Source code for colour.models.rgb.transfer_functions.itur_bt_1886
"""
Recommendation ITU-R BT.1886
============================
Define the *Recommendation ITU-R BT.1886* electro-optical transfer function
(EOTF) and its inverse:
- :func:`colour.models.eotf_inverse_BT1886`
- :func:`colour.models.eotf_BT1886`
References
----------
- :cite:`InternationalTelecommunicationUnion2011h` : International
Telecommunication Union. (2011). Recommendation ITU-R BT.1886 - Reference
electro-optical transfer function for flat panel displays used in HDTV
studio production BT Series Broadcasting service.
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.1886-0-201103-I!!PDF-E.pdf
"""
from __future__ import annotations
import numpy as np
from colour.algebra import spow
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float, from_range_1, to_domain_1
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"eotf_inverse_BT1886",
"eotf_BT1886",
]
[docs]
def eotf_inverse_BT1886(L: ArrayLike, L_B: float = 0, L_W: float = 1) -> NDArrayFloat:
"""
Define *Recommendation ITU-R BT.1886* inverse electro-optical transfer
function (EOTF).
Parameters
----------
L
Screen luminance in :math:`cd/m^2`.
L_B
Screen luminance for black.
L_W
Screen luminance for white.
Returns
-------
:class:`numpy.ndarray`
Input video signal level (normalised, black at :math:`V = 0`, to white
at :math:`V = 1`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``L`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``V`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2011h`
Examples
--------
>>> eotf_inverse_BT1886(0.11699185725296059) # doctest: +ELLIPSIS
0.4090077...
"""
L = to_domain_1(L)
gamma = 2.40
gamma_d = 1 / gamma
n = L_W**gamma_d - L_B**gamma_d
a = n**gamma
b = L_B**gamma_d / n
V = spow(L / a, gamma_d) - b
return as_float(from_range_1(V))
[docs]
def eotf_BT1886(V: ArrayLike, L_B: float = 0, L_W: float = 1) -> NDArrayFloat:
"""
Define *Recommendation ITU-R BT.1886* electro-optical transfer function
(EOTF).
Parameters
----------
V
Input video signal level (normalised, black at :math:`V = 0`, to white
at :math:`V = 1`. For content mastered per
*Recommendation ITU-R BT.709*, 10-bit digital code values :math:`D` map
into values of :math:`V` per the following equation:
:math:`V = (D-64)/876`
L_B
Screen luminance for black.
L_W
Screen luminance for white.
Returns
-------
:class:`numpy.ndarray`
Screen luminance in :math:`cd/m^2`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``V`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``L`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2011h`
Examples
--------
>>> eotf_BT1886(0.409007728864150) # doctest: +ELLIPSIS
0.1169918...
"""
V = to_domain_1(V)
gamma = 2.40
gamma_d = 1 / gamma
n = L_W**gamma_d - L_B**gamma_d
a = n**gamma
b = L_B**gamma_d / n
L = a * spow(np.maximum(V + b, 0), gamma)
return as_float(from_range_1(L))
