
"""
Lab = np.asarray(Lab)
Lab_s = np.roll(np.copy(Lab), -3)
_L, a, b = tsplit(Lab)
_L_s, a_s, b_s = tsplit(Lab_s)
A = np.linalg.norm(Lab[..., 1:3], axis=-1)
B = np.linalg.norm(Lab_s[..., 1:3], axis=-1)
C = np.linalg.norm(np.dstack((a_s - a, b_s - b)), axis=-1)
t = (A + B + C) / 2
S = np.sqrt(t * (t - A) * (t - B) * (t - C))
return np.sum(S)
def vs_colorimetry_data(spd_test,
spd_reference,
spds_vs,
cmfs,
chromatic_adaptation=False):
"""
Returns the *VS test colour samples* colorimetry data.
Parameters
----------
spd_test : SpectralPowerDistribution
Test spectral power distribution.
spd_reference : SpectralPowerDistribution
Reference spectral power distribution.
spds_vs : dict
*VS test colour samples* spectral power distributions.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
chromatic_adaptation : bool, optional
Perform chromatic adaptation.
Returns
-------
list
*VS test colour samples* colorimetry data.
"""
XYZ_t = spectral_to_XYZ(spd_test, cmfs)
XYZ_t /= XYZ_t[1]
XYZ_r = spectral_to_XYZ(spd_reference, cmfs)
XYZ_r /= XYZ_r[1]
xy_r = XYZ_to_xy(XYZ_r)
vs_data = []
for _key, value in sorted(VS_INDEXES_TO_NAMES.items()):
spd_vs = spds_vs[value]
XYZ_vs = spectral_to_XYZ(spd_vs, cmfs, spd_test)
XYZ_vs /= 100
if chromatic_adaptation:
XYZ_vs = chromatic_adaptation_VonKries(
XYZ_vs, XYZ_t, XYZ_r, transform='CMCCAT2000')
Lab_vs = XYZ_to_Lab(XYZ_vs, illuminant=xy_r)
_L_vs, C_vs, _Hab = Lab_to_LCHab(Lab_vs)
vs_data.append(VS_ColorimetryData(spd_vs.name, XYZ_vs, Lab_vs, C_vs))
return vs_data
def CCT_factor(reference_data, XYZ_r):
"""
Returns the correlated colour temperature factor penalizing lamps with
extremely low correlated colour temperatures.
Parameters
----------
reference_data : VS_ColorimetryData
Reference colorimetry data.
XYZ_r : array_like
*CIE XYZ* tristimulus values for reference.
Returns
-------
numeric
Correlated colour temperature factor.
"""
xy_w = ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['D65']
XYZ_w = xy_to_XYZ(xy_w)
Labs = []
for vs_colorimetry_data_ in reference_data:
_name, XYZ, _Lab, _C = vs_colorimetry_data_
XYZ_a = chromatic_adaptation_VonKries(
XYZ, XYZ_r, XYZ_w, transform='CMCCAT2000')
Lab = XYZ_to_Lab(XYZ_a, illuminant=xy_w)
Labs.append(Lab)
G_r = gamut_area(Labs) / D65_GAMUT_AREA
CCT_f = 1 if G_r > 1 else G_r
return CCT_f
def scale_conversion(D_E_ab, CCT_f, scaling_f=3.104):
"""
Returns the *Colour Quality Scale* (CQS) for given :math:`\Delta E_{ab}`
value and given correlated colour temperature penalizing factor.
Parameters
----------
D_E_ab : numeric
:math:`\Delta E_{ab}` value.
CCT_f : numeric
Correlated colour temperature penalizing factor.
scaling_f : numeric, optional
Scaling factor constant.
Returns
-------
numeric
*Colour Quality Scale* (CQS).
"""
Q_a = 10 * np.log(np.exp((100 - scaling_f * D_E_ab) / 10) + 1) * CCT_f
return Q_a
def delta_E_RMS(cqs_data, attribute):
"""
Computes the root-mean-square average for given *Colour Quality Scale*
(CQS) data.
Parameters
----------
cqs_data : VS_ColourQualityScaleData
*Colour Quality Scale* (CQS) data.
attribute : unicode
Colorimetry data attribute to use to compute the root-mean-square
average.
Returns
-------
numeric
Root-mean-square average.
"""
return np.sqrt(1 / len(cqs_data) * np.sum(
[getattr(sample_data, attribute) ** 2
for sample_data in cqs_data.values()])) # yapf: disable
def colour_quality_scales(test_data, reference_data, CCT_f):
"""
Returns the *VS test colour samples* rendering scales.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
CCT_f : numeric
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
dict
*VS Test colour samples* colour rendering scales.
"""
Q_as = {}
for i, _ in enumerate(test_data):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = euclidean_distance(test_data[i].Lab, reference_data[i].Lab)
if D_C_ab > 0:
D_Ep_ab = np.sqrt(D_E_ab ** 2 - D_C_ab ** 2)
else:
D_Ep_ab = D_E_ab
Q_a = scale_conversion(D_Ep_ab, CCT_f)
Q_as[i + 1] = VS_ColourQualityScaleData(test_data[i].name, Q_a, D_C_ab,
D_E_ab, D_Ep_ab)
return Q_as