Source code for colour.models.rgb.transfer_functions.st_2084

"""
SMPTE ST 2084:2014
==================

Defines the *SMPTE ST 2084:2014* opto-electrical transfer function
(OETF) and electro-optical transfer function (EOTF):

-   :func:`colour.models.eotf_ST2084`
-   :func:`colour.models.eotf_inverse_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 numpy as np

from colour.algebra import spow
from colour.hints import Floating, FloatingOrArrayLike, FloatingOrNDArray
from colour.utilities import Structure, as_float_array, as_float

__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 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__ = [
    "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: FloatingOrArrayLike, L_p: Floating = 10000, constants: Structure = CONSTANTS_ST2084, ) -> FloatingOrNDArray: """ Define *SMPTE ST 2084:2014* optimised perceptual 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 :math:`cd/m^2`, this parameter should stay at its default :math:`10000 cd/m^2` value for practical applications. It is exposed so that the definition can be used as a fitting function. constants *SMPTE ST 2084:2014* constants. Returns ------- :class:`numpy.floating` or :class:`numpy.ndarray` Color value abbreviated as :math:`N`, that is directly proportional to the encoded signal representation, and which is 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 *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) 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: FloatingOrArrayLike, L_p: Floating = 10000, constants: Structure = CONSTANTS_ST2084, ) -> FloatingOrNDArray: """ Define *SMPTE ST 2084:2014* optimised perceptual electro-optical transfer function (EOTF). This perceptual quantizer (PQ) has been modeled by Dolby Laboratories using *Barten (1999)* contrast sensitivity function. Parameters ---------- N Color value abbreviated as :math:`N`, that is directly proportional to the encoded signal representation, and which is not directly proportional to the optical output of a display device. L_p System peak luminance :math:`cd/m^2`, this parameter should stay at its default :math:`10000 cd/m^2` value for practical applications. It is exposed so that the definition can be used as a fitting function. constants *SMPTE ST 2084:2014* constants. Returns ------- :class:`numpy.floating` or :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) 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)