"""
CAM16 Colour Appearance Model
=============================
Define the *CAM16* colour appearance model for predicting perceptual colour
attributes under varying viewing conditions.
- :class:`colour.appearance.InductionFactors_CAM16`
- :attr:`colour.VIEWING_CONDITIONS_CAM16`
- :class:`colour.CAM_Specification_CAM16`
- :func:`colour.XYZ_to_CAM16`
- :func:`colour.CAM16_to_XYZ`
References
----------
- :cite:`Li2017` : Li, C., Li, Z., Wang, Z., Xu, Y., Luo, M. R., Cui, G.,
Melgosa, M., Brill, M. H., & Pointer, M. (2017). Comprehensive color
solutions: CAM16, CAT16, and CAM16-UCS. Color Research & Application,
42(6), 703-718. doi:10.1002/col.22131
"""
from __future__ import annotations
from dataclasses import astuple, dataclass, field
import numpy as np
from colour.adaptation import CAT_CAT16
from colour.algebra import sdiv, sdiv_mode, spow, vecmul
from colour.appearance.ciecam02 import (
VIEWING_CONDITIONS_CIECAM02,
InductionFactors_CIECAM02,
hue_quadrature,
)
from colour.constants import EPSILON
from colour.hints import ( # noqa: TC001
Annotated,
ArrayLike,
Domain100,
NDArrayFloat,
Range100,
)
from colour.utilities import (
CanonicalMapping,
MixinDataclassArithmetic,
MixinDataclassIterable,
array_namespace,
as_float,
from_range_100,
from_range_degrees,
has_only_nan,
ones,
to_domain_100,
to_domain_degrees,
tsplit,
tstack,
xp_as_float_array,
xp_degrees,
xp_radians,
)
__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__ = [
"MATRIX_16",
"MATRIX_INVERSE_16",
"InductionFactors_CAM16",
"VIEWING_CONDITIONS_CAM16",
"CAM_Specification_CAM16",
"XYZ_to_CAM16",
"CAM16_to_XYZ",
]
MATRIX_16: NDArrayFloat = CAT_CAT16
"""Adaptation matrix :math:`M_{16}`."""
MATRIX_INVERSE_16: NDArrayFloat = np.linalg.inv(MATRIX_16)
"""Inverse adaptation matrix :math:`M^{-1}_{16}`."""
[docs]
@dataclass(frozen=True)
class InductionFactors_CAM16(MixinDataclassIterable):
"""
Define the *CAM16* colour appearance model induction factors.
Parameters
----------
F
Maximum degree of adaptation :math:`F`.
c
Exponential non-linearity :math:`c`.
N_c
Chromatic induction factor :math:`N_c`.
Notes
-----
- The *CAM16* colour appearance model induction factors are
identical to the *CIECAM02* colour appearance model
induction factors.
References
----------
:cite:`Li2017`
"""
F: float
c: float
N_c: float
VIEWING_CONDITIONS_CAM16: CanonicalMapping = CanonicalMapping(
VIEWING_CONDITIONS_CIECAM02
)
VIEWING_CONDITIONS_CAM16.__doc__ = """
Define the reference *CAM16* colour appearance model viewing conditions.
References
----------
:cite:`Li2017`
"""
[docs]
@dataclass
class CAM_Specification_CAM16(MixinDataclassArithmetic):
"""
Define the *CAM16* colour appearance model specification.
Parameters
----------
J
Correlate of *lightness* :math:`J`.
C
Correlate of *chroma* :math:`C`.
h
*Hue* angle :math:`h` in degrees.
s
Correlate of *saturation* :math:`s`.
Q
Correlate of *brightness* :math:`Q`.
M
Correlate of *colourfulness* :math:`M`.
H
*Hue* :math:`h` quadrature :math:`H`.
HC
*Hue* :math:`h` composition :math:`H^C`.
References
----------
:cite:`Li2017`
"""
J: float | NDArrayFloat | None = field(default_factory=lambda: None)
C: float | NDArrayFloat | None = field(default_factory=lambda: None)
h: float | NDArrayFloat | None = field(default_factory=lambda: None)
s: float | NDArrayFloat | None = field(default_factory=lambda: None)
Q: float | NDArrayFloat | None = field(default_factory=lambda: None)
M: float | NDArrayFloat | None = field(default_factory=lambda: None)
H: float | NDArrayFloat | None = field(default_factory=lambda: None)
HC: float | NDArrayFloat | None = field(default_factory=lambda: None)
[docs]
def XYZ_to_CAM16(
XYZ: Domain100,
XYZ_w: Domain100,
L_A: ArrayLike,
Y_b: ArrayLike,
surround: (
InductionFactors_CIECAM02 | InductionFactors_CAM16
) = VIEWING_CONDITIONS_CAM16["Average"],
discount_illuminant: bool = False,
compute_H: bool = False,
) -> Annotated[CAM_Specification_CAM16, (100, 100, 360, 100, 100, 100, 400)]:
"""
Compute the *CAM16* colour appearance model correlates from the specified
*CIE XYZ* tristimulus values.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often
taken to be 20% of the luminance of a white object in the scene).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 \\times L_b / L_w` where :math:`L_w` is the
luminance of the light source and :math:`L_b` is the luminance of
the background. For viewing images, :math:`Y_b` can be the average
:math:`Y` value for the pixels in the entire image, or frequently,
a :math:`Y` value of 20, approximating an :math:`L^*` of 50 is
used.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
compute_H
When *True*, compute the *Hue Quadrature* :math:`H` correlate
via :func:`colour.appearance.ciecam02.hue_quadrature`. Defaults to
*False* because :math:`H` is rarely consumed downstream and
skipping the bin search is a measurable cost saving.
Returns
-------
:class:`colour.CAM_Specification_CAM16`
*CAM16* colour appearance model specification.
Notes
-----
+---------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``XYZ`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``XYZ_w`` | 100 | 1 |
+---------------------+-----------------------+---------------+
+---------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``specification.J`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.C`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.h`` | 360 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.s`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.Q`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.M`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.H`` | 400 | 1 |
+---------------------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> surround = VIEWING_CONDITIONS_CAM16["Average"]
>>> XYZ_to_CAM16(
... XYZ, XYZ_w, L_A, Y_b, surround,
... compute_H=True,
... ) # doctest: +ELLIPSIS
CAM_Specification_CAM16(J=np.float64(41.7312079...), \
C=np.float64(0.1033557...), h=np.float64(217.0679597...), \
s=np.float64(2.3450150...), Q=np.float64(195.3717089...), \
M=np.float64(0.1074367...), H=np.float64(275.5949861...), HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
xp = array_namespace(XYZ, XYZ_w, L_A, Y_b)
XYZ = xp_as_float_array(XYZ, xp=xp)
XYZ_w = xp_as_float_array(XYZ_w, xp=xp, like=XYZ)
L_A = xp_as_float_array(L_A, xp=xp, like=XYZ)
Y_b = xp_as_float_array(Y_b, xp=xp, like=XYZ)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Viewing condition dependent parameters: background induction
# factor :math:`n`, luminance level adaptation factor :math:`F_L`,
# chromatic induction factors :math:`N_{bb}` and :math:`N_{cb}`,
# base exponential non-linearity :math:`z`. Same formulation as
# in *CIECAM02*.
with sdiv_mode():
n = sdiv(Y_b, Y_w)
k = 1 / (5 * L_A + 1)
k4 = k**4
F_L = 0.2 * k4 * (5 * L_A) + 0.1 * (1 - k4) ** 2 * spow(5 * L_A, 1 / 3)
with sdiv_mode():
N_bb = 0.725 * spow(sdiv(1, n), 0.2)
N_cb = N_bb
z = 1.48 + xp.sqrt(n)
# Converting *CIE XYZ* tristimulus values to *CAT16* sharpened *RGB*
# values for the stimulus and reference white. *CAM16* uses the
# *CAT16* matrix directly rather than *CIECAM02*'s *CAT02*
# sharpening followed by *Hunt-Pointer-Estevez* transform.
RGB = vecmul(MATRIX_16, XYZ)
RGB_w = vecmul(MATRIX_16, XYZ_w)
# Computing degree of adaptation :math:`D`, same formulation as in
# *CIECAM02*, clipped to :math:`[0, 1]` and bypassed entirely when
# ``discount_illuminant`` is set.
if discount_illuminant:
D = xp_as_float_array(ones(L_A.shape), xp=xp, like=XYZ)
else:
F = xp_as_float_array(surround.F, xp=xp, like=XYZ)
D = xp.clip(F * (1 - (1 / 3.6) * xp.exp((-L_A - 42) / 92)), 0, 1)
# Computing full chromatic adaptation, applied to the stimulus and
# the reference white via a shared adaptation factor.
D_RGB = D[..., None] * Y_w[..., None] / RGB_w + 1 - D[..., None]
RGB_c = D_RGB * RGB
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non-linear response compression,
# same sign-preserving form as in *CIECAM02* per *Luo (2013)*. In
# *CAM16* the compression is applied directly to the chromatically
# adapted *RGB* (no intermediate *HPE* transform).
F_L_RGB_c = spow(F_L[..., None] * xp.abs(RGB_c) / 100, 0.42)
RGB_a = (400 * xp.sign(RGB_c) * F_L_RGB_c) / (27.13 + F_L_RGB_c) + 0.1
F_L_RGB_wc = spow(F_L[..., None] * xp.abs(RGB_wc) / 100, 0.42)
RGB_aw = (400 * xp.sign(RGB_wc) * F_L_RGB_wc) / (27.13 + F_L_RGB_wc) + 0.1
# Computing the opponent colour dimensions :math:`a` and :math:`b`,
# same formulation as in *CIECAM02*.
Ra, Ga, Ba = tsplit(RGB_a)
a = Ra - 12 * Ga / 11 + Ba / 11
b = (Ra + Ga - 2 * Ba) / 9
# Computing the *hue* angle :math:`h` in degrees in
# :math:`[0, 360)`, same as in *CIECAM02*.
h = xp_degrees(xp.atan2(b, a)) % 360
# Computing eccentricity factor :math:`e_t`, same as in *CIECAM02*.
e_t = 1 / 4 * (xp.cos(2 + xp_radians(h)) + 3.8)
# Computing achromatic responses :math:`A` for the stimulus and
# :math:`A_w` for the whitepoint, same as in *CIECAM02*.
A = (2 * Ra + Ga + (1 / 20) * Ba - 0.305) * N_bb
Raw, Gaw, Baw = tsplit(RGB_aw)
A_w = (2 * Raw + Gaw + (1 / 20) * Baw - 0.305) * N_bb
# Computing the correlate of *Lightness* :math:`J`, same form as
# in *CIECAM02*.
c = surround.c
with sdiv_mode():
J = 100 * spow(sdiv(A, A_w), c * z)
# Computing the correlate of *brightness* :math:`Q`, same form as
# in *CIECAM02*.
Q = (4 / c) * xp.sqrt(J / 100) * (A_w + 4) * spow(F_L, 0.25)
# Computing the temporary magnitude quantity :math:`t` and the
# correlate of *chroma* :math:`C`, same forms as in *CIECAM02*.
N_c = surround.N_c
with sdiv_mode():
t = ((50000 / 13) * N_c * N_cb) * sdiv(
e_t * spow(a**2 + b**2, 0.5), Ra + Ga + 21 * Ba / 20
)
C = spow(t, 0.9) * spow(J / 100, 0.5) * spow(1.64 - 0.29**n, 0.73)
# Computing the correlate of *colourfulness* :math:`M` and the
# correlate of *saturation* :math:`s`, same forms as in *CIECAM02*.
M = C * spow(F_L, 0.25)
with sdiv_mode():
s = 100 * spow(sdiv(M, Q), 0.5)
# Computing hue :math:`h` quadrature :math:`H` only when requested
# via ``compute_H``; the bin search is shared with *CIECAM02* and
# delegates to :func:`hue_quadrature`.
# TODO: Compute hue composition.
H = hue_quadrature(h) if compute_H else xp.full_like(h, float("nan"))
return CAM_Specification_CAM16(
J=as_float(from_range_100(J)),
C=as_float(from_range_100(C)),
h=as_float(from_range_degrees(h)),
s=as_float(from_range_100(s)),
Q=as_float(from_range_100(Q)),
M=as_float(from_range_100(M)),
H=as_float(from_range_degrees(H, 400)),
HC=None,
)
[docs]
def CAM16_to_XYZ(
specification: Annotated[
CAM_Specification_CAM16, (100, 100, 360, 100, 100, 100, 400)
],
XYZ_w: Domain100,
L_A: ArrayLike,
Y_b: ArrayLike,
surround: (
InductionFactors_CIECAM02 | InductionFactors_CAM16
) = VIEWING_CONDITIONS_CAM16["Average"],
discount_illuminant: bool = False,
) -> Range100:
"""
Convert the *CAM16* colour appearance model specification to *CIE XYZ*
tristimulus values.
Parameters
----------
specification
*CAM16* colour appearance model specification. Correlate of
*lightness* :math:`J`, correlate of *chroma* :math:`C` or correlate
of *colourfulness* :math:`M` and *hue* angle :math:`h` in degrees
must be specified, e.g., :math:`JCh` or :math:`JMh`.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often
taken to be 20% of the luminance of a white object in the scene).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 \\times L_b / L_w` where :math:`L_w` is the
luminance of the light source and :math:`L_b` is the luminance of
the background. For viewing images, :math:`Y_b` can be the average
:math:`Y` value for the pixels in the entire image, or frequently,
a :math:`Y` value of 20, approximating an :math:`L^*` of 50 is
used.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither :math:`C` nor :math:`M` correlates have been defined
in the ``specification`` argument.
Notes
-----
+---------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``specification.J`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.C`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.h`` | 360 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.s`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.Q`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.M`` | 100 | 1 |
+---------------------+-----------------------+---------------+
| ``specification.H`` | 360 | 1 |
+---------------------+-----------------------+---------------+
| ``XYZ_w`` | 100 | 1 |
+---------------------+-----------------------+---------------+
+---------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+=====================+=======================+===============+
| ``XYZ`` | 100 | 1 |
+---------------------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> specification = CAM_Specification_CAM16(
... J=41.731207905126638, C=0.103355738709070, h=217.067959767393010
... )
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> CAM16_to_XYZ(specification, XYZ_w, L_A, Y_b) # doctest: +ELLIPSIS
array([19.01..., 20... , 21.78...])
"""
J, C, h, _s, _Q, M, _H, _HC = astuple(specification)
J = to_domain_100(J)
C = to_domain_100(C)
h = to_domain_degrees(h)
M = to_domain_100(M)
XYZ_w = to_domain_100(XYZ_w)
xp = array_namespace(J, C, h, M, XYZ_w, L_A)
J = xp_as_float_array(J, xp=xp)
C = xp_as_float_array(C, xp=xp, like=J)
h = xp_as_float_array(h, xp=xp, like=J)
M = xp_as_float_array(M, xp=xp, like=J)
XYZ_w = xp_as_float_array(XYZ_w, xp=xp, like=J)
L_A = xp_as_float_array(L_A, xp=xp, like=J)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Viewing condition dependent parameters: background induction
# factor :math:`n`, luminance level adaptation factor :math:`F_L`,
# chromatic induction factors :math:`N_{bb}` and :math:`N_{cb}`,
# base exponential non-linearity :math:`z`. Same formulation as
# in *CIECAM02*.
with sdiv_mode():
n = sdiv(Y_b, Y_w)
k = 1 / (5 * L_A + 1)
k4 = k**4
F_L = 0.2 * k4 * (5 * L_A) + 0.1 * (1 - k4) ** 2 * spow(5 * L_A, 1 / 3)
with sdiv_mode():
N_bb = 0.725 * spow(sdiv(1, n), 0.2)
N_cb = N_bb
z = 1.48 + xp.sqrt(n)
# Converting *CIE XYZ* tristimulus values to *CAT16* sharpened *RGB*
# values for the reference white.
RGB_w = vecmul(MATRIX_16, XYZ_w)
# Computing degree of adaptation :math:`D`, same formulation as in
# *CIECAM02*, clipped to :math:`[0, 1]` and bypassed entirely when
# ``discount_illuminant`` is set.
if discount_illuminant:
D = xp_as_float_array(ones(L_A.shape), xp=xp, like=J)
else:
F = xp_as_float_array(surround.F, xp=xp, like=J)
D = xp.clip(F * (1 - (1 / 3.6) * xp.exp((-L_A - 42) / 92)), 0, 1)
# Computing full chromatic adaptation for the reference white.
D_RGB = D[..., None] * Y_w[..., None] / RGB_w + 1 - D[..., None]
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non-linear response compression
# to the whitepoint, same form as in *CIECAM02*.
F_L_RGB_wc = spow(F_L[..., None] * xp.abs(RGB_wc) / 100, 0.42)
RGB_aw = (400 * xp.sign(RGB_wc) * F_L_RGB_wc) / (27.13 + F_L_RGB_wc) + 0.1
# Computing achromatic response :math:`A_w` for the whitepoint,
# same as in *CIECAM02*.
Raw, Gaw, Baw = tsplit(RGB_aw)
A_w = (2 * Raw + Gaw + (1 / 20) * Baw - 0.305) * N_bb
# Recovering the correlate of *chroma* :math:`C` from the correlate
# of *colourfulness* :math:`M` when only :math:`M` has been
# provided.
if has_only_nan(C) and not has_only_nan(M):
C = M / spow(F_L, 0.25)
elif has_only_nan(C):
error = (
'Either "C" or "M" correlate must be defined in '
'the "CAM_Specification_CAM16" argument!'
)
raise ValueError(error)
# Computing temporary magnitude quantity :math:`t`, same form as
# in *CIECAM02*.
J_prime = xp.clip(J, min=EPSILON)
t = spow(C / (xp.sqrt(J_prime / 100) * spow(1.64 - 0.29**n, 0.73)), 1 / 0.9)
# Computing eccentricity factor :math:`e_t`, same as in *CIECAM02*.
e_t = 1 / 4 * (xp.cos(2 + xp_radians(h)) + 3.8)
# Computing achromatic response :math:`A` for the stimulus, same
# inverse form as in *CIECAM02*.
c = surround.c
A = A_w * spow(J / 100, 1 / (c * z))
# Computing points :math:`P_1`, :math:`P_2`, :math:`P_3`, same
# form as in *CIECAM02*.
N_c = surround.N_c
with sdiv_mode():
P_1 = sdiv((50000 / 13) * N_c * N_cb * e_t, t)
P_2 = A / N_bb + 0.305
P_3 = xp.full_like(P_1, 21 / 20)
# Computing opponent colour dimensions :math:`a` and :math:`b`
# via the sin / cos branching protecting against the numerical
# singularity near the hue axis. Same as in *CIECAM02*.
hr = xp_radians(h)
sin_hr = xp.sin(hr)
cos_hr = xp.cos(hr)
with sdiv_mode():
cos_hr_sin_hr = sdiv(cos_hr, sin_hr)
sin_hr_cos_hr = sdiv(sin_hr, cos_hr)
P_4 = sdiv(P_1, sin_hr)
P_5 = sdiv(P_1, cos_hr)
n_ab = P_2 * (2 + P_3) * (460 / 1403)
abs_sin_ge_cos = xp.abs(sin_hr) >= xp.abs(cos_hr)
abs_sin_lt_cos = xp.abs(sin_hr) < xp.abs(cos_hr)
a = xp.zeros_like(hr)
b = xp.zeros_like(hr)
b = xp.where(
abs_sin_ge_cos,
n_ab
/ (
P_4
+ (2 + P_3) * (220 / 1403) * cos_hr_sin_hr
- (27 / 1403)
+ P_3 * (6300 / 1403)
),
b,
)
a = xp.where(abs_sin_ge_cos, b * cos_hr_sin_hr, a)
a = xp.where(
abs_sin_lt_cos,
n_ab
/ (
P_5
+ (2 + P_3) * (220 / 1403)
- ((27 / 1403) - P_3 * (6300 / 1403)) * sin_hr_cos_hr
),
a,
)
b = xp.where(abs_sin_lt_cos, a * sin_hr_cos_hr, b)
t_mask = xp.where(t == 0, 0, 1)
a = a * t_mask
b = b * t_mask
# Applying post-adaptation non-linear response compression matrix
# to recover the compressed *RGB* array. Same as in *CIECAM02*.
RGB_a = (
vecmul(
[
[460, 451, 288],
[460, -891, -261],
[460, -220, -6300],
],
tstack([P_2, a, b]),
)
/ 1403
)
# Applying inverse post-adaptation non-linear response compression,
# same form as in *CIECAM02*.
RGB_c = (
xp.sign(RGB_a - 0.1)
* 100
/ F_L[..., None]
* spow(
(27.13 * xp.abs(RGB_a - 0.1)) / (400 - xp.abs(RGB_a - 0.1)),
1 / 0.42,
)
)
# Applying inverse full chromatic adaptation, using the precomputed
# ``D_RGB`` adaptation factor.
RGB = RGB_c / D_RGB
# Converting *CAT16* sharpened *RGB* values back to *CIE XYZ*
# tristimulus values.
XYZ = vecmul(MATRIX_INVERSE_16, RGB)
return from_range_100(XYZ)
