#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
ATD (1995) Colour Vision Model
==============================
Defines ATD (1995) colour vision model objects:
- :class:`ATD95_Specification`
- :func:`XYZ_to_ATD95`
See Also
--------
`ATD (1995) Colour Vision Model IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/appearance/atd95.ipynb>`_ # noqa
Notes
-----
- According to CIE TC1-34 definition of a colour appearance model, the
*ATD95* model cannot be considered as a colour appearance model. It was
developed with different aims and is described as a model of colour vision.
References
----------
.. [1] Fairchild, M. D. (2013). ATD Model. In Color Appearance Models
(3rd ed., pp. 5852–5991). Wiley. ASIN:B00DAYO8E2
.. [2] Guth, S. L. (1995). Further applications of the ATD model for color
vision. In E. Walowit (Ed.), IS&T/SPIE’s Symposium on Electronic …
(Vol. 2414, pp. 12–26). doi:10.1117/12.206546
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.utilities.array import tsplit, tstack
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - Colour Developers'
__license__ = 'GPL V3.0 - http://www.gnu.org/licenses/'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['ATD95_ReferenceSpecification',
'ATD95_Specification',
'XYZ_to_ATD95',
'luminance_to_retinal_illuminance',
'XYZ_to_LMS_ATD95',
'opponent_colour_dimensions',
'final_response']
[docs]class ATD95_ReferenceSpecification(
namedtuple('ATD95_ReferenceSpecification',
('H', 'C', 'Br', 'A_1', 'T_1', 'D_1', 'A_2', 'T_2', 'D_2'))):
"""
Defines the ATD (1995) colour vision model reference specification.
This specification has field names consistent with Fairchild (2013)
reference.
Parameters
----------
H : numeric or array_like
*Hue* angle :math:`H` in degrees.
C : numeric or array_like
Correlate of *saturation* :math:`C`. Guth (1995) incorrectly uses the
terms saturation and chroma interchangeably. However, :math:`C` is here
a measure of saturation rather than chroma since it is measured
relative to the achromatic response for the stimulus rather than that
of a similarly illuminated white.
Br : numeric or array_like
Correlate of *brightness* :math:`Br`.
A_1 : numeric or array_like
First stage :math:`A_1` response.
T_1 : numeric or array_like
First stage :math:`T_1` response.
D_1 : numeric or array_like
First stage :math:`D_1` response.
A_2 : numeric or array_like
Second stage :math:`A_2` response.
T_2 : numeric or array_like
Second stage :math:`A_2` response.
D_2 : numeric or array_like
Second stage :math:`D_2` response.
"""
[docs]class ATD95_Specification(
namedtuple('ATD95_Specification',
('h', 'C', 'Q', 'A_1', 'T_1', 'D_1', 'A_2', 'T_2', 'D_2'))):
"""
Defines the ATD (1995) colour vision model specification.
This specification has field names consistent with the remaining colour
appearance models in :mod:`colour.appearance` but diverge from Fairchild
(2013) reference.
Notes
-----
- This specification is the one used in the current model implementation.
Parameters
----------
h : numeric or array_like
*Hue* angle :math:`H` in degrees.
C : numeric or array_like
Correlate of *saturation* :math:`C`. Guth (1995) incorrectly uses the
terms saturation and chroma interchangeably. However, :math:`C` is here
a measure of saturation rather than chroma since it is measured
relative to the achromatic response for the stimulus rather than that
of a similarly illuminated white.
Q : numeric or array_like
Correlate of *brightness* :math:`Br`.
A_1 : numeric or array_like
First stage :math:`A_1` response.
T_1 : numeric or array_like
First stage :math:`T_1` response.
D_1 : numeric or array_like
First stage :math:`D_1` response.
A_2 : numeric or array_like
Second stage :math:`A_2` response.
T_2 : numeric or array_like
Second stage :math:`A_2` response.
D_2 : numeric or array_like
Second stage :math:`D_2` response.
"""
[docs]def XYZ_to_ATD95(XYZ, XYZ_0, Y_0, k_1, k_2, sigma=300):
"""
Computes the ATD (1995) colour vision model correlates.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus in domain
[0, 100].
XYZ_0 : array_like
*CIE XYZ* tristimulus values of reference white in domain [0, 100].
Y_0 : numeric or array_like
Absolute adapting field luminance in :math:`cd/m^2`.
k_1 : numeric or array_like
Application specific weight :math:`k_1`.
k_2 : numeric or array_like
Application specific weight :math:`k_2`.
sigma : numeric or array_like, optional
Constant :math:`\sigma` varied to predict different types of data.
Returns
-------
ATD95_Specification
ATD (1995) colour vision model specification.
Warning
-------
The input domain of that definition is non standard!
Notes
-----
- Input *CIE XYZ* tristimulus values are in domain [0, 100].
- Input *CIE XYZ_0* tristimulus values are in domain [0, 100].
- For unrelated colors, there is only self-adaptation, and :math:`k_1` is
set to 1.0 while :math:`k_2` is set to 0.0. For related colors such as
typical colorimetric applications, :math:`k_1` is set to 0.0 and
:math:`k_2` is set to a value between 15 and 50 *(Guth, 1995)*.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_0 = np.array([95.05, 100.00, 108.88])
>>> Y_0 = 318.31
>>> k_1 = 0.0
>>> k_2 = 50.0
>>> XYZ_to_ATD95(XYZ, XYZ_0, Y_0, k_1, k_2) # doctest: +ELLIPSIS
ATD95_Specification(h=1.9089869..., C=1.2064060..., Q=0.1814003..., \
A_1=0.1787931... T_1=0.0286942..., D_1=0.0107584..., A_2=0.0192182..., \
T_2=0.0205377..., D_2=0.0107584...)
"""
Y_0 = np.asarray(Y_0)
k_1 = np.asarray(k_1)
k_2 = np.asarray(k_2)
sigma = np.asarray(sigma)
XYZ = luminance_to_retinal_illuminance(XYZ, Y_0)
XYZ_0 = luminance_to_retinal_illuminance(XYZ_0, Y_0)
# Computing adaptation model.
LMS = XYZ_to_LMS_ATD95(XYZ)
XYZ_a = k_1[..., np.newaxis] * XYZ + k_2[..., np.newaxis] * XYZ_0
LMS_a = XYZ_to_LMS_ATD95(XYZ_a)
LMS_g = LMS * (sigma[..., np.newaxis] / (sigma[..., np.newaxis] + LMS_a))
# Computing opponent colour dimensions.
A_1, T_1, D_1, A_2, T_2, D_2 = tsplit(
opponent_colour_dimensions(LMS_g))
# -------------------------------------------------------------------------
# Computing the correlate of *brightness* :math:`Br`.
# -------------------------------------------------------------------------
Br = (A_1 ** 2 + T_1 ** 2 + D_1 ** 2) ** 0.5
# -------------------------------------------------------------------------
# Computing the correlate of *saturation* :math:`C`.
# -------------------------------------------------------------------------
C = (T_2 ** 2 + D_2 ** 2) ** 0.5 / A_2
# -------------------------------------------------------------------------
# Computing the *hue* :math:`H`.
# -------------------------------------------------------------------------
H = T_2 / D_2
return ATD95_Specification(H, C, Br, A_1, T_1, D_1, A_2, T_2, D_2)
[docs]def luminance_to_retinal_illuminance(XYZ, Y_c):
"""
Converts from luminance in :math:`cd/m^2` to retinal illuminance in
trolands.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Y_c : numeric or array_like
Absolute adapting field luminance in :math:`cd/m^2`.
Returns
-------
ndarray
Converted *CIE XYZ* tristimulus values in trolands.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> Y_0 = 318.31
>>> luminance_to_retinal_illuminance(XYZ, Y_0) # doctest: +ELLIPSIS
array([ 479.4445924..., 499.3174313..., 534.5631673...])
"""
XYZ = np.asarray(XYZ)
Y_c = np.asarray(Y_c)
return 18 * (Y_c[..., np.newaxis] * XYZ / 100.) ** 0.8
[docs]def XYZ_to_LMS_ATD95(XYZ):
"""
Converts from *CIE XYZ* tristimulus values to *LMS* cone responses.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Returns
-------
ndarray
*LMS* cone responses.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_to_LMS_ATD95(XYZ) # doctest: +ELLIPSIS
array([ 6.2283272..., 7.4780666..., 3.8859772...])
"""
X, Y, Z = tsplit(XYZ)
L = ((0.66 * (0.2435 * X + 0.8524 * Y - 0.0516 * Z)) ** 0.7) + 0.024
M = ((-0.3954 * X + 1.1642 * Y + 0.0837 * Z) ** 0.7) + 0.036
S = ((0.43 * (0.04 * Y + 0.6225 * Z)) ** 0.7) + 0.31
LMS = tstack((L, M, S))
return LMS
[docs]def opponent_colour_dimensions(LMS_g):
"""
Returns opponent colour dimensions from given post adaptation cone signals.
Parameters
----------
LMS_g : array_like
Post adaptation cone signals.
Returns
-------
ndarray
Opponent colour dimensions.
Examples
--------
>>> LMS_g = np.array([6.95457922, 7.08945043, 6.44069316])
>>> opponent_colour_dimensions(LMS_g) # doctest: +ELLIPSIS
array([ 0.1787931..., 0.0286942..., 0.0107584..., 0.0192182..., ...])
"""
L_g, M_g, S_g = tsplit(LMS_g)
A_1i = 3.57 * L_g + 2.64 * M_g
T_1i = 7.18 * L_g - 6.21 * M_g
D_1i = -0.7 * L_g + 0.085 * M_g + S_g
A_2i = 0.09 * A_1i
T_2i = 0.43 * T_1i + 0.76 * D_1i
D_2i = D_1i
A_1 = final_response(A_1i)
T_1 = final_response(T_1i)
D_1 = final_response(D_1i)
A_2 = final_response(A_2i)
T_2 = final_response(T_2i)
D_2 = final_response(D_2i)
return tstack((A_1, T_1, D_1, A_2, T_2, D_2))
[docs]def final_response(value):
"""
Returns the final response of given opponent colour dimension.
Parameters
----------
value : numeric or array_like
Opponent colour dimension.
Returns
-------
numeric or ndarray
Final response of opponent colour dimension.
Examples
--------
>>> final_response(43.54399695501678) # doctest: +ELLIPSIS
0.1787931...
"""
value = np.asarray(value)
return value / (200 + np.abs(value))
Colour 0.3