#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Colour Quality Scale
====================
Defines *colour quality scale* computation objects:
- :class:`CQS_Specification`
- :func:`colour_quality_scale`
See Also
--------
`Colour Quality Scale IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/quality/cqs.ipynb>`_ # noqa
References
----------
.. [1] Davis, W., & Ohno, Y. (2010). Color quality scale. Optical
Engineering, 49(3), 33602–33616. doi:10.1117/1.3360335
.. [2] Ohno, Y., & Davis, W. (2008). NIST CQS simulation 7.4. Retrieved from
http://cie2.nist.gov/TC1-69/NIST CQS simulation 7.4.xls
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.colorimetry import STANDARD_OBSERVERS_CMFS
from colour.colorimetry import (
ILLUMINANTS,
D_illuminant_relative_spd,
blackbody_spd,
spectral_to_XYZ)
from colour.quality.dataset.vs import VS_SPDS, VS_INDEXES_TO_NAMES
from colour.models import (
UCS_to_uv,
XYZ_to_UCS,
XYZ_to_xy,
XYZ_to_Lab,
Lab_to_LCHab,
xy_to_XYZ)
from colour.temperature import CCT_to_xy_CIE_D, uv_to_CCT_Ohno2013
from colour.adaptation import chromatic_adaptation_VonKries
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - 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']
D65_GAMUT_AREA = 8210
[docs]class VS_ColorimetryData(namedtuple('VS_ColorimetryData',
('name', 'XYZ', 'Lab', 'C'))):
"""
Defines the the class holding *VS test colour samples* colorimetry data.
"""
[docs]class VS_ColourQualityScaleData(
namedtuple('VS_ColourQualityScaleData',
('name', 'Q_a', 'D_C_ab', 'D_E_ab', 'D_Ep_ab'))):
"""
Defines the the class holding *VS test colour samples* colour quality
scale data.
"""
[docs]class CQS_Specification(
namedtuple(
'CQS_Specification',
('Q_a', 'Q_f', 'Q_p', 'Q_g', 'Q_d', 'Q_as', 'colorimetry_data'))):
"""
Defines the *CQS* colour quality specification.
Parameters
----------
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 LAB* object
colourspace.
Q_d : numeric
Relative gamut area scale :math:`Q_d`.
Q_as : dict
Individual *CQS* data for each sample.
colorimetry_data : tuple
Colorimetry data for the test and reference computations.
"""
[docs]def colour_quality_scale(spd_test, additional_data=False):
"""
Returns the *colour quality scale* 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.
Examples
--------
>>> from colour import ILLUMINANTS_RELATIVE_SPDS
>>> spd = ILLUMINANTS_RELATIVE_SPDS.get('F2')
>>> colour_quality_scale(spd) # doctest: +ELLIPSIS
64.6860580...
"""
cmfs = STANDARD_OBSERVERS_CMFS.get(
'CIE 1931 2 Degree Standard Observer')
shape = cmfs.shape
spd_test = spd_test.clone().align(shape)
vs_spds = {}
for index, vs_spd in VS_SPDS.items():
vs_spds[index] = vs_spd.clone().align(shape)
XYZ = spectral_to_XYZ(spd_test, cmfs)
uv = UCS_to_uv(XYZ_to_UCS(XYZ))
CCT, _ = 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_factor = _CCT_factor(reference_vs_colorimetry_data, XYZ_r)
Q_as = _colour_quality_scales(
test_vs_colorimetry_data, reference_vs_colorimetry_data, CCT_factor)
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_factor)
Q_f = _scale_conversion(D_E_RMS, CCT_factor, 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()])
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_factor * 100
if additional_data:
return CQS_Specification(Q_a,
Q_f,
Q_p,
Q_g,
Q_d,
Q_as,
(test_vs_colorimetry_data,
reference_vs_colorimetry_data))
else:
return Q_a
[docs]def gamut_area(Labs):
"""
Returns the gamut area :math:`G` covered by given *CIE Lab* matrices.
Parameters
----------
Labs : array_like
*CIE Lab* colourspace matrices.
Returns
-------
numeric
Gamut area :math:`G`.
Examples
--------
>>> Labs = [
... 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, -29.5465555, -20.50177194]),
... np.array([55.73912101, -43.39520959, -5.08956953]),
... np.array([56.2077687, -53.68997662, 20.2113441]),
... np.array([66.16683122, -38.64600327, 42.77396631]),
... np.array([76.7295211, -23.9214821, 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, 27.4671817]),
... np.array([40.52565174, 48.87449192, 3.4512168])]
>>> gamut_area(Labs) # doctest: +ELLIPSIS
8335.9482018...
"""
Labs_s = Labs[:]
Labs_s.append(Labs_s.pop(0))
G = 0
for i, _ in enumerate(Labs):
L, a, b = Labs[i]
L_s, a_s, b_s = Labs_s[i]
A = np.sqrt(a ** 2 + b ** 2)
B = np.sqrt(a_s ** 2 + b_s ** 2)
C = np.sqrt((a_s - a) ** 2 + (b_s - b) ** 2)
t = (A + B + C) / 2
S = np.sqrt(t * (t - A) * (t - B) * (t - C))
G += S
return G
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.get(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)
_, chroma_vs, _ = Lab_to_LCHab(Lab_vs)
vs_data.append(
VS_ColorimetryData(spd_vs.name,
XYZ_vs,
Lab_vs,
chroma_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* colourspace matrix for reference.
Returns
-------
numeric
Correlated colour temperature factor.
"""
xy_w = ILLUMINANTS.get('CIE 1931 2 Degree Standard Observer').get('D65')
XYZ_w = xy_to_XYZ(xy_w)
Labs = []
for vs_colorimetry_data in reference_data:
_, XYZ, _, _ = 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_factor = 1 if G_r > 1 else G_r
return CCT_factor
def _scale_conversion(D_E_ab, CCT_factor, scaling_factor=3.104):
"""
Returns the correlated colour temperature factor penalizing lamps with
extremely low correlated colour temperatures.
Parameters
----------
reference_data : VS_ColorimetryData
Reference colorimetry data.
spd_reference : SpectralPowerDistribution
Reference spectral power distribution.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
Returns
-------
numeric
Correlated colour temperature factor.
"""
Q_a = (10 * np.log(np.exp((100 - scaling_factor * D_E_ab) / 10) + 1) *
CCT_factor)
return Q_a
def _delta_E_RMS(cqs_data, attribute):
"""
Computes the root-mean-square average for given *CQS* data.
Parameters
----------
cqs_data : VS_ColourQualityScaleData
*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()]))
def _colour_quality_scales(test_data, reference_data, CCT_factor):
"""
Returns the *VS test colour samples* rendering scales.
Parameters
----------
test_data : list
Test data.
reference_data : list
Reference data.
CCT_factor : numeric
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
dict
*VS Test colour samples* colour rendering scales.
"""
colour_quality_scales = {}
for i, _ in enumerate(test_data):
D_C_ab = test_data[i].C - reference_data[i].C
D_E_ab = np.sqrt(
np.sum((test_data[i].Lab - reference_data[i].Lab) ** 2))
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_factor)
colour_quality_scales[i + 1] = VS_ColourQualityScaleData(
test_data[i].name, Q_a, D_C_ab, D_E_ab, D_Ep_ab)
return colour_quality_scales
Colour 0.3