Source code for colour.models.igpgtg

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

Defines the :math:`I_GP_GT_G` colourspace transformations:

-   :func:`colour.XYZ_to_IgPgTg`
-   :func:`colour.IgPgTg_to_XYZ`

References
----------
-   :cite:`Hellwig2020` : Hellwig, L., & Fairchild, M. D. (2020). Using
    Gaussian Spectra to Derive a Hue-linear Color Space. Journal of Perceptual
    Imaging. doi:10.2352/J.Percept.Imaging.2020.3.2.020401
"""

import numpy as np

from colour.algebra import spow, vector_dot
from colour.utilities import from_range_1, to_domain_1

__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__ = [
    'MATRIX_IGPGTG_XYZ_TO_LMS', 'MATRIX_IGPGTG_LMS_TO_XYZ',
    'MATRIX_IGPGTG_LMS_TO_IGPGTG', 'MATRIX_IGPGTG_IGPGTG_TO_LMS',
    'XYZ_to_IgPgTg', 'IgPgTg_to_XYZ'
]

MATRIX_IGPGTG_XYZ_TO_LMS = np.array([
    [2.968, 2.741, -0.649],
    [1.237, 5.969, -0.173],
    [-0.318, 0.387, 2.311],
])
"""
*CIE XYZ* tristimulus values to normalised cone responses matrix.

MATRIX_IGPGTG_XYZ_TO_LMS : array_like, (3, 3)
"""

MATRIX_IGPGTG_LMS_TO_XYZ = np.linalg.inv(MATRIX_IGPGTG_XYZ_TO_LMS)
"""
Normalised cone responses to *CIE XYZ* tristimulus values matrix.

MATRIX_IGPGTG_LMS_TO_XYZ : array_like, (3, 3)
"""

MATRIX_IGPGTG_LMS_TO_IGPGTG = np.array([
    [0.117, 1.464, 0.130],
    [8.285, -8.361, 21.400],
    [-1.208, 2.412, -36.530],
])
"""
Normalised cone responses to :math:`I_GP_GT_G` colourspace matrix.

MATRIX_IGPGTG_LMS_TO_IGPGTG : array_like, (3, 3)
"""

MATRIX_IGPGTG_IGPGTG_TO_LMS = np.linalg.inv(MATRIX_IGPGTG_LMS_TO_IGPGTG)
"""
:math:`I_GP_GT_G` colourspace to normalised cone responses matrix.

MATRIX_IGPGTG_IGPGTG_TO_LMS : array_like, (3, 3)
"""


[docs]def XYZ_to_IgPgTg(XYZ): """ Converts from *CIE XYZ* tristimulus values to :math:`I_GP_GT_G` colourspace. Parameters ---------- XYZ : array_like *CIE XYZ* tristimulus values. Returns ------- ndarray :math:`I_GP_GT_G` colourspace array. Notes ----- +------------+-----------------------+-----------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``XYZ`` | [0, 1] | [0, 1] | +------------+-----------------------+-----------------+ +------------+-----------------------+-----------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``IgPgTg`` | ``IG`` : [0, 1] | ``IG`` : [0, 1] | | | | | | | ``PG`` : [-1, 1] | ``PG`` : [-1, 1]| | | | | | | ``TG`` : [-1, 1] | ``TG`` : [-1, 1]| +------------+-----------------------+-----------------+ - Input *CIE XYZ* tristimulus values must be adapted to *CIE Standard Illuminant D Series* *D65*. References ---------- :cite:`Hellwig2020` Examples -------- >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> XYZ_to_IgPgTg(XYZ) # doctest: +ELLIPSIS array([ 0.4242125..., 0.1863249..., 0.1068922...]) """ XYZ = to_domain_1(XYZ) LMS = vector_dot(MATRIX_IGPGTG_XYZ_TO_LMS, XYZ) LMS_prime = spow(LMS / np.array([18.36, 21.46, 19435]), 0.427) IgPgTg = vector_dot(MATRIX_IGPGTG_LMS_TO_IGPGTG, LMS_prime) return from_range_1(IgPgTg)
[docs]def IgPgTg_to_XYZ(IgPgTg): """ Converts from :math:`I_GP_GT_G` colourspace to *CIE XYZ* tristimulus values. Parameters ---------- IgPgTg : array_like :math:`I_GP_GT_G` colourspace array. Returns ------- ndarray *CIE XYZ* tristimulus values. Notes ----- +------------+-----------------------+-----------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``IgPgTg`` | ``IG`` : [0, 1] | ``IG`` : [0, 1] | | | | | | | ``PG`` : [-1, 1] | ``PG`` : [-1, 1]| | | | | | | ``TG`` : [-1, 1] | ``TG`` : [-1, 1]| +------------+-----------------------+-----------------+ +------------+-----------------------+-----------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``XYZ`` | [0, 1] | [0, 1] | +------------+-----------------------+-----------------+ References ---------- :cite:`Hellwig2020` Examples -------- >>> IgPgTg = np.array([0.42421258, 0.18632491, 0.10689223]) >>> IgPgTg_to_XYZ(IgPgTg) # doctest: +ELLIPSIS array([ 0.2065400..., 0.1219722..., 0.0513695...]) """ IgPgTg = to_domain_1(IgPgTg) LMS = vector_dot(MATRIX_IGPGTG_IGPGTG_TO_LMS, IgPgTg) LMS_prime = spow(LMS, 1 / 0.427) * np.array([18.36, 21.46, 19435]) XYZ = vector_dot(MATRIX_IGPGTG_LMS_TO_XYZ, LMS_prime) return from_range_1(XYZ)