Source code for colour.models.jzazbz

"""
:math:`J_za_zb_z` Colourspace
=============================

Define the :math:`J_za_zb_z` colourspace:

-   :func:`colour.models.IZAZBZ_METHODS`
-   :func:`colour.models.XYZ_to_Izazbz`
-   :func:`colour.models.Izazbz_to_XYZ`
-   :func:`colour.XYZ_to_Jzazbz`
-   :func:`colour.Jzazbz_to_XYZ`

References
----------
-   :cite:`Safdar2017` : Safdar, M., Cui, G., Kim, Y. J., & Luo, M. R. (2017).
    Perceptually uniform color space for image signals including high dynamic
    range and wide gamut. Optics Express, 25(13), 15131.
    doi:10.1364/OE.25.015131
-   :cite:`Safdar2021` : Safdar, M., Hardeberg, J. Y., & Ronnier Luo, M.
    (2021). ZCAM, a colour appearance model based on a high dynamic range
    uniform colour space. Optics Express, 29(4), 6036. doi:10.1364/OE.413659
"""

from __future__ import annotations

import numpy as np

from colour.algebra import vecmul
from colour.hints import ArrayLike, Literal, NDArrayFloat
from colour.models.rgb.transfer_functions import (
    eotf_inverse_ST2084,
    eotf_ST2084,
)
from colour.models.rgb.transfer_functions.st_2084 import CONSTANTS_ST2084
from colour.utilities import (
    Structure,
    as_float_array,
    domain_range_scale,
    optional,
    tsplit,
    tstack,
    validate_method,
)
from colour.utilities.documentation import (
    DocstringTuple,
    is_documentation_building,
)

__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__ = [
    "CONSTANTS_JZAZBZ_SAFDAR2017",
    "CONSTANTS_JZAZBZ_SAFDAR2021",
    "MATRIX_JZAZBZ_XYZ_TO_LMS",
    "MATRIX_JZAZBZ_LMS_TO_XYZ",
    "MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2017",
    "MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2017",
    "MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2021",
    "MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2021",
    "IZAZBZ_METHODS",
    "XYZ_to_Izazbz",
    "Izazbz_to_XYZ",
    "XYZ_to_Jzazbz",
    "Jzazbz_to_XYZ",
]

CONSTANTS_JZAZBZ_SAFDAR2017: Structure = Structure(
    b=1.15, g=0.66, d=-0.56, d_0=1.6295499532821566 * 10**-11
)
CONSTANTS_JZAZBZ_SAFDAR2017.update(CONSTANTS_ST2084)
CONSTANTS_JZAZBZ_SAFDAR2017.m_2 = 1.7 * 2523 / 2**5
"""
Constants for :math:`J_za_zb_z` colourspace and its variant of the perceptual
quantizer (PQ) from Dolby Laboratories.

Notes
-----
-   The :math:`m2` constant, i.e. the power factor has been re-optimized during
    the development of the :math:`J_za_zb_z` colourspace.
"""

CONSTANTS_JZAZBZ_SAFDAR2021: Structure = Structure(**CONSTANTS_JZAZBZ_SAFDAR2017)
CONSTANTS_JZAZBZ_SAFDAR2021.d_0 = 3.7035226210190005 * 10**-11
""":math:`J_za_zb_z` colourspace constants for the *ZCAM* colour appearance model."""

MATRIX_JZAZBZ_XYZ_TO_LMS: NDArrayFloat = np.array(
    [
        [0.41478972, 0.579999, 0.0146480],
        [-0.2015100, 1.120649, 0.0531008],
        [-0.0166008, 0.264800, 0.6684799],
    ]
)
"""
:math:`J_za_zb_z` *CIE XYZ* tristimulus values to normalised cone responses
matrix.
"""

MATRIX_JZAZBZ_LMS_TO_XYZ: NDArrayFloat = np.linalg.inv(MATRIX_JZAZBZ_XYZ_TO_LMS)
"""
:math:`J_za_zb_z` normalised cone responses to *CIE XYZ* tristimulus values
matrix.
"""

MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2017: NDArrayFloat = np.array(
    [
        [0.500000, 0.500000, 0.000000],
        [3.524000, -4.066708, 0.542708],
        [0.199076, 1.096799, -1.295875],
    ]
)
"""
:math:`LMS_p` *SMPTE ST 2084:2014* encoded normalised cone responses to
:math:`I_za_zb_z` intermediate colourspace matrix.
"""

MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2017: NDArrayFloat = np.linalg.inv(
    MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2017
)
"""
:math:`I_za_zb_z` intermediate colourspace to :math:`LMS_p`
*SMPTE ST 2084:2014* encoded normalised cone responses matrix.
"""

MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2021: NDArrayFloat = np.array(
    [
        [0.000000, 1.000000, 0.000000],
        [3.524000, -4.066708, 0.542708],
        [0.199076, 1.096799, -1.295875],
    ]
)
"""
:math:`LMS_p` *SMPTE ST 2084:2014* encoded normalised cone responses to
:math:`I_za_zb_z` intermediate colourspace matrix.

References
----------
:cite:`Safdar2021`
"""

MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2021: NDArrayFloat = np.linalg.inv(
    MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2021
)
"""
:math:`I_za_zb_z` intermediate colourspace to :math:`LMS_p`
*SMPTE ST 2084:2014* encoded normalised cone responses matrix.

References
----------
:cite:`Safdar2021`
"""

IZAZBZ_METHODS: tuple = ("Safdar 2017", "Safdar 2021", "ZCAM")
if is_documentation_building():  # pragma: no cover
    IZAZBZ_METHODS = DocstringTuple(IZAZBZ_METHODS)
    IZAZBZ_METHODS.__doc__ = """
Supported :math:`I_za_zb_z` computation methods.

References
----------
:cite:`Safdar2017`, :cite:`Safdar2021`
"""


[docs] def XYZ_to_Izazbz( XYZ_D65: ArrayLike, constants: Structure | None = None, method: (Literal["Safdar 2017", "Safdar 2021", "ZCAM"] | str) = "Safdar 2017", ) -> NDArrayFloat: """ Convert from *CIE XYZ* tristimulus values to :math:`I_za_zb_z` colourspace. Parameters ---------- XYZ_D65 *CIE XYZ* tristimulus values under *CIE Standard Illuminant D Series D65*. constants :math:`J_za_zb_z` colourspace constants. method Computation method, *Safdar 2021* and *ZCAM* methods are equivalent. Returns ------- :class:`numpy.ndarray` :math:`I_za_zb_z` colourspace array where :math:`I_z` is the achromatic response, :math:`a_z` is redness-greenness and :math:`b_z` is yellowness-blueness. 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* 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** | +============+=======================+==================+ | ``Izazbz`` | ``Iz`` : [0, 1] | ``Iz`` : [0, 1] | | | | | | | ``az`` : [-1, 1] | ``az`` : [-1, 1] | | | | | | | ``bz`` : [-1, 1] | ``bz`` : [-1, 1] | +------------+-----------------------+------------------+ References ---------- :cite:`Safdar2017`, :cite:`Safdar2021` Examples -------- >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> XYZ_to_Izazbz(XYZ) # doctest: +ELLIPSIS array([ 0.0120779..., 0.0092430..., 0.0052600...]) """ X_D65, Y_D65, Z_D65 = tsplit(as_float_array(XYZ_D65)) method = validate_method(method, IZAZBZ_METHODS) constants = optional( constants, ( CONSTANTS_JZAZBZ_SAFDAR2017 if method == "safdar 2017" else CONSTANTS_JZAZBZ_SAFDAR2021 ), ) X_p_D65 = constants.b * X_D65 - (constants.b - 1) * Z_D65 Y_p_D65 = constants.g * Y_D65 - (constants.g - 1) * X_D65 XYZ_p_D65 = tstack([X_p_D65, Y_p_D65, Z_D65]) LMS = vecmul(MATRIX_JZAZBZ_XYZ_TO_LMS, XYZ_p_D65) with domain_range_scale("ignore"): LMS_p = eotf_inverse_ST2084(LMS, 10000, constants) if method == "safdar 2017": Izazbz = vecmul(MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2017, LMS_p) else: Izazbz = vecmul(MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ_SAFDAR2021, LMS_p) Izazbz[..., 0] -= constants.d_0 return Izazbz
[docs] def Izazbz_to_XYZ( Izazbz: ArrayLike, constants: Structure | None = None, method: (Literal["Safdar 2017", "Safdar 2021", "ZCAM"] | str) = "Safdar 2017", ) -> NDArrayFloat: """ Convert from :math:`I_za_zb_z` colourspace to *CIE XYZ* tristimulus values. Parameters ---------- Izazbz :math:`I_za_zb_z` colourspace array where :math:`I_z` is the achromatic response, :math:`a_z` is redness-greenness and :math:`b_z` is yellowness-blueness. constants :math:`J_za_zb_z` colourspace constants. method Computation method, *Safdar 2021* and *ZCAM* methods are equivalent. Returns ------- :class:`numpy.ndarray` *CIE XYZ* tristimulus values under *CIE Standard Illuminant D Series D65*. 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* and *1* scales are only indicative that the data is not affected by scale transformations. +------------+-----------------------+------------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``Izazbz`` | ``Iz`` : [0, 1] | ``Iz`` : [0, 1] | | | | | | | ``az`` : [-1, 1] | ``az`` : [-1, 1] | | | | | | | ``bz`` : [-1, 1] | ``bz`` : [-1, 1] | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``XYZ`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ References ---------- :cite:`Safdar2017`, :cite:`Safdar2021` Examples -------- >>> Izazbz = np.array([0.01207793, 0.00924302, 0.00526007]) >>> Izazbz_to_XYZ(Izazbz) # doctest: +ELLIPSIS array([ 0.2065401..., 0.1219723..., 0.0513696...]) """ Izazbz = as_float_array(Izazbz) method = validate_method(method, IZAZBZ_METHODS) constants = optional( constants, ( CONSTANTS_JZAZBZ_SAFDAR2017 if method == "safdar 2017" else CONSTANTS_JZAZBZ_SAFDAR2021 ), ) if method == "safdar 2017": LMS_p = vecmul(MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2017, Izazbz) else: Izazbz[..., 0] += constants.d_0 LMS_p = vecmul(MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P_SAFDAR2021, Izazbz) with domain_range_scale("ignore"): LMS = eotf_ST2084(LMS_p, 10000, constants) X_p_D65, Y_p_D65, Z_p_D65 = tsplit(vecmul(MATRIX_JZAZBZ_LMS_TO_XYZ, LMS)) X_D65 = (X_p_D65 + (constants.b - 1) * Z_p_D65) / constants.b Y_D65 = (Y_p_D65 + (constants.g - 1) * X_D65) / constants.g XYZ_D65 = tstack([X_D65, Y_D65, Z_p_D65]) return XYZ_D65
[docs] def XYZ_to_Jzazbz( XYZ_D65: ArrayLike, constants: Structure = CONSTANTS_JZAZBZ_SAFDAR2017 ) -> NDArrayFloat: """ Convert from *CIE XYZ* tristimulus values to :math:`J_za_zb_z` colourspace. Parameters ---------- XYZ_D65 *CIE XYZ* tristimulus values under *CIE Standard Illuminant D Series D65*. constants :math:`J_za_zb_z` colourspace constants. Returns ------- :class:`numpy.ndarray` :math:`J_za_zb_z` colourspace array where :math:`J_z` is Lightness, :math:`a_z` is redness-greenness and :math:`b_z` is yellowness-blueness. 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* 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** | +============+=======================+==================+ | ``Jzazbz`` | ``Jz`` : [0, 1] | ``Jz`` : [0, 1] | | | | | | | ``az`` : [-1, 1] | ``az`` : [-1, 1] | | | | | | | ``bz`` : [-1, 1] | ``bz`` : [-1, 1] | +------------+-----------------------+------------------+ References ---------- :cite:`Safdar2017` Examples -------- >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> XYZ_to_Jzazbz(XYZ) # doctest: +ELLIPSIS array([ 0.0053504..., 0.0092430..., 0.0052600...]) """ XYZ_D65 = as_float_array(XYZ_D65) with domain_range_scale("ignore"): I_z, a_z, b_z = tsplit( XYZ_to_Izazbz(XYZ_D65, CONSTANTS_JZAZBZ_SAFDAR2017, "Safdar 2017") ) J_z = ((1 + constants.d) * I_z) / (1 + constants.d * I_z) - constants.d_0 Jzazbz = tstack([J_z, a_z, b_z]) return Jzazbz
[docs] def Jzazbz_to_XYZ( Jzazbz: ArrayLike, constants: Structure = CONSTANTS_JZAZBZ_SAFDAR2017 ) -> NDArrayFloat: """ Convert from :math:`J_za_zb_z` colourspace to *CIE XYZ* tristimulus values. Parameters ---------- Jzazbz :math:`J_za_zb_z` colourspace array where :math:`J_z` is Lightness, :math:`a_z` is redness-greenness and :math:`b_z` is yellowness-blueness. constants :math:`J_za_zb_z` colourspace constants. Returns ------- :class:`numpy.ndarray` *CIE XYZ* tristimulus values under *CIE Standard Illuminant D Series D65*. 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* and *1* scales are only indicative that the data is not affected by scale transformations. +------------+-----------------------+------------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``Jzazbz`` | ``Jz`` : [0, 1] | ``Jz`` : [0, 1] | | | | | | | ``az`` : [-1, 1] | ``az`` : [-1, 1] | | | | | | | ``bz`` : [-1, 1] | ``bz`` : [-1, 1] | +------------+-----------------------+------------------+ +------------+-----------------------+------------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+==================+ | ``XYZ`` | ``UN`` | ``UN`` | +------------+-----------------------+------------------+ References ---------- :cite:`Safdar2017` Examples -------- >>> Jzazbz = np.array([0.00535048, 0.00924302, 0.00526007]) >>> Jzazbz_to_XYZ(Jzazbz) # doctest: +ELLIPSIS array([ 0.2065402..., 0.1219723..., 0.0513696...]) """ J_z, a_z, b_z = tsplit(as_float_array(Jzazbz)) I_z = (J_z + constants.d_0) / ( 1 + constants.d - constants.d * (J_z + constants.d_0) ) with domain_range_scale("ignore"): XYZ_D65 = Izazbz_to_XYZ( tstack([I_z, a_z, b_z]), CONSTANTS_JZAZBZ_SAFDAR2017, "Safdar 2017" ) return XYZ_D65