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
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
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..., 0.0205377...,
0.0107584...])
"""
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))
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))
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)
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)
