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 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(
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: 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 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,
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)
