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

# -*- coding: utf-8 -*-
"""
ITU-R BT.2020
=============

Defines *ITU-R BT.2020* opto-electrical transfer function (OETF / OECF) and
electro-optical transfer function (EOTF / EOCF):

-   :func:`colour.models.eotf_inverse_BT2020`
-   :func:`colour.models.eotf_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 division, unicode_literals

import numpy as np

from colour.algebra import spow
from colour.utilities import (Structure, as_float, domain_range_scale,
                              from_range_1, to_domain_1)

__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__ = [
    'BT2020_CONSTANTS', 'BT2020_CONSTANTS_PRECISE', 'eotf_inverse_BT2020',
    'eotf_BT2020'
]

BT2020_CONSTANTS = 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.

BT2020_CONSTANTS : Structure
"""

BT2020_CONSTANTS_PRECISE = 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`

BT2020_CONSTANTS_PRECISE : Structure
"""


[docs]def eotf_inverse_BT2020(E, is_12_bits_system=False, constants=BT2020_CONSTANTS): """ Defines *Recommendation ITU-R BT.2020* inverse electro-optical transfer function (EOTF / EOCF). Parameters ---------- E : numeric or array_like 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 : bool, optional *BT.709* *alpha* and *beta* constants are used if system is not 12-bit. constants : Structure, optional *Recommendation ITU-R BT.2020* constants. Returns ------- numeric or 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 -------- >>> eotf_inverse_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 eotf_BT2020(E_p, is_12_bits_system=False, constants=BT2020_CONSTANTS): """ Defines *Recommendation ITU-R BT.2020* electro-optical transfer function (EOTF / EOCF). Parameters ---------- E_p : numeric or array_like Non-linear signal :math:`E'`. is_12_bits_system : bool, optional *BT.709* *alpha* and *beta* constants are used if system is not 12-bit. constants : Structure, optional *Recommendation ITU-R BT.2020* constants. Returns ------- numeric or 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 -------- >>> eotf_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 < eotf_inverse_BT2020(b), E_p / 4.5, spow((E_p + (a - 1)) / a, 1 / 0.45), ) return as_float(from_range_1(E))