Source code for colour.models.rgb.transfer_functions.st_2084
"""
SMPTE ST 2084:2014
==================
Define the *SMPTE ST 2084:2014* electro-optical transfer function (EOTF) and
its inverse.
- :func:`colour.models.eotf_inverse_ST2084`
- :func:`colour.models.eotf_ST2084`
References
----------
- :cite:`Miller2014a` : Miller, S. (2014). A Perceptual EOTF for Extended
Dynamic Range Imagery (pp. 1-17).
https://www.smpte.org/sites/default/files/\
2014-05-06-EOTF-Miller-1-2-handout.pdf
- :cite:`SocietyofMotionPictureandTelevisionEngineers2014a` : Society of
Motion Picture and Television Engineers. (2014). SMPTE ST 2084:2014 -
Dynamic Range Electro-Optical Transfer Function of Mastering Reference
Displays (pp. 1-14). doi:10.5594/SMPTE.ST2084.2014
"""
from __future__ import annotations
import typing
import numpy as np
from colour.algebra import spow
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import Structure, as_float, as_float_array, optional
__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__ = [
"CONSTANTS_ST2084",
"eotf_inverse_ST2084",
"eotf_ST2084",
]
CONSTANTS_ST2084: Structure = Structure(
m_1=2610 / 4096 * (1 / 4),
m_2=2523 / 4096 * 128,
c_1=3424 / 4096,
c_2=2413 / 4096 * 32,
c_3=2392 / 4096 * 32,
)
"""
Constants for *SMPTE ST 2084:2014* inverse electro-optical transfer function
(EOTF) and electro-optical transfer function (EOTF).
"""
[docs]
def eotf_inverse_ST2084(
C: ArrayLike,
L_p: float = 10000,
constants: Structure | None = None,
) -> NDArrayFloat:
"""
Apply the *SMPTE ST 2084:2014* perceptual quantizer (PQ) inverse
electro-optical transfer function (EOTF).
Parameters
----------
C
Target optical output :math:`C` in :math:`cd/m^2` of the ideal
reference display.
L_p
System peak luminance in :math:`cd/m^2`. This parameter should remain
at its default value of :math:`10000 cd/m^2` for practical
applications. It is exposed to enable the definition's use as a
fitting function.
constants
*SMPTE ST 2084:2014* constants.
Returns
-------
:class:`numpy.ndarray`
Colour value abbreviated as :math:`N`, directly proportional to the
encoded signal representation and not directly proportional to the
optical output of a display device.
Warnings
--------
*SMPTE ST 2084:2014* is an absolute transfer function.
Notes
-----
- *SMPTE ST 2084:2014* is an absolute transfer function; thus, the
domain and range values for the *Reference* and *1* scales are only
indicative that the data is not affected by scale transformations.
The effective domain of the *SMPTE ST 2084:2014* inverse
electro-optical transfer function (EOTF) is [0.0001, 10000].
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``C`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``N`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Miller2014a`,
:cite:`SocietyofMotionPictureandTelevisionEngineers2014a`
Examples
--------
>>> eotf_inverse_ST2084(100) # doctest: +ELLIPSIS
0.5080784...
"""
C = as_float_array(C)
constants = optional(constants, CONSTANTS_ST2084)
c_1 = constants.c_1
c_2 = constants.c_2
c_3 = constants.c_3
m_1 = constants.m_1
m_2 = constants.m_2
Y_p = spow(C / L_p, m_1)
N = spow((c_1 + c_2 * Y_p) / (c_3 * Y_p + 1), m_2)
return as_float(N)
[docs]
def eotf_ST2084(
N: ArrayLike,
L_p: float = 10000,
constants: Structure | None = None,
) -> NDArrayFloat:
"""
Apply the *SMPTE ST 2084:2014* perceptual quantizer (PQ) electro-optical
transfer function (EOTF).
Parameters
----------
N
Colour value abbreviated as :math:`N`, directly proportional to the
encoded signal representation and not directly proportional to the
optical output of a display device.
L_p
System peak luminance in :math:`cd/m^2`. This parameter should remain
at its default value of :math:`10000 cd/m^2` for practical
applications. It is exposed to enable the definition's use as a
fitting function.
constants
*SMPTE ST 2084:2014* constants.
Returns
-------
:class:`numpy.ndarray`
Target optical output :math:`C` in :math:`cd/m^2` of the ideal
reference display.
Warnings
--------
*SMPTE ST 2084:2014* is an absolute transfer function.
Notes
-----
- *SMPTE ST 2084:2014* is an absolute transfer function, thus the
domain and range values for the *Reference* and *1* scales are only
indicative that the data is not affected by scale transformations.
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``N`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``C`` | ``UN`` | ``UN`` |
+------------+-----------------------+---------------+
References
----------
:cite:`Miller2014a`,
:cite:`SocietyofMotionPictureandTelevisionEngineers2014a`
Examples
--------
>>> eotf_ST2084(0.508078421517399) # doctest: +ELLIPSIS
100.0000000...
"""
N = as_float_array(N)
constants = optional(constants, CONSTANTS_ST2084)
c_1 = constants.c_1
c_2 = constants.c_2
c_3 = constants.c_3
m_1 = constants.m_1
m_2 = constants.m_2
m_1_d = 1 / m_1
m_2_d = 1 / m_2
V_p = spow(N, m_2_d)
n = np.maximum(0, V_p - c_1)
L = spow((n / (c_2 - c_3 * V_p)), m_1_d)
C = L_p * L
return as_float(C)
