"""
: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
"""
from __future__ import annotations
import numpy as np
from colour.algebra import spow, vector_dot
from colour.hints import ArrayLike, NDArray
from colour.utilities import from_range_1, to_domain_1
__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_IGPGTG_XYZ_TO_LMS",
"MATRIX_IGPGTG_LMS_TO_XYZ",
"MATRIX_IGPGTG_LMS_P_TO_IGPGTG",
"MATRIX_IGPGTG_IGPGTG_TO_LMS_P",
"XYZ_to_IgPgTg",
"IgPgTg_to_XYZ",
]
MATRIX_IGPGTG_XYZ_TO_LMS: NDArray = 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_LMS_TO_XYZ: NDArray = np.linalg.inv(MATRIX_IGPGTG_XYZ_TO_LMS)
"""Normalised cone responses to *CIE XYZ* tristimulus values matrix."""
MATRIX_IGPGTG_LMS_P_TO_IGPGTG: NDArray = np.array(
[
[0.117, 1.464, 0.130],
[8.285, -8.361, 21.400],
[-1.208, 2.412, -36.530],
]
)
"""Normalised non-linear cone responses to :math:`I_GP_GT_G` colourspace matrix."""
MATRIX_IGPGTG_IGPGTG_TO_LMS_P: NDArray = np.linalg.inv(
MATRIX_IGPGTG_LMS_P_TO_IGPGTG
)
""":math:`I_GP_GT_G` colourspace to normalised non-linear cone responses matrix."""
[docs]def XYZ_to_IgPgTg(XYZ: ArrayLike) -> NDArray:
"""
Convert from *CIE XYZ* tristimulus values to :math:`I_GP_GT_G`
colourspace.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
Returns
-------
:class:`numpy.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_P_TO_IGPGTG, LMS_prime)
return from_range_1(IgPgTg)
[docs]def IgPgTg_to_XYZ(IgPgTg: ArrayLike) -> NDArray:
"""
Convert from :math:`I_GP_GT_G` colourspace to *CIE XYZ* tristimulus
values.
Parameters
----------
IgPgTg
:math:`I_GP_GT_G` colourspace array.
Returns
-------
:class:`numpy.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_P, 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)