Source code for colour.models.rgb.transfer_functions.itur_bt_2100

# -*- coding: utf-8 -*-
"""
ITU-R BT.2100
=============

Defines *ITU-R BT.2100* opto-electrical transfer functions (OETF / OECF),
opto-optical transfer functions (OOTF / OOCF) and electro-optical transfer
functions (EOTF / EOCF) and their reverse:

-   :func:`colour.models.oetf_BT2100_PQ`
-   :func:`colour.models.oetf_reverse_BT2100_PQ`
-   :func:`colour.models.eotf_BT2100_PQ`
-   :func:`colour.models.eotf_reverse_BT2100_PQ`
-   :func:`colour.models.ootf_BT2100_PQ`
-   :func:`colour.models.ootf_reverse_BT2100_PQ`
-   :func:`colour.models.oetf_BT2100_HLG`
-   :func:`colour.models.oetf_reverse_BT2100_HLG`
-   :func:`colour.models.eotf_BT2100_HLG`
-   :func:`colour.models.eotf_reverse_BT2100_HLG`
-   :func:`colour.models.ootf_BT2100_HLG`
-   :func:`colour.models.ootf_reverse_BT2100_HLG`

See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_

References
----------
-   :cite:`Borer2017a` : Borer, T. (2017). Private Discussion with
    Mansencal, T. and Shaw, N.
-   :cite:`InternationalTelecommunicationUnion2016a` : International
    Telecommunication Union. (2016). Recommendation ITU-R BT.2100-1 - Image
    parameter values for high dynamic range television for use in production
    and international programme exchange. Retrieved from
    https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2100-1-201706-I!!PDF-E.pdf
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.models.rgb.transfer_functions import (
    eotf_BT1886, eotf_ST2084, eotf_reverse_BT1886, oetf_ARIBSTDB67, oetf_BT709,
    oetf_ST2084, oetf_reverse_ARIBSTDB67, oetf_reverse_BT709)
from colour.models.rgb.transfer_functions.arib_std_b67 import (
    ARIBSTDB67_CONSTANTS)
from colour.utilities import (Structure, as_float_array, as_float,
                              from_range_1, to_domain_1, tsplit, tstack,
                              usage_warning)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'

__all__ = [
    'oetf_BT2100_PQ', 'oetf_reverse_BT2100_PQ', 'eotf_BT2100_PQ',
    'eotf_reverse_BT2100_PQ', 'ootf_BT2100_PQ', 'ootf_reverse_BT2100_PQ',
    'BT2100_HLG_WEIGHTS', 'BT2100_HLG_CONSTANTS', 'gamma_function_BT2100_HLG',
    'oetf_BT2100_HLG', 'oetf_reverse_BT2100_HLG', 'eotf_BT2100_HLG',
    'eotf_reverse_BT2100_HLG', 'ootf_BT2100_HLG', 'ootf_reverse_BT2100_HLG'
]


[docs]def oetf_BT2100_PQ(E): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* opto-electrical transfer function (OETF / OECF). The OETF maps relative scene linear light into the non-linear *PQ* signal value. Parameters ---------- E : numeric or array_like :math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by scene light and scaled by camera exposure. Returns ------- numeric or ndarray :math:`E'` is the resulting non-linear signal (:math:`R'`, :math:`G'`, :math:`B'`). Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> oetf_BT2100_PQ(0.1) # doctest: +ELLIPSIS 0.7247698... """ return oetf_ST2084(ootf_BT2100_PQ(E), 10000)
[docs]def oetf_reverse_BT2100_PQ(E_p): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* reverse opto-electrical transfer function (OETF / OECF). Parameters ---------- E_p : numeric or array_like :math:`E'` is the resulting non-linear signal (:math:`R'`, :math:`G'`, :math:`B'`). Returns ------- numeric or ndarray :math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by scene light and scaled by camera exposure. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> oetf_reverse_BT2100_PQ(0.724769816665726) # doctest: +ELLIPSIS 0.0999999... """ return ootf_reverse_BT2100_PQ(eotf_ST2084(E_p, 10000))
[docs]def eotf_BT2100_PQ(E_p): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* electro-optical transfer function (EOTF / EOCF). The EOTF maps the non-linear *PQ* signal into display light. Parameters ---------- E_p : numeric or array_like :math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or :math:`{L', M', S'}` in *PQ* space [0, 1]. Returns ------- numeric or ndarray :math:`F_D` is the luminance of a displayed linear component :math:`{R_D, G_D, B_D}` or :math:`Y_D` or :math:`I_D`, in :math:`cd/m^2`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> eotf_BT2100_PQ(0.724769816665726) # doctest: +ELLIPSIS 779.9883608... """ return eotf_ST2084(E_p, 10000)
[docs]def eotf_reverse_BT2100_PQ(F_D): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* reverse electro-optical transfer function (EOTF / EOCF). Parameters ---------- F_D : numeric or array_like :math:`F_D` is the luminance of a displayed linear component :math:`{R_D, G_D, B_D}` or :math:`Y_D` or :math:`I_D`, in :math:`cd/m^2`. Returns ------- numeric or ndarray :math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or :math:`{L', M', S'}` in *PQ* space [0, 1]. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> eotf_reverse_BT2100_PQ(779.988360834085370) # doctest: +ELLIPSIS 0.7247698... """ return oetf_ST2084(F_D, 10000)
[docs]def ootf_BT2100_PQ(E): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* opto-optical transfer function (OOTF / OOCF). The OOTF maps relative scene linear light to display linear light. Parameters ---------- E : numeric or array_like :math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by scene light and scaled by camera exposure. Returns ------- numeric or ndarray :math:`F_D` is the luminance of a displayed linear component (:math:`R_D`, :math:`G_D`, :math:`B_D`; :math:`Y_D`; or :math:`I_D`). Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> ootf_BT2100_PQ(0.1) # doctest: +ELLIPSIS 779.9883608... """ E = as_float_array(E) return 100 * eotf_BT1886(oetf_BT709(59.5208 * E))
[docs]def ootf_reverse_BT2100_PQ(F_D): """ Defines *Recommendation ITU-R BT.2100* *Reference PQ* reverse opto-optical transfer function (OOTF / OOCF). Parameters ---------- F_D : numeric or array_like :math:`F_D` is the luminance of a displayed linear component (:math:`R_D`, :math:`G_D`, :math:`B_D`; :math:`Y_D`; or :math:`I_D`). Returns ------- numeric or ndarray :math:`E = {R_S, G_S, B_S; Y_S; or I_S}` is the signal determined by scene light and scaled by camera exposure. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> ootf_reverse_BT2100_PQ(779.988360834115840) # doctest: +ELLIPSIS 0.1000000... """ F_D = as_float_array(F_D) return oetf_reverse_BT709(eotf_reverse_BT1886(F_D / 100)) / 59.5208
BT2100_HLG_WEIGHTS = np.array([0.2627, 0.6780, 0.0593]) """ Luminance weights for *Recommendation ITU-R BT.2100* *Reference HLG*. BT2100_HLG_WEIGHTS : ndarray """ BT2100_HLG_CONSTANTS = Structure( a=ARIBSTDB67_CONSTANTS.a, b=1 - 4 * ARIBSTDB67_CONSTANTS.a, c=0.5 - ARIBSTDB67_CONSTANTS.a * np.log(4 * ARIBSTDB67_CONSTANTS.a)) """ *Recommendation ITU-R BT.2100* *Reference HLG* constants expressed in their analytical form in contrast to the *ARIB STD-B67 (Hybrid Log-Gamma)* numerical reference. Those constants are not currently in use and are provided as a reference only. References ---------- :cite:`InternationalTelecommunicationUnion2016a` BT2100_HLG_CONSTANTS : Structure """ def gamma_function_BT2100_HLG(L_W=1000): """ Returns the *Reference HLG* system gamma value for given display nominal peak luminance. Parameters ---------- L_W : numeric, optional :math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2` for achromatic pixels. Returns ------- numeric *Reference HLG* system gamma value. Examples -------- >>> gamma_function_BT2100_HLG() 1.2 >>> gamma_function_BT2100_HLG(2000) # doctest: +ELLIPSIS 1.3264325... >>> gamma_function_BT2100_HLG(4000) # doctest: +ELLIPSIS 1.4528651... """ gamma = 1.2 + 0.42 * np.log10(L_W / 1000) return gamma
[docs]def oetf_BT2100_HLG(E): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF / OECF). The OETF maps relative scene linear light into the non-linear *HLG* signal value. Parameters ---------- E : numeric or array_like :math:`E` is the signal for each colour component :math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled by camera exposure. Returns ------- numeric or ndarray :math:`E'` is the resulting non-linear signal :math:`{R', G', B'}`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> oetf_BT2100_HLG(0.18 / 12) # doctest: +ELLIPSIS 0.2121320... """ return oetf_ARIBSTDB67(12 * E)
[docs]def oetf_reverse_BT2100_HLG(E): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* reverse opto-electrical transfer function (OETF / OECF). Parameters ---------- E_p : numeric or array_like :math:`E'` is the resulting non-linear signal :math:`{R', G', B'}`. Returns ------- numeric or ndarray :math:`E` is the signal for each colour component :math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled by camera exposure. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> oetf_reverse_BT2100_HLG(0.212132034355964) # doctest: +ELLIPSIS 0.0149999... """ return oetf_reverse_ARIBSTDB67(E) / 12
[docs]def eotf_BT2100_HLG(E_p, L_B=0, L_W=1000, gamma=None): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* electro-optical transfer function (EOTF / EOCF). The EOTF maps the non-linear *HLG* signal into display light. Parameters ---------- E_p : numeric or array_like :math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or :math:`{L', M', S'}` in *HLG* space. L_B : numeric, optional :math:`L_B` is the display luminance for black in :math:`cd/m^2`. L_W : numeric, optional :math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2` for achromatic pixels. gamma : numeric, optional System gamma value, 1.2 at the nominal display peak luminance of :math:`1000 cd/m^2`. Returns ------- numeric or ndarray Luminance :math:`F_D` of a displayed linear component :math:`{R_D, G_D, B_D}` or :math:`Y_D` or :math:`I_D`, in :math:`cd/m^2`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> eotf_BT2100_HLG(0.212132034355964) # doctest: +ELLIPSIS 6.4760398... """ return ootf_BT2100_HLG(oetf_reverse_ARIBSTDB67(E_p) / 12, L_B, L_W, gamma)
[docs]def eotf_reverse_BT2100_HLG(F_D, L_B=0, L_W=1000, gamma=None): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* reverse electro-optical transfer function (EOTF / EOCF). Parameters ---------- F_D : numeric or array_like Luminance :math:`F_D` of a displayed linear component :math:`{R_D, G_D, B_D}` or :math:`Y_D` or :math:`I_D`, in :math:`cd/m^2`. L_B : numeric, optional :math:`L_B` is the display luminance for black in :math:`cd/m^2`. L_W : numeric, optional :math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2` for achromatic pixels. gamma : numeric, optional System gamma value, 1.2 at the nominal display peak luminance of :math:`1000 cd/m^2`. Returns ------- numeric or ndarray :math:`E'` denotes a non-linear colour value :math:`{R', G', B'}` or :math:`{L', M', S'}` in *HLG* space. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E_p`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> eotf_reverse_BT2100_HLG(6.476039825649814) # doctest: +ELLIPSIS 0.2121320... """ return oetf_ARIBSTDB67(ootf_reverse_BT2100_HLG(F_D, L_B, L_W, gamma) * 12)
[docs]def ootf_BT2100_HLG(E, L_B=0, L_W=1000, gamma=None): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* opto-optical transfer function (OOTF / OOCF). The OOTF maps relative scene linear light to display linear light. Parameters ---------- E : numeric or array_like :math:`E` is the signal for each colour component :math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled by camera exposure. L_B : numeric, optional :math:`L_B` is the display luminance for black in :math:`cd/m^2`. L_W : numeric, optional :math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2` for achromatic pixels. gamma : numeric, optional System gamma value, 1.2 at the nominal display peak luminance of :math:`1000 cd/m^2`. Returns ------- numeric or ndarray :math:`F_D` is the luminance of a displayed linear component :math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> ootf_BT2100_HLG(0.1) # doctest: +ELLIPSIS 63.0957344... """ E = np.atleast_1d(to_domain_1(E)) if E.shape[-1] != 3: usage_warning( '"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses ' 'RGB Luminance in computations and expects a vector input, thus ' 'the given input array will be stacked to compose a vector for ' 'internal computations but a single component will be output.') R_S = G_S = B_S = E else: R_S, G_S, B_S = tsplit(E) alpha = L_W - L_B beta = L_B Y_S = np.sum(BT2100_HLG_WEIGHTS * tstack([R_S, G_S, B_S]), axis=-1) if gamma is None: gamma = gamma_function_BT2100_HLG(L_W) R_D = alpha * R_S * np.abs(Y_S) ** (gamma - 1) + beta G_D = alpha * G_S * np.abs(Y_S) ** (gamma - 1) + beta B_D = alpha * B_S * np.abs(Y_S) ** (gamma - 1) + beta if E.shape[-1] != 3: return as_float(from_range_1(R_D)) else: RGB_D = tstack([R_D, G_D, B_D]) return from_range_1(RGB_D)
[docs]def ootf_reverse_BT2100_HLG(F_D, L_B=0, L_W=1000, gamma=None): """ Defines *Recommendation ITU-R BT.2100* *Reference HLG* reverse opto-optical transfer function (OOTF / OOCF). Parameters ---------- F_D : numeric or array_like :math:`F_D` is the luminance of a displayed linear component :math:`{R_D, G_D, or B_D}`, in :math:`cd/m^2`. L_B : numeric, optional :math:`L_B` is the display luminance for black in :math:`cd/m^2`. L_W : numeric, optional :math:`L_W` is nominal peak luminance of the display in :math:`cd/m^2` for achromatic pixels. gamma : numeric, optional System gamma value, 1.2 at the nominal display peak luminance of :math:`1000 cd/m^2`. Returns ------- numeric or ndarray :math:`E` is the signal for each colour component :math:`{R_S, G_S, B_S}` proportional to scene linear light and scaled by camera exposure. Notes ----- +------------+-----------------------+---------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``F_D`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ +------------+-----------------------+---------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+===============+ | ``E`` | [0, 1] | [0, 1] | +------------+-----------------------+---------------+ References ---------- :cite:`Borer2017a`, :cite:`InternationalTelecommunicationUnion2016a` Examples -------- >>> ootf_reverse_BT2100_HLG(63.095734448019336) # doctest: +ELLIPSIS 0.1000000... """ F_D = np.atleast_1d(to_domain_1(F_D)) if F_D.shape[-1] != 3: usage_warning( '"Recommendation ITU-R BT.2100" "Reference HLG OOTF" uses ' 'RGB Luminance in computations and expects a vector input, thus ' 'the given input array will be stacked to compose a vector for ' 'internal computations but a single component will be output.') R_D = G_D = B_D = F_D else: R_D, G_D, B_D = tsplit(F_D) Y_D = np.sum(BT2100_HLG_WEIGHTS * tstack([R_D, G_D, B_D]), axis=-1) alpha = L_W - L_B beta = L_B if gamma is None: gamma = gamma_function_BT2100_HLG(L_W) R_S = np.where( Y_D == beta, 0.0, (np.abs((Y_D - beta) / alpha) ** ((1 - gamma) / gamma)) * (R_D - beta) / alpha, ) G_S = np.where( Y_D == beta, 0.0, (np.abs((Y_D - beta) / alpha) ** ((1 - gamma) / gamma)) * (G_D - beta) / alpha, ) B_S = np.where( Y_D == beta, 0.0, (np.abs((Y_D - beta) / alpha) ** ((1 - gamma) / gamma)) * (B_D - beta) / alpha, ) if F_D.shape[-1] != 3: return as_float(from_range_1(R_S)) else: RGB_S = tstack([R_S, G_S, B_S]) return from_range_1(RGB_S)