# -*- coding: utf-8 -*-
"""
ITU-R BT.2100
=============
Defines *ITU-R BT.2100* opto-electrical transfer functions (OETF / OECF),
opto-optical transfer functions (OOTF / OOCF) and electro-optical transfer
functions (EOTF / EOCF) and their inverse:
- :func:`colour.models.oetf_PQ_BT2100`
- :func:`colour.models.oetf_inverse_PQ_BT2100`
- :func:`colour.models.eotf_PQ_BT2100`
- :func:`colour.models.eotf_inverse_PQ_BT2100`
- :func:`colour.models.ootf_PQ_BT2100`
- :func:`colour.models.ootf_inverse_PQ_BT2100`
- :func:`colour.models.oetf_HLG_BT2100`
- :func:`colour.models.oetf_inverse_HLG_BT2100`
- :func:`colour.models.eotf_HLG_BT2100_1`
- :func:`colour.models.eotf_HLG_BT2100_2`
- :attr:`colour.models.BT2100_HLG_EOTF_METHODS`
- :func:`colour.models.eotf_HLG_BT2100`
- :func:`colour.models.eotf_inverse_HLG_BT2100_1`
- :func:`colour.models.eotf_inverse_HLG_BT2100_2`
- :attr:`colour.models.BT2100_HLG_EOTF_INVERSE_METHODS`
- :func:`colour.models.eotf_inverse_HLG_BT2100`
- :func:`colour.models.ootf_HLG_BT2100`
- :func:`colour.models.ootf_inverse_HLG_BT2100`
- :func:`colour.models.ootf_HLG_BT2100_1`
- :func:`colour.models.ootf_HLG_BT2100_2`
- :attr:`colour.models.BT2100_HLG_OOTF_METHODS`
- :func:`colour.models.ootf_HLG_BT2100`
- :func:`colour.models.ootf_inverse_HLG_BT2100_1`
- :func:`colour.models.ootf_inverse_HLG_BT2100_2`
- :attr:`colour.models.BT2100_HLG_OOTF_INVERSE_METHODS`
- :func:`colour.models.ootf_inverse_HLG_BT2100`
See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_
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. Retrieved from
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. Retrieved from
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2100-2-201807-I!!PDF-E.pdf
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import spow
from colour.models.rgb.transfer_functions import (
eotf_BT1886, eotf_ST2084, eotf_inverse_BT1886, oetf_ARIBSTDB67, oetf_BT709,
eotf_inverse_ST2084, oetf_inverse_ARIBSTDB67, oetf_inverse_BT709)
from colour.models.rgb.transfer_functions.arib_std_b67 import (
ARIBSTDB67_CONSTANTS)
from colour.utilities import (
CaseInsensitiveMapping, Structure, as_float_array, as_float, filter_kwargs,
from_range_1, to_domain_1, tsplit, tstack, usage_warning)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - Colour Developers'
__license__ = 'New BSD License - https://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-developers@colour-science.org'
__status__ = 'Production'
__all__ = [
'oetf_PQ_BT2100', 'oetf_inverse_PQ_BT2100', 'eotf_PQ_BT2100',
'eotf_inverse_PQ_BT2100', 'ootf_PQ_BT2100', 'ootf_inverse_PQ_BT2100',
'BT2100_HLG_WEIGHTS', 'BT2100_HLG_CONSTANTS', 'gamma_function_HLG_BT2100',
'oetf_HLG_BT2100', 'oetf_inverse_HLG_BT2100',
'black_level_lift_HLG_BT2100', 'eotf_HLG_BT2100_1', 'eotf_HLG_BT2100_2',
'BT2100_HLG_EOTF_METHODS', 'eotf_HLG_BT2100', 'eotf_inverse_HLG_BT2100_1',
'eotf_inverse_HLG_BT2100_2', 'BT2100_HLG_EOTF_INVERSE_METHODS',
'eotf_inverse_HLG_BT2100', 'ootf_HLG_BT2100_1', 'ootf_HLG_BT2100_2',
'BT2100_HLG_OOTF_METHODS', 'ootf_HLG_BT2100', 'ootf_inverse_HLG_BT2100_1',
'ootf_inverse_HLG_BT2100_2', 'BT2100_HLG_OOTF_INVERSE_METHODS',
'ootf_inverse_HLG_BT2100'
]
[docs]def oetf_PQ_BT2100(E):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* opto-electrical
transfer function (OETF / OECF).
The OETF maps relative scene linear light into the non-linear *PQ* signal
value.
Parameters
----------
E : numeric or array_like
:math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by
scene light and scaled by camera exposure.
Returns
-------
numeric or ndarray
:math:`E'` is the resulting non-linear signal (:math:`R'`, :math:`G'`,
:math:`B'`).
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_PQ_BT2100(0.1) # doctest: +ELLIPSIS
0.7247698...
"""
return eotf_inverse_ST2084(ootf_PQ_BT2100(E), 10000)
[docs]def oetf_inverse_PQ_BT2100(E_p):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* inverse
opto-electrical transfer function (OETF / OECF).
Parameters
----------
E_p : numeric or array_like
:math:`E'` is the resulting non-linear signal (:math:`R'`, :math:`G'`,
:math:`B'`).
Returns
-------
numeric or ndarray
:math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by
scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_inverse_PQ_BT2100(0.724769816665726) # doctest: +ELLIPSIS
0.0999999...
"""
return ootf_inverse_PQ_BT2100(eotf_ST2084(E_p, 10000))
[docs]def eotf_PQ_BT2100(E_p):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* electro-optical
transfer function (EOTF / EOCF).
The EOTF maps the non-linear *PQ* signal into display light.
Parameters
----------
E_p : numeric or array_like
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *PQ* space [0, 1].
Returns
-------
numeric or ndarray
:math:`F_D` is the luminance 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_PQ_BT2100(0.724769816665726) # doctest: +ELLIPSIS
779.9883608...
"""
return eotf_ST2084(E_p, 10000)
[docs]def eotf_inverse_PQ_BT2100(F_D):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* inverse
electro-optical transfer function (EOTF / EOCF).
Parameters
----------
F_D : numeric or array_like
:math:`F_D` is the luminance 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
-------
numeric or ndarray
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *PQ* space [0, 1].
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_inverse_PQ_BT2100(779.988360834085370) # doctest: +ELLIPSIS
0.7247698...
"""
return eotf_inverse_ST2084(F_D, 10000)
[docs]def ootf_PQ_BT2100(E):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* opto-optical transfer
function (OOTF / OOCF).
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E : numeric or array_like
:math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by
scene light and scaled by camera exposure.
Returns
-------
numeric or ndarray
:math:`F_D` is the luminance of a displayed linear component
(:math:`R_D`, :math:`G_D`, :math:`B_D`; :math:`Y_D`; or :math:`I_D`).
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_PQ_BT2100(0.1) # doctest: +ELLIPSIS
779.9883608...
"""
E = as_float_array(E)
return 100 * eotf_BT1886(oetf_BT709(59.5208 * E))
[docs]def ootf_inverse_PQ_BT2100(F_D):
"""
Defines *Recommendation ITU-R BT.2100* *Reference PQ* inverse opto-optical
transfer function (OOTF / OOCF).
Parameters
----------
F_D : numeric or array_like
:math:`F_D` is the luminance of a displayed linear component
(:math:`R_D`, :math:`G_D`, :math:`B_D`; :math:`Y_D`; or :math:`I_D`).
Returns
-------
numeric or ndarray
:math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by
scene light and scaled by camera exposure.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_inverse_PQ_BT2100(779.988360834115840) # doctest: +ELLIPSIS
0.1000000...
"""
F_D = as_float_array(F_D)
return oetf_inverse_BT709(eotf_inverse_BT1886(F_D / 100)) / 59.5208
BT2100_HLG_WEIGHTS = np.array([0.2627, 0.6780, 0.0593])
"""
Luminance weights for *Recommendation ITU-R BT.2100* *Reference HLG*.
BT2100_HLG_WEIGHTS : ndarray
"""
BT2100_HLG_CONSTANTS = Structure(
a=ARIBSTDB67_CONSTANTS.a,
b=1 - 4 * ARIBSTDB67_CONSTANTS.a,
c=0.5 - ARIBSTDB67_CONSTANTS.a * np.log(4 * ARIBSTDB67_CONSTANTS.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`
BT2100_HLG_CONSTANTS : Structure
"""
def gamma_function_HLG_BT2100(L_W=1000):
"""
Returns the *Reference HLG* system gamma value for given display nominal
peak luminance.
Parameters
----------
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
Returns
-------
numeric
*Reference HLG* system gamma value.
Examples
--------
>>> gamma_function_HLG_BT2100()
1.2
>>> gamma_function_HLG_BT2100(2000) # doctest: +ELLIPSIS
1.3264325...
>>> gamma_function_HLG_BT2100(4000) # doctest: +ELLIPSIS
1.4528651...
"""
gamma = 1.2 + 0.42 * np.log10(L_W / 1000)
return gamma
[docs]def oetf_HLG_BT2100(E, constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical
transfer function (OETF / OECF).
The OETF maps relative scene linear light into the non-linear *HLG* signal
value.
Parameters
----------
E : numeric or array_like
:math:`E` is the signal for each colour component
:math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled
by camera exposure.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or ndarray
:math:`E'` is the resulting non-linear signal :math:`{R', G', B'}`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_HLG_BT2100(0.18 / 12) # doctest: +ELLIPSIS
0.2121320...
"""
return oetf_ARIBSTDB67(12 * E, constants=constants)
[docs]def oetf_inverse_HLG_BT2100(E_p, constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse
opto-electrical transfer function (OETF / OECF).
Parameters
----------
E_p : numeric or array_like
:math:`E'` is the resulting non-linear signal :math:`{R', G', B'}`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or ndarray
:math:`E` is 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** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> oetf_inverse_HLG_BT2100(0.212132034355964) # doctest: +ELLIPSIS
0.0149999...
"""
return oetf_inverse_ARIBSTDB67(E_p, constants=constants) / 12
def black_level_lift_HLG_BT2100(L_B=0, L_W=1000, gamma=None):
"""
Returns the *Reference HLG* black level lift :math:`\\Beta` for given
display luminance for black, nominal peak luminance and system gamma value.
Parameters
----------
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
Returns
-------
numeric
*Reference HLG* black level lift :math:`\\Beta`.
Examples
--------
>>> black_level_lift_HLG_BT2100()
0.0
>>> black_level_lift_HLG_BT2100(0.01) # doctest: +ELLIPSIS
0.0142964...
>>> black_level_lift_HLG_BT2100(0.001, 2000) # doctest: +ELLIPSIS
0.0073009...
>>> black_level_lift_HLG_BT2100(0.01, gamma=1.4) # doctest: +ELLIPSIS
0.0283691...
"""
if gamma is None:
gamma = gamma_function_HLG_BT2100(L_W)
beta = np.sqrt(3 * spow((L_B / L_W), 1 / gamma))
return beta
def eotf_HLG_BT2100_1(E_p,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF / EOCF) as given in *ITU-R BT.2100-1*.
The EOTF maps the non-linear *HLG* signal into display light.
Parameters
----------
E_p : numeric or array_like
:math:`E'` is the non-linear signal :math:`{R', G', B'}` as defined for
the OETF.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_HLG_BT2100_1(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_HLG_BT2100_1(0.212132034355964, 0.01) # doctest: +ELLIPSIS
6.4859750...
"""
return ootf_HLG_BT2100_1(
oetf_inverse_ARIBSTDB67(E_p, constants=constants) / 12, L_B, L_W,
gamma)
def eotf_HLG_BT2100_2(E_p,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF / EOCF) as given in *ITU-R BT.2100-2* with the
modified black level behaviour.
The EOTF maps the non-linear *HLG* signal into display light.
Parameters
----------
E_p : numeric or array_like
:math:`E'` is the non-linear signal :math:`{R', G', B'}` as defined for
the *HLG Reference* OETF.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_HLG_BT2100_2(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_HLG_BT2100_2(0.212132034355964, 0.01) # doctest: +ELLIPSIS
7.3321975...
"""
beta = black_level_lift_HLG_BT2100(L_B, L_W, gamma)
return ootf_HLG_BT2100_2(
oetf_inverse_ARIBSTDB67(
(1 - beta) * E_p + beta, constants=constants) / 12, L_W, gamma)
BT2100_HLG_EOTF_METHODS = CaseInsensitiveMapping({
'ITU-R BT.2100-1': eotf_HLG_BT2100_1,
'ITU-R BT.2100-2': eotf_HLG_BT2100_2,
})
BT2100_HLG_EOTF_METHODS.__doc__ = """
Supported *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF / EOCF).
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
BT2100_HLG_EOTF_METHODS : CaseInsensitiveMapping
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**
"""
[docs]def eotf_HLG_BT2100(E_p,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS,
method='ITU-R BT.2100-2'):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical
transfer function (EOTF / EOCF).
The EOTF maps the non-linear *HLG* signal into display light.
Parameters
----------
E_p : numeric or array_like
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *HLG* space.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
method : unicode, optional
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**,
Computation method.
Returns
-------
numeric or 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_HLG_BT2100(0.212132034355964) # doctest: +ELLIPSIS
6.4760398...
>>> eotf_HLG_BT2100(0.212132034355964, method='ITU-R BT.2100-1')
... # doctest: +ELLIPSIS
6.4760398...
>>> eotf_HLG_BT2100(0.212132034355964, 0.01)
... # doctest: +ELLIPSIS
7.3321975...
"""
return BT2100_HLG_EOTF_METHODS[method](E_p, L_B, L_W, gamma, constants)
def eotf_inverse_HLG_BT2100_1(F_D,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF / EOCF) as given in
*ITU-R BT.2100-1*.
Parameters
----------
F_D : numeric or array_like
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 : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or ndarray
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *HLG* space.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> eotf_inverse_HLG_BT2100_1(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_HLG_BT2100_1(6.485975065251558, 0.01)
... # doctest: +ELLIPSIS
0.2121320...
"""
return oetf_ARIBSTDB67(
ootf_inverse_HLG_BT2100_1(F_D, L_B, L_W, gamma) * 12,
constants=constants)
def eotf_inverse_HLG_BT2100_2(F_D,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF / EOCF) as given in
*ITU-R BT.2100-2* with the modified black level behaviour.
Parameters
----------
F_D : numeric or array_like
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 : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
Returns
-------
numeric or ndarray
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *HLG* space.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_inverse_HLG_BT2100_2(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_HLG_BT2100_2(7.332197528353875, 0.01)
... # doctest: +ELLIPSIS
0.2121320...
"""
beta = black_level_lift_HLG_BT2100(L_B, L_W, gamma)
return (oetf_ARIBSTDB67(
ootf_inverse_HLG_BT2100_2(F_D, L_W, gamma) * 12, constants=constants) -
beta) / (1 - beta)
BT2100_HLG_EOTF_INVERSE_METHODS = CaseInsensitiveMapping({
'ITU-R BT.2100-1': eotf_inverse_HLG_BT2100_1,
'ITU-R BT.2100-2': eotf_inverse_HLG_BT2100_2,
})
BT2100_HLG_EOTF_INVERSE_METHODS.__doc__ = """
Supported *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF / EOCF).
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
BT2100_HLG_EOTF_INVERSE_METHODS : CaseInsensitiveMapping
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**
"""
[docs]def eotf_inverse_HLG_BT2100(F_D,
L_B=0,
L_W=1000,
gamma=None,
constants=BT2100_HLG_CONSTANTS,
method='ITU-R BT.2100-2'):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse
electro-optical transfer function (EOTF / EOCF).
Parameters
----------
F_D : numeric or array_like
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 : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
constants : Structure, optional
*Recommendation ITU-R BT.2100* *Reference HLG* constants.
method : unicode, optional
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**,
Computation method.
Returns
-------
numeric or ndarray
:math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or
:math:`{L', M', S'}` in *HLG* space.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> eotf_inverse_HLG_BT2100(6.476039825649814) # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_HLG_BT2100(6.476039825649814, method='ITU-R BT.2100-1')
... # doctest: +ELLIPSIS
0.2121320...
>>> eotf_inverse_HLG_BT2100(7.332197528353875, 0.01) # doctest: +ELLIPSIS
0.2121320...
"""
return BT2100_HLG_EOTF_INVERSE_METHODS[method](F_D, L_B, L_W, gamma,
constants)
def ootf_HLG_BT2100_1(E, L_B=0, L_W=1000, gamma=None):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical
transfer function (OOTF / OOCF) as given in *ITU-R BT.2100-1*.
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E : numeric or array_like
:math:`E` is the signal for each colour component
:math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled
by camera exposure.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
Returns
-------
numeric or ndarray
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_HLG_BT2100_1(0.1) # doctest: +ELLIPSIS
63.0957344...
>>> ootf_HLG_BT2100_1(0.1, 0.01)
... # doctest: +ELLIPSIS
63.1051034...
"""
E = np.atleast_1d(to_domain_1(E))
if E.shape[-1] != 3:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
'RGB Luminance in computations and expects a vector input, thus '
'the given 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(BT2100_HLG_WEIGHTS * tstack([R_S, G_S, B_S]), axis=-1)
if gamma is None:
gamma = gamma_function_HLG_BT2100(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 E.shape[-1] != 3:
return as_float(from_range_1(R_D))
else:
RGB_D = tstack([R_D, G_D, B_D])
return from_range_1(RGB_D)
def ootf_HLG_BT2100_2(E, L_W=1000, gamma=None):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical
transfer function (OOTF / OOCF) as given in *ITU-R BT.2100-2*.
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E : numeric or array_like
:math:`E` is the signal for each colour component
:math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled
by camera exposure.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
Returns
-------
numeric or ndarray
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_HLG_BT2100_2(0.1) # doctest: +ELLIPSIS
63.0957344...
"""
E = np.atleast_1d(to_domain_1(E))
if E.shape[-1] != 3:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
'RGB Luminance in computations and expects a vector input, thus '
'the given 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(BT2100_HLG_WEIGHTS * tstack([R_S, G_S, B_S]), axis=-1)
if gamma is None:
gamma = gamma_function_HLG_BT2100(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 E.shape[-1] != 3:
return as_float(from_range_1(R_D))
else:
RGB_D = tstack([R_D, G_D, B_D])
return from_range_1(RGB_D)
BT2100_HLG_OOTF_METHODS = CaseInsensitiveMapping({
'ITU-R BT.2100-1': ootf_HLG_BT2100_1,
'ITU-R BT.2100-2': ootf_HLG_BT2100_2,
})
BT2100_HLG_OOTF_METHODS.__doc__ = """
Supported *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical transfer
function (OOTF / OOCF).
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
BT2100_HLG_OOTF_METHODS : CaseInsensitiveMapping
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**
"""
[docs]def ootf_HLG_BT2100(E, L_B=0, L_W=1000, gamma=None, method='ITU-R BT.2100-2'):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical
transfer function (OOTF / OOCF).
The OOTF maps relative scene linear light to display linear light.
Parameters
----------
E : numeric or array_like
:math:`E` is the signal for each colour component
:math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled
by camera exposure.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
method : unicode, optional
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**,
Computation method.
Returns
-------
numeric or ndarray
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``F_D`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_HLG_BT2100(0.1) # doctest: +ELLIPSIS
63.0957344...
>>> ootf_HLG_BT2100(0.1, 0.01, method='ITU-R BT.2100-1')
... # doctest: +ELLIPSIS
63.1051034...
"""
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_HLG_BT2100_1(F_D, L_B=0, L_W=1000, gamma=None):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse opto-optical
transfer function (OOTF / OOCF) as given in *ITU-R BT.2100-1*.
Parameters
----------
F_D : numeric or array_like
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
Returns
-------
numeric or ndarray
:math:`E` is 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`
Examples
--------
>>> ootf_inverse_HLG_BT2100_1(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
>>> ootf_inverse_HLG_BT2100_1(63.105103490674857, 0.01)
... # doctest: +ELLIPSIS
0.0999999...
"""
F_D = np.atleast_1d(to_domain_1(F_D))
if F_D.shape[-1] != 3:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
'RGB Luminance in computations and expects a vector input, thus '
'the given 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(BT2100_HLG_WEIGHTS * tstack([R_D, G_D, B_D]), axis=-1)
alpha = L_W - L_B
beta = L_B
if gamma is None:
gamma = gamma_function_HLG_BT2100(L_W)
R_S = np.where(
Y_D == beta,
0.0,
(np.abs((Y_D - beta) / alpha) **
((1 - gamma) / gamma)) * (R_D - beta) / alpha,
)
G_S = np.where(
Y_D == beta,
0.0,
(np.abs((Y_D - beta) / alpha) **
((1 - gamma) / gamma)) * (G_D - beta) / alpha,
)
B_S = np.where(
Y_D == beta,
0.0,
(np.abs((Y_D - beta) / alpha) **
((1 - gamma) / gamma)) * (B_D - beta) / alpha,
)
if F_D.shape[-1] != 3:
return as_float(from_range_1(R_S))
else:
RGB_S = tstack([R_S, G_S, B_S])
return from_range_1(RGB_S)
def ootf_inverse_HLG_BT2100_2(F_D, L_W=1000, gamma=None):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse opto-optical
transfer function (OOTF / OOCF) as given in *ITU-R BT.2100-2*.
Parameters
----------
F_D : numeric or array_like
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
Returns
-------
numeric or ndarray
:math:`E` is 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_inverse_HLG_BT2100_2(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
"""
F_D = np.atleast_1d(to_domain_1(F_D))
if F_D.shape[-1] != 3:
usage_warning(
'"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses '
'RGB Luminance in computations and expects a vector input, thus '
'the given 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(BT2100_HLG_WEIGHTS * tstack([R_D, G_D, B_D]), axis=-1)
alpha = L_W
if gamma is None:
gamma = gamma_function_HLG_BT2100(L_W)
R_S = np.where(
Y_D == 0,
0.0,
(np.abs(Y_D / alpha) ** ((1 - gamma) / gamma)) * R_D / alpha,
)
G_S = np.where(
Y_D == 0,
0.0,
(np.abs(Y_D / alpha) ** ((1 - gamma) / gamma)) * G_D / alpha,
)
B_S = np.where(
Y_D == 0,
0.0,
(np.abs(Y_D / alpha) ** ((1 - gamma) / gamma)) * B_D / alpha,
)
if F_D.shape[-1] != 3:
return as_float(from_range_1(R_S))
else:
RGB_S = tstack([R_S, G_S, B_S])
return from_range_1(RGB_S)
BT2100_HLG_OOTF_INVERSE_METHODS = CaseInsensitiveMapping({
'ITU-R BT.2100-1': ootf_inverse_HLG_BT2100_1,
'ITU-R BT.2100-2': ootf_inverse_HLG_BT2100_2,
})
BT2100_HLG_OOTF_INVERSE_METHODS.__doc__ = """
Supported *Recommendation ITU-R BT.2100* *Reference HLG* inverse opto-optical
transfer function (OOTF / OOCF).
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
BT2100_HLG_OOTF_INVERSE_METHODS : CaseInsensitiveMapping
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**
"""
[docs]def ootf_inverse_HLG_BT2100(F_D,
L_B=0,
L_W=1000,
gamma=None,
method='ITU-R BT.2100-2'):
"""
Defines *Recommendation ITU-R BT.2100* *Reference HLG* inverse opto-optical
transfer function (OOTF / OOCF).
Parameters
----------
F_D : numeric or array_like
:math:`F_D` is the luminance of a displayed linear component
:math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`.
L_B : numeric, optional
:math:`L_B` is the display luminance for black in :math:`cd/m^2`.
L_W : numeric, optional
:math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2`
for achromatic pixels.
gamma : numeric, optional
System gamma value, 1.2 at the nominal display peak luminance of
:math:`1000 cd/m^2`.
method : unicode, optional
**{'ITU-R BT.2100-1', 'ITU-R BT.2100-2'}**,
Computation method.
Returns
-------
numeric or ndarray
:math:`E` is 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`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2017`,
:cite:`InternationalTelecommunicationUnion2018`
Examples
--------
>>> ootf_inverse_HLG_BT2100(63.095734448019336) # doctest: +ELLIPSIS
0.1000000...
>>> ootf_inverse_HLG_BT2100(
... 63.105103490674857, 0.01, method='ITU-R BT.2100-1')
... # doctest: +ELLIPSIS
0.0999999...
"""
function = BT2100_HLG_OOTF_INVERSE_METHODS[method]
return function(
F_D,
**filter_kwargs(function, **{
'L_B': L_B,
'L_W': L_W,
'gamma': gamma
}))