def XYZ_to_RLAB(XYZ,
XYZ_n,
Y_n,
sigma=RLAB_VIEWING_CONDITIONS['Average'],
D=RLAB_D_FACTOR['Hard Copy Images']):
"""
Computes the *RLAB* model color appearance correlates.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus in domain
[0, 100].
XYZ_n : array_like
*CIE XYZ* tristimulus values of reference white in domain [0, 100].
Y_n : numeric or array_like
Absolute adapting luminance in :math:`cd/m^2`.
sigma : numeric or array_like, optional
Relative luminance of the surround, see
:attr:`colour.RLAB_VIEWING_CONDITIONS` for reference.
D : numeric or array_like, optional
*Discounting-the-Illuminant* factor in domain [0, 1].
Returns
-------
RLAB_Specification
*RLAB* 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_n* tristimulus values are in domain [0, 100].
References
----------
- :cite:`Fairchild1996a`
- :cite:`Fairchild2013w`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_n = np.array([109.85, 100, 35.58])
>>> Y_n = 31.83
>>> sigma = RLAB_VIEWING_CONDITIONS['Average']
>>> D = RLAB_D_FACTOR['Hard Copy Images']
>>> XYZ_to_RLAB(XYZ, XYZ_n, Y_n, sigma, D) # doctest: +ELLIPSIS
RLAB_Specification(J=49.8347069..., C=54.8700585..., h=286.4860208..., \
s=1.1010410..., HC=None, a=15.5711021..., b=-52.6142956...)
"""
Y_n = np.asarray(Y_n)
D = np.asarray(D)
sigma = np.asarray(sigma)
# Converting to cone responses.
LMS_n = XYZ_to_rgb(XYZ_n)
# Computing the :math:`A` matrix.
LMS_l_E = (3 * LMS_n) / (LMS_n[0] + LMS_n[1] + LMS_n[2])
LMS_p_L = ((1 + (Y_n[..., np.newaxis] ** (1 / 3)) + LMS_l_E) /
(1 + (Y_n[..., np.newaxis] ** (1 / 3)) + (1 / LMS_l_E)))
LMS_a_L = (LMS_p_L + D[..., np.newaxis] * (1 - LMS_p_L)) / LMS_n
aR = row_as_diagonal(LMS_a_L)
M = dot_matrix(dot_matrix(R_MATRIX, aR), XYZ_TO_HPE_MATRIX)
XYZ_ref = dot_vector(M, XYZ)
X_ref, Y_ref, Z_ref = tsplit(XYZ_ref)
# Computing the correlate of *Lightness* :math:`L^R`.
LR = 100 * (Y_ref ** sigma)
# Computing opponent colour dimensions :math:`a^R` and :math:`b^R`.
aR = 430 * ((X_ref ** sigma) - (Y_ref ** sigma))
bR = 170 * ((Y_ref ** sigma) - (Z_ref ** sigma))
# Computing the *hue* angle :math:`h^R`.
hR = np.degrees(np.arctan2(bR, aR)) % 360
# TODO: Implement hue composition computation.
# Computing the correlate of *chroma* :math:`C^R`.
CR = np.hypot(aR, bR)
# Computing the correlate of *saturation* :math:`s^R`.
sR = CR / LR
return RLAB_Specification(LR, CR, hR, sR, None, aR, bR)
def XYZ_to_RLAB(XYZ,
XYZ_n,
Y_n,
sigma=VIEWING_CONDITIONS_RLAB['Average'],
D=D_FACTOR_RLAB['Hard Copy Images']):
"""
Computes the *RLAB* model color appearance correlates.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_n : array_like
*CIE XYZ* tristimulus values of reference white.
Y_n : numeric or array_like
Absolute adapting luminance in :math:`cd/m^2`.
sigma : numeric or array_like, optional
Relative luminance of the surround, see
:attr:`colour.VIEWING_CONDITIONS_RLAB` for reference.
D : numeric or array_like, optional
*Discounting-the-Illuminant* factor normalised to domain [0, 1].
Returns
-------
CAM_Specification_RLAB
*RLAB* colour appearance model specification.
Notes
-----
+--------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+==========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
| ``XYZ_n`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
+------------------------------+-----------------------\
+---------------+
| **Range** | **Scale - Reference** \
| **Scale - 1** |
+==============================+=======================\
+===============+
| ``CAM_Specification_RLAB.h`` | [0, 360] \
| [0, 1] |
+------------------------------+-----------------------\
+---------------+
References
----------
:cite:`Fairchild1996a`, :cite:`Fairchild2013w`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_n = np.array([109.85, 100, 35.58])
>>> Y_n = 31.83
>>> sigma = VIEWING_CONDITIONS_RLAB['Average']
>>> D = D_FACTOR_RLAB['Hard Copy Images']
>>> XYZ_to_RLAB(XYZ, XYZ_n, Y_n, sigma, D) # doctest: +ELLIPSIS
CAM_Specification_RLAB(J=49.8347069..., C=54.8700585..., \
h=286.4860208..., s=1.1010410..., HC=None, a=15.5711021..., b=-52.6142956...)
"""
XYZ = to_domain_100(XYZ)
XYZ_n = to_domain_100(XYZ_n)
Y_n = as_float_array(Y_n)
D = as_float_array(D)
sigma = as_float_array(sigma)
# Converting to cone responses.
LMS_n = XYZ_to_rgb(XYZ_n)
# Computing the :math:`A` matrix.
LMS_l_E = (3 * LMS_n) / (LMS_n[0] + LMS_n[1] + LMS_n[2])
LMS_p_L = ((1 + spow(Y_n[..., np.newaxis], 1 / 3) + LMS_l_E) /
(1 + spow(Y_n[..., np.newaxis], 1 / 3) + (1 / LMS_l_E)))
LMS_a_L = (LMS_p_L + D[..., np.newaxis] * (1 - LMS_p_L)) / LMS_n
aR = row_as_diagonal(LMS_a_L)
M = matrix_dot(matrix_dot(MATRIX_R, aR), MATRIX_XYZ_TO_HPE)
XYZ_ref = vector_dot(M, XYZ)
X_ref, Y_ref, Z_ref = tsplit(XYZ_ref)
# Computing the correlate of *Lightness* :math:`L^R`.
LR = 100 * spow(Y_ref, sigma)
# Computing opponent colour dimensions :math:`a^R` and :math:`b^R`.
aR = 430 * (spow(X_ref, sigma) - spow(Y_ref, sigma))
bR = 170 * (spow(Y_ref, sigma) - spow(Z_ref, sigma))
# Computing the *hue* angle :math:`h^R`.
hR = np.degrees(np.arctan2(bR, aR)) % 360
# TODO: Implement hue composition computation.
# Computing the correlate of *chroma* :math:`C^R`.
CR = np.hypot(aR, bR)
# Computing the correlate of *saturation* :math:`s^R`.
sR = CR / LR
return CAM_Specification_RLAB(LR, CR, from_range_degrees(hR), sR, None, aR,
bR)
def XYZ_to_RLAB(XYZ,
XYZ_n,
Y_n,
sigma=RLAB_VIEWING_CONDITIONS.get('Average'),
D=RLAB_D_FACTOR.get('Hard Copy Images')):
"""
Computes the RLAB model color appearance correlates.
Parameters
----------
XYZ : array_like, (3, n)
*CIE XYZ* colourspace matrix of test sample / stimulus in domain
[0, 100].
XYZ_n : array_like, (3,)
*CIE XYZ* colourspace matrix of reference white in domain [0, 100].
Y_n : numeric
Absolute adapting luminance in :math:`cd/m^2`.
sigma : numeric, optional
Relative luminance of the surround, see :attr:`RLAB_VIEWING_CONDITIONS`
for reference.
D : numeric, optional
*Discounting-the-Illuminant* factor in domain [0, 1].
Returns
-------
RLAB_Specification
*RLAB* colour appearance model specification.
Warning
-------
The input domain of that definition is non standard!
Notes
-----
- Input *CIE XYZ* colourspace matrix is in domain [0, 100].
- Input *CIE XYZ_n* colourspace matrix is in domain [0, 100].
Examples
--------
>>> XYZ = np.array([19.01, 20, 21.78])
>>> XYZ_n = np.array([109.85, 100, 35.58])
>>> Y_n = 31.83
>>> sigma = RLAB_VIEWING_CONDITIONS['Average']
>>> D = RLAB_D_FACTOR['Hard Copy Images']
>>> XYZ_to_RLAB(XYZ, XYZ_n, Y_n, sigma, D) # doctest: +ELLIPSIS
RLAB_Specification(J=49.8347069..., C=54.8700585..., h=286.4860208..., s=1.1010410..., HC=None, a=15.5711021..., b=-52.6142956...)
"""
X, Y, Z = np.ravel(XYZ)
# Converting to cone responses.
LMS = XYZ_to_rgb(XYZ)
LMS_n = XYZ_to_rgb(XYZ_n)
# Computing the :math:`A` matrix.
LMS_l_E = (3 * LMS_n) / (LMS_n[0] + LMS_n[1] + LMS_n[2])
LMS_p_L = ((1 + (Y_n**(1 / 3)) + LMS_l_E) / (1 + (Y_n**(1 / 3)) +
(1 / LMS_l_E)))
LMS_a_L = (LMS_p_L + D * (1 - LMS_p_L)) / LMS_n
# Special handling here to allow *array_like* variable input.
if len(np.shape(X)) == 0:
# *numeric* case.
# Implementation as per reference.
aR = np.diag(LMS_a_L)
XYZ_ref = R_MATRIX.dot(aR).dot(XYZ_TO_HPE_MATRIX).dot(XYZ)
else:
# *array_like* case.
# Constructing huge multidimensional arrays might not be the best idea,
# we handle each input dimension separately.
# First figure out how many values we have to deal with.
dimension = len(X)
# Then create the output array that will be filled layer by layer.
XYZ_ref = np.zeros((3, dimension))
for layer in range(dimension):
aR = np.diag(LMS_a_L[..., layer])
XYZ_ref[..., layer] = (R_MATRIX.dot(aR).dot(XYZ_TO_HPE_MATRIX).dot(
XYZ[..., layer]))
X_ref, Y_ref, Z_ref = XYZ_ref
# -------------------------------------------------------------------------
# Computing the correlate of *Lightness* :math:`L^R`.
# -------------------------------------------------------------------------
LR = 100 * (Y_ref**sigma)
# Computing opponent colour dimensions :math:`a^R` and :math:`b^R`.
aR = 430 * ((X_ref**sigma) - (Y_ref**sigma))
bR = 170 * ((Y_ref**sigma) - (Z_ref**sigma))
# -------------------------------------------------------------------------
# Computing the *hue* angle :math:`h^R`.
# -------------------------------------------------------------------------
hR = math.degrees(np.arctan2(bR, aR)) % 360
# TODO: Implement hue composition computation.
# -------------------------------------------------------------------------
# Computing the correlate of *chroma* :math:`C^R`.
# -------------------------------------------------------------------------
CR = np.sqrt((aR**2) + (bR**2))
# -------------------------------------------------------------------------
# Computing the correlate of *saturation* :math:`s^R`.
# -------------------------------------------------------------------------
sR = CR / LR
return RLAB_Specification(LR, CR, hR, sR, None, aR, bR)