Source code for colour.models.rgb.ictcp

"""
:math:`IC_TC_P` Colour Encoding
===============================

Defines the :math:`IC_TC_P` colour encoding related transformations:

-   :func:`colour.RGB_to_ICtCp`
-   :func:`colour.ICtCp_to_RGB`
-   :func:`colour.XYZ_to_ICtCp`
-   :func:`colour.ICtCp_to_XYZ`

References
----------
-   :cite:`Dolby2016a` : Dolby. (2016). WHAT IS ICtCp? - INTRODUCTION.
    https://www.dolby.com/us/en/technologies/dolby-vision/ICtCp-white-paper.pdf
-   :cite:`InternationalTelecommunicationUnion2018` : International
    Telecommunication Union. (2018). Recommendation ITU-R BT.2100-2 - Image
    parameter values for high dynamic range television for use in production
    and international programme exchange.
    https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.2100-2-201807-I!!PDF-E.pdf
-   :cite:`Lu2016c` : Lu, T., Pu, F., Yin, P., Chen, T., Husak, W., Pytlarz,
    J., Atkins, R., Froehlich, J., & Su, G.-M. (2016). ITP Colour Space and Its
    Compression Performance for High Dynamic Range and Wide Colour Gamut Video
    Distribution. ZTE Communications, 14(1), 32-38.
"""

from __future__ import annotations

import numpy as np

from colour.algebra import vector_dot
from colour.colorimetry import CCS_ILLUMINANTS
from colour.hints import ArrayLike, Floating, Literal, NDArray, Optional, Union
from colour.models.rgb import RGB_COLOURSPACES, RGB_to_XYZ, XYZ_to_RGB
from colour.models.rgb.transfer_functions import (
    eotf_ST2084,
    eotf_inverse_ST2084,
    oetf_BT2100_HLG,
    oetf_inverse_BT2100_HLG,
)
from colour.utilities import (
    as_float_array,
    domain_range_scale,
    validate_method,
)

__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__ = [
    "MATRIX_ICTCP_RGB_TO_LMS",
    "MATRIX_ICTCP_LMS_TO_RGB",
    "MATRIX_ICTCP_LMS_P_TO_ICTCP",
    "MATRIX_ICTCP_ICTCP_TO_LMS_P",
    "MATRIX_ICTCP_LMS_P_TO_ICTCP_BT2100_HLG_2",
    "MATRIX_ICTCP_ICTCP_TO_LMS_P_BT2100_HLG_2",
    "RGB_to_ICtCp",
    "ICtCp_to_RGB",
    "XYZ_to_ICtCp",
    "ICtCp_to_XYZ",
]

MATRIX_ICTCP_RGB_TO_LMS: NDArray = (
    np.array(
        [
            [1688, 2146, 262],
            [683, 2951, 462],
            [99, 309, 3688],
        ]
    )
    / 4096
)
"""*ITU-R BT.2020* colourspace to normalised cone responses matrix."""

MATRIX_ICTCP_LMS_TO_RGB: NDArray = np.linalg.inv(MATRIX_ICTCP_RGB_TO_LMS)
"""
:math:`IC_TC_P` colourspace normalised cone responses to *ITU-R BT.2020*
colourspace matrix.
"""

MATRIX_ICTCP_LMS_P_TO_ICTCP: NDArray = (
    np.array(
        [
            [2048, 2048, 0],
            [6610, -13613, 7003],
            [17933, -17390, -543],
        ]
    )
    / 4096
)
"""
:math:`LMS_p` *SMPTE ST 2084:2014* encoded normalised cone responses to
:math:`IC_TC_P` colour encoding matrix.
"""

MATRIX_ICTCP_ICTCP_TO_LMS_P: NDArray = np.linalg.inv(
    MATRIX_ICTCP_LMS_P_TO_ICTCP
)
"""
:math:`IC_TC_P` colour encoding to :math:`LMS_p` *SMPTE ST 2084:2014* encoded
normalised cone responses matrix.
"""

MATRIX_ICTCP_LMS_P_TO_ICTCP_BT2100_HLG_2: NDArray = (
    np.array(
        [
            [2048, 2048, 0],
            [3625, -7465, 3840],
            [9500, -9212, -288],
        ]
    )
    / 4096
)
"""
:math:`LMS_p` *SMPTE ST 2084:2014* encoded normalised cone responses to
:math:`IC_TC_P` colour encoding matrix as given in *ITU-R BT.2100-2*.
"""

MATRIX_ICTCP_ICTCP_TO_LMS_P_BT2100_HLG_2: NDArray = np.linalg.inv(
    MATRIX_ICTCP_LMS_P_TO_ICTCP_BT2100_HLG_2
)
"""
:math:`IC_TC_P` colour encoding to :math:`LMS_p` *SMPTE ST 2084:2014* encoded
normalised cone responses matrix as given in *ITU-R BT.2100-2*.
"""


[docs]def RGB_to_ICtCp( RGB: ArrayLike, method: Union[ Literal[ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], str, ] = "Dolby 2016", L_p: Floating = 10000, ) -> NDArray: """ Convert from *ITU-R BT.2020* colourspace to :math:`IC_TC_P` colour encoding. Parameters ---------- RGB *ITU-R BT.2020* colourspace array. method Computation method. *Recommendation ITU-R BT.2100* defines multiple variants of the :math:`IC_TC_P` colour encoding: - *ITU-R BT.2100-1* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *ITU-R BT.2100-1 HLG* method. - *ITU-R BT.2100-2* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and a custom :math:`IC_TC_P` matrix from :cite:`InternationalTelecommunicationUnion2018`: *ITU-R BT.2100-2 HLG* method. L_p Display peak luminance :math:`cd/m^2` for *SMPTE ST 2084:2014* non-linear encoding. 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. Returns ------- :class:`numpy.ndarray` :math:`IC_TC_P` colour encoding array. Warnings -------- The underlying *SMPTE ST 2084:2014* transfer function is an absolute transfer function. Notes ----- - The *ITU-R BT.2100-1 PQ* and *ITU-R BT.2100-2 PQ* methods are aliases for the *Dolby 2016* method. - The underlying *SMPTE ST 2084:2014* transfer function 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. The effective domain of *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) is [0.0001, 10000]. +------------+-----------------------+------------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``RGB`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``ICtCp`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``CT`` : [-1, 1] | ``CT`` : [-1, 1] | | | | | | | ``CP`` : [-1, 1] | ``CP`` : [-1, 1] | +------------+-----------------------+------------------+ References ---------- :cite:`Dolby2016a`, :cite:`Lu2016c` Examples -------- >>> RGB = np.array([0.45620519, 0.03081071, 0.04091952]) >>> RGB_to_ICtCp(RGB) # doctest: +ELLIPSIS array([ 0.0735136..., 0.0047525..., 0.0935159...]) >>> RGB_to_ICtCp(RGB, method='ITU-R BT.2100-2 HLG') # doctest: +ELLIPSIS array([ 0.6256789..., -0.0198449..., 0.3591125...]) """ RGB = as_float_array(RGB) method = validate_method( method, [ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], ) is_hlg_method = "hlg" in method is_BT2100_2_method = "2100-2" in method LMS = vector_dot(MATRIX_ICTCP_RGB_TO_LMS, RGB) with domain_range_scale("ignore"): LMS_p = ( oetf_BT2100_HLG(LMS) if is_hlg_method else eotf_inverse_ST2084(LMS, L_p) ) ICtCp = ( vector_dot(MATRIX_ICTCP_LMS_P_TO_ICTCP_BT2100_HLG_2, LMS_p) if (is_hlg_method and is_BT2100_2_method) else vector_dot(MATRIX_ICTCP_LMS_P_TO_ICTCP, LMS_p) ) return ICtCp
[docs]def ICtCp_to_RGB( ICtCp: ArrayLike, method: Union[ Literal[ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], str, ] = "Dolby 2016", L_p: Floating = 10000, ) -> NDArray: """ Convert from :math:`IC_TC_P` colour encoding to *ITU-R BT.2020* colourspace. Parameters ---------- ICtCp :math:`IC_TC_P` colour encoding array. method Computation method. *Recommendation ITU-R BT.2100* defines multiple variants of the :math:`IC_TC_P` colour encoding: - *ITU-R BT.2100-1* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *ITU-R BT.2100-1 HLG* method. - *ITU-R BT.2100-2* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and a custom :math:`IC_TC_P` matrix from :cite:`InternationalTelecommunicationUnion2018`: *ITU-R BT.2100-2 HLG* method. L_p Display peak luminance :math:`cd/m^2` for *SMPTE ST 2084:2014* non-linear encoding. 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. Returns ------- :class:`numpy.ndarray` *ITU-R BT.2020* colourspace array. Warnings -------- The underlying *SMPTE ST 2084:2014* transfer function is an absolute transfer function. Notes ----- - The *ITU-R BT.2100-1 PQ* and *ITU-R BT.2100-2 PQ* methods are aliases for the *Dolby 2016* method. - The underlying *SMPTE ST 2084:2014* transfer function 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** | +============+=======================+==================+ | ``ICtCp`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``CT`` : [-1, 1] | ``CT`` : [-1, 1] | | | | | | | ``CP`` : [-1, 1] | ``CP`` : [-1, 1] | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``RGB`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ References ---------- :cite:`Dolby2016a`, :cite:`Lu2016c` Examples -------- >>> ICtCp = np.array([0.07351364, 0.00475253, 0.09351596]) >>> ICtCp_to_RGB(ICtCp) # doctest: +ELLIPSIS array([ 0.4562052..., 0.0308107..., 0.0409195...]) >>> ICtCp = np.array([0.62567899, -0.01984490, 0.35911259]) >>> ICtCp_to_RGB(ICtCp, method='ITU-R BT.2100-2 HLG') # doctest: +ELLIPSIS array([ 0.4562052..., 0.0308107..., 0.0409195...]) """ ICtCp = as_float_array(ICtCp) method = validate_method( method, [ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], ) is_hlg_method = "hlg" in method is_BT2100_2_method = "2100-2" in method LMS_p = ( vector_dot(MATRIX_ICTCP_ICTCP_TO_LMS_P_BT2100_HLG_2, ICtCp) if (is_hlg_method and is_BT2100_2_method) else vector_dot(MATRIX_ICTCP_ICTCP_TO_LMS_P, ICtCp) ) with domain_range_scale("ignore"): LMS = ( oetf_inverse_BT2100_HLG(LMS_p) if is_hlg_method else eotf_ST2084(LMS_p, L_p) ) RGB = vector_dot(MATRIX_ICTCP_LMS_TO_RGB, LMS) return RGB
[docs]def XYZ_to_ICtCp( XYZ: ArrayLike, illuminant=CCS_ILLUMINANTS["CIE 1931 2 Degree Standard Observer"]["D65"], chromatic_adaptation_transform: Optional[ Union[ Literal[ "Bianco 2010", "Bianco PC 2010", "Bradford", "CAT02 Brill 2008", "CAT02", "CAT16", "CMCCAT2000", "CMCCAT97", "Fairchild", "Sharp", "Von Kries", "XYZ Scaling", ], str, ] ] = "CAT02", method: Union[ Literal[ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], str, ] = "Dolby 2016", L_p: Floating = 10000, ) -> NDArray: """ Convert from *CIE XYZ* tristimulus values to :math:`IC_TC_P` colour encoding. Parameters ---------- XYZ *CIE XYZ* tristimulus values. illuminant Source illuminant chromaticity coordinates. chromatic_adaptation_transform *Chromatic adaptation* transform. method Computation method. *Recommendation ITU-R BT.2100* defines multiple variants of the :math:`IC_TC_P` colour encoding: - *ITU-R BT.2100-1* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *ITU-R BT.2100-1 HLG* method. - *ITU-R BT.2100-2* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and a custom :math:`IC_TC_P` matrix from :cite:`InternationalTelecommunicationUnion2018`: *ITU-R BT.2100-2 HLG* method. L_p Display peak luminance :math:`cd/m^2` for *SMPTE ST 2084:2014* non-linear encoding. 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. Returns ------- :class:`numpy.ndarray` :math:`IC_TC_P` colour encoding array. Warnings -------- The underlying *SMPTE ST 2084:2014* transfer function is an absolute transfer function. Notes ----- - The underlying *SMPTE ST 2084:2014* transfer function is an absolute transfer function, thus the domain and range values for the *Reference* - The *ITU-R BT.2100-1 PQ* and *ITU-R BT.2100-2 PQ* methods are aliases for the *Dolby 2016* method. and *1* scales are only indicative that the data is not affected by scale transformations. The effective domain of *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) is [0.0001, 10000]. +------------+-----------------------+------------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``XYZ`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``ICtCp`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``CT`` : [-1, 1] | ``CT`` : [-1, 1] | | | | | | | ``CP`` : [-1, 1] | ``CP`` : [-1, 1] | +------------+-----------------------+------------------+ References ---------- :cite:`Dolby2016a`, :cite:`Lu2016c` Examples -------- >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> XYZ_to_ICtCp(XYZ) # doctest: +ELLIPSIS array([ 0.0685809..., -0.0028384..., 0.0602098...]) >>> XYZ_to_ICtCp(XYZ, method='ITU-R BT.2100-2 HLG') # doctest: +ELLIPSIS array([ 0.5924279..., -0.0374073..., 0.2512267...]) """ BT2020 = RGB_COLOURSPACES["ITU-R BT.2020"] RGB = XYZ_to_RGB( XYZ, illuminant, BT2020.whitepoint, BT2020.matrix_XYZ_to_RGB, chromatic_adaptation_transform, ) return RGB_to_ICtCp(RGB, method, L_p)
[docs]def ICtCp_to_XYZ( ICtCp: ArrayLike, illuminant=CCS_ILLUMINANTS["CIE 1931 2 Degree Standard Observer"]["D65"], chromatic_adaptation_transform: Optional[ Union[ Literal[ "Bianco 2010", "Bianco PC 2010", "Bradford", "CAT02 Brill 2008", "CAT02", "CAT16", "CMCCAT2000", "CMCCAT97", "Fairchild", "Sharp", "Von Kries", "XYZ Scaling", ], str, ] ] = "CAT02", method: Union[ Literal[ "Dolby 2016", "ITU-R BT.2100-1 HLG", "ITU-R BT.2100-1 PQ", "ITU-R BT.2100-2 HLG", "ITU-R BT.2100-2 PQ", ], str, ] = "Dolby 2016", L_p: Floating = 10000, ) -> NDArray: """ Convert from :math:`IC_TC_P` colour encoding to *CIE XYZ* tristimulus values. Parameters ---------- ICtCp :math:`IC_TC_P` colour encoding array. illuminant Source illuminant chromaticity coordinates. chromatic_adaptation_transform *Chromatic adaptation* transform. method Computation method. *Recommendation ITU-R BT.2100* defines multiple variants of the :math:`IC_TC_P` colour encoding: - *ITU-R BT.2100-1* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *ITU-R BT.2100-1 HLG* method. - *ITU-R BT.2100-2* - *SMPTE ST 2084:2014* inverse electro-optical transfer function (EOTF) and the :math:`IC_TC_P` matrix from :cite:`Dolby2016a`: *Dolby 2016*, *ITU-R BT.2100-1 PQ*, *ITU-R BT.2100-2 PQ* methods. - *Recommendation ITU-R BT.2100* *Reference HLG* opto-electrical transfer function (OETF) and a custom :math:`IC_TC_P` matrix from :cite:`InternationalTelecommunicationUnion2018`: *ITU-R BT.2100-2 HLG* method. L_p Display peak luminance :math:`cd/m^2` for *SMPTE ST 2084:2014* non-linear encoding. 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. Returns ------- :class:`numpy.ndarray` *CIE XYZ* tristimulus values. Warnings -------- The underlying *SMPTE ST 2084:2014* transfer function is an absolute transfer function. Notes ----- - The *ITU-R BT.2100-1 PQ* and *ITU-R BT.2100-2 PQ* methods are aliases for the *Dolby 2016* method. - The underlying *SMPTE ST 2084:2014* transfer function 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** | +============+=======================+==================+ | ``ICtCp`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``CT`` : [-1, 1] | ``CT`` : [-1, 1] | | | | | | | ``CP`` : [-1, 1] | ``CP`` : [-1, 1] | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``XYZ`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ References ---------- :cite:`Dolby2016a`, :cite:`Lu2016c` Examples -------- >>> ICtCp = np.array([0.06858097, -0.00283842, 0.06020983]) >>> ICtCp_to_XYZ(ICtCp) # doctest: +ELLIPSIS array([ 0.2065400..., 0.1219722..., 0.0513695...]) >>> ICtCp = np.array([0.59242792, -0.03740730, 0.25122675]) >>> ICtCp_to_XYZ(ICtCp, method='ITU-R BT.2100-2 HLG') # doctest: +ELLIPSIS array([ 0.2065400..., 0.1219722..., 0.0513695...]) """ RGB = ICtCp_to_RGB(ICtCp, method, L_p) BT2020 = RGB_COLOURSPACES["ITU-R BT.2020"] XYZ = RGB_to_XYZ( RGB, BT2020.whitepoint, illuminant, BT2020.matrix_RGB_to_XYZ, chromatic_adaptation_transform, ) return XYZ