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

# -*- coding: utf-8 -*-
"""
SMPTE ST 2084:2014
==================

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

-   :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 division, unicode_literals

import numpy as np

from colour.algebra import spow
from colour.utilities import Structure, 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__ = ['CONSTANTS_ST2084', 'eotf_inverse_ST2084', 'eotf_ST2084']

CONSTANTS_ST2084 = 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 / EOCF) and electro-optical transfer function (EOTF / EOCF).

CONSTANTS_ST2084 : Structure
"""


[docs]def eotf_inverse_ST2084(C, L_p=10000, constants=CONSTANTS_ST2084): """ Defines *SMPTE ST 2084:2014* optimised perceptual inverse electro-optical transfer function (EOTF / EOCF). Parameters ---------- C : numeric or array_like Target optical output :math:`C` in :math:`cd/m^2` of the ideal reference display. L_p : numeric, optional 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 : Structure, optional *SMPTE ST 2084:2014* constants. Returns ------- numeric or 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. +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``C`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``N`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Miller2014a`, :cite:`SocietyofMotionPictureandTelevisionEngineers2014a` Examples -------- >>> eotf_inverse_ST2084(100) # doctest: +ELLIPSIS 0.5080784... """ C = to_domain_1(C) Y_p = spow(C / L_p, constants.m_1) N = spow((constants.c_1 + constants.c_2 * Y_p) / (constants.c_3 * Y_p + 1), constants.m_2) return from_range_1(N)
[docs]def eotf_ST2084(N, L_p=10000, constants=CONSTANTS_ST2084): """ Defines *SMPTE ST 2084:2014* optimised perceptual electro-optical transfer function (EOTF / EOCF). This perceptual quantizer (PQ) has been modeled by Dolby Laboratories using *Barten (1999)* contrast sensitivity function. Parameters ---------- N : numeric or array_like 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 : numeric, optional 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 : Structure, optional *SMPTE ST 2084:2014* constants. Returns ------- numeric or 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`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``C`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Miller2014a`, :cite:`SocietyofMotionPictureandTelevisionEngineers2014a` Examples -------- >>> eotf_ST2084(0.508078421517399) # doctest: +ELLIPSIS 100.0000000... """ N = to_domain_1(N) m_1_d = 1 / constants.m_1 m_2_d = 1 / constants.m_2 V_p = spow(N, m_2_d) n = V_p - constants.c_1 # Limiting negative values. n = np.where(n < 0, 0, n) L = spow((n / (constants.c_2 - constants.c_3 * V_p)), m_1_d) C = L_p * L return from_range_1(C)