"""
Recommendation ITU-R BT.2100
============================
Define the *Recommendation ITU-R BT.2100* opto-electrical transfer functions
(OETF), opto-optical transfer functions (OOTF / OOCF) and electro-optical
transfer functions (EOTF) and their inverse.
- :func:`colour.models.oetf_BT2100_PQ`
- :func:`colour.models.oetf_inverse_BT2100_PQ`
- :func:`colour.models.eotf_BT2100_PQ`
- :func:`colour.models.eotf_inverse_BT2100_PQ`
- :func:`colour.models.ootf_BT2100_PQ`
- :func:`colour.models.ootf_inverse_BT2100_PQ`
- :func:`colour.models.oetf_BT2100_HLG`
- :func:`colour.models.oetf_inverse_BT2100_HLG`
- :func:`colour.models.eotf_BT2100_HLG_1`
- :func:`colour.models.eotf_BT2100_HLG_2`
- :attr:`colour.models.BT2100_HLG_EOTF_METHODS`
- :func:`colour.models.eotf_BT2100_HLG`
- :func:`colour.models.eotf_inverse_BT2100_HLG_1`
- :func:`colour.models.eotf_inverse_BT2100_HLG_2`
- :attr:`colour.models.BT2100_HLG_EOTF_INVERSE_METHODS`
- :func:`colour.models.eotf_inverse_BT2100_HLG`
- :func:`colour.models.ootf_BT2100_HLG`
- :func:`colour.models.ootf_inverse_BT2100_HLG`
- :func:`colour.models.ootf_BT2100_HLG_1`
- :func:`colour.models.ootf_BT2100_HLG_2`
- :attr:`colour.models.BT2100_HLG_OOTF_METHODS`
- :func:`colour.models.ootf_BT2100_HLG`
- :func:`colour.models.ootf_inverse_BT2100_HLG_1`
- :func:`colour.models.ootf_inverse_BT2100_HLG_2`
- :attr:`colour.models.BT2100_HLG_OOTF_INVERSE_METHODS`
- :func:`colour.models.ootf_inverse_BT2100_HLG`
References
----------
- :cite:`Borer2017a` : Borer, T. (2017). Private Discussion with Mansencal,
T. and Shaw, N.
- :cite:`InternationalTelecommunicationUnion2017` : International
Telecommunication Union. (2017). Recommendation ITU-R BT.2100-1 - Image
parameter values for high dynamic range television for use in production
and international programme exchange.
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2100-1-201706-I!!PDF-E.pdf
- :cite:`InternationalTelecommunicationUnion2018` : International
Telecommunication Union. (2018). Recommendation ITU-R BT.2100-2 - Image
parameter values for high dynamic range television for use in production
and international programme exchange.
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2100-2-201807-I!!PDF-E.pdf
"""
from __future__ import annotations
import typing
import numpy as np
from colour.algebra import spow
if typing.TYPE_CHECKING:
from colour.hints import Literal
from colour.hints import ( # noqa: TC001
ArrayLike,
Domain1,
NDArrayFloat,
Range1,
)
from colour.models.rgb.transfer_functions import (
eotf_BT1886,
eotf_inverse_BT1886,
eotf_inverse_ST2084,
eotf_ST2084,
oetf_ARIBSTDB67,
oetf_BT709,
oetf_inverse_ARIBSTDB67,
oetf_inverse_BT709,
)
from colour.models.rgb.transfer_functions.arib_std_b67 import CONSTANTS_ARIBSTDB67
from colour.utilities import (
CanonicalMapping,
Structure,
as_float,
as_float_array,
as_float_scalar,
domain_range_scale,
filter_kwargs,
from_range_1,
optional,
to_domain_1,
tsplit,
tstack,
usage_warning,
validate_method,
)
__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__ = [
"oetf_BT2100_PQ",
"oetf_inverse_BT2100_PQ",
"eotf_BT2100_PQ",
"eotf_inverse_BT2100_PQ",
"ootf_BT2100_PQ",
"ootf_inverse_BT2100_PQ",
"WEIGHTS_BT2100_HLG",
"CONSTANTS_BT2100_HLG",
"gamma_function_BT2100_HLG",
"oetf_BT2100_HLG",
"oetf_inverse_BT2100_HLG",
"black_level_lift_BT2100_HLG",
"eotf_BT2100_HLG_1",
"eotf_BT2100_HLG_2",
"BT2100_HLG_EOTF_METHODS",
"eotf_BT2100_HLG",
"eotf_inverse_BT2100_HLG_1",
"eotf_inverse_BT2100_HLG_2",
"BT2100_HLG_EOTF_INVERSE_METHODS",
"eotf_inverse_BT2100_HLG",
"ootf_BT2100_HLG_1",
"ootf_BT2100_HLG_2",
"BT2100_HLG_OOTF_METHODS",
"ootf_BT2100_HLG",
"ootf_inverse_BT2100_HLG_1",
"ootf_inverse_BT2100_HLG_2",
"BT2100_HLG_OOTF_INVERSE_METHODS",
"ootf_inverse_BT2100_HLG",
]
[docs]
def oetf_BT2100_PQ(E: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* opto-electronic
transfer function (OETF).
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_BT2100_PQ(0.1) # doctest: +ELLIPSIS
0.7247698...
"""
return eotf_inverse_ST2084(ootf_BT2100_PQ(E), 10000)
[docs]
def oetf_inverse_BT2100_PQ(E_p: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* inverse
opto-electrical transfer function (OETF).
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Returns
-------
:class:`numpy.ndarray`
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_inverse_BT2100_PQ(0.724769816665726) # doctest: +ELLIPSIS
0.0999999...
"""
return ootf_inverse_BT2100_PQ(eotf_ST2084(E_p, 10000))
[docs]
def eotf_BT2100_PQ(E_p: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* electro-optical
transfer function (EOTF).
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_BT2100_PQ(0.724769816665726) # doctest: +ELLIPSIS
779.9883608...
"""
return eotf_ST2084(E_p, 10000)
[docs]
def eotf_inverse_BT2100_PQ(F_D: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* inverse
electro-optical transfer function (EOTF).
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` denotes a non-linear colour value :math:`\\{R', G', B'\\}`
or :math:`\\{L', M', S'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`,
:cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_inverse_BT2100_PQ(779.988360834085370) # doctest: +ELLIPSIS
0.7247698...
"""
return eotf_inverse_ST2084(F_D, 10000)
[docs]
def ootf_BT2100_PQ(E: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* opto-optical
transfer function (OOTF).
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_BT2100_PQ(0.1) # doctest: +ELLIPSIS
779.9883608...
"""
E = as_float_array(E)
with domain_range_scale("ignore"):
return 100 * eotf_BT1886(oetf_BT709(59.5208 * E))
[docs]
def ootf_inverse_BT2100_PQ(F_D: ArrayLike) -> NDArrayFloat:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference PQ* inverse
opto-optical transfer function (OOTF).
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
:math:`E = \\{R_S, G_S, B_S; Y_S; or I_S\\}` denotes the signal
determined by scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_inverse_BT2100_PQ(779.988360834115840) # doctest: +ELLIPSIS
0.1000000...
"""
F_D = as_float_array(F_D)
with domain_range_scale("ignore"):
return oetf_inverse_BT709(eotf_inverse_BT1886(F_D / 100)) / 59.5208
WEIGHTS_BT2100_HLG: NDArrayFloat = np.array([0.2627, 0.6780, 0.0593])
"""Luminance weights for *Recommendation ITU-R BT.2100* *Reference HLG*."""
CONSTANTS_BT2100_HLG: Structure = Structure(
a=CONSTANTS_ARIBSTDB67.a,
b=1 - 4 * CONSTANTS_ARIBSTDB67.a,
c=0.5 - CONSTANTS_ARIBSTDB67.a * np.log(4 * CONSTANTS_ARIBSTDB67.a),
)
"""
*Recommendation ITU-R BT.2100* *Reference HLG* constants expressed in their
analytical form in contrast to the *ARIB STD-B67 (Hybrid Log-Gamma)* numerical
reference.
References
----------
:cite:`InternationalTelecommunicationUnion2017`
"""
def gamma_function_BT2100_HLG(L_W: float = 1000) -> float:
"""
Compute the *Reference HLG* system gamma value for the specified display
nominal peak luminance.
Parameters
----------
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
Returns
-------
:class:`float`
*Reference HLG* system gamma value.
Examples
--------
>>> gamma_function_BT2100_HLG()
1.2
>>> gamma_function_BT2100_HLG(2000) # doctest: +ELLIPSIS
1.3264325...
>>> gamma_function_BT2100_HLG(4000) # doctest: +ELLIPSIS
1.4528651...
"""
gamma = 1.2 + 0.42 * np.log10(L_W / 1000)
return as_float_scalar(gamma)
[docs]
def oetf_BT2100_HLG(E: Domain1, constants: Structure | None = None) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical
transfer function (OETF).
The OETF maps relative scene linear light into the non-linear *HLG* signal
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` is the resulting non-linear signal :math:`\\{R', G', B'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_BT2100_HLG(0.18 / 12) # doctest: +ELLIPSIS
0.2121320...
"""
E = as_float_array(E)
constants = optional(constants, CONSTANTS_BT2100_HLG)
return oetf_ARIBSTDB67(12 * E, constants=constants)
[docs]
def oetf_inverse_BT2100_HLG(E_p: Domain1, constants: Structure | None = None) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
opto-electrical transfer function (OETF).
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_inverse_BT2100_HLG(0.212132034355964) # doctest: +ELLIPSIS
0.0149999...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
return oetf_inverse_ARIBSTDB67(E_p, constants=constants) / 12
def black_level_lift_BT2100_HLG(
L_B: float = 0, L_W: float = 1000, gamma: float | None = None
) -> float:
"""
Compute the *Reference HLG* black level lift :math:`\\beta` for the
specified display luminance for black, nominal peak luminance, and system
gamma value.
Parameters
----------
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`float`
*Reference HLG* black level lift :math:`\\beta`.
Examples
--------
>>> black_level_lift_BT2100_HLG()
0.0
>>> black_level_lift_BT2100_HLG(0.01) # doctest: +ELLIPSIS
0.0142964...
>>> black_level_lift_BT2100_HLG(0.001, 2000) # doctest: +ELLIPSIS
0.0073009...
>>> black_level_lift_BT2100_HLG(0.01, gamma=1.4) # doctest: +ELLIPSIS
0.0283691...
"""
gamma = optional(gamma, gamma_function_BT2100_HLG(L_W))
beta = np.sqrt(3 * spow((L_B / L_W), 1 / gamma))
return as_float_scalar(beta)
def eotf_BT2100_HLG_1(
E_p: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF) as specified in *ITU-R BT.2100-1*.
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_BT2100_HLG_1(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_BT2100_HLG_1(0.212132034355964, 0.01) # doctest: +ELLIPSIS
6.4859750...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
return ootf_BT2100_HLG_1(
oetf_inverse_ARIBSTDB67(E_p, constants=constants) / 12, L_B, L_W, gamma
)
def eotf_BT2100_HLG_2(
E_p: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF) as specified in *ITU-R BT.2100-2* with
modified black level behaviour.
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_BT2100_HLG_2(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_BT2100_HLG_2(0.212132034355964, 0.01) # doctest: +ELLIPSIS
7.3321975...
"""
E_p = as_float_array(E_p)
constants = optional(constants, CONSTANTS_BT2100_HLG)
beta = black_level_lift_BT2100_HLG(L_B, L_W, gamma)
return ootf_BT2100_HLG_2(
oetf_inverse_ARIBSTDB67((1 - beta) * E_p + beta, constants=constants) / 12,
L_W,
gamma,
)
BT2100_HLG_EOTF_METHODS: CanonicalMapping = CanonicalMapping(
{
"ITU-R BT.2100-1": eotf_BT2100_HLG_1,
"ITU-R BT.2100-2": eotf_BT2100_HLG_2,
}
)
BT2100_HLG_EOTF_METHODS.__doc__ = """
Define supported *ITU-R BT.2100* *Reference HLG* electro-optical transfer
function (EOTF) methods.
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
"""
[docs]
def eotf_BT2100_HLG(
E_p: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
method: (Literal["ITU-R BT.2100-1", "ITU-R BT.2100-2"] | str) = "ITU-R BT.2100-2",
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG*
electro-optical transfer function (EOTF).
Parameters
----------
E_p
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
method
Computation method.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_BT2100_HLG(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_BT2100_HLG(0.212132034355964, method="ITU-R BT.2100-1")
... # doctest: +ELLIPSIS
6.4760398...
>>> eotf_BT2100_HLG(0.212132034355964, 0.01)
... # doctest: +ELLIPSIS
7.3321975...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
method = validate_method(method, tuple(BT2100_HLG_EOTF_METHODS))
return BT2100_HLG_EOTF_METHODS[method](E_p, L_B, L_W, gamma, constants)
def eotf_inverse_BT2100_HLG_1(
F_D: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF) as specified in
*ITU-R BT.2100-1*.
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_inverse_BT2100_HLG_1(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_BT2100_HLG_1(6.485975065251558, 0.01)
... # doctest: +ELLIPSIS
0.2121320...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
return oetf_ARIBSTDB67(
ootf_inverse_BT2100_HLG_1(F_D, L_B, L_W, gamma) * 12,
constants=constants,
)
def eotf_inverse_BT2100_HLG_2(
F_D: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF) as specified in *ITU-R BT.2100-2*
with modified black level behaviour.
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_inverse_BT2100_HLG_2(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_BT2100_HLG_2(7.332197528353875, 0.01)
... # doctest: +ELLIPSIS
0.2121320...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
beta = black_level_lift_BT2100_HLG(L_B, L_W, gamma)
return (
oetf_ARIBSTDB67(
ootf_inverse_BT2100_HLG_2(F_D, L_W, gamma) * 12,
constants=constants,
)
- beta
) / (1 - beta)
BT2100_HLG_EOTF_INVERSE_METHODS: CanonicalMapping = CanonicalMapping(
{
"ITU-R BT.2100-1": eotf_inverse_BT2100_HLG_1,
"ITU-R BT.2100-2": eotf_inverse_BT2100_HLG_2,
}
)
BT2100_HLG_EOTF_INVERSE_METHODS.__doc__ = """
Define the supported *ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF) methods.
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
"""
[docs]
def eotf_inverse_BT2100_HLG(
F_D: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
constants: Structure | None = None,
method: (Literal["ITU-R BT.2100-1", "ITU-R BT.2100-2"] | str) = "ITU-R BT.2100-2",
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF).
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
constants
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
method
Computation method.
Returns
-------
:class:`numpy.ndarray`
:math:`E'` denotes the non-linear signal :math:`\\{R', G', B'\\}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_inverse_BT2100_HLG(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_BT2100_HLG(6.476039825649814, method="ITU-R BT.2100-1")
... # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_BT2100_HLG(7.332197528353875, 0.01) # doctest: +ELLIPSIS
0.2121320...
"""
constants = optional(constants, CONSTANTS_BT2100_HLG)
method = validate_method(method, tuple(BT2100_HLG_EOTF_INVERSE_METHODS))
return BT2100_HLG_EOTF_INVERSE_METHODS[method](F_D, L_B, L_W, gamma, constants)
def ootf_BT2100_HLG_1(
E: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG*
opto-optical transfer function
(OOTF) as specified in *ITU-R BT.2100-1*.
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_BT2100_HLG_1(0.1) # doctest: +ELLIPSIS
63.0957344...
>>> ootf_BT2100_HLG_1(0.1, 0.01)
... # doctest: +ELLIPSIS
63.1051034...
"""
E = to_domain_1(E)
is_single_channel = np.atleast_1d(E).shape[-1] != 3
if is_single_channel:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
"RGB Luminance in computations and expects a vector input, thus "
"the specified input array will be stacked to compose a vector for "
"internal computations but a single component will be output."
)
R_S = G_S = B_S = E
else:
R_S, G_S, B_S = tsplit(E)
alpha = L_W - L_B
beta = L_B
Y_S = np.sum(WEIGHTS_BT2100_HLG * tstack([R_S, G_S, B_S]), axis=-1)
gamma = optional(gamma, gamma_function_BT2100_HLG(L_W))
R_D = alpha * R_S * np.abs(Y_S) ** (gamma - 1) + beta
G_D = alpha * G_S * np.abs(Y_S) ** (gamma - 1) + beta
B_D = alpha * B_S * np.abs(Y_S) ** (gamma - 1) + beta
if is_single_channel:
return as_float(from_range_1(R_D))
RGB_D = tstack([R_D, G_D, B_D])
return from_range_1(RGB_D)
def ootf_BT2100_HLG_2(
E: Domain1,
L_W: float = 1000,
gamma: float | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical
transfer function (OOTF) as specified in *ITU-R BT.2100-2*.
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_BT2100_HLG_2(0.1) # doctest: +ELLIPSIS
63.0957344...
"""
E = to_domain_1(E)
is_single_channel = np.atleast_1d(E).shape[-1] != 3
if is_single_channel:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
"RGB Luminance in computations and expects a vector input, thus "
"the specified input array will be stacked to compose a vector for "
"internal computations but a single component will be output."
)
R_S = G_S = B_S = E
else:
R_S, G_S, B_S = tsplit(E)
alpha = L_W
Y_S = np.sum(WEIGHTS_BT2100_HLG * tstack([R_S, G_S, B_S]), axis=-1)
gamma = optional(gamma, gamma_function_BT2100_HLG(L_W))
R_D = alpha * R_S * np.abs(Y_S) ** (gamma - 1)
G_D = alpha * G_S * np.abs(Y_S) ** (gamma - 1)
B_D = alpha * B_S * np.abs(Y_S) ** (gamma - 1)
if is_single_channel:
return as_float(from_range_1(R_D))
RGB_D = tstack([R_D, G_D, B_D])
return from_range_1(RGB_D)
BT2100_HLG_OOTF_METHODS: CanonicalMapping = CanonicalMapping(
{
"ITU-R BT.2100-1": ootf_BT2100_HLG_1,
"ITU-R BT.2100-2": ootf_BT2100_HLG_2,
}
)
BT2100_HLG_OOTF_METHODS.__doc__ = """
Map *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical transfer
function (OOTF) methods.
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
"""
[docs]
def ootf_BT2100_HLG(
E: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
method: (Literal["ITU-R BT.2100-1", "ITU-R BT.2100-2"] | str) = "ITU-R BT.2100-2",
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical
transfer function (OOTF).
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2`
for achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_BT2100_HLG(0.1) # doctest: +ELLIPSIS
63.0957344...
>>> ootf_BT2100_HLG(0.1, 0.01, method="ITU-R BT.2100-1")
... # doctest: +ELLIPSIS
63.1051034...
"""
method = validate_method(method, tuple(BT2100_HLG_OOTF_METHODS))
function = BT2100_HLG_OOTF_METHODS[method]
return function(
E,
**filter_kwargs(function, L_B=L_B, L_W=L_W, gamma=gamma),
)
def ootf_inverse_BT2100_HLG_1(
F_D: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
opto-optical transfer function (OOTF) as defined in *ITU-R BT.2100-1*.
The inverse OOTF maps display linear light to relative scene linear light.
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
:math:`E = \\{R_S, G_S, B_S; Y_S; \\text{or } I_S\\}` denotes the
signal determined by scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_inverse_BT2100_HLG_1(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
>>> ootf_inverse_BT2100_HLG_1(63.105103490674857, 0.01)
... # doctest: +ELLIPSIS
0.0999999...
"""
F_D = to_domain_1(F_D)
is_single_channel = np.atleast_1d(F_D).shape[-1] != 3
if is_single_channel:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
"RGB Luminance in computations and expects a vector input, thus "
"the specified input array will be stacked to compose a vector for "
"internal computations but a single component will be output."
)
R_D = G_D = B_D = F_D
else:
R_D, G_D, B_D = tsplit(F_D)
Y_D = np.sum(WEIGHTS_BT2100_HLG * tstack([R_D, G_D, B_D]), axis=-1)
alpha = L_W - L_B
beta = L_B
gamma = optional(gamma, gamma_function_BT2100_HLG(L_W))
Y_D_beta = np.abs((Y_D - beta) / alpha) ** ((1 - gamma) / gamma)
R_S = np.where(
beta == Y_D,
0.0,
Y_D_beta * (R_D - beta) / alpha,
)
G_S = np.where(
beta == Y_D,
0.0,
Y_D_beta * (G_D - beta) / alpha,
)
B_S = np.where(
beta == Y_D,
0.0,
Y_D_beta * (B_D - beta) / alpha,
)
if is_single_channel:
return as_float(from_range_1(R_S))
RGB_S = tstack([R_S, G_S, B_S])
return from_range_1(RGB_S)
def ootf_inverse_BT2100_HLG_2(
F_D: Domain1,
L_W: float = 1000,
gamma: float | None = None,
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
opto-optical transfer function (OOTF) according to *ITU-R BT.2100-2*.
The inverse OOTF maps display linear light to relative scene linear light.
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
Returns
-------
:class:`numpy.ndarray`
:math:`E` denotes the signal for each colour component
:math:`\\{R_S, G_S, B_S\\}` proportional to scene linear light and
scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_inverse_BT2100_HLG_2(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
"""
F_D = to_domain_1(F_D)
is_single_channel = np.atleast_1d(F_D).shape[-1] != 3
if is_single_channel:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
"RGB Luminance in computations and expects a vector input, thus "
"the specified input array will be stacked to compose a vector for "
"internal computations but a single component will be output."
)
R_D = G_D = B_D = F_D
else:
R_D, G_D, B_D = tsplit(F_D)
Y_D = np.sum(WEIGHTS_BT2100_HLG * tstack([R_D, G_D, B_D]), axis=-1)
alpha = L_W
gamma = optional(gamma, gamma_function_BT2100_HLG(L_W))
Y_D_alpha = np.abs(Y_D / alpha) ** ((1 - gamma) / gamma)
R_S = np.where(
Y_D == 0,
0.0,
Y_D_alpha * R_D / alpha,
)
G_S = np.where(
Y_D == 0,
0.0,
Y_D_alpha * G_D / alpha,
)
B_S = np.where(
Y_D == 0,
0.0,
Y_D_alpha * B_D / alpha,
)
if is_single_channel:
return as_float(from_range_1(R_S))
RGB_S = tstack([R_S, G_S, B_S])
return from_range_1(RGB_S)
BT2100_HLG_OOTF_INVERSE_METHODS: CanonicalMapping = CanonicalMapping(
{
"ITU-R BT.2100-1": ootf_inverse_BT2100_HLG_1,
"ITU-R BT.2100-2": ootf_inverse_BT2100_HLG_2,
}
)
BT2100_HLG_OOTF_INVERSE_METHODS.__doc__ = """
Support methods for the *ITU-R BT.2100* *Reference HLG* inverse
opto-optical transfer function (OOTF).
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
"""
[docs]
def ootf_inverse_BT2100_HLG(
F_D: Domain1,
L_B: float = 0,
L_W: float = 1000,
gamma: float | None = None,
method: (Literal["ITU-R BT.2100-1", "ITU-R BT.2100-2"] | str) = "ITU-R BT.2100-2",
) -> Range1:
"""
Apply the *Recommendation ITU-R BT.2100* *Reference HLG* inverse
opto-optical transfer function (OOTF).
The inverse OOTF maps display linear light to relative scene linear light.
Parameters
----------
F_D
Luminance :math:`F_D` of a displayed linear component
:math:`\\{R_D, G_D, B_D\\}` or :math:`Y_D` or :math:`I_D`, in
:math:`cd/m^2`.
L_B
Display luminance for black :math:`L_B` in :math:`cd/m^2`.
L_W
Nominal peak luminance :math:`L_W` of the display in :math:`cd/m^2` for
achromatic pixels.
gamma
System gamma value, defaults to 1.2 at the nominal display peak
luminance of :math:`1000 cd/m^2`.
method
Computation method.
Returns
-------
:class:`numpy.ndarray`
:math:`E` denotes the signal for each colour component
:math:`\\{R_S, G_S, B_S\\}` proportional to scene linear light and
scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | 1 | 1 |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | 1 | 1 |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_inverse_BT2100_HLG(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
>>> ootf_inverse_BT2100_HLG(63.105103490674857, 0.01, method="ITU-R BT.2100-1")
... # doctest: +ELLIPSIS
0.0999999...
"""
method = validate_method(method, tuple(BT2100_HLG_OOTF_INVERSE_METHODS))
function = BT2100_HLG_OOTF_INVERSE_METHODS[method]
return function(
F_D,
**filter_kwargs(function, L_B=L_B, L_W=L_W, gamma=gamma),
)
