Source code for colour.models.jzazbz

# -*- coding: utf-8 -*-
"""
:math:`J_zA_zB_z` Colourspace
=============================

Defines the :math:`J_zA_zB_z` colourspace:

-   :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
"""

import numpy as np

from colour.algebra import vector_dot
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, domain_range_scale, from_range_1,
                              to_domain_1, tsplit, tstack)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2021 - 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_JZAZBZ', 'MATRIX_JZAZBZ_XYZ_TO_LMS', 'MATRIX_JZAZBZ_LMS_TO_XYZ',
    'MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ', 'MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P',
    'XYZ_to_JzAzBz', 'JzAzBz_to_XYZ'
]

CONSTANTS_JZAZBZ = Structure(
    b=1.15, g=0.66, d=-0.56, d_0=1.6295499532821566 * 10 ** -11)
CONSTANTS_JZAZBZ.update(CONSTANTS_ST2084)
CONSTANTS_JZAZBZ.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 : Structure
"""

MATRIX_JZAZBZ_XYZ_TO_LMS = 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_XYZ_TO_LMS : array_like, (3, 3)
"""

MATRIX_JZAZBZ_LMS_TO_XYZ = 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_TO_XYZ : array_like, (3, 3)
"""

MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ = 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_LMS_P_TO_IZAZBZ : array_like, (3, 3)
"""

MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P = np.linalg.inv(MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ)
"""
:math:`I_zA_zB_z` intermediate colourspace to :math:`LMS_p`
*SMPTE ST 2084:2014* encoded normalised cone responses matrix.

MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P : array_like, (3, 3)
"""


[docs]def XYZ_to_JzAzBz(XYZ_D65, constants=CONSTANTS_JZAZBZ): """ Converts from *CIE XYZ* tristimulus values to :math:`J_zA_zB_z` colourspace. Parameters ---------- XYZ_D65 : array_like *CIE XYZ* tristimulus values under *CIE Standard Illuminant D Series D65*. constants : Structure, optional :math:`J_zA_zB_z` colourspace constants. Returns ------- 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 / EOCF) 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...]) """ X_D65, Y_D65, Z_D65 = tsplit(to_domain_1(XYZ_D65)) 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 = vector_dot(MATRIX_JZAZBZ_XYZ_TO_LMS, XYZ_p_D65) with domain_range_scale('ignore'): LMS_p = eotf_inverse_ST2084(LMS, 10000, constants) I_z, A_z, B_z = tsplit(vector_dot(MATRIX_JZAZBZ_LMS_P_TO_IZAZBZ, LMS_p)) J_z = ((1 + constants.d) * I_z) / (1 + constants.d * I_z) - constants.d_0 JzAzBz = tstack([J_z, A_z, B_z]) return from_range_1(JzAzBz)
[docs]def JzAzBz_to_XYZ(JzAzBz, constants=CONSTANTS_JZAZBZ): """ Converts from :math:`J_zA_zB_z` colourspace to *CIE XYZ* tristimulus values. Parameters ---------- JzAzBz : array_like :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 : Structure, optional :math:`J_zA_zB_z` colourspace constants. Returns ------- 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(to_domain_1(JzAzBz)) I_z = ((J_z + constants.d_0) / (1 + constants.d - constants.d * (J_z + constants.d_0))) LMS_p = vector_dot(MATRIX_JZAZBZ_IZAZBZ_TO_LMS_P, tstack([I_z, A_z, B_z])) with domain_range_scale('ignore'): LMS = eotf_ST2084(LMS_p, 10000, constants) X_p_D65, Y_p_D65, Z_p_D65 = tsplit( vector_dot(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 from_range_1(XYZ_D65)