"""
Colour Quality Scale
====================
Define the *Colour Quality Scale* (CQS) computation objects:
- :class:`colour.quality.ColourRendering_Specification_CQS`
- :func:`colour.colour_quality_scale`
References
----------
- :cite:`Davis2010a` : Davis, W., & Ohno, Y. (2010). Color quality scale.
Optical Engineering, 49(3), 033602. doi:10.1117/1.3360335
- :cite:`Ohno2008a` : Ohno, Yoshiro, & Davis, W. (2008). NIST CQS simulation
(Version 7.4) [Computer software].
https://drive.google.com/file/d/1PsuU6QjUJjCX6tQyCud6ul2Tbs8rYWW9/view?\
usp=sharing
- :cite:`Ohno2013` : Ohno, Yoshiro, & Davis, W. (2008). NIST CQS simulation
(Version 7.4) [Computer software].
https://drive.google.com/file/d/1PsuU6QjUJjCX6tQyCud6ul2Tbs8rYWW9/view?\
usp=sharing
"""
from __future__ import annotations
import typing
from dataclasses import dataclass
import numpy as np
from colour.adaptation import chromatic_adaptation_VonKries
from colour.algebra import euclidean_distance, sdiv, sdiv_mode
from colour.colorimetry import (
CCS_ILLUMINANTS,
MSDS_CMFS,
SPECTRAL_SHAPE_DEFAULT,
MultiSpectralDistributions,
SpectralDistribution,
reshape_msds,
reshape_sd,
sd_blackbody,
sd_CIE_illuminant_D_series,
sd_to_XYZ,
)
if typing.TYPE_CHECKING:
from colour.hints import (
ArrayLike,
Dict,
Literal,
NDArrayFloat,
Tuple,
)
from colour.hints import cast
from colour.models import Lab_to_LCHab # pyright: ignore
from colour.models import UCS_to_uv, XYZ_to_Lab, XYZ_to_UCS, XYZ_to_xy, xy_to_XYZ
from colour.quality.datasets.vs import INDEXES_TO_NAMES_VS, SDS_VS
from colour.temperature import CCT_to_xy_CIE_D, uv_to_CCT_Ohno2013
from colour.utilities import as_float_array, domain_range_scale, tsplit, validate_method
from colour.utilities.documentation import DocstringTuple, is_documentation_building
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"GAMUT_AREA_D65",
"DataColorimetry_VS",
"DataColourQualityScale_VS",
"ColourRendering_Specification_CQS",
"COLOUR_QUALITY_SCALE_METHODS",
"colour_quality_scale",
"gamut_area",
"vs_colorimetry_data",
"CCT_factor",
"scale_conversion",
"delta_E_RMS",
"colour_quality_scales",
]
GAMUT_AREA_D65: int = 8210
"""Gamut area for *CIE Illuminant D Series D65*."""
@dataclass
class DataColorimetry_VS:
"""Define the class storing *VS test colour samples* colorimetry data."""
name: str
XYZ: NDArrayFloat
Lab: NDArrayFloat
C: NDArrayFloat
@dataclass
class DataColourQualityScale_VS:
"""
Define the class storing *VS test colour samples* colour quality scale
data.
"""
name: str
Q_a: float
D_C_ab: float
D_E_ab: float
D_Ep_ab: float
[docs]
@dataclass
class ColourRendering_Specification_CQS:
"""
Define the *Colour Quality Scale* (CQS) colour rendering (quality)
specification.
Parameters
----------
name
Name of the test spectral distribution.
Q_a
Colour quality scale :math:`Q_a`.
Q_f
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
Colour preference scale :math:`Q_p` similar to colour quality scale
:math:`Q_a` but placing additional weight on preference of object
colour appearance, set to *None* in *NIST CQS 9.0* method. This metric
is based on the notion that increases in chroma are generally preferred
and should be rewarded.
Q_g
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
Relative gamut area scale :math:`Q_d`, set to *None* in *NIST CQS 9.0*
method.
Q_as
Individual *Colour Quality Scale* (CQS) data for each sample.
colorimetry_data
Colorimetry data for the test and reference computations.
References
----------
:cite:`Davis2010a`, :cite:`Ohno2008a`, :cite:`Ohno2013`
"""
name: str
Q_a: float
Q_f: float
Q_p: float | None
Q_g: float
Q_d: float | None
Q_as: Dict[int, DataColourQualityScale_VS]
colorimetry_data: Tuple[
Tuple[DataColorimetry_VS, ...], Tuple[DataColorimetry_VS, ...]
]
COLOUR_QUALITY_SCALE_METHODS: tuple = ("NIST CQS 7.4", "NIST CQS 9.0")
if is_documentation_building(): # pragma: no cover
COLOUR_QUALITY_SCALE_METHODS = DocstringTuple(COLOUR_QUALITY_SCALE_METHODS)
COLOUR_QUALITY_SCALE_METHODS.__doc__ = """
Supported *Colour Quality Scale* (CQS) computation methods.
References
----------
:cite:`Davis2010a`, :cite:`Ohno2008a`, :cite:`Ohno2013`
"""
@typing.overload
def colour_quality_scale(
sd_test: SpectralDistribution,
*,
additional_data: Literal[False],
method: Literal["NIST CQS 7.4", "NIST CQS 9.0"] | str = ...,
) -> float: ...
@typing.overload
def colour_quality_scale(
sd_test: SpectralDistribution,
additional_data: Literal[True] = True,
method: Literal["NIST CQS 7.4", "NIST CQS 9.0"] | str = ...,
) -> ColourRendering_Specification_CQS: ...
@typing.overload
def colour_quality_scale(
sd_test: SpectralDistribution,
additional_data: Literal[False],
method: Literal["NIST CQS 7.4", "NIST CQS 9.0"] | str = ...,
) -> float: ...
[docs]
def colour_quality_scale(
sd_test: SpectralDistribution,
additional_data: bool = False,
method: Literal["NIST CQS 7.4", "NIST CQS 9.0"] | str = "NIST CQS 9.0",
) -> float | ColourRendering_Specification_CQS:
"""
Return the *Colour Quality Scale* (CQS) of given spectral distribution
using given method.
Parameters
----------
sd_test
Test spectral distribution.
additional_data
Whether to output additional data.
method
Computation method.
Returns
-------
:class:`float` or \
:class:`colour.quality.ColourRendering_Specification_CQS`
*Colour Quality Scale* (CQS).
References
----------
:cite:`Davis2010a`, :cite:`Ohno2008a`, :cite:`Ohno2013`
Examples
--------
>>> from colour import SDS_ILLUMINANTS
>>> sd = SDS_ILLUMINANTS["FL2"]
>>> colour_quality_scale(sd) # doctest: +ELLIPSIS
64.1118220...
"""
method = validate_method(method, tuple(COLOUR_QUALITY_SCALE_METHODS))
cmfs = reshape_msds(
MSDS_CMFS["CIE 1931 2 Degree Standard Observer"],
SPECTRAL_SHAPE_DEFAULT,
copy=False,
)
shape = cmfs.shape
sd_test = reshape_sd(sd_test, shape, copy=False)
vs_sds = {
sd.name: reshape_sd(sd, shape, copy=False) for sd in SDS_VS[method].values()
}
with domain_range_scale("1"):
XYZ = sd_to_XYZ(sd_test, cmfs)
uv = UCS_to_uv(XYZ_to_UCS(XYZ))
CCT, _D_uv = uv_to_CCT_Ohno2013(uv)
if CCT < 5000:
sd_reference = sd_blackbody(CCT, shape)
else:
xy = CCT_to_xy_CIE_D(CCT)
sd_reference = sd_CIE_illuminant_D_series(xy)
sd_reference.align(shape)
test_vs_colorimetry_data = vs_colorimetry_data(
sd_test, sd_reference, vs_sds, cmfs, chromatic_adaptation=True
)
reference_vs_colorimetry_data = vs_colorimetry_data(
sd_reference, sd_reference, vs_sds, cmfs
)
CCT_f: float
if method == "nist cqs 9.0":
CCT_f = 1
scaling_f = 3.2
else:
XYZ_r = sd_to_XYZ(sd_reference, cmfs)
XYZ_r /= XYZ_r[1]
CCT_f = CCT_factor(reference_vs_colorimetry_data, XYZ_r)
scaling_f = 3.104
Q_as = colour_quality_scales(
test_vs_colorimetry_data,
reference_vs_colorimetry_data,
scaling_f,
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, scaling_f)
scaling_f = 2.93 * 1.0343 if method == "nist cqs 9.0" else 2.928
Q_f = scale_conversion(D_E_RMS, CCT_f, scaling_f)
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 / GAMUT_AREA_D65 * 100
if method == "nist cqs 9.0":
Q_p = Q_d = None
else:
p_delta_C = cast(
float,
np.average([max(0, sample_data.D_C_ab) for sample_data in Q_as.values()]),
)
Q_p = 100 - 3.6 * (D_Ep_RMS - p_delta_C)
Q_d = G_t / G_r * CCT_f * 100
if additional_data:
return ColourRendering_Specification_CQS(
sd_test.name,
Q_a,
Q_f,
Q_p,
Q_g,
Q_d,
Q_as,
(test_vs_colorimetry_data, reference_vs_colorimetry_data),
)
return Q_a
def gamut_area(Lab: ArrayLike) -> float:
"""
Return the gamut area :math:`G` covered by given *CIE L\\*a\\*b\\**
matrices.
Parameters
----------
Lab
*CIE L\\*a\\*b\\** colourspace matrices.
Returns
-------
:class:`float`
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 = as_float_array(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(
sd_test: SpectralDistribution,
sd_reference: SpectralDistribution,
sds_vs: Dict[str, SpectralDistribution],
cmfs: MultiSpectralDistributions,
chromatic_adaptation: bool = False,
) -> Tuple[DataColorimetry_VS, ...]:
"""
Return the *VS test colour samples* colorimetry data.
Parameters
----------
sd_test
Test spectral distribution.
sd_reference
Reference spectral distribution.
sds_vs
*VS test colour samples* spectral reflectance distributions.
cmfs
Standard observer colour matching functions.
chromatic_adaptation
Whether to perform chromatic adaptation.
Returns
-------
:class:`tuple`
*VS test colour samples* colorimetry data.
"""
XYZ_t = sd_to_XYZ(sd_test, cmfs)
with sdiv_mode():
XYZ_t = sdiv(XYZ_t, XYZ_t[1])
XYZ_r = sd_to_XYZ(sd_reference, cmfs)
with sdiv_mode():
XYZ_r = sdiv(XYZ_r, XYZ_r[1])
xy_r = XYZ_to_xy(XYZ_r)
vs_data = []
for _key, value in sorted(INDEXES_TO_NAMES_VS.items()):
sd_vs = sds_vs[value]
with domain_range_scale("1"):
XYZ_vs = sd_to_XYZ(sd_vs, cmfs, sd_test)
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(DataColorimetry_VS(sd_vs.name, XYZ_vs, Lab_vs, C_vs))
return tuple(vs_data)
def CCT_factor(
reference_data: Tuple[DataColorimetry_VS, ...], XYZ_r: ArrayLike
) -> float:
"""
Return the correlated colour temperature factor penalizing lamps with
extremely low correlated colour temperatures.
Parameters
----------
reference_data
Reference colorimetry data.
XYZ_r
*CIE XYZ* tristimulus values for reference.
Returns
-------
:class:`float`
Correlated colour temperature factor.
"""
xy_w = CCS_ILLUMINANTS["CIE 1931 2 Degree Standard Observer"]["D65"]
XYZ_w = xy_to_XYZ(xy_w)
Lab = XYZ_to_Lab(
chromatic_adaptation_VonKries(
[colorimetry_data.XYZ for colorimetry_data in reference_data],
XYZ_r,
XYZ_w,
transform="CMCCAT2000",
),
illuminant=xy_w,
)
G_r = gamut_area(Lab) / GAMUT_AREA_D65
return min(G_r, 1)
def scale_conversion(D_E_ab: float, CCT_f: float, scaling_f: float) -> float:
"""
Return the *Colour Quality Scale* (CQS) for given :math:`\\Delta E_{ab}`
value and given correlated colour temperature penalizing factor.
Parameters
----------
D_E_ab
:math:`\\Delta E_{ab}` value.
CCT_f
Correlated colour temperature penalizing factor.
scaling_f
Scaling factor constant.
Returns
-------
:class:`float`
*Colour Quality Scale* (CQS).
"""
return 10 * np.log1p(np.exp((100 - scaling_f * D_E_ab) / 10)) * CCT_f
def delta_E_RMS(
CQS_data: Dict[int, DataColourQualityScale_VS], attribute: str
) -> float:
"""
Compute the root-mean-square average for given *Colour Quality Scale*
(CQS) data.
Parameters
----------
CQS_data
*Colour Quality Scale* (CQS) data.
attribute
Colorimetry data attribute to use to compute the root-mean-square
average.
Returns
-------
:class:`float`
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: Tuple[DataColorimetry_VS, ...],
reference_data: Tuple[DataColorimetry_VS, ...],
scaling_f: float,
CCT_f: float,
) -> Dict[int, DataColourQualityScale_VS]:
"""
Return the *VS test colour samples* rendering scales.
Parameters
----------
test_data
Test data.
reference_data
Reference data.
scaling_f
Scaling factor constant.
CCT_f
Factor penalizing lamps with extremely low correlated colour
temperatures.
Returns
-------
:class:`dict`
*VS Test colour samples* colour rendering scales.
"""
Q_as = {}
for i in range(len(test_data)):
D_C_ab = cast(float, test_data[i].C - reference_data[i].C)
D_E_ab = cast(
float, euclidean_distance(test_data[i].Lab, reference_data[i].Lab)
)
D_Ep_ab = cast(float, np.sqrt(D_E_ab**2 - D_C_ab**2) if D_C_ab > 0 else D_E_ab)
Q_a = scale_conversion(D_Ep_ab, CCT_f, scaling_f)
Q_as[i + 1] = DataColourQualityScale_VS(
test_data[i].name, Q_a, D_C_ab, D_E_ab, D_Ep_ab
)
return Q_as
