Source code for colour.models.rgb.transfer_functions.itur_bt_2020

"""
ITU-R BT.2020
=============

Defines the *ITU-R BT.2020* opto-electrical transfer function (OETF) and its
inverse:

-   :func:`colour.models.oetf_BT2020`
-   :func:`colour.models.oetf_inverse_BT2020`

References
----------
-   :cite:`InternationalTelecommunicationUnion2015h` : International
    Telecommunication Union. (2015). Recommendation ITU-R BT.2020 - Parameter
    values for ultra-high definition television systems for production and
    international programme exchange (pp. 1-8).
    https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2020-2-201510-I!!PDF-E.pdf
"""

from __future__ import annotations

import numpy as np

from colour.algebra import spow
from colour.hints import Boolean, FloatingOrArrayLike, FloatingOrNDArray
from colour.utilities import (
    Structure,
    as_float,
    domain_range_scale,
    from_range_1,
    to_domain_1,
)

__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_BT2020",
    "CONSTANTS_BT2020_PRECISE",
    "oetf_BT2020",
    "oetf_inverse_BT2020",
]

CONSTANTS_BT2020: Structure = Structure(
    alpha=lambda x: 1.0993 if x else 1.099,
    beta=lambda x: 0.0181 if x else 0.018,
)
"""*BT.2020* colourspace constants."""

CONSTANTS_BT2020_PRECISE: Structure = Structure(
    alpha=lambda x: 1.09929682680944, beta=lambda x: 0.018053968510807
)
"""
*BT.2020* colourspace constants at double precision to connect the two curve
segments smoothly.

References
----------
:cite:`InternationalTelecommunicationUnion2015h`
"""


[docs]def oetf_BT2020( E: FloatingOrArrayLike, is_12_bits_system: Boolean = False, constants: Structure = CONSTANTS_BT2020, ) -> FloatingOrNDArray: """ Define *Recommendation ITU-R BT.2020* opto-electronic transfer function (OETF). Parameters ---------- E Voltage :math:`E` normalised by the reference white level and proportional to the implicit light intensity that would be detected with a reference camera colour channel R, G, B. is_12_bits_system *BT.709* *alpha* and *beta* constants are used if system is not 12-bit. constants *Recommendation ITU-R BT.2020* constants. Returns ------- :class:`numpy.floating` or :class:`numpy.ndarray` Resulting non-linear signal :math:`E'`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`InternationalTelecommunicationUnion2015h` Examples -------- >>> oetf_BT2020(0.18) # doctest: +ELLIPSIS 0.4090077... """ E = to_domain_1(E) a = constants.alpha(is_12_bits_system) b = constants.beta(is_12_bits_system) E_p = np.where(E < b, E * 4.5, a * spow(E, 0.45) - (a - 1)) return as_float(from_range_1(E_p))
[docs]def oetf_inverse_BT2020( E_p: FloatingOrArrayLike, is_12_bits_system: Boolean = False, constants: Structure = CONSTANTS_BT2020, ) -> FloatingOrNDArray: """ Define *Recommendation ITU-R BT.2020* inverse opto-electronic transfer function (OETF). Parameters ---------- E_p Non-linear signal :math:`E'`. is_12_bits_system *BT.709* *alpha* and *beta* constants are used if system is not 12-bit. constants *Recommendation ITU-R BT.2020* constants. Returns ------- :class:`numpy.floating` or :class:`numpy.ndarray` Resulting voltage :math:`E`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`InternationalTelecommunicationUnion2015h` Examples -------- >>> oetf_inverse_BT2020(0.705515089922121) # doctest: +ELLIPSIS 0.4999999... """ E_p = to_domain_1(E_p) a = constants.alpha(is_12_bits_system) b = constants.beta(is_12_bits_system) with domain_range_scale("ignore"): E = np.where( E_p < oetf_BT2020(b), E_p / 4.5, spow((E_p + (a - 1)) / a, 1 / 0.45), ) return as_float(from_range_1(E))