def CAM16_to_XYZ(CAM16_specification,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Converts from *CAM16* specification to *CIE XYZ* tristimulus values.
This is the *inverse* implementation.
Parameters
----------
CAM16_specification : CAM16_Specification
*CAM16* colour appearance model specification. Correlate of
*Lightness* :math:`J`, correlate of *chroma* :math:`C` or correlate of
*colourfulness* :math:`M` and *hue* angle :math:`h` in degrees must be
specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions.
discount_illuminant : bool, optional
Discount the illuminant.
Returns
-------
XYZ : ndarray
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM16_specification`` argument.
Notes
-----
+---------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``CAM16_specification.J`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.C`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.h`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.s`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.Q`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.M`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.H`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
+---------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
- ``CAM16_specification`` can also be passed as a compatible argument
to :func:`colour.utilities.as_namedtuple` definition.
References
----------
:cite:`Li2017`
Examples
--------
>>> specification = CAM16_Specification(J=41.731207905126638,
... C=0.103355738709070,
... h=217.067959767393010)
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> CAM16_to_XYZ(specification, XYZ_w, L_A, Y_b) # doctest: +ELLIPSIS
array([ 19.01..., 20... , 21.78...])
"""
J, C, h, _s, _Q, M, _H, _HC = as_namedtuple(CAM16_specification,
CAM16_Specification)
J = to_domain_100(J)
C = to_domain_100(C) if C is not None else C
h = to_domain_degrees(h)
M = to_domain_100(M) if M is not None else M
L_A = as_float_array(L_A)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else np.ones(L_A.shape))
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
if C is None and M is not None:
C = M / spow(F_L, 0.25)
elif C is None:
raise ValueError('Either "C" or "M" correlate must be defined in '
'the "CAM16_specification" argument!')
# Step 2
# Computing temporary magnitude quantity :math:`t`.
t = temporary_magnitude_quantity_inverse(C, J, n)
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing achromatic response :math:`A` for the stimulus.
A = achromatic_response_inverse(A_w, J, surround.c, z)
# Computing *P_1* to *P_3*.
P_n = P(surround.N_c, N_cb, e_t, t, A, N_bb)
_P_1, P_2, _P_3 = tsplit(P_n)
# Step 3
# Computing opponent colour dimensions :math:`a` and :math:`b`.
a, b = tsplit(opponent_colour_dimensions_inverse(P_n, h))
# Step 4
# Computing post-adaptation non linear response compression matrix.
RGB_a = post_adaptation_non_linear_response_compression_matrix(P_2, a, b)
# Step 5
# Applying inverse post-adaptation non linear response compression.
RGB_c = post_adaptation_non_linear_response_compression_inverse(RGB_a, F_L)
# Step 6
RGB = RGB_c / D_RGB
# Step 7
XYZ = dot_vector(M_16_INVERSE, RGB)
return from_range_100(XYZ)
def CAM16_to_XYZ(CAM16_specification,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Converts *CAM16* specification to *CIE XYZ* tristimulus values.
This is the *reverse* implementation.
Parameters
----------
CAM16_specification : CAM16_Specification
*CAM16* colour appearance model specification. Correlate of
*Lightness* :math:`J`, correlate of *chroma* :math:`C` or correlate of
*colourfulness* :math:`M` and *hue* angle :math:`h` in degrees must be
specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions.
discount_illuminant : bool, optional
Discount the illuminant.
Returns
-------
XYZ : ndarray
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM16_specification`` argument.
Notes
-----
+---------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``CAM16_specification.h`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.H`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
+---------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
- ``CAM16_specification`` can also be passed as a compatible argument
to :func:`colour.utilities.as_namedtuple` definition.
References
----------
:cite:`Li2017`
Examples
--------
>>> specification = CAM16_Specification(J=41.731207905126638,
... C=0.103355738709070,
... h=217.067959767393010)
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> CAM16_to_XYZ(specification, XYZ_w, L_A, Y_b) # doctest: +ELLIPSIS
array([ 19.01..., 20... , 21.78...])
"""
J, C, h, _s, _Q, M, _H, _HC = as_namedtuple(CAM16_specification,
CAM16_Specification)
L_A = as_float_array(L_A)
h = to_domain_degrees(h)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else np.ones(L_A.shape))
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
if C is None and M is not None:
C = M / spow(F_L, 0.25)
elif C is None:
raise ValueError('Either "C" or "M" correlate must be defined in '
'the "CAM16_specification" argument!')
# Step 2
# Computing temporary magnitude quantity :math:`t`.
t = temporary_magnitude_quantity_reverse(C, J, n)
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing achromatic response :math:`A` for the stimulus.
A = achromatic_response_reverse(A_w, J, surround.c, z)
# Computing *P_1* to *P_3*.
P_n = P(surround.N_c, N_cb, e_t, t, A, N_bb)
_P_1, P_2, _P_3 = tsplit(P_n)
# Step 3
# Computing opponent colour dimensions :math:`a` and :math:`b`.
a, b = tsplit(opponent_colour_dimensions_reverse(P_n, h))
# Step 4
# Computing post-adaptation non linear response compression matrix.
RGB_a = post_adaptation_non_linear_response_compression_matrix(P_2, a, b)
# Step 5
# Applying reverse post-adaptation non linear response compression.
RGB_c = post_adaptation_non_linear_response_compression_reverse(RGB_a, F_L)
# Step 6
RGB = RGB_c / D_RGB
# Step 7
XYZ = dot_vector(M_16_INVERSE, RGB)
return from_range_100(XYZ)
def XYZ_to_CAM16(XYZ,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Computes the *CAM16* colour appearance model correlates from given
*CIE XYZ* tristimulus values.
This is the *forward* implementation.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions induction factors.
discount_illuminant : bool, optional
Truth value indicating if the illuminant should be discounted.
Returns
-------
CAM16_Specification
*CAM16* colour appearance model specification.
Notes
-----
+---------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
+---------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``CAM16_specification.J`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.C`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.h`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.s`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.Q`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.M`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_specification.H`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> surround = CAM16_VIEWING_CONDITIONS['Average']
>>> XYZ_to_CAM16(XYZ, XYZ_w, L_A, Y_b, surround) # doctest: +ELLIPSIS
CAM16_Specification(J=41.7312079..., C=0.1033557..., h=217.0679597..., \
s=2.3450150..., Q=195.3717089..., M=0.1074367..., H=275.5949861..., HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
Y_b = as_float_array(Y_b)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else np.ones(L_A.shape))
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB = dot_vector(M_16, XYZ)
# Step 2
RGB_c = D_RGB * RGB
# Step 3
# Applying forward post-adaptation non linear response compression.
RGB_a = post_adaptation_non_linear_response_compression_forward(RGB_c, F_L)
# Step 4
# Converting to preliminary cartesian coordinates.
a, b = tsplit(opponent_colour_dimensions_forward(RGB_a))
# Computing the *hue* angle :math:`h`.
h = hue_angle(a, b)
# Step 5
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing hue :math:`h` quadrature :math:`H`.
H = hue_quadrature(h)
# TODO: Compute hue composition.
# Step 6
# Computing achromatic responses for the stimulus.
A = achromatic_response_forward(RGB_a, N_bb)
# Step 7
# Computing the correlate of *Lightness* :math:`J`.
J = lightness_correlate(A, A_w, surround.c, z)
# Step 8
# Computing the correlate of *brightness* :math:`Q`.
Q = brightness_correlate(surround.c, J, A_w, F_L)
# Step 9
# Computing the correlate of *chroma* :math:`C`.
C = chroma_correlate(J, n, surround.N_c, N_cb, e_t, a, b, RGB_a)
# Computing the correlate of *colourfulness* :math:`M`.
M = colourfulness_correlate(C, F_L)
# Computing the correlate of *saturation* :math:`s`.
s = saturation_correlate(M, Q)
return CAM16_Specification(from_range_100(J), from_range_100(C),
from_range_degrees(h), from_range_100(s),
from_range_100(Q), from_range_100(M),
from_range_degrees(H), None)
def CAM16_to_XYZ(
specification: CAM_Specification_CAM16,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
Y_b: FloatingOrArrayLike,
surround: Union[
InductionFactors_CIECAM02,
InductionFactors_CAM16] = VIEWING_CONDITIONS_CAM16["Average"],
discount_illuminant: Boolean = False,
) -> NDArray:
"""
Convert from *CAM16* specification to *CIE XYZ* tristimulus values.
Parameters
----------
specification : CAM_Specification_CAM16
*CAM16* colour appearance model specification. Correlate of
*Lightness* :math:`J`, correlate of *chroma* :math:`C` or correlate of
*colourfulness* :math:`M` and *hue* angle :math:`h` in degrees must be
specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 x L_b / L_w` where :math:`L_w` is the luminance of the
light source and :math:`L_b` is the luminance of the background. For
viewing images, :math:`Y_b` can be the average :math:`Y` value for the
pixels in the entire image, or frequently, a :math:`Y` value of 20,
approximate an :math:`L^*` of 50 is used.
surround
Surround viewing conditions.
discount_illuminant
Discount the illuminant.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM_Specification_CAM16`` argument.
Notes
-----
+-------------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+===============================+=======================+===============+
| ``CAM_Specification_CAM16.J`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.C`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.h`` | [0, 360] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.s`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.Q`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.M`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.H`` | [0, 360] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> specification = CAM_Specification_CAM16(J=41.731207905126638,
... C=0.103355738709070,
... h=217.067959767393010)
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> CAM16_to_XYZ(specification, XYZ_w, L_A, Y_b) # doctest: +ELLIPSIS
array([ 19.01..., 20... , 21.78...])
"""
J, C, h, _s, _Q, M, _H, _HC = astuple(specification)
J = to_domain_100(J)
C = to_domain_100(C)
h = to_domain_degrees(h)
M = to_domain_100(M)
L_A = as_float_array(L_A)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = vector_dot(MATRIX_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else ones(L_A.shape))
n, F_L, N_bb, N_cb, z = viewing_condition_dependent_parameters(
Y_b, Y_w, L_A)
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non-linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
if has_only_nan(C) and not has_only_nan(M):
C = M / spow(F_L, 0.25)
elif has_only_nan(C):
raise ValueError('Either "C" or "M" correlate must be defined in '
'the "CAM_Specification_CAM16" argument!')
# Step 2
# Computing temporary magnitude quantity :math:`t`.
t = temporary_magnitude_quantity_inverse(C, J, n)
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing achromatic response :math:`A` for the stimulus.
A = achromatic_response_inverse(A_w, J, surround.c, z)
# Computing *P_1* to *P_3*.
P_n = P(surround.N_c, N_cb, e_t, t, A, N_bb)
_P_1, P_2, _P_3 = tsplit(P_n)
# Step 3
# Computing opponent colour dimensions :math:`a` and :math:`b`.
a, b = tsplit(opponent_colour_dimensions_inverse(P_n, h))
# Step 4
# Applying post-adaptation non-linear response compression matrix.
RGB_a = matrix_post_adaptation_non_linear_response_compression(P_2, a, b)
# Step 5
# Applying inverse post-adaptation non-linear response compression.
RGB_c = post_adaptation_non_linear_response_compression_inverse(RGB_a, F_L)
# Step 6
RGB = RGB_c / D_RGB
# Step 7
XYZ = vector_dot(MATRIX_INVERSE_16, RGB)
return from_range_100(XYZ)
def XYZ_to_CAM16(XYZ,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Computes the *CAM16* colour appearance model correlates from given
*CIE XYZ* tristimulus values.
This is the *forward* implementation.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions induction factors.
discount_illuminant : bool, optional
Truth value indicating if the illuminant should be discounted.
Returns
-------
CAM16_Specification
*CAM16* colour appearance model specification.
Notes
-----
+---------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+---------------------------+-----------------------+---------------+
+---------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========================+=======================+===============+
| ``CAM16_Specification.h`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
| ``CAM16_Specification.H`` | [0, 360] | [0, 1] |
+---------------------------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> surround = CAM16_VIEWING_CONDITIONS['Average']
>>> XYZ_to_CAM16(XYZ, XYZ_w, L_A, Y_b, surround) # doctest: +ELLIPSIS
CAM16_Specification(J=41.7312079..., C=0.1033557..., h=217.0679597..., \
s=2.3450150..., Q=195.3717089..., M=0.1074367..., H=275.5949861..., HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
Y_b = as_float_array(Y_b)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else np.ones(L_A.shape))
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB = dot_vector(M_16, XYZ)
# Step 2
RGB_c = D_RGB * RGB
# Step 3
# Applying forward post-adaptation non linear response compression.
RGB_a = post_adaptation_non_linear_response_compression_forward(RGB_c, F_L)
# Step 4
# Converting to preliminary cartesian coordinates.
a, b = tsplit(opponent_colour_dimensions_forward(RGB_a))
# Computing the *hue* angle :math:`h`.
h = hue_angle(a, b)
# Step 5
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing hue :math:`h` quadrature :math:`H`.
H = hue_quadrature(h)
# TODO: Compute hue composition.
# Step 6
# Computing achromatic responses for the stimulus.
A = achromatic_response_forward(RGB_a, N_bb)
# Step 7
# Computing the correlate of *Lightness* :math:`J`.
J = lightness_correlate(A, A_w, surround.c, z)
# Step 8
# Computing the correlate of *brightness* :math:`Q`.
Q = brightness_correlate(surround.c, J, A_w, F_L)
# Step 9
# Computing the correlate of *chroma* :math:`C`.
C = chroma_correlate(J, n, surround.N_c, N_cb, e_t, a, b, RGB_a)
# Computing the correlate of *colourfulness* :math:`M`.
M = colourfulness_correlate(C, F_L)
# Computing the correlate of *saturation* :math:`s`.
s = saturation_correlate(M, Q)
return CAM16_Specification(J, C, from_range_degrees(h), s, Q, M,
from_range_degrees(H), None)
def CAM16_to_XYZ(CAM16_specification,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Converts *CAM16* specification to *CIE XYZ* tristimulus values.
This is the *reverse* implementation.
Parameters
----------
CAM16_specification : CAM16_Specification
*CAM16* colour appearance model specification. Correlate of
*Lightness* :math:`J`, correlate of *chroma* :math:`C` or correlate of
*colourfulness* :math:`M` and *hue* angle :math:`h` in degrees must be
specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions.
discount_illuminant : bool, optional
Discount the illuminant.
Returns
-------
XYZ : ndarray
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM16_specification`` argument.
Warning
-------
The output range of that definition is non standard!
Notes
-----
- ``CAM16_specification`` can also be passed as a compatible argument
:func:`colour.utilities.as_namedtuple` definition.
- Input *CIE XYZ_w* tristimulus values are in domain [0, 100].
- Output *CIE XYZ* tristimulus values are in range [0, 100].
References
----------
- :cite:`Li2017`
Examples
--------
>>> specification = CAM16_Specification(J=41.718025051415616,
... C=11.941344635245843,
... h=210.38389558131118)
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> CAM16_to_XYZ(specification, XYZ_w, L_A, Y_b) # doctest: +ELLIPSIS
array([ 19.01..., 20... , 21.78...])
"""
J, C, h, _s, _Q, M, _H, _HC = as_namedtuple(CAM16_specification,
CAM16_Specification)
_X_w, Y_w, _Zw = tsplit(XYZ_w)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else 1)
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = D[..., np.newaxis] * XYZ_w / RGB_w + 1 - D[..., np.newaxis]
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
if C is None and M is not None:
C = M / F_L**0.25
elif C is None:
raise ValueError('Either "C" or "M" correlate must be defined in '
'the "CAM16_specification" argument!')
# Step 2
# Computing temporary magnitude quantity :math:`t`.
t = temporary_magnitude_quantity_reverse(C, J, n)
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing achromatic response :math:`A` for the stimulus.
A = achromatic_response_reverse(A_w, J, surround.c, z)
# Computing *P_1* to *P_3*.
P_n = P(surround.N_c, N_cb, e_t, t, A, N_bb)
_P_1, P_2, _P_3 = tsplit(P_n)
# Step 3
# Computing opponent colour dimensions :math:`a` and :math:`b`.
a, b = tsplit(opponent_colour_dimensions_reverse(P_n, h))
# Step 4
# Computing post-adaptation non linear response compression matrix.
RGB_a = post_adaptation_non_linear_response_compression_matrix(P_2, a, b)
# Step 5
# Applying reverse post-adaptation non linear response compression.
RGB_c = post_adaptation_non_linear_response_compression_reverse(RGB_a, F_L)
# Step 6
RGB = RGB_c / D_RGB
# Step 7
XYZ = dot_vector(M_16_INVERSE, RGB)
return XYZ
def XYZ_to_CAM16(
XYZ: ArrayLike,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
Y_b: FloatingOrArrayLike,
surround: Union[
InductionFactors_CIECAM02,
InductionFactors_CAM16] = VIEWING_CONDITIONS_CAM16["Average"],
discount_illuminant: Boolean = False,
) -> CAM_Specification_CAM16:
"""
Compute the *CAM16* colour appearance model correlates from given
*CIE XYZ* tristimulus values.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 x L_b / L_w` where :math:`L_w` is the luminance of the
light source and :math:`L_b` is the luminance of the background. For
viewing images, :math:`Y_b` can be the average :math:`Y` value for the
pixels in the entire image, or frequently, a :math:`Y` value of 20,
approximate an :math:`L^*` of 50 is used.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
Returns
-------
:class:`colour.CAM_Specification_CAM16`
*CAM16* colour appearance model specification.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
+-------------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===============================+=======================+===============+
| ``CAM_Specification_CAM16.J`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.C`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.h`` | [0, 360] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.s`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.Q`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.M`` | [0, 100] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_CAM16.H`` | [0, 400] | [0, 1] |
+-------------------------------+-----------------------+---------------+
References
----------
:cite:`Li2017`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> surround = VIEWING_CONDITIONS_CAM16['Average']
>>> XYZ_to_CAM16(XYZ, XYZ_w, L_A, Y_b, surround) # doctest: +ELLIPSIS
CAM_Specification_CAM16(J=41.7312079..., C=0.1033557..., \
h=217.0679597..., s=2.3450150..., Q=195.3717089..., M=0.1074367..., \
H=275.5949861..., HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
Y_b = as_float_array(Y_b)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = vector_dot(MATRIX_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else ones(L_A.shape))
n, F_L, N_bb, N_cb, z = viewing_condition_dependent_parameters(
Y_b, Y_w, L_A)
D_RGB = (D[..., np.newaxis] * Y_w[..., np.newaxis] / RGB_w + 1 -
D[..., np.newaxis])
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non-linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB = vector_dot(MATRIX_16, XYZ)
# Step 2
RGB_c = D_RGB * RGB
# Step 3
# Applying forward post-adaptation non-linear response compression.
RGB_a = post_adaptation_non_linear_response_compression_forward(RGB_c, F_L)
# Step 4
# Converting to preliminary cartesian coordinates.
a, b = tsplit(opponent_colour_dimensions_forward(RGB_a))
# Computing the *hue* angle :math:`h`.
h = hue_angle(a, b)
# Step 5
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing hue :math:`h` quadrature :math:`H`.
H = hue_quadrature(h)
# TODO: Compute hue composition.
# Step 6
# Computing achromatic responses for the stimulus.
A = achromatic_response_forward(RGB_a, N_bb)
# Step 7
# Computing the correlate of *Lightness* :math:`J`.
J = lightness_correlate(A, A_w, surround.c, z)
# Step 8
# Computing the correlate of *brightness* :math:`Q`.
Q = brightness_correlate(surround.c, J, A_w, F_L)
# Step 9
# Computing the correlate of *chroma* :math:`C`.
C = chroma_correlate(J, n, surround.N_c, N_cb, e_t, a, b, RGB_a)
# Computing the correlate of *colourfulness* :math:`M`.
M = colourfulness_correlate(C, F_L)
# Computing the correlate of *saturation* :math:`s`.
s = saturation_correlate(M, Q)
return CAM_Specification_CAM16(
as_float(from_range_100(J)),
as_float(from_range_100(C)),
as_float(from_range_degrees(h)),
as_float(from_range_100(s)),
as_float(from_range_100(Q)),
as_float(from_range_100(M)),
as_float(from_range_degrees(H, 400)),
None,
)
def XYZ_to_CAM16(XYZ,
XYZ_w,
L_A,
Y_b,
surround=CAM16_VIEWING_CONDITIONS['Average'],
discount_illuminant=False):
"""
Computes the *CAM16* colour appearance model correlates from given
*CIE XYZ* tristimulus values.
This is the *forward* implementation.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus in domain
[0, 100].
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white in domain [0, 100].
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
Y_b : numeric or array_like
Relative luminance of background :math:`Y_b` in :math:`cd/m^2`.
surround : CAM16_InductionFactors, optional
Surround viewing conditions induction factors.
discount_illuminant : bool, optional
Truth value indicating if the illuminant should be discounted.
Returns
-------
CAM16_Specification
*CAM16* colour appearance 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_w* tristimulus values are in domain [0, 100].
References
----------
- :cite:`Li2017`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> Y_b = 20.0
>>> surround = CAM16_VIEWING_CONDITIONS['Average']
>>> XYZ_to_CAM16(XYZ, XYZ_w, L_A, Y_b, surround) # doctest: +ELLIPSIS
CAM16_Specification(J=41.7180250..., C=11.9413446..., h=210.3838955..., \
s=25.3564036..., Q=193.0617673..., M=12.4128523..., H=267.0983345..., HC=None)
"""
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = np.asarray(L_A)
Y_b = np.asarray(Y_b)
# Step 0
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB_w = dot_vector(M_16, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (np.clip(degree_of_adaptation(surround.F, L_A), 0, 1)
if not discount_illuminant else 1)
n, F_L, N_bb, N_cb, z = tsplit(
viewing_condition_dependent_parameters(Y_b, Y_w, L_A))
D_RGB = D[..., np.newaxis] * XYZ_w / RGB_w + 1 - D[..., np.newaxis]
RGB_wc = D_RGB * RGB_w
# Applying forward post-adaptation non linear response compression.
RGB_aw = post_adaptation_non_linear_response_compression_forward(
RGB_wc, F_L)
# Computing achromatic responses for the whitepoint.
A_w = achromatic_response_forward(RGB_aw, N_bb)
# Step 1
# Converting *CIE XYZ* tristimulus values to sharpened *RGB* values.
RGB = dot_vector(M_16, XYZ)
# Step 2
RGB_c = D_RGB * RGB
# Step 3
# Applying forward post-adaptation non linear response compression.
RGB_a = post_adaptation_non_linear_response_compression_forward(RGB_c, F_L)
# Step 4
# Converting to preliminary cartesian coordinates.
a, b = tsplit(opponent_colour_dimensions_forward(RGB_a))
# Computing the *hue* angle :math:`h`.
h = hue_angle(a, b)
# Step 5
# Computing eccentricity factor *e_t*.
e_t = eccentricity_factor(h)
# Computing hue :math:`h` quadrature :math:`H`.
H = hue_quadrature(h)
# TODO: Compute hue composition.
# Step 6
# Computing achromatic responses for the stimulus.
A = achromatic_response_forward(RGB_a, N_bb)
# Step 7
# Computing the correlate of *Lightness* :math:`J`.
J = lightness_correlate(A, A_w, surround.c, z)
# Step 8
# Computing the correlate of *brightness* :math:`Q`.
Q = brightness_correlate(surround.c, J, A_w, F_L)
# Step 9
# Computing the correlate of *chroma* :math:`C`.
C = chroma_correlate(J, n, surround.N_c, N_cb, e_t, a, b, RGB_a)
# Computing the correlate of *colourfulness* :math:`M`.
M = colourfulness_correlate(C, F_L)
# Computing the correlate of *saturation* :math:`s`.
s = saturation_correlate(M, Q)
return CAM16_Specification(J, C, h, s, Q, M, H, None)
def ZCAM_to_XYZ(
specification: CAM_Specification_ZCAM,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
Y_b: FloatingOrArrayLike,
surround: InductionFactors_ZCAM = VIEWING_CONDITIONS_ZCAM["Average"],
discount_illuminant: Boolean = False,
) -> NDArray:
"""
Convert from *ZCAM* specification to *CIE XYZ* tristimulus values.
Parameters
----------
specification
*ZCAM* colour appearance model specification.
Correlate of *Lightness* :math:`J`, correlate of *chroma* :math:`C` or
correlate of *colourfulness* :math:`M` and *hue* angle :math:`h` in
degrees must be specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w
Absolute *CIE XYZ* tristimulus values of the white under reference
illuminant.
L_A
Test adapting field *luminance* :math:`L_A` in :math:`cd/m^2` such as
:math:`L_A = L_w * Y_b / 100` (where :math:`L_w` is luminance of the
reference white and :math:`Y_b` is the background luminance factor).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 x L_b / L_w` where :math:`L_w` is the luminance of the
light source and :math:`L_b` is the luminance of the background. For
viewing images, :math:`Y_b` can be the average :math:`Y` value for the
pixels in the entire image, or frequently, a :math:`Y` value of 20,
approximate an :math:`L^*` of 50 is used.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM_Specification_ZCAM`` argument.
Warnings
--------
The underlying *SMPTE ST 2084:2014* transfer function is an absolute
transfer function.
Notes
-----
- *Safdar, Hardeberg and Luo (2021)* does not specify how the chromatic
adaptation to *CIE Standard Illuminant D65* in *Step 0* should be
performed. A one-step *Von Kries* chromatic adaptation transform is not
symetrical or transitive when a degree of adptation is involved.
*Safdar, Hardeberg and Luo (2018)* uses *Zhai and Luo (2018)* two-steps
chromatic adaptation transform, thus it seems sensible to adopt this
transform for the *ZCAM* colour appearance model until more information
is available. It is worth noting that a one-step *Von Kries* chromatic
adaptation transform with support for degree of adaptation produces
values closer to the supplemental document compared to the
*Zhai and Luo (2018)* two-steps chromatic adaptation transform but then
the *ZCAM* colour appearance model does not round-trip properly.
- *Step 4* of the inverse model uses a rounded exponent of 1.3514
preventing the model to round-trip properly. Given that this
implementation takes some liberties with respect to the chromatic
adaptation transform to use, it was deemed appropriate to use an
exponent value that enables the *ZCAM* colour appearance model to
round-trip.
- 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** |
+===============================+=======================+===============+
| ``CAM_Specification_ZCAM.J`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.C`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.h`` | [0, 360] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.s`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.Q`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.M`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.H`` | [0, 400] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.HC`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.V`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.K`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.H`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [UN] | [UN] |
+-----------+-----------------------+---------------+
References
----------
:cite:`Safdar2018`, :cite:`Safdar2021`, :cite:`Zhai2018`
Examples
--------
>>> specification = CAM_Specification_ZCAM(J=92.250443780723629,
... C=3.0216926733329013,
... h=196.32457375575581)
>>> XYZ_w = np.array([256, 264, 202])
>>> L_A = 264
>>> Y_b = 100
>>> surround = VIEWING_CONDITIONS_ZCAM['Average']
>>> ZCAM_to_XYZ(specification, XYZ_w, L_A, Y_b, surround)
... # doctest: +ELLIPSIS
array([ 185., 206., 163.])
"""
J_z, C_z, h_z, _S_z, _Q_z, M_z, _H, _H_Z, _V_z, _K_z, _W_z = astuple(
specification)
J_z = to_domain_1(J_z)
C_z = to_domain_1(C_z)
h_z = to_domain_degrees(h_z)
M_z = to_domain_1(M_z)
XYZ_w = to_domain_1(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
Y_b = as_float_array(Y_b)
F_s, F, c, N_c = surround
# Step 0 (Forward) - Chromatic adaptation from reference illuminant to
# "CIE Standard Illuminant D65" illuminant using "CAT02".
# Computing degree of adaptation :math:`D`.
D = (degree_of_adaptation(surround.F, L_A)
if not discount_illuminant else ones(L_A.shape))
# Step 1 (Forward) - Computing factors related with viewing conditions and
# independent of the test stimulus.
# Background factor :math:`F_b`
F_b = np.sqrt(Y_b / Y_w)
# Luminance level adaptation factor :math:`F_L`
F_L = 0.171 * spow(L_A, 1 / 3) * (1 - np.exp(-48 / 9 * L_A))
# Step 2 (Forward) - Computing achromatic response (:math:`I_{z,w}`),
# redness-greenness (:math:`a_{z,w}`), and yellowness-blueness
# (:math:`b_{z,w}`).
with domain_range_scale("ignore"):
I_z_w, _A_z_w, B_z_w = tsplit(
XYZ_to_Izazbz(XYZ_w, method="Safdar 2021"))
# Step 1 (Inverse) - Computing achromatic response (:math:`I_z`).
Q_z_p = (1.6 * F_s) / F_b**0.12
Q_z_m = F_s**2.2 * F_b**0.5 * spow(F_L, 0.2)
Q_z_w = 2700 * spow(I_z_w, Q_z_p) * Q_z_m
I_z_p = (F_b**0.12) / (1.6 * F_s)
I_z_d = 2700 * 100 * Q_z_m
I_z = spow((J_z * Q_z_w) / I_z_d, I_z_p)
# Step 2 (Inverse) - Computing chroma :math:`C_z`.
if has_only_nan(M_z) and not has_only_nan(C_z):
M_z = (C_z * Q_z_w) / 100
elif has_only_nan(M_z):
raise ValueError('Either "C" or "M" correlate must be defined in '
'the "CAM_Specification_ZCAM" argument!')
# Step 3 (Inverse) - Computing hue angle :math:`h_z`
# :math:`h_z` is currently required as an input.
# Computing eccentricity factor :math:`e_z`.
e_z = 1.015 + np.cos(np.radians(89.038 + h_z % 360))
h_z_r = np.radians(h_z)
# Step 4 (Inverse) - Computing redness-greenness (:math:`a_z`), and
# yellowness-blueness (:math:`b_z`).
# C_z_p_e = 1.3514
C_z_p_e = 50 / 37
C_z_p = spow(
(M_z * spow(I_z_w, 0.78) * F_b**0.1) /
(100 * e_z**0.068 * spow(F_L, 0.2)),
C_z_p_e,
)
a_z = C_z_p * np.cos(h_z_r)
b_z = C_z_p * np.sin(h_z_r)
# Step 5 (Inverse) - Computing tristimulus values :math:`XYZ_{D65}`.
with domain_range_scale("ignore"):
XYZ_D65 = Izazbz_to_XYZ(tstack([I_z, a_z, b_z]), method="Safdar 2021")
XYZ = chromatic_adaptation_Zhai2018(XYZ_D65,
TVS_D65,
XYZ_w,
D,
D,
transform="CAT02")
return from_range_1(XYZ)
def XYZ_to_ZCAM(
XYZ: ArrayLike,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
Y_b: FloatingOrArrayLike,
surround: InductionFactors_ZCAM = VIEWING_CONDITIONS_ZCAM["Average"],
discount_illuminant: Boolean = False,
) -> CAM_Specification_ZCAM:
"""
Compute the *ZCAM* colour appearance model correlates from given *CIE XYZ*
tristimulus values.
Parameters
----------
XYZ
Absolute *CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w
Absolute *CIE XYZ* tristimulus values of the white under reference
illuminant.
L_A
Test adapting field *luminance* :math:`L_A` in :math:`cd/m^2` such as
:math:`L_A = L_w * Y_b / 100` (where :math:`L_w` is luminance of the
reference white and :math:`Y_b` is the background luminance factor).
Y_b
Luminous factor of background :math:`Y_b` such as
:math:`Y_b = 100 * L_b / L_w` where :math:`L_w` is the luminance of the
light source and :math:`L_b` is the luminance of the background. For
viewing images, :math:`Y_b` can be the average :math:`Y` value for the
pixels in the entire image, or frequently, a :math:`Y` value of 20,
approximate an :math:`L^*` of 50 is used.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
Returns
-------
:class:`colour.CAM_Specification_ZCAM`
*ZCAM* colour appearance model specification.
Warnings
--------
The underlying *SMPTE ST 2084:2014* transfer function is an absolute
transfer function.
Notes
-----
- *Safdar, Hardeberg and Luo (2021)* does not specify how the chromatic
adaptation to *CIE Standard Illuminant D65* in *Step 0* should be
performed. A one-step *Von Kries* chromatic adaptation transform is not
symmetrical or transitive when a degree of adaptation is involved.
*Safdar, Hardeberg and Luo (2018)* uses *Zhai and Luo (2018)* two-steps
chromatic adaptation transform, thus it seems sensible to adopt this
transform for the *ZCAM* colour appearance model until more information
is available. It is worth noting that a one-step *Von Kries* chromatic
adaptation transform with support for degree of adaptation produces
values closer to the supplemental document compared to the
*Zhai and Luo (2018)* two-steps chromatic adaptation transform but then
the *ZCAM* colour appearance model does not round-trip properly.
- 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** |
+============+=======================+===============+
| ``XYZ`` | [UN] | [UN] |
+------------+-----------------------+---------------+
| ``XYZ_tw`` | [UN] | [UN] |
+------------+-----------------------+---------------+
| ``XYZ_rw`` | [UN] | [UN] |
+------------+-----------------------+---------------+
+-------------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===============================+=======================+===============+
| ``CAM_Specification_ZCAM.J`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.C`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.h`` | [0, 360] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.s`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.Q`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.M`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.H`` | [0, 400] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.HC`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.V`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.K`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
| ``CAM_Specification_ZCAM.H`` | [UN] | [0, 1] |
+-------------------------------+-----------------------+---------------+
References
----------
:cite:`Safdar2018`, :cite:`Safdar2021`, :cite:`Zhai2018`
Examples
--------
>>> XYZ = np.array([185, 206, 163])
>>> XYZ_w = np.array([256, 264, 202])
>>> L_A = 264
>>> Y_b = 100
>>> surround = VIEWING_CONDITIONS_ZCAM['Average']
>>> XYZ_to_ZCAM(XYZ, XYZ_w, L_A, Y_b, surround)
... # doctest: +ELLIPSIS
CAM_Specification_ZCAM(J=92.2504437..., C=3.0216926..., h=196.3245737..., \
s=19.1319556..., Q=321.3408463..., M=10.5256217..., H=237.6114442..., \
HC=None, V=34.7006776..., K=25.8835968..., W=91.6821728...)
"""
XYZ = to_domain_1(XYZ)
XYZ_w = to_domain_1(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
Y_b = as_float_array(Y_b)
F_s, _F, _c, _N_c = surround
# Step 0 (Forward) - Chromatic adaptation from reference illuminant to
# "CIE Standard Illuminant D65" illuminant using "CAT02".
# Computing degree of adaptation :math:`D`.
D = (degree_of_adaptation(surround.F, L_A)
if not discount_illuminant else ones(L_A.shape))
XYZ_D65 = chromatic_adaptation_Zhai2018(XYZ,
XYZ_w,
TVS_D65,
D,
D,
transform="CAT02")
# Step 1 (Forward) - Computing factors related with viewing conditions and
# independent of the test stimulus.
# Background factor :math:`F_b`
F_b = np.sqrt(Y_b / Y_w)
# Luminance level adaptation factor :math:`F_L`
F_L = 0.171 * spow(L_A, 1 / 3) * (1 - np.exp(-48 / 9 * L_A))
# Step 2 (Forward) - Computing achromatic response (:math:`I_z` and
# :math:`I_{z,w}`), redness-greenness (:math:`a_z` and :math:`a_{z,w}`),
# and yellowness-blueness (:math:`b_z`, :math:`b_{z,w}`).
with domain_range_scale("ignore"):
I_z, a_z, b_z = tsplit(XYZ_to_Izazbz(XYZ_D65, method="Safdar 2021"))
I_z_w, _a_z_w, b_z_w = tsplit(
XYZ_to_Izazbz(XYZ_w, method="Safdar 2021"))
# Step 3 (Forward) - Computing hue angle :math:`h_z`
h_z = hue_angle(a_z, b_z)
# Step 4 (Forward) - Computing hue quadrature :math:`H`.
H = hue_quadrature(h_z)
# Computing eccentricity factor :math:`e_z`.
e_z = 1.015 + np.cos(np.radians(89.038 + h_z % 360))
# Step 5 (Forward) - Computing brightness :math:`Q_z`,
# lightness :math:`J_z`, colourfulness :math`M_z`, and chroma :math:`C_z`
Q_z_p = (1.6 * F_s) / F_b**0.12
Q_z_m = F_s**2.2 * F_b**0.5 * spow(F_L, 0.2)
Q_z = 2700 * spow(I_z, Q_z_p) * Q_z_m
Q_z_w = 2700 * spow(I_z_w, Q_z_p) * Q_z_m
J_z = 100 * (Q_z / Q_z_w)
M_z = (100 * (a_z**2 + b_z**2)**0.37 *
((spow(e_z, 0.068) * spow(F_L, 0.2)) /
(F_b**0.1 * spow(I_z_w, 0.78))))
C_z = 100 * (M_z / Q_z_w)
# Step 6 (Forward) - Computing saturation :math:`S_z`,
# vividness :math:`V_z`, blackness :math:`K_z`, and whiteness :math:`W_z`.
S_z = 100 * spow(F_L, 0.6) * np.sqrt(M_z / Q_z)
V_z = np.sqrt((J_z - 58)**2 + 3.4 * C_z**2)
K_z = 100 - 0.8 * np.sqrt(J_z**2 + 8 * C_z**2)
W_z = 100 - np.sqrt((100 - J_z)**2 + C_z**2)
return CAM_Specification_ZCAM(
as_float(from_range_1(J_z)),
as_float(from_range_1(C_z)),
as_float(from_range_degrees(h_z)),
as_float(from_range_1(S_z)),
as_float(from_range_1(Q_z)),
as_float(from_range_1(M_z)),
as_float(from_range_degrees(H, 400)),
None,
as_float(from_range_1(V_z)),
as_float(from_range_1(K_z)),
as_float(from_range_1(W_z)),
)
def Kim2009_to_XYZ(
specification: CAM_Specification_Kim2009,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
media: MediaParameters_Kim2009 = MEDIA_PARAMETERS_KIM2009["CRT Displays"],
surround: InductionFactors_Kim2009 = VIEWING_CONDITIONS_KIM2009["Average"],
discount_illuminant: Boolean = False,
n_c: Floating = 0.57,
) -> NDArray:
"""
Convert from *Kim, Weyrich and Kautz (2009)* specification to *CIE XYZ*
tristimulus values.
Parameters
----------
specification
*Kim, Weyrich and Kautz (2009)* colour appearance model specification.
Correlate of *Lightness* :math:`J`, correlate of *chroma* :math:`C` or
correlate of *colourfulness* :math:`M` and *hue* angle :math:`h` in
degrees must be specified, e.g. :math:`JCh` or :math:`JMh`.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
media
Media parameters.
surroundl
Surround viewing conditions induction factors.
discount_illuminant
Discount the illuminant.
n_c
Cone response sigmoidal curve modulating factor :math:`n_c`.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If neither *C* or *M* correlates have been defined in the
``CAM_Specification_Kim2009`` argument.
Notes
-----
+---------------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+=================================+=======================+===============+
| ``CAM_Specification_Kim2009.J`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.C`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.h`` | [0, 360] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.s`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.Q`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.M`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.H`` | [0, 360] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`Kim2009`
Examples
--------
>>> specification = CAM_Specification_Kim2009(J=28.861908975839647,
... C=0.5592455924373706,
... h=219.04806677662953)
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> media = MEDIA_PARAMETERS_KIM2009['CRT Displays']
>>> surround = VIEWING_CONDITIONS_KIM2009['Average']
>>> Kim2009_to_XYZ(specification, XYZ_w, L_A, media, surround)
... # doctest: +ELLIPSIS
array([ 19.0099995..., 19.9999999..., 21.7800000...])
"""
J, C, h, _s, _Q, M, _H, _HC = astuple(specification)
J = to_domain_100(J)
C = to_domain_100(C)
h = to_domain_degrees(h)
M = to_domain_100(M)
L_A = as_float_array(L_A)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
# Converting *CIE XYZ* tristimulus values to *CMCCAT2000* transform
# sharpened *RGB* values.
RGB_w = vector_dot(CAT_CAT02, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (
degree_of_adaptation(surround.F, L_A)
if not discount_illuminant
else ones(L_A.shape)
)
# Computing full chromatic adaptation.
XYZ_wc = full_chromatic_adaptation_forward(RGB_w, RGB_w, Y_w, D)
# Converting to *Hunt-Pointer-Estevez* colourspace.
LMS_w = RGB_to_rgb(XYZ_wc)
# n_q = 0.1308
# J = Q / spow(Y_w, n_q)
if has_only_nan(C) and not has_only_nan(M):
a_m, b_m = 0.11, 0.61
C = M / (a_m * np.log10(Y_w) + b_m)
elif has_only_nan(C):
raise ValueError(
'Either "C" or "M" correlate must be defined in '
'the "CAM_Specification_Kim2009" argument!'
)
# Cones absolute response.
LMS_w_n_c = spow(LMS_w, n_c)
L_A_n_c = spow(L_A, n_c)
LMS_wp = LMS_w_n_c / (LMS_w_n_c + L_A_n_c)
# Achromatic signal :math:`A_w`
v_A = np.array([40, 20, 1])
A_w = np.sum(v_A * LMS_wp, axis=-1) / 61
# Perceived *Lightness* :math:`J_p`.
J_p = (J / 100 - 1) / media.E + 1
# Achromatic signal :math:`A`.
a_j, b_j, n_j, o_j = 0.89, 0.24, 3.65, 0.65
J_p_n_j = spow(J_p, n_j)
A = A_w * ((a_j * J_p_n_j) / (J_p_n_j + spow(o_j, n_j)) + b_j)
# Opponent signals :math:`a` and :math:`b`.
a_k, n_k = 456.5, 0.62
C_a_k_n_k = spow(C / a_k, 1 / n_k)
hr = np.radians(h)
a, b = np.cos(hr) * C_a_k_n_k, np.sin(hr) * C_a_k_n_k
# Cones absolute response.
M = np.array(
[
[1.0000, 0.3215, 0.2053],
[1.0000, -0.6351, -0.1860],
[1.0000, -0.1568, -4.4904],
]
)
LMS_p = vector_dot(M, tstack([A, a, b]))
LMS = spow((-spow(L_A, n_c) * LMS_p) / (LMS_p - 1), 1 / n_c)
# Converting to *Hunt-Pointer-Estevez* colourspace.
RGB_c = rgb_to_RGB(LMS)
# Applying inverse full chromatic adaptation.
RGB = full_chromatic_adaptation_inverse(RGB_c, RGB_w, Y_w, D)
XYZ = vector_dot(CAT_INVERSE_CAT02, RGB)
return from_range_100(XYZ)
def XYZ_to_Kim2009(
XYZ: ArrayLike,
XYZ_w: ArrayLike,
L_A: FloatingOrArrayLike,
media: MediaParameters_Kim2009 = MEDIA_PARAMETERS_KIM2009["CRT Displays"],
surround: InductionFactors_Kim2009 = VIEWING_CONDITIONS_KIM2009["Average"],
discount_illuminant: Boolean = False,
n_c: Floating = 0.57,
) -> CAM_Specification_Kim2009:
"""
Compute the *Kim, Weyrich and Kautz (2009)* colour appearance model
correlates from given *CIE XYZ* tristimulus values.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w
*CIE XYZ* tristimulus values of reference white.
L_A
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`, (often taken
to be 20% of the luminance of a white object in the scene).
media
Media parameters.
surround
Surround viewing conditions induction factors.
discount_illuminant
Truth value indicating if the illuminant should be discounted.
n_c
Cone response sigmoidal curve modulating factor :math:`n_c`.
Returns
-------
:class:`colour.CAM_Specification_Kim2009`
*Kim, Weyrich and Kautz (2009)* colour appearance model specification.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+------------+-----------------------+---------------+
+---------------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+=================================+=======================+===============+
| ``CAM_Specification_Kim2009.J`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.C`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.h`` | [0, 360] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.s`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.Q`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.M`` | [0, 100] | [0, 1] |
+---------------------------------+-----------------------+---------------+
| ``CAM_Specification_Kim2009.H`` | [0, 400] | [0, 1] |
+---------------------------------+-----------------------+---------------+
References
----------
:cite:`Kim2009`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> media = MEDIA_PARAMETERS_KIM2009['CRT Displays']
>>> surround = VIEWING_CONDITIONS_KIM2009['Average']
>>> XYZ_to_Kim2009(XYZ, XYZ_w, L_A, media, surround)
... # doctest: +ELLIPSIS
CAM_Specification_Kim2009(J=28.8619089..., C=0.5592455..., \
h=219.0480667..., s=9.3837797..., Q=52.7138883..., M=0.4641738..., \
H=278.0602824..., HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
L_A = as_float_array(L_A)
# Converting *CIE XYZ* tristimulus values to *CMCCAT2000* transform
# sharpened *RGB* values.
RGB = vector_dot(CAT_CAT02, XYZ)
RGB_w = vector_dot(CAT_CAT02, XYZ_w)
# Computing degree of adaptation :math:`D`.
D = (
degree_of_adaptation(surround.F, L_A)
if not discount_illuminant
else ones(L_A.shape)
)
# Computing full chromatic adaptation.
XYZ_c = full_chromatic_adaptation_forward(RGB, RGB_w, Y_w, D)
XYZ_wc = full_chromatic_adaptation_forward(RGB_w, RGB_w, Y_w, D)
# Converting to *Hunt-Pointer-Estevez* colourspace.
LMS = RGB_to_rgb(XYZ_c)
LMS_w = RGB_to_rgb(XYZ_wc)
# Cones absolute response.
LMS_n_c = spow(LMS, n_c)
LMS_w_n_c = spow(LMS_w, n_c)
L_A_n_c = spow(L_A, n_c)
LMS_p = LMS_n_c / (LMS_n_c + L_A_n_c)
LMS_wp = LMS_w_n_c / (LMS_w_n_c + L_A_n_c)
# Achromatic signal :math:`A` and :math:`A_w`.
v_A = np.array([40, 20, 1])
A = np.sum(v_A * LMS_p, axis=-1) / 61
A_w = np.sum(v_A * LMS_wp, axis=-1) / 61
# Perceived *Lightness* :math:`J_p`.
a_j, b_j, o_j, n_j = 0.89, 0.24, 0.65, 3.65
A_A_w = A / A_w
J_p = spow(
(-(A_A_w - b_j) * spow(o_j, n_j)) / (A_A_w - b_j - a_j), 1 / n_j
)
# Computing the media dependent *Lightness* :math:`J`.
J = 100 * (media.E * (J_p - 1) + 1)
# Computing the correlate of *brightness* :math:`Q`.
n_q = 0.1308
Q = J * spow(Y_w, n_q)
# Opponent signals :math:`a` and :math:`b`.
a = (1 / 11) * np.sum(np.array([11, -12, 1]) * LMS_p, axis=-1)
b = (1 / 9) * np.sum(np.array([1, 1, -2]) * LMS_p, axis=-1)
# Computing the correlate of *chroma* :math:`C`.
a_k, n_k = 456.5, 0.62
C = a_k * spow(np.sqrt(a**2 + b**2), n_k)
# Computing the correlate of *colourfulness* :math:`M`.
a_m, b_m = 0.11, 0.61
M = C * (a_m * np.log10(Y_w) + b_m)
# Computing the correlate of *saturation* :math:`s`.
s = 100 * np.sqrt(M / Q)
# Computing the *hue* angle :math:`h`.
h = np.degrees(np.arctan2(b, a)) % 360
# Computing hue :math:`h` quadrature :math:`H`.
H = hue_quadrature(h)
return CAM_Specification_Kim2009(
as_float(from_range_100(J)),
as_float(from_range_100(C)),
as_float(from_range_degrees(h)),
as_float(from_range_100(s)),
as_float(from_range_100(Q)),
as_float(from_range_100(M)),
as_float(from_range_degrees(H, 400)),
None,
)