def spd_to_power(data, ptype='ru', cieobs=_CIEOBS):
"""
Calculate power of spectral data in radiometric, photometric
or quantal energy units.
Args:
:data:
| ndarray with spectral data
:ptype:
| 'ru' or str, optional
| str: - 'ru': in radiometric units
| - 'pu': in photometric units
| - 'pusa': in photometric units with Km corrected
| to standard air (cfr. CIE TN003-2015)
| - 'qu': in quantal energy units
:cieobs:
| _CIEOBS or str, optional
| Type of cmf set to use for photometric units.
Returns:
returns:
| ndarray with normalized spectral data (SI units)
"""
# get wavelength spacing:
dl = getwld(data[0])
if ptype == 'ru': #normalize to radiometric units
p = np2d(np.dot(data[1:], dl * np.ones(data.shape[1]))).T
elif ptype == 'pusa': # normalize in photometric units with correction of Km to standard air
# Calculate correction factor for Km in standard air:
na = _BB['na'] # n for standard air
c = _BB['c'] # m/s light speed
lambdad = c / (na * 54 * 1e13) / (1e-9
) # 555 nm lambda in standard air
Km_correction_factor = 1 / (
1 - (1 - 0.9998567) *
(lambdad - 555)) # correction factor for Km in standard air
# Get Vlambda and Km (for E):
Vl, Km = vlbar(cieobs=cieobs, wl_new=data[0], out=2)
Km *= Km_correction_factor
p = Km * np2d(np.dot(data[1:], dl * Vl[1])).T
elif ptype == 'pu': # normalize in photometric units
# Get Vlambda and Km (for E):
Vl, Km = vlbar(cieobs=cieobs, wl_new=data[0], out=2)
p = Km * np2d(np.dot(data[1:], dl * Vl[1])).T
elif ptype == 'qu': # normalize to quantual units
# Get Quantal conversion factor:
fQ = ((1e-9) / (_BB['h'] * _BB['c']))
p = np2d(fQ * np.dot(data[1:], dl * data[0])).T
return p
def dot(self, S):
"""
Take dot product with instance of SPD.
"""
if isinstance(S, SPD):
self.value = np.dot(self.value, S.value)
else:
self.value = np.dot(self.value, M)
self.shape = self.value.shape
self.N = self.shape[0]
return self
def line_intersect(a1, a2, b1, b2):
"""
Line intersections of series of two line segments a and b.
Args:
:a1:
| ndarray (.shape = (N,2)) specifying end-point 1 of line a
:a2:
| ndarray (.shape = (N,2)) specifying end-point 2 of line a
:b1:
| ndarray (.shape = (N,2)) specifying end-point 1 of line b
:b2:
| ndarray (.shape = (N,2)) specifying end-point 2 of line b
Note:
N is the number of line segments a and b.
Returns:
:returns:
| ndarray with line-intersections (.shape = (N,2))
References:
1. https://stackoverflow.com/questions/3252194/numpy-and-line-intersections
"""
T = np.array([[0.0, -1.0], [1.0, 0.0]])
da = np.atleast_2d(a2 - a1)
db = np.atleast_2d(b2 - b1)
dp = np.atleast_2d(a1 - b1)
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1)
num = np.sum(dap * dp, axis=1)
return np.atleast_2d(num / denom).T * db + b1
def check_posdef(A, atol = 1.0e-9, rtol = 1.0e-9):
"""
Checks positive definiteness of a matrix via Cholesky.
Args:
:A:
| ndarray
:atol:
| float, optional
| The absolute tolerance parameter (see Notes of numpy.allclose())
:rtol:
| float, optional
| The relative tolerance parameter (see Notes of numpy.allclose())
Returns:
:returns:
| Bool
| True: the array is positive-definite within the given tolerance
"""
try:
R = np.linalg.cholesky(A)
if np.allclose(A, np.dot(R,R.T), atol = atol,rtol = rtol):
return True
else:
return False
except np.linalg.LinAlgError:
return False
def rgb_to_xyz(rgb, M, tr, xyz_black, tr_type = 'lut'):
"""
Convert input rgb to xyz.
Args:
:rgb:
| ndarray [Nx3] with RGB values
:M:
| linear rgb to xyz conversion matrix
:tr:
| Tone Response function parameters or lut
:xyz_black:
| ndarray with XYZ tristimulus values of black
:tr_type:
| 'lut', optional
| Type of Tone Response in tr input argument
| options:
| - 'lut': Tone-Response as a look-up-table
| - 'gog': Tone-Response as a gain-offset-gamma function
Returns:
:xyz:
| ndarray [Nx3] of XYZ tristimulus values
"""
return np.dot(M, _rgb_linearizer(rgb, tr, tr_type = tr_type).T).T + xyz_black
def xyz_to_rgb(xyz,N,tr, xyz_black, tr_type = 'lut'):
"""
Convert xyz to input rgb.
Args:
:xyz:
| ndarray [Nx3] with XYZ tristimulus values
:N:
| xyz to linear rgb conversion matrix
:tr:
| Tone Response function parameters or lut
:xyz_black:
| ndarray with XYZ tristimulus values of black
:tr_type:
| 'lut', optional
| Type of Tone Response in tr input argument
| options:
| - 'lut': Tone-Response as a look-up-table
| - 'gog': Tone-Response as a gain-offset-gamma function
Returns:
:rgb:
| ndarray [Nx3] of display RGB values
"""
rgblin = _clamp0(np.dot(N,(xyz - xyz_black).T).T) # calculate rgblin and clamp to zero (on separate line for speed)
return np.round(_rgb_delinearizer(rgblin,tr, tr_type = tr_type)) # delinearize rgblin
def dot(self, M):
"""
Take dot product with instance.
"""
self.value = np.dot(M, self.value.T).T
self.shape = self.value.shape
return self
def polyarea(x,y):
"""
Calculates area of polygon.
| First coordinate should also be last.
Args:
:x:
| ndarray of x-coordinates of polygon vertices.
:y:
| ndarray of x-coordinates of polygon vertices.
Returns:
:returns:
| float (area or polygon)
"""
return 0.5*np.abs(np.dot(x,np.roll(y,1).T)-np.dot(y,np.roll(x,1).T))
def normalize_3x3_matrix(M, xyz0 = np.array([[1.0,1.0,1.0]])):
"""
Normalize 3x3 matrix M to xyz0 -- > [1,1,1]
| If M.shape == (1,9): M is reshaped to (3,3)
Args:
:M:
| ndarray((3,3) or ndarray((1,9))
:xyz0:
| 2darray, optional
Returns:
:returns:
| normalized matrix such that M*xyz0 = [1,1,1]
"""
M = np2d(M)
if M.shape[-1]==9:
M = M.reshape(3,3)
if xyz0.shape[0] == 1:
return np.dot(np.diagflat(1/(np.dot(M,xyz0.T))),M)
else:
return np.concatenate([np.dot(np.diagflat(1/(np.dot(M,xyz0[1].T))),M) for i in range(xyz0.shape[0])],axis=0).reshape(xyz0.shape[0],3,3)
def spd_to_ler(data, cieobs=_CIEOBS, K=None):
"""
Calculates Luminous efficacy of radiation (LER) from spectral data.
Args:
:data:
| ndarray or pandas.dataframe with spectral data
| (.shape = (number of spectra + 1, number of wavelengths))
| Note that :data: is never interpolated, only CMFs and RFLs.
| This way interpolation errors due to peaky spectra are avoided.
| Conform CIE15-2018.
:cieobs:
| luxpy._CIEOBS, optional
| Determines the color matching function set used in the
| calculation of LER. For cieobs = '1931_2' the ybar CMF curve equals
| the CIE 1924 Vlambda curve.
:K:
| None, optional
| e.g. K = 683 lm/W for '1931_2'
Returns:
:ler:
| ndarray of LER values.
References:
1. `CIE15:2018, “Colorimetry,” CIE, Vienna, Austria, 2018. <https://doi.org/10.25039/TR.015.2018>`_
"""
if isinstance(cieobs, str):
if K == None: K = _CMF[cieobs]['K']
Vl = vlbar(cieobs=cieobs, scr='dict', wl_new=data[0],
kind='np')[1:2] #also interpolate to wl of data
else:
Vl = spd(wl=data[0], data=cieobs, interpolation='cmf', kind='np')[1:2]
if K is None:
raise Exception(
"spd_to_ler: User defined Vlambda, but no K scaling factor has been supplied."
)
dl = getwld(data[0])
return ((K * np.dot(
(Vl * dl), data[1:].T)) / np.sum(data[1:] * dl, axis=data.ndim - 1)).T
def lmsb_to_xyzb(lms, fieldsize=10, out='XYZ', allow_negative_values=False):
"""
Convert from LMS cone fundamentals to XYZ color matching functions.
Args:
:lms:
| ndarray with lms cone fundamentals, optional
:fieldsize:
| fieldsize in degrees, optional
| Defaults to 10°.
:out:
| 'xyz' or str, optional
| Determines output.
:allow_negative_values:
| False, optional
| XYZ color matching functions should not have negative values.
| If False: xyz[xyz<0] = 0.
Returns:
:returns:
| LMS
| - LMS: ndarray with population XYZ color matching functions.
Note:
For intermediate field sizes (2° < fieldsize < 10°) a conversion matrix
is calculated by linear interpolation between
the _INDVCMF_M_2d and _INDVCMF_M_10d matrices.
"""
wl = lms[None, 0] #store wavelengths
M = get_lms_to_xyz_matrix(fieldsize=fieldsize)
if lms.ndim > 2:
xyz = np.vstack((wl, math.dot23(M, lms[1:, ...], keepdims=False)))
else:
xyz = np.vstack((wl, np.dot(M, lms[1:, ...])))
if allow_negative_values == False:
xyz[np.where(xyz < 0)] = 0
return xyz
def fit_ellipse(xy, center_on_mean_xy = False):
"""
Fit an ellipse to supplied data points.
Args:
:xy:
| coordinates of points to fit (Nx2 array)
:center_on_mean_xy:
| False, optional
| Center ellipse on mean of xy
| (otherwise it might be offset due to solving
| the contrained minization problem: aT*S*a, see ref below.)
Returns:
:v:
| vector with ellipse parameters [Rmax,Rmin, xc,yc, theta (rad.)]
Reference:
1. Fitzgibbon, A.W., Pilu, M., and Fischer R.B.,
Direct least squares fitting of ellipsees,
Proc. of the 13th Internation Conference on Pattern Recognition,
pp 253–257, Vienna, 1996.
"""
# remove centroid:
# center = xy.mean(axis=0)
# xy = xy - center
# Fit ellipse:
x, y = xy[:,0:1], xy[:,1:2]
D = np.hstack((x * x, x * y, y * y, x, y, np.ones_like(x)))
S, C = np.dot(D.T, D), np.zeros([6, 6])
C[0, 2], C[2, 0], C[1, 1] = 2, 2, -1
U, s, V = np.linalg.svd(np.dot(np.linalg.inv(S), C))
e = U[:, 0]
# E, V = np.linalg.eig(np.dot(np.linalg.inv(S), C))
# n = np.argmax(np.abs(E))
# e = V[:,n]
# get ellipse axis lengths, center and orientation:
b, c, d, f, g, a = e[1] / 2, e[2], e[3] / 2, e[4] / 2, e[5], e[0]
# get ellipse center:
num = b * b - a * c
if num == 0:
xc = 0
yc = 0
else:
xc = ((c * d - b * f) / num)
yc = ((a * f - b * d) / num)
# get ellipse orientation:
theta = np.arctan2(np.array(2 * b), np.array((a - c))) / 2
# if b == 0:
# if a > c:
# theta = 0
# else:
# theta = np.pi/2
# else:
# if a > c:
# theta = np.arctan2(2*b,(a-c))/2
# else:
# theta = np.arctan2(2*b,(a-c))/2 + np.pi/2
# axis lengths:
up = 2 * (a * f * f + c * d * d + g * b * b - 2 * b * d * f - a * c * g)
down1 = (b * b - a * c) * ((c - a) * np.sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
down2 = (b * b - a * c) * ((a - c) * np.sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
a, b = np.sqrt((up / down1)), np.sqrt((up / down2))
# assert that a is the major axis (otherwise swap and correct angle)
if(b > a):
b, a = a, b
# ensure the angle is betwen 0 and 2*pi
theta = fmod(theta, 2.0 * np.pi)
if center_on_mean_xy == True:
xc,yc = xy.mean(axis=0)
return np.hstack((a, b, xc, yc, theta))
def test_model():
import pandas as pd
import luxpy as lx
# Read selected set of Munsell samples and LMS10(lambda):
M = pd.read_csv('Munsell_LMS_nonlin_Nov18_2015_version.dat',
header=None,
sep='\t').values
YLMS10_ = pd.read_csv('YLMS10_LMS_nonlin_Nov18_2015_version.dat',
header=None,
sep='\t').values
Y10_ = YLMS10_[[0, 1], :].copy()
LMS10_ = YLMS10_[[0, 2, 3, 4], :].copy()
# Calculate lms:
Y10 = cie_interp(_CMF['1964_10']['bar'].copy(),
getwlr([400, 700, 5]),
kind='cmf')[[0, 2], :]
XYZ10_lx = _CMF['2006_10']['bar'].copy()
XYZ10_lx = cie_interp(XYZ10_lx, getwlr([400, 700, 5]), kind='cmf')
LMS10_lx = np.vstack(
(XYZ10_lx[:1, :],
np.dot(
math.normalize_3x3_matrix(_CMF['2006_10']['M'],
np.array([[1, 1, 1]])),
XYZ10_lx[1:, :])))
LMS10 = cie_interp(LMS10_lx, getwlr([400, 700, 5]), kind='cmf')
#LMS10 = np.vstack((XYZ10[:1,:],np.dot(lx.math.normalize_3x3_matrix(_CMF['2006_10']['M'],np.array([[1,1,1]])),XYZ10_lx[1:,:])))
#LMS10[1:,:] = LMS10[1:,:]/LMS10[1:,:].sum(axis=1,keepdims=True)*Y10[1:,:].sum()
# test python model vs excel calculator:
def spdBB(CCT=5500, wl=[400, 700, 5], Lw=25000, cieobs='1964_10'):
wl = getwlr(wl)
dl = wl[1] - wl[0]
spd = 2 * np.pi * 6.626068E-34 * (299792458**2) / (
(wl * 0.000000001)**
5) / (np.exp(6.626068E-34 * 299792458 /
(wl * 0.000000001) / 1.3806503E-23 / CCT) - 1)
spd = Lw * spd / (dl * 683 * (spd * cie_interp(
_CMF[cieobs]['bar'].copy(), wl, kind='cmf')[2, :]).sum())
return np.vstack((wl, spd))
# Create long term and applied spds:
spd5500 = spdBB(5500, Lw=25000, wl=[400, 700, 5], cieobs='1964_10')
spd6500 = spdBB(6500, Lw=400, wl=[400, 700, 5], cieobs='1964_10')
# Calculate lms0 as a check:
clms = np.array(
[0.98446776, 0.98401909, 0.98571412]
) # correction factor for slight differences in _CMF and the cmfs from the excel calculator
lms0 = 5 * 683 * (spd5500[1:] * LMS10[1:, :] * 0.2).sum(axis=1).T
# Full excel parameters for testing:
parameters = {
'cLMS':
np.array([1, 1, 1]),
'lms0':
np.array([4985.02802565, 5032.49518502, 4761.27272226]) * 1,
'Cc':
0.251617118325755,
'Cf':
-0.4,
'clambda': [0.5, 0.5, 0.0],
'calpha': [1.0, -1.0, 0.0],
'cbeta': [0.5, 0.5, -1.0],
'cga1': [26.1047711317923, 33.9721745703298],
'cgb1': [6.76038379211498, 10.9220216677629],
'cga2': [0.587271269247578],
'cgb2': [-0.952412544980473],
'cl_int': [14.0035243121804, 1.0],
'cab_int': [4.99218965716342, 65.7869547646456],
'cab_out': [-0.1, -1.0],
'Ccwb':
None,
'Mxyz2lms': [[0.21701045, 0.83573367, -0.0435106],
[-0.42997951, 1.2038895, 0.08621089],
[0., 0., 0.46579234]]
}
# Note cLMS is a relative scaling factor between CIE2006 10° and 1964 10°:
# clms = np.array([1.00164919, 1.00119269, 1.0029173 ]) = (Y10[1:,:].sum(axis=1)/LMS10[1:,:].sum(axis=1))*(406.98099078/400)
#parameters =_CAM_SWW16_PARAMETERS['JOSA']
# Calculate Munsell spectra multiplied with spd6500:
spd6500xM = np.vstack((spd6500[:1, :], spd6500[1:, :] * M[1:, :]))
# Test spectral input:
print('SPD INPUT -----')
jab = cam_sww16(spd6500xM,
dataw=spd6500,
Yb=20.0,
Lw=400.0,
Ccwb=1,
relative=True,
inputtype='spd',
direction='forward',
parameters=parameters,
cieobs='2006_10',
match_to_conversionmatrix_to_cieobs=True)
# # Test xyz input:
print('\nXYZ INPUT -----')
xyz = lx.spd_to_xyz(spd6500xM, cieobs='2006_10', relative=False)
xyzw = lx.spd_to_xyz(spd6500, cieobs='2006_10', relative=False)
xyz2, xyzw2 = lx.spd_to_xyz(spd6500,
cieobs='2006_10',
relative=False,
rfl=M,
out=2)
print(xyzw)
jab = cam_sww16(xyz,
dataw=xyzw,
Yb=20.0,
Lw=400,
Ccwb=1,
relative=True,
inputtype='xyz',
direction='forward',
parameters=parameters,
cieobs='2006_10',
match_to_conversionmatrix_to_cieobs=True)
def symmM_to_posdefM(A = None, atol = 1.0e-9, rtol = 1.0e-9, method = 'make', forcesymm = True):
"""
Convert a symmetric matrix to a positive definite one.
Args:
:A:
| ndarray
:atol:
| float, optional
| The absolute tolerance parameter (see Notes of numpy.allclose())
:rtol:
| float, optional
| The relative tolerance parameter (see Notes of numpy.allclose())
:method:
| 'make' or 'nearest', optional (see notes for more info)
:forcesymm:
| True or False, optional
| If A is not symmetric, force symmetry using:
| A = numpy.triu(A) + numpy.triu(A).T - numpy.diag(numpy.diag(A))
Returns:
:returns:
| ndarray with positive-definite matrix.
Notes on supported methods:
1. `'make': A Python/Numpy port of Muhammad Asim Mubeen's matlab function
Spd_Mat.m
<https://nl.mathworks.com/matlabcentral/fileexchange/45873-positive-definite-matrix>`_
2. `'nearest': A Python/Numpy port of John D'Errico's `nearestSPD`
MATLAB code.
<https://stackoverflow.com/questions/43238173/python-convert-matrix-to-positive-semi-definite>`_
"""
if A is not None:
A = np2d(A)
# Make sure matrix A is symmetric up to a certain tolerance:
sn = check_symmetric(A, atol = atol, rtol = rtol)
if ((A.shape[0] != A.shape[1]) | (sn != True)):
if (forcesymm == True) & (A.shape[0] == A.shape[1]):
A = np.triu(A) + np.triu(A).T - np.diag(np.diag(A))
else:
raise Exception('symmM_to_posdefM(): matrix A not symmetric.')
if check_posdef(A, atol = atol, rtol = rtol) == True:
return A
else:
if method == 'make':
# A Python/Numpy port of Muhammad Asim Mubeen's matlab function Spd_Mat.m
#
# See: https://nl.mathworks.com/matlabcentral/fileexchange/45873-positive-definite-matrix
Val, Vec = np.linalg.eig(A)
Val = np.real(Val)
Vec = np.real(Vec)
Val[np.where(Val==0)] = _EPS #making zero eigenvalues non-zero
p = np.where(Val<0)
Val[p] = -Val[p] #making negative eigenvalues positive
return np.dot(Vec,np.dot(np.diag(Val) , Vec.T))
elif method == 'nearest':
# A Python/Numpy port of John D'Errico's `nearestSPD` MATLAB code [1], which
# credits [2].
#
# [1] https://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd
#
# [2] N.J. Higham, "Computing a nearest symmetric positive semidefinite
# matrix" (1988): https://doi.org/10.1016/0024-3795(88)90223-6
#
# See: https://stackoverflow.com/questions/43238173/python-convert-matrix-to-positive-semi-definite
B = (A + A.T) / 2.0
_, s, V = np.linalg.svd(B)
H = np.dot(V.T, np.dot(np.diag(s), V))
A2 = (B + H) / 2.0
A3 = (A2 + A2.T) / 2.0
if check_posdef(A3, atol = atol, rtol = rtol) == True:
return A3
spacing = np.spacing(np.linalg.norm(A))
I = np.eye(A.shape[0])
k = 1
while not check_posdef(A3, atol = atol, rtol = rtol):
mineig = np.min(np.real(np.linalg.eigvals(A3)))
A3 += I * (-mineig * k**2.0+ spacing)
k += 1
return A3
def cam_sww16(data, dataw = None, Yb = 20.0, Lw = 400.0, Ccwb = None, relative = True, \
parameters = None, inputtype = 'xyz', direction = 'forward', \
cieobs = '2006_10'):
"""
A simple principled color appearance model based on a mapping
of the Munsell color system.
| This function implements the JOSA A (parameters = 'JOSA') published model.
Args:
:data:
| ndarray with input tristimulus values
| or spectral data
| or input color appearance correlates
| Can be of shape: (N [, xM], x 3), whereby:
| N refers to samples and M refers to light sources.
| Note that for spectral input shape is (N x (M+1) x wl)
:dataw:
| None or ndarray, optional
| Input tristimulus values or spectral data of white point.
| None defaults to the use of CIE illuminant C.
:Yb:
| 20.0, optional
| Luminance factor of background (perfect white diffuser, Yw = 100)
:Lw:
| 400.0, optional
| Luminance (cd/m²) of white point.
:Ccwb:
| None, optional
| Degree of cognitive adaptation (white point balancing)
| If None: use [..,..] from parameters dict.
:relative:
| True or False, optional
| True: xyz tristimulus values are relative (Yw = 100)
:parameters:
| None or str or dict, optional
| Dict with model parameters.
| - None: defaults to luxpy.cam._CAM_SWW_2016_PARAMETERS['JOSA']
| - str: 'best-fit-JOSA' or 'best-fit-all-Munsell'
| - dict: user defined model parameters
| (dict should have same structure)
:inputtype:
| 'xyz' or 'spd', optional
| Specifies the type of input:
| tristimulus values or spectral data for the forward mode.
:direction:
| 'forward' or 'inverse', optional
| -'forward': xyz -> cam_sww_2016
| -'inverse': cam_sww_2016 -> xyz
:cieobs:
| '2006_10', optional
| CMF set to use to perform calculations where spectral data
is involved (inputtype == 'spd'; dataw = None)
| Other options: see luxpy._CMF['types']
Returns:
:returns:
| ndarray with color appearance correlates (:direction: == 'forward')
| or
| XYZ tristimulus values (:direction: == 'inverse')
Notes:
| This function implements the JOSA A (parameters = 'JOSA')
published model.
| With:
| 1. A correction for the parameter
| in Eq.4 of Fig. 11: 0.952 --> -0.952
|
| 2. The delta_ac and delta_bc white-balance shifts in Eq. 5e & 5f
| should be: -0.028 & 0.821
|
| (cfr. Ccwb = 0.66 in:
| ab_test_out = ab_test_int - Ccwb*ab_gray_adaptation_field_int))
References:
1. `Smet, K. A. G., Webster, M. A., & Whitehead, L. A. (2016).
A simple principled approach for modeling and understanding uniform color metrics.
Journal of the Optical Society of America A, 33(3), A319–A331.
<https://doi.org/10.1364/JOSAA.33.00A319>`_
"""
# get model parameters
args = locals().copy()
if parameters is None:
parameters = _CAM_SWW16_PARAMETERS['JOSA']
if isinstance(parameters, str):
parameters = _CAM_SWW16_PARAMETERS[parameters]
parameters = put_args_in_db(
parameters,
args) #overwrite parameters with other (not-None) args input
#unpack model parameters:
Cc, Ccwb, Cf, Mxyz2lms, cLMS, cab_int, cab_out, calpha, cbeta, cga1, cga2, cgb1, cgb2, cl_int, clambda, lms0 = [
parameters[x] for x in sorted(parameters.keys())
]
# setup default adaptation field:
if (dataw is None):
dataw = _CIE_ILLUMINANTS['C'].copy() # get illuminant C
xyzw = spd_to_xyz(dataw, cieobs=cieobs,
relative=False) # get abs. tristimulus values
if relative == False: #input is expected to be absolute
dataw[1:] = Lw * dataw[
1:] / xyzw[:, 1:2] #dataw = Lw*dataw # make absolute
else:
dataw = dataw # make relative (Y=100)
if inputtype == 'xyz':
dataw = spd_to_xyz(dataw, cieobs=cieobs, relative=relative)
# precomputations:
Mxyz2lms = np.dot(
np.diag(cLMS),
math.normalize_3x3_matrix(Mxyz2lms, np.array([[1, 1, 1]]))
) # normalize matrix for xyz-> lms conversion to ill. E weighted with cLMS
invMxyz2lms = np.linalg.inv(Mxyz2lms)
MAab = np.array([clambda, calpha, cbeta])
invMAab = np.linalg.inv(MAab)
#initialize data and camout:
data = np2d(data).copy(
) # stimulus data (can be upto NxMx3 for xyz, or [N x (M+1) x wl] for spd))
dataw = np2d(dataw).copy(
) # white point (can be upto Nx3 for xyz, or [(N+1) x wl] for spd)
# make axis 1 of dataw have 'same' dimensions as data:
if (data.ndim == 2):
data = np.expand_dims(data, axis=1) # add light source axis 1
if inputtype == 'xyz':
if dataw.shape[
0] == 1: #make dataw have same lights source dimension size as data
dataw = np.repeat(dataw, data.shape[1], axis=0)
else:
if dataw.shape[0] == 2:
dataw = np.vstack(
(dataw[0], np.repeat(dataw[1:], data.shape[1], axis=0)))
# Flip light source dim to axis 0:
data = np.transpose(data, axes=(1, 0, 2))
# Initialize output array:
dshape = list(data.shape)
dshape[-1] = 3 # requested number of correlates: l_int, a_int, b_int
if (inputtype != 'xyz') & (direction == 'forward'):
dshape[-2] = dshape[
-2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral
camout = np.zeros(dshape)
camout.fill(np.nan)
# apply forward/inverse model for each row in data:
for i in range(data.shape[0]):
# stage 1: calculate photon rates of stimulus and adapting field, lmst & lmsf:
if (inputtype != 'xyz'):
if relative == True:
xyzw_abs = spd_to_xyz(np.vstack((dataw[0], dataw[i + 1])),
cieobs=cieobs,
relative=False)
dataw[i +
1] = Lw * dataw[i + 1] / xyzw_abs[0, 1] # make absolute
xyzw = spd_to_xyz(np.vstack((dataw[0], dataw[i + 1])),
cieobs=cieobs,
relative=False)
lmsw = 683.0 * np.dot(Mxyz2lms, xyzw.T).T / _CMF[cieobs]['K']
lmsf = (Yb / 100.0
) * lmsw # calculate adaptation field and convert to l,m,s
if (direction == 'forward'):
if relative == True:
data[i, 1:, :] = Lw * data[i, 1:, :] / xyzw_abs[
0, 1] # make absolute
xyzt = spd_to_xyz(data[i], cieobs=cieobs,
relative=False) / _CMF[cieobs]['K']
lmst = 683.0 * np.dot(Mxyz2lms, xyzt.T).T # convert to l,m,s
else:
lmst = lmsf # put lmsf in lmst for inverse-mode
elif (inputtype == 'xyz'):
if relative == True:
dataw[i] = Lw * dataw[i] / 100.0 # make absolute
lmsw = 683.0 * np.dot(
Mxyz2lms, dataw[i].T).T / _CMF[cieobs]['K'] # convert to lms
lmsf = (Yb / 100.0) * lmsw
if (direction == 'forward'):
if relative == True:
data[i] = Lw * data[i] / 100.0 # make absolute
lmst = 683.0 * np.dot(
Mxyz2lms,
data[i].T).T / _CMF[cieobs]['K'] # convert to lms
else:
lmst = lmsf # put lmsf in lmst for inverse-mode
# stage 2: calculate cone outputs of stimulus lmstp
lmstp = math.erf(Cc * (np.log(lmst / lms0) + Cf * np.log(lmsf / lms0)))
lmsfp = math.erf(Cc * (np.log(lmsf / lms0) + Cf * np.log(lmsf / lms0)))
lmstp = np.vstack(
(lmsfp, lmstp)
) # add adaptation field lms temporarily to lmsp for quick calculation
# stage 3: calculate optic nerve signals, lam*, alphp, betp:
lstar, alph, bet = asplit(np.dot(MAab, lmstp.T).T)
alphp = cga1[0] * alph
alphp[alph < 0] = cga1[1] * alph[alph < 0]
betp = cgb1[0] * bet
betp[bet < 0] = cgb1[1] * bet[bet < 0]
# stage 4: calculate recoded nerve signals, alphapp, betapp:
alphpp = cga2[0] * (alphp + betp)
betpp = cgb2[0] * (alphp - betp)
# stage 5: calculate conscious color perception:
lstar_int = cl_int[0] * (lstar + cl_int[1])
alph_int = cab_int[0] * (np.cos(cab_int[1] * np.pi / 180.0) * alphpp -
np.sin(cab_int[1] * np.pi / 180.0) * betpp)
bet_int = cab_int[0] * (np.sin(cab_int[1] * np.pi / 180.0) * alphpp +
np.cos(cab_int[1] * np.pi / 180.0) * betpp)
lstar_out = lstar_int
if direction == 'forward':
if Ccwb is None:
alph_out = alph_int - cab_out[0]
bet_out = bet_int - cab_out[1]
else:
Ccwb = Ccwb * np.ones((2))
Ccwb[Ccwb < 0.0] = 0.0
Ccwb[Ccwb > 1.0] = 1.0
alph_out = alph_int - Ccwb[0] * alph_int[
0] # white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation
bet_out = bet_int - Ccwb[1] * bet_int[0]
camout[i] = np.vstack(
(lstar_out[1:], alph_out[1:], bet_out[1:])
).T # stack together and remove adaptation field from vertical stack
elif direction == 'inverse':
labf_int = np.hstack((lstar_int[0], alph_int[0], bet_int[0]))
# get lstar_out, alph_out & bet_out for data:
lstar_out, alph_out, bet_out = asplit(data[i])
# stage 5 inverse:
# undo cortical white-balance:
if Ccwb is None:
alph_int = alph_out + cab_out[0]
bet_int = bet_out + cab_out[1]
else:
Ccwb = Ccwb * np.ones((2))
Ccwb[Ccwb < 0.0] = 0.0
Ccwb[Ccwb > 1.0] = 1.0
alph_int = alph_out + Ccwb[0] * alph_int[
0] # inverse white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation
bet_int = bet_out + Ccwb[1] * bet_int[0]
lstar_int = lstar_out
alphpp = (1.0 / cab_int[0]) * (
np.cos(-cab_int[1] * np.pi / 180.0) * alph_int -
np.sin(-cab_int[1] * np.pi / 180.0) * bet_int)
betpp = (1.0 / cab_int[0]) * (
np.sin(-cab_int[1] * np.pi / 180.0) * alph_int +
np.cos(-cab_int[1] * np.pi / 180.0) * bet_int)
lstar_int = lstar_out
lstar = (lstar_int / cl_int[0]) - cl_int[1]
# stage 4 inverse:
alphp = 0.5 * (alphpp / cga2[0] + betpp / cgb2[0]
) # <-- alphpp = (Cga2.*(alphp+betp));
betp = 0.5 * (alphpp / cga2[0] - betpp / cgb2[0]
) # <-- betpp = (Cgb2.*(alphp-betp));
# stage 3 invers:
alph = alphp / cga1[0]
bet = betp / cgb1[0]
sa = np.sign(cga1[1])
sb = np.sign(cgb1[1])
alph[(sa * alphp) < 0.0] = alphp[(sa * alphp) < 0] / cga1[1]
bet[(sb * betp) < 0.0] = betp[(sb * betp) < 0] / cgb1[1]
lab = ajoin((lstar, alph, bet))
# stage 2 inverse:
lmstp = np.dot(invMAab, lab.T).T
lmstp[lmstp < -1.0] = -1.0
lmstp[lmstp > 1.0] = 1.0
lmstp = math.erfinv(lmstp) / Cc - Cf * np.log(lmsf / lms0)
lmst = np.exp(lmstp) * lms0
# stage 1 inverse:
xyzt = np.dot(invMxyz2lms, lmst.T).T
if relative == True:
xyzt = (100.0 / Lw) * xyzt
camout[i] = xyzt
# if flipaxis0and1 == True: # loop over shortest dim.
# camout = np.transpose(camout, axes = (1,0,2))
# Flip light source dim back to axis 1:
camout = np.transpose(camout, axes=(1, 0, 2))
if camout.shape[0] == 1:
camout = np.squeeze(camout, axis=0)
return camout
def run(data,
xyzw=_DEFAULT_WHITE_POINT,
Yw=None,
outin='J,aM,bM',
conditions=None,
forward=True,
yellowbluepurplecorrect=False,
mcat='cat02'):
"""
Run CIECAM02 color appearance model in forward or backward modes.
Args:
:data:
| ndarray with relative sample xyz values (forward mode) or J'a'b' coordinates (inverse mode)
:xyzw:
| ndarray with relative white point tristimulus values
:Yw:
| None, optional
| Luminance factor of white point.
| If None: xyz (in data) and xyzw are entered as relative tristimulus values
| (normalized to Yw = 100).
| If not None: input tristimulus are absolute and Yw is used to
| rescale the absolute values to relative ones
| (relative to a reference perfect white diffuser
| with Ywr = 100).
| Yw can be < 100 for e.g. paper as white point. If Yw is None, it
| is assumed that the relative Y-tristimulus value in xyzw
| represents the luminance factor Yw.
:conditions:
| None, optional
| Dictionary with viewing condition parameters for:
| La, Yb, D and surround.
| surround can contain:
| - str (options: 'avg','dim','dark') or
| - dict with keys c, Nc, F.
| None results in:
| {'La':100, 'Yb':20, 'D':1, 'surround':'avg'}
:forward:
| True, optional
| If True: run in CAM in forward mode, else: inverse mode.
:outin:
| 'J,aM,bM', optional
| String with requested output (e.g. "J,aM,bM,M,h") [Forward mode]
| - attributes: 'J': lightness,'Q': brightness,
| 'M': colorfulness,'C': chroma, 's': saturation,
| 'h': hue angle, 'H': hue quadrature/composition,
| String with inputs in data [inverse mode].
| Input must have data.shape[-1]==3 and last dim of data must have
| the following structure for inverse mode:
| * data[...,0] = J or Q,
| * data[...,1:] = (aM,bM) or (aC,bC) or (aS,bS) or (M,h) or (C, h), ...
:yellowbluepurplecorrect:
| False, optional
| If False: don't correct for yellow-blue and purple problems in ciecam02.
| If 'brill-suss':
| for yellow-blue problem, see:
| - Brill [Color Res Appl, 2006; 31, 142-145] and
| - Brill and Süsstrunk [Color Res Appl, 2008; 33, 424-426]
| If 'jiang-luo':
| for yellow-blue problem + purple line problem, see:
| - Jiang, Jun et al. [Color Res Appl 2015: 40(5), 491-503]
:mcat:
| 'cat02', optional
| Specifies CAT sensor space.
| - options:
| - None defaults to 'cat02'
| (others e.g. 'cat02-bs', 'cat02-jiang',
| all trying to correct gamut problems of original cat02 matrix)
| - str: see see luxpy.cat._MCATS.keys() for options
| (details on type, ?luxpy.cat)
| - ndarray: matrix with sensor primaries
Returns:
:camout:
| ndarray with color appearance correlates (forward mode)
| or
| XYZ tristimulus values (inverse mode)
References:
1. `N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, (2002),
"The CIECAM02 color appearance model,”
IS&T/SID Tenth Color Imaging Conference. p. 23, 2002.
<http://rit-mcsl.org/fairchild/PDFs/PRO19.pdf>`_
"""
outin = outin.split(',') if isinstance(outin, str) else outin
#--------------------------------------------
# Get condition parameters:
if conditions is None:
conditions = _DEFAULT_CONDITIONS
D, Dtype, La, Yb, surround = (conditions[x]
for x in sorted(conditions.keys()))
surround_parameters = _SURROUND_PARAMETERS
if isinstance(surround, str):
surround = surround_parameters[conditions['surround']]
F, FLL, Nc, c = [surround[x] for x in sorted(surround.keys())]
#--------------------------------------------
# Define sensor space and cat matrices:
# Hunt-Pointer-Estevez sensors (cone fundamentals)
mhpe = cat._MCATS['hpe']
# chromatic adaptation sensors:
if (mcat is None) | (mcat == 'cat02'):
mcat = cat._MCATS['cat02']
if yellowbluepurplecorrect == 'brill-suss':
mcat = cat._MCATS[
'cat02-bs'] # for yellow-blue problem, Brill [Color Res Appl 2006;31:142-145] and Brill and Süsstrunk [Color Res Appl 2008;33:424-426]
elif yellowbluepurplecorrect == 'jiang-luo':
mcat = cat._MCATS[
'cat02-jiang-luo'] # for yellow-blue problem + purple line problem
elif isinstance(mcat, str):
mcat = cat._MCATS[mcat]
#--------------------------------------------
# pre-calculate some matrices:
invmcat = np.linalg.inv(mcat)
mhpe_x_invmcat = np.dot(mhpe, invmcat)
if not forward: mcat_x_invmhpe = np.dot(mcat, np.linalg.inv(mhpe))
#--------------------------------------------
# Set Yw:
if Yw is not None:
Yw = (Yw * np.ones_like(xyzw2[..., 1:2]).T)
else:
Yw = xyzw[..., 1:2].T
#--------------------------------------------
# calculate condition dependent parameters:
k = 1.0 / (5.0 * La + 1.0)
FL = 0.2 * (k**4.0) * (5.0 * La) + 0.1 * ((1.0 - k**4.0)**2.0) * (
(5.0 * La)**(1.0 / 3.0)) # luminance adaptation factor
n = Yb / Yw
Nbb = 0.725 * (1 / n)**0.2
Ncb = Nbb
z = 1.48 + FLL * n**0.5
yw = xyzw[..., 1:2].T # original Y in xyzw (pre-transposed)
#--------------------------------------------
# Calculate degree of chromatic adaptation:
if D is None:
D = F * (1.0 - (1.0 / 3.6) * np.exp((-La - 42.0) / 92.0))
#===================================================================
# WHITE POINT transformations (common to forward and inverse modes):
#--------------------------------------------
# Normalize white point (keep transpose for next step):
xyzw = Yw * xyzw.T / yw
#--------------------------------------------
# transform from xyzw to cat sensor space:
rgbw = math.dot23(mcat, xyzw)
#--------------------------------------------
# apply von Kries cat:
rgbwc = (
(D * Yw / rgbw) + (1 - D)
) * rgbw # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbwp = math.dot23(mhpe_x_invmcat, rgbwc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression to white:
NK = lambda x, forward: naka_rushton(x,
scaling=400,
n=0.42,
sig=27.13**(1 / 0.42),
noise=0.1,
forward=forward)
pw = np.where(rgbwp < 0)
# if requested apply yellow-blue correction:
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
rgbwp[pw] = 0.0
rgbwpa = NK(FL * rgbwp / 100.0, True)
rgbwpa[pw] = 0.1 - (NK(FL * np.abs(rgbwp[pw]) / 100.0, True) - 0.1)
#--------------------------------------------
# Calculate achromatic signal of white:
Aw = (2.0 * rgbwpa[..., 0] + rgbwpa[..., 1] +
(1.0 / 20.0) * rgbwpa[..., 2] - 0.305) * Nbb
# massage shape of data for broadcasting:
original_ndim = data.ndim
if data.ndim == 2: data = data[:, None]
#===================================================================
# STIMULUS transformations
if forward:
#--------------------------------------------
# Normalize xyz (keep transpose for matrix multiplication in next step):
xyz = (Yw / yw)[..., None] * data.T
#--------------------------------------------
# transform from xyz to cat sensor space:
rgb = math.dot23(mcat, xyz)
#--------------------------------------------
# apply von Kries cat:
rgbc = (
(D * Yw / rgbw)[..., None] + (1 - D)
) * rgb # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbp = math.dot23(mhpe_x_invmcat, rgbc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression:
p = np.where(rgbp < 0)
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
rgbp[p] = 0.0
rgbpa = NK(FL * rgbp / 100.0, forward)
rgbpa[p] = 0.1 - (NK(FL * np.abs(rgbp[p]) / 100.0, forward) - 0.1)
#--------------------------------------------
# Calculate achromatic signal:
A = (2.0 * rgbpa[..., 0] + rgbpa[..., 1] +
(1.0 / 20.0) * rgbpa[..., 2] - 0.305) * Nbb
#--------------------------------------------
# calculate initial opponent channels:
a = rgbpa[..., 0] - 12.0 * rgbpa[..., 1] / 11.0 + rgbpa[..., 2] / 11.0
b = (1.0 / 9.0) * (rgbpa[..., 0] + rgbpa[..., 1] - 2.0 * rgbpa[..., 2])
#--------------------------------------------
# calculate hue h and eccentricity factor, et:
h = hue_angle(a, b, htype='deg')
et = (1.0 / 4.0) * (np.cos(h * np.pi / 180 + 2.0) + 3.8)
#--------------------------------------------
# calculate Hue quadrature (if requested in 'out'):
if 'H' in outin:
H = hue_quadrature(h, unique_hue_data=_UNIQUE_HUE_DATA)
else:
H = None
#--------------------------------------------
# calculate lightness, J:
J = 100.0 * (A / Aw)**(c * z)
#--------------------------------------------
# calculate brightness, Q:
Q = (4.0 / c) * ((J / 100.0)**0.5) * (Aw + 4.0) * (FL**0.25)
#--------------------------------------------
# calculate chroma, C:
t = ((50000.0 / 13.0) * Nc * Ncb * et *
((a**2.0 + b**2.0)**0.5)) / (rgbpa[..., 0] + rgbpa[..., 1] +
(21.0 / 20.0 * rgbpa[..., 2]))
C = (t**0.9) * ((J / 100.0)**0.5) * (1.64 - 0.29**n)**0.73
#--------------------------------------------
# calculate colorfulness, M:
M = C * FL**0.25
#--------------------------------------------
# calculate saturation, s:
s = 100.0 * (M / Q)**0.5
S = s # make extra variable, jsut in case 'S' is called
#--------------------------------------------
# calculate cartesian coordinates:
if ('aS' in outin):
aS = s * np.cos(h * np.pi / 180.0)
bS = s * np.sin(h * np.pi / 180.0)
if ('aC' in outin):
aC = C * np.cos(h * np.pi / 180.0)
bC = C * np.sin(h * np.pi / 180.0)
if ('aM' in outin):
aM = M * np.cos(h * np.pi / 180.0)
bM = M * np.sin(h * np.pi / 180.0)
#--------------------------------------------
if outin != ['J', 'aM', 'bM']:
camout = eval('ajoin((' + ','.join(outin) + '))')
else:
camout = ajoin((J, aM, bM))
if (camout.shape[1] == 1) & (original_ndim < 3):
camout = camout[:, 0, :]
return camout
elif forward == False:
#--------------------------------------------
# Get Lightness J from data:
if ('J' in outin[0]):
J = data[..., 0].copy()
elif ('Q' in outin[0]):
Q = data[..., 0].copy()
J = 100.0 * (Q / ((Aw + 4.0) * (FL**0.25) * (4.0 / c)))**2.0
else:
raise Exception(
'No lightness or brightness values in data. Inverse CAM-transform not possible!'
)
#--------------------------------------------
if 'a' in outin[1]:
# calculate hue h:
h = hue_angle(data[..., 1], data[..., 2], htype='deg')
#--------------------------------------------
# calculate Colorfulness M or Chroma C or Saturation s from a,b:
MCs = (data[..., 1]**2.0 + data[..., 2]**2.0)**0.5
else:
h = data[..., 2]
MCs = data[..., 1]
if ('S' in outin[1]):
Q = (4.0 / c) * ((J / 100.0)**0.5) * (Aw + 4.0) * (FL**0.25)
M = Q * (MCs / 100.0)**2.0
C = M / (FL**0.25)
if ('M' in outin[1]): # convert M to C:
C = MCs / (FL**0.25)
if ('C' in outin[1]):
C = MCs
#--------------------------------------------
# calculate t from J, C:
t = (C / ((J / 100.0)**(1.0 / 2.0) * (1.64 - 0.29**n)**0.73))**(1.0 /
0.9)
#--------------------------------------------
# calculate eccentricity factor, et:
et = (np.cos(h * np.pi / 180.0 + 2.0) + 3.8) / 4.0
#--------------------------------------------
# calculate achromatic signal, A:
A = Aw * (J / 100.0)**(1.0 / (c * z))
#--------------------------------------------
# calculate temporary cart. co. at, bt and p1,p2,p3,p4,p5:
at = np.cos(h * np.pi / 180.0)
bt = np.sin(h * np.pi / 180.0)
p1 = (50000.0 / 13.0) * Nc * Ncb * et / t
p2 = A / Nbb + 0.305
p3 = 21.0 / 20.0
p4 = p1 / bt
p5 = p1 / at
#--------------------------------------------
#q = np.where(np.abs(bt) < np.abs(at))[0]
q = (np.abs(bt) < np.abs(at))
b = p2 * (2.0 + p3) * (460.0 / 1403.0) / (p4 + (2.0 + p3) *
(220.0 / 1403.0) *
(at / bt) -
(27.0 / 1403.0) + p3 *
(6300.0 / 1403.0))
a = b * (at / bt)
a[q] = p2[q] * (2.0 + p3) * (460.0 / 1403.0) / (p5[q] + (2.0 + p3) *
(220.0 / 1403.0) -
((27.0 / 1403.0) - p3 *
(6300.0 / 1403.0)) *
(bt[q] / at[q]))
b[q] = a[q] * (bt[q] / at[q])
#--------------------------------------------
# calculate post-adaptation values
rpa = (460.0 * p2 + 451.0 * a + 288.0 * b) / 1403.0
gpa = (460.0 * p2 - 891.0 * a - 261.0 * b) / 1403.0
bpa = (460.0 * p2 - 220.0 * a - 6300.0 * b) / 1403.0
#--------------------------------------------
# join values:
rgbpa = ajoin((rpa, gpa, bpa))
#--------------------------------------------
# decompress signals:
rgbp = (100.0 / FL) * NK(rgbpa, forward)
# apply yellow-blue correction:
if (yellowbluepurplecorrect == 'brill-suss'
): # Brill & Susstrunck approach, for purple line problem
p = np.where(rgbp < 0.0)
rgbp[p] = 0.0
#--------------------------------------------
# convert from to cone sensors (hpe) cat02 sensor space:
rgbc = math.dot23(mcat_x_invmhpe, rgbp.T)
#--------------------------------------------
# apply inverse von Kries cat:
rgb = rgbc / ((D * Yw / rgbw)[..., None] + (1.0 - D))
#--------------------------------------------
# transform from cat sensor space to xyz:
xyz = math.dot23(invmcat, rgb)
#--------------------------------------------
# unnormalize xyz:
xyz = ((yw / Yw)[..., None] * xyz).T
return xyz
def cam15u(data,
fov=10.0,
inputtype='xyz',
direction='forward',
outin='Q,aW,bW',
parameters=None):
"""
Convert between CIE 2006 10° XYZ tristimulus values (or spectral data)
and CAM15u color appearance correlates.
Args:
:data:
| ndarray of CIE 2006 10° XYZ tristimulus values or spectral data
| or color appearance attributes
:fov:
| 10.0, optional
| Field-of-view of stimulus (for size effect on brightness)
:inputtpe:
| 'xyz' or 'spd', optional
| Specifies the type of input:
| tristimulus values or spectral data for the forward mode.
:direction:
| 'forward' or 'inverse', optional
| -'forward': xyz -> cam15u
| -'inverse': cam15u -> xyz
:outin:
| 'Q,aW,bW' or str, optional
| 'Q,aW,bW' (brightness and opponent signals for amount-of-neutral)
| other options: 'Q,aM,bM' (colorfulness) and 'Q,aS,bS' (saturation)
| Str specifying the type of
| input (:direction: == 'inverse') and
| output (:direction: == 'forward')
:parameters:
| None or dict, optional
| Set of model parameters.
| - None: defaults to luxpy.cam._CAM15U_PARAMETERS
| (see references below)
Returns:
:returns:
| ndarray with color appearance correlates (:direction: == 'forward')
| or
| XYZ tristimulus values (:direction: == 'inverse')
References:
1. `M. Withouck, K. A. G. Smet, W. R. Ryckaert, and P. Hanselaer,
“Experimental driven modelling of the color appearance of
unrelated self-luminous stimuli: CAM15u,”
Opt. Express, vol. 23, no. 9, pp. 12045–12064, 2015.
<https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-9-12045&origin=search>`_
2. `M. Withouck, K. A. G. Smet, and P. Hanselaer, (2015),
“Brightness prediction of different sized unrelated self-luminous stimuli,”
Opt. Express, vol. 23, no. 10, pp. 13455–13466.
<https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-10-13455&origin=search>`_
"""
if parameters is None:
parameters = _CAM15U_PARAMETERS
outin = outin.split(',')
#unpack model parameters:
Mxyz2rgb, cA, cAlms, cHK, cM, cW, ca, calms, cb, cblms, cfov, cp, k, unique_hue_data = [
parameters[x] for x in sorted(parameters.keys())
]
# precomputations:
invMxyz2rgb = np.linalg.inv(Mxyz2rgb)
MAab = np.array([cAlms, calms, cblms])
invMAab = np.linalg.inv(MAab)
#initialize data and camout:
data = np2d(data)
if len(data.shape) == 2:
data = np.expand_dims(data, axis=0) # avoid looping if not necessary
if (data.shape[0] > data.shape[1]): # loop over shortest dim.
flipaxis0and1 = True
data = np.transpose(data, axes=(1, 0, 2))
else:
flipaxis0and1 = False
dshape = list(data.shape)
dshape[-1] = len(outin) # requested number of correlates
if (inputtype != 'xyz') & (direction == 'forward'):
dshape[-2] = dshape[
-2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral
camout = np.zeros(dshape)
camout.fill(np.nan)
for i in range(data.shape[0]):
if (inputtype != 'xyz') & (direction == 'forward'):
xyz = spd_to_xyz(data[i], cieobs='2006_10', relative=False)
lms = np.dot(_CMF['2006_10']['M'], xyz.T).T # convert to l,m,s
rgb = (lms /
_CMF['2006_10']['K']) * k # convert to rho, gamma, beta
elif (inputtype == 'xyz') & (direction == 'forward'):
rgb = np.dot(Mxyz2rgb, data[i].T).T
if direction == 'forward':
# apply cube-root compression:
rgbc = rgb**(cp)
# calculate achromatic and color difference signals, A, a, b:
Aab = np.dot(MAab, rgbc.T).T
A, a, b = asplit(Aab)
A = cA * A
a = ca * a
b = cb * b
# calculate colorfullness like signal M:
M = cM * ((a**2.0 + b**2.0)**0.5)
# calculate brightness Q:
Q = A + cHK[0] * M**cHK[
1] # last term is contribution of Helmholtz-Kohlrausch effect on brightness
# calculate saturation, s:
s = M / Q
# calculate amount of white, W:
W = 100.0 / (1.0 + cW[0] * (s**cW[1]))
# adjust Q for size (fov) of stimulus (matter of debate whether to do this before or after calculation of s or W, there was no data on s, M or W for different sized stimuli: after)
Q = Q * (fov / 10.0)**cfov
# calculate hue, h and Hue quadrature, H:
h = hue_angle(a, b, htype='deg')
if 'H' in outin:
H = hue_quadrature(h, unique_hue_data=unique_hue_data)
else:
H = None
# calculate cart. co.:
if 'aM' in outin:
aM = M * np.cos(h * np.pi / 180.0)
bM = M * np.sin(h * np.pi / 180.0)
if 'aS' in outin:
aS = s * np.cos(h * np.pi / 180.0)
bS = s * np.sin(h * np.pi / 180.0)
if 'aW' in outin:
aW = W * np.cos(h * np.pi / 180.0)
bW = W * np.sin(h * np.pi / 180.0)
if (outin != ['Q', 'aW', 'bW']):
camout[i] = eval('ajoin((' + ','.join(outin) + '))')
else:
camout[i] = ajoin((Q, aW, bW))
elif direction == 'inverse':
# get Q, M and a, b depending on input type:
if 'aW' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
W = (a**2.0 + b**2.0)**0.5
s = (((100 / W) - 1.0) / cW[0])**(1.0 / cW[1])
M = s * Q
if 'aM' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
M = (a**2.0 + b**2.0)**0.5
if 'aS' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
s = (a**2.0 + b**2.0)**0.5
M = s * Q
if 'h' in outin:
Q, WsM, h = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
if 'W' in outin:
s = (((100.0 / WsM) - 1.0) / cW[0])**(1.0 / cW[1])
M = s * Q
elif 's' in outin:
M = WsM * Q
elif 'M' in outin:
M = WsM
# calculate achromatic signal, A from Q and M:
A = Q - cHK[0] * M**cHK[1]
A = A / cA
# calculate hue angle:
h = hue_angle(a, b, htype='rad')
# calculate a,b from M and h:
a = (M / cM) * np.cos(h)
b = (M / cM) * np.sin(h)
a = a / ca
b = b / cb
# create Aab:
Aab = ajoin((A, a, b))
# calculate rgbc:
rgbc = np.dot(invMAab, Aab.T).T
# decompress rgbc to rgb:
rgb = rgbc**(1 / cp)
# convert rgb to xyz:
xyz = np.dot(invMxyz2rgb, rgb.T).T
camout[i] = xyz
if flipaxis0and1 == True: # loop over shortest dim.
camout = np.transpose(camout, axes=(1, 0, 2))
if camout.shape[0] == 1:
camout = np.squeeze(camout, axis=0)
return camout
def _polyarea(x, y):
return 0.5 * np.abs(
np.dot(x, np.roll(y, 1, axis=0)) - np.dot(y, np.roll(x, 1, axis=0)))
def _simple_cam(
data,
dataw=None,
Lw=100.0,
relative=True,
inputtype='xyz',
direction='forward',
cie_illuminant='D65',
parameters={
'cA': 1,
'ca': np.array([1, -1, 0]),
'cb': (1 / 3) * np.array([0.5, 0.5, -1]),
'n': 1 / 3,
'Mxyz2lms': _CMF['1931_2']['M'].copy()
},
cieobs='2006_10',
match_to_conversionmatrix_to_cieobs=True):
"""
An example CAM illustration the usage of the functions in luxpy.cam.helpers
| Note that this example uses NO chromatic adaptation
| and SIMPLE compression, opponent and correlate processing.
| THIS IS ONLY FOR ILLUSTRATION PURPOSES !!!
Args:
:data:
| ndarray with input:
| - tristimulus values
| or
| - spectral data
| or
| - input color appearance correlates
| Can be of shape: (N [, xM], x 3), whereby:
| N refers to samples and M refers to light sources.
| Note that for spectral input shape is (N x (M+1) x wl)
:dataw:
| None or ndarray, optional
| Input tristimulus values or spectral data of white point.
| None defaults to the use of :cie_illuminant:
:cie_illuminant:
| 'D65', optional
| String corresponding to one of the illuminants (keys)
| in luxpy._CIE_ILLUMINANT
| If ndarray, then use this one.
| This is ONLY USED WHEN dataw is NONE !!!
:Lw:
| 100.0, optional
| Luminance (cd/m²) of white point.
:relative:
| True or False, optional
| True: data and dataw input is relative (i.e. Yw = 100)
:parameters:
| {'cA': 1, 'ca':np.array([1,-1,0]), 'cb':(1/3)*np.array([0.5,0.5,-1]),
| 'n': 1/3, 'Mxyz2lms': _CMF['1931_2']['M'].copy()}
| Dict with model parameters
| (For illustration purposes of match_conversionmatrix_to_cieobs,
| the conversion matrix luxpy._CMF['1931_2']['M'] does NOT match
| the default observer specification of the input data in :cieobs: !!!)
:inputtype:
| 'xyz' or 'spd', optional
| Specifies the type of input:
| tristimulus values or spectral data for the forward mode.
:direction:
| 'forward' or 'inverse', optional
| -'forward': xyz -> cam
| -'inverse': cam -> xyz
:cieobs:
| '2006_10', optional
| CMF set to use to perform calculations where spectral data
| is involved (inputtype == 'spd'; dataw = None)
| Other options: see luxpy._CMF['types']
:match_conversionmatrix_to_cieobs:
| True, optional
| When changing to a different CIE observer, change the xyz_to_lms
| matrix to the one corresponding to that observer.
| Set to False to keep the one in the parameter dict!
Returns:
:returns:
| ndarray with:
| - color appearance correlates (:direction: == 'forward')
| or
| - XYZ tristimulus values (:direction: == 'inverse')
"""
#--------------------------------------------------------------------------
# Get model parameters:
#--------------------------------------------------------------------------
args = locals().copy(
) # gets all local variables (i.e. the function arguments)
parameters = _update_parameter_dict(
args,
parameters=parameters,
cieobs=cieobs,
match_conversionmatrix_to_cieobs=match_to_conversionmatrix_to_cieobs,
Mxyz2lms_whitepoint=np.array([[1, 1, 1]]))
#unpack model parameters:
(Mxyz2lms, cA, ca, cb,
n) = [parameters[x] for x in sorted(parameters.keys())]
#--------------------------------------------------------------------------
# Setup default white point / adaptation field:
#--------------------------------------------------------------------------
dataw = _setup_default_adaptation_field(dataw=dataw,
Lw=Lw,
cie_illuminant='C',
inputtype=inputtype,
relative=relative,
cieobs=cieobs)
#--------------------------------------------------------------------------
# Redimension input data to ensure most appropriate sizes
# for easy and efficient looping and initialize output array:
#--------------------------------------------------------------------------
n_out = 5 # this example outputs 5 'correlates': J, a, b, C, h
(data, dataw, camout,
originalshape) = _massage_input_and_init_output(data,
dataw,
inputtype=inputtype,
direction=direction,
n_out=n_out)
#--------------------------------------------------------------------------
# Do precomputations needed for both the forward and inverse model,
# and which do not depend on sample or light source data:
#--------------------------------------------------------------------------
# Create matrix with scale factors for L, M, S
# for quick matrix multiplications to obtain neural signals:
MAab = np.array([[cA, cA, cA], ca, cb])
if direction == 'inverse':
invMxyz2lms = np.linalg.inv(
Mxyz2lms) # Calculate the inverse lms-to-xyz conversion matrix
invMAab = np.linalg.inv(
MAab) # Pre-calculate its inverse to avoid repeat in loop.
#--------------------------------------------------------------------------
# Apply forward/inverse model by looping over each row (=light source dim.)
# in data:
#--------------------------------------------------------------------------
N = data.shape[0]
for i in range(N):
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# START FORWARD MODE and common part of inverse mode
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#-----------------------------------------------------------------------------
# Get tristimulus values for stimulus field and white point for row i:
#-----------------------------------------------------------------------------
# Note that xyzt will contain a None in case of inverse mode !!!
xyzt, xyzw, xyzw_abs = _get_absolute_xyz_xyzw(data,
dataw,
i=i,
Lw=Lw,
direction=direction,
cieobs=cieobs,
inputtype=inputtype,
relative=relative)
#---------------------------------------------------------------------
# stage 1 (white point): calculate lms values of white:
#----------------------------------------------------------------------
lmsw = np.dot(Mxyz2lms, xyzw.T).T
#------------------------------------------------------------------
# stage 2 (white): apply simple chromatic adaptation:
#------------------------------------------------------------------
lmsw_a = lmsw / lmsw
#----------------------------------------------------------------------
# stage 3 (white point): apply simple compression to lms values
#----------------------------------------------------------------------
lmsw_ac = lmsw_a**n
#----------------------------------------------------------------------
# stage 4 (white point): calculate achromatic A, and opponent signals a,b):
#----------------------------------------------------------------------
Aabw = np.dot(MAab, lmsw_ac.T).T
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# SPLIT CALCULATION STEPS IN FORWARD AND INVERSE MODES:
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if direction == 'forward':
#------------------------------------------------------------------
# stage 1 (stimulus): calculate lms values
#------------------------------------------------------------------
lms = np.dot(Mxyz2lms, xyzt.T).T
#------------------------------------------------------------------
# stage 2 (stimulus): apply simple chromatic adaptation:
#------------------------------------------------------------------
lms_a = lms / lmsw
#------------------------------------------------------------------
# stage 3 (stimulus): apply simple compression to lms values
#------------------------------------------------------------------
lms_ac = lms_a**n
#------------------------------------------------------------------
# stage 3 (stimulus): calculate achromatic A, and opponent signals a,b:
#------------------------------------------------------------------
Aab = np.dot(MAab, lms_ac.T).T
#------------------------------------------------------------------
# stage 4 (stimulus): calculate J, C, h
#------------------------------------------------------------------
J = Aab[..., 0] / Aabw[..., 0]
C = (Aab[..., 1]**2 + Aab[..., 2]**2)**0.5
h = math.positive_arctan(Aab[..., 1], Aab[..., 2])
# # stack together:
camout[i] = np.vstack((J, Aab[..., 1], Aab[..., 2], C, h)).T
#--------------------------------------
# INVERSE MODE FROM PERCEPTUAL SIGNALS:
#--------------------------------------
elif direction == 'inverse':
pass
return _massage_output_data_to_original_shape(camout, originalshape)
def plotellipse(v, cspace_in = 'Yxy', cspace_out = None, nsamples = 100, \
show = True, axh = None, \
line_color = 'darkgray', line_style = ':', line_width = 1, line_marker = '', line_markersize = 4,\
plot_center = False, center_marker = 'o', center_color = 'darkgray', center_markersize = 4,\
show_grid = False, llabel = '', label_fontname = 'Times New Roman', label_fontsize = 12,\
out = None):
"""
Plot ellipse(s) given in v-format [Rmax,Rmin,xc,yc,theta].
Args:
:v:
| (Nx5) ndarray
| ellipse parameters [Rmax,Rmin,xc,yc,theta]
:cspace_in:
| 'Yxy', optional
| Color space of v.
| If None: no color space assumed. Axis labels assumed ('x','y').
:cspace_out:
| None, optional
| Color space to plot ellipse(s) in.
| If None: plot in cspace_in.
:nsamples:
| 100 or int, optional
| Number of points (samples) in ellipse boundary
:show:
| True or boolean, optional
| Plot ellipse(s) (True) or not (False)
:axh:
| None, optional
| Ax-handle to plot ellipse(s) in.
| If None: create new figure with axes.
:line_color:
| 'darkgray', optional
| Color to plot ellipse(s) in.
:line_style:
| ':', optional
| Linestyle of ellipse(s).
:line_width':
| 1, optional
| Width of ellipse boundary line.
:line_marker:
| 'none', optional
| Marker for ellipse boundary.
:line_markersize:
| 4, optional
| Size of markers in ellipse boundary.
:plot_center:
| False, optional
| Plot center of ellipse: yes (True) or no (False)
:center_color:
| 'darkgray', optional
| Color to plot ellipse center in.
:center_marker:
| 'o', optional
| Marker for ellipse center.
:center_markersize:
| 4, optional
| Size of marker of ellipse center.
:show_grid:
| False, optional
| Show grid (True) or not (False)
:llabel:
| None,optional
| Legend label for ellipse boundary.
:label_fontname:
| 'Times New Roman', optional
| Sets font type of axis labels.
:label_fontsize:
| 12, optional
| Sets font size of axis labels.
:out:
| None, optional
| Output of function
| If None: returns None. Can be used to output axh of newly created
| figure axes or to return Yxys an ndarray with coordinates of
| ellipse boundaries in cspace_out (shape = (nsamples,3,N))
Returns:
:returns: None, or whatever set by :out:.
"""
Yxys = np.zeros((nsamples, 3, v.shape[0]))
ellipse_vs = np.zeros((v.shape[0], 5))
for i, vi in enumerate(v):
# Set sample density of ellipse boundary:
t = np.linspace(0, 2 * np.pi, int(nsamples))
a = vi[0] # major axis
b = vi[1] # minor axis
xyc = vi[2:4, None] # center
theta = vi[-1] # rotation angle
# define rotation matrix:
R = np.hstack((np.vstack((np.cos(theta), np.sin(theta))),
np.vstack((-np.sin(theta), np.cos(theta)))))
# Calculate ellipses:
Yxyc = np.vstack((1, xyc)).T
Yxy = np.vstack(
(np.ones((1, nsamples)),
xyc + np.dot(R, np.vstack((a * np.cos(t), b * np.sin(t)))))).T
Yxys[:, :, i] = Yxy
# Convert to requested color space:
if (cspace_out is not None) & (cspace_in is not None):
Yxy = colortf(Yxy, cspace_in + '>' + cspace_out)
Yxyc = colortf(Yxyc, cspace_in + '>' + cspace_out)
Yxys[:, :, i] = Yxy
# get ellipse parameters in requested color space:
ellipse_vs[i, :] = math.fit_ellipse(Yxy[:, 1:])
#de = np.sqrt((Yxy[:,1]-Yxyc[:,1])**2 + (Yxy[:,2]-Yxyc[:,2])**2)
#ellipse_vs[i,:] = np.hstack((de.max(),de.min(),Yxyc[:,1],Yxyc[:,2],np.nan)) # nan because orientation is xy, but request is some other color space. Change later to actual angle when fitellipse() has been implemented
# plot ellipses:
if show == True:
if (axh is None) & (i == 0):
fig = plt.figure()
axh = fig.add_subplot(111)
if (cspace_in is None):
xlabel = 'x'
ylabel = 'y'
else:
xlabel = _CSPACE_AXES[cspace_in][1]
ylabel = _CSPACE_AXES[cspace_in][2]
if (cspace_out is not None):
xlabel = _CSPACE_AXES[cspace_out][1]
ylabel = _CSPACE_AXES[cspace_out][2]
if plot_center == True:
axh.plot(Yxyc[:, 1],
Yxyc[:, 2],
color=center_color,
linestyle='none',
marker=center_marker,
markersize=center_markersize)
if llabel is None:
axh.plot(Yxy[:, 1],
Yxy[:, 2],
color=line_color,
linestyle=line_style,
linewidth=line_width,
marker=line_marker,
markersize=line_markersize)
else:
axh.plot(Yxy[:, 1],
Yxy[:, 2],
color=line_color,
linestyle=line_style,
linewidth=line_width,
marker=line_marker,
markersize=line_markersize,
label=llabel)
axh.set_xlabel(xlabel,
fontname=label_fontname,
fontsize=label_fontsize)
axh.set_ylabel(ylabel,
fontname=label_fontname,
fontsize=label_fontsize)
if show_grid == True:
plt.grid(True)
#plt.show()
Yxys = np.transpose(Yxys, axes=(0, 2, 1))
if out is not None:
return eval(out)
else:
return None
def _xyz_to_jab_cam02ucs(xyz, xyzw, ucs=True, conditions=None):
"""
Calculate CAM02-UCS J'a'b' coordinates from xyz tristimulus values of sample and white point.
Args:
:xyz:
| ndarray with sample tristimulus values
:xyzw:
| ndarray with white point tristimulus values
:conditions:
| None, optional
| Dictionary with viewing conditions.
| None results in:
| {'La':100, 'Yb':20, 'D':1, 'surround':'avg'}
| For more info see luxpy.cam.ciecam02()?
Returns:
:jab:
| ndarray with J'a'b' coordinates.
"""
#--------------------------------------------
# Get/ set conditions parameters:
if conditions is not None:
surround_parameters = {
'surrounds': ['avg', 'dim', 'dark'],
'avg': {
'c': 0.69,
'Nc': 1.0,
'F': 1.0,
'FLL': 1.0
},
'dim': {
'c': 0.59,
'Nc': 0.9,
'F': 0.9,
'FLL': 1.0
},
'dark': {
'c': 0.525,
'Nc': 0.8,
'F': 0.8,
'FLL': 1.0
}
}
La = conditions['La']
Yb = conditions['Yb']
D = conditions['D']
surround = conditions['surround']
if isinstance(surround, str):
surround = surround_parameters[conditions['surround']]
F, FLL, Nc, c = [surround[x] for x in sorted(surround.keys())]
else:
# set defaults:
La, Yb, D, F, FLL, Nc, c = 100, 20, 1, 1, 1, 1, 0.69
#--------------------------------------------
# Define sensor space and cat matrices:
mhpe = np.array([[0.38971, 0.68898, -0.07868], [-0.22981, 1.1834, 0.04641],
[0.0, 0.0, 1.0]
]) # Hunt-Pointer-Estevez sensors (cone fundamentals)
mcat = np.array([[0.7328, 0.4296, -0.1624], [-0.7036, 1.6975, 0.0061],
[0.0030, 0.0136, 0.9834]]) # CAT02 sensor space
#--------------------------------------------
# pre-calculate some matrices:
invmcat = np.linalg.inv(mcat)
mhpe_x_invmcat = np.dot(mhpe, invmcat)
#--------------------------------------------
# calculate condition dependent parameters:
Yw = xyzw[..., 1:2].T
k = 1.0 / (5.0 * La + 1.0)
FL = 0.2 * (k**4.0) * (5.0 * La) + 0.1 * ((1.0 - k**4.0)**2.0) * (
(5.0 * La)**(1.0 / 3.0)) # luminance adaptation factor
n = Yb / Yw
Nbb = 0.725 * (1 / n)**0.2
Ncb = Nbb
z = 1.48 + FLL * n**0.5
if D is None:
D = F * (1.0 - (1.0 / 3.6) * np.exp((-La - 42.0) / 92.0))
#--------------------------------------------
# transform from xyz, xyzw to cat sensor space:
rgb = math.dot23(mcat, xyz.T)
rgbw = mcat @ xyzw.T
#--------------------------------------------
# apply von Kries cat:
rgbc = (
(D * Yw / rgbw)[..., None] + (1 - D)
) * rgb # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
rgbwc = (
(D * Yw / rgbw) + (1 - D)
) * rgbw # factor 100 from ciecam02 is replaced with Yw[i] in ciecam16, but see 'note' in Fairchild's "Color Appearance Models" (p291 ni 3ed.)
#--------------------------------------------
# convert from cat02 sensor space to cone sensors (hpe):
rgbp = math.dot23(mhpe_x_invmcat, rgbc).T
rgbwp = (mhpe_x_invmcat @ rgbwc).T
#--------------------------------------------
# apply Naka_rushton repsonse compression:
naka_rushton = lambda x: 400 * x**0.42 / (x**0.42 + 27.13) + 0.1
rgbpa = naka_rushton(FL * rgbp / 100.0)
p = np.where(rgbp < 0)
rgbpa[p] = 0.1 - (naka_rushton(FL * np.abs(rgbp[p]) / 100.0) - 0.1)
rgbwpa = naka_rushton(FL * rgbwp / 100.0)
pw = np.where(rgbwp < 0)
rgbwpa[pw] = 0.1 - (naka_rushton(FL * np.abs(rgbwp[pw]) / 100.0) - 0.1)
#--------------------------------------------
# Calculate achromatic signal:
A = (2.0 * rgbpa[..., 0] + rgbpa[..., 1] +
(1.0 / 20.0) * rgbpa[..., 2] - 0.305) * Nbb
Aw = (2.0 * rgbwpa[..., 0] + rgbwpa[..., 1] +
(1.0 / 20.0) * rgbwpa[..., 2] - 0.305) * Nbb
#--------------------------------------------
# calculate initial opponent channels:
a = rgbpa[..., 0] - 12.0 * rgbpa[..., 1] / 11.0 + rgbpa[..., 2] / 11.0
b = (1.0 / 9.0) * (rgbpa[..., 0] + rgbpa[..., 1] - 2.0 * rgbpa[..., 2])
#--------------------------------------------
# calculate hue h and eccentricity factor, et:
h = np.arctan2(b, a)
et = (1.0 / 4.0) * (np.cos(h + 2.0) + 3.8)
#--------------------------------------------
# calculate lightness, J:
J = 100.0 * (A / Aw)**(c * z)
#--------------------------------------------
# calculate chroma, C:
t = ((50000.0 / 13.0) * Nc * Ncb * et *
((a**2.0 + b**2.0)**0.5)) / (rgbpa[..., 0] + rgbpa[..., 1] +
(21.0 / 20.0 * rgbpa[..., 2]))
C = (t**0.9) * ((J / 100.0)**0.5) * (1.64 - 0.29**n)**0.73
#--------------------------------------------
# Calculate colorfulness, M:
M = C * FL**0.25
#--------------------------------------------
# convert to cam02ucs J', aM', bM':
if ucs == True:
KL, c1, c2 = 1.0, 0.007, 0.0228
Jp = (1.0 + 100.0 * c1) * J / (1.0 + c1 * J)
Mp = (1.0 / c2) * np.log(1.0 + c2 * M)
else:
Jp = J
Mp = M
aMp = Mp * np.cos(h)
bMp = Mp * np.sin(h)
return np.dstack((Jp, aMp, bMp))
def spd_to_xyz(data,
relative=True,
rfl=None,
cieobs=_CIEOBS,
K=None,
out=None,
cie_std_dev_obs=None):
"""
Calculates xyz tristimulus values from spectral data.
Args:
:data:
| ndarray or pandas.dataframe with spectral data
| (.shape = (number of spectra + 1, number of wavelengths))
| Note that :data: is never interpolated, only CMFs and RFLs.
| This way interpolation errors due to peaky spectra are avoided.
| Conform CIE15-2018.
:relative:
| True or False, optional
| Calculate relative XYZ (Yw = 100) or absolute XYZ (Y = Luminance)
:rfl:
| ndarray with spectral reflectance functions.
| Will be interpolated if wavelengths do not match those of :data:
:cieobs:
| luxpy._CIEOBS or str, optional
| Determines the color matching functions to be used in the
| calculation of XYZ.
:K:
| None, optional
| e.g. K = 683 lm/W for '1931_2' (relative == False)
| or K = 100/sum(spd*dl) (relative == True)
:out:
| None or 1 or 2, optional
| Determines number and shape of output. (see :returns:)
:cie_std_dev_obs:
| None or str, optional
| - None: don't use CIE Standard Deviate Observer function.
| - 'f1': use F1 function.
Returns:
:returns:
| If rfl is None:
| If out is None: ndarray of xyz values
| (.shape = (data.shape[0],3))
| If out == 1: ndarray of xyz values
| (.shape = (data.shape[0],3))
| If out == 2: (ndarray of xyz, ndarray of xyzw) values
| Note that xyz == xyzw, with (.shape = (data.shape[0],3))
| If rfl is not None:
| If out is None: ndarray of xyz values
| (.shape = (rfl.shape[0],data.shape[0],3))
| If out == 1: ndarray of xyz values
| (.shape = (rfl.shape[0]+1,data.shape[0],3))
| The xyzw values of the light source spd are the first set
| of values of the first dimension. The following values
| along this dimension are the sample (rfl) xyz values.
| If out == 2: (ndarray of xyz, ndarray of xyzw) values
| with xyz.shape = (rfl.shape[0],data.shape[0],3)
| and with xyzw.shape = (data.shape[0],3)
References:
1. `CIE15:2018, “Colorimetry,” CIE, Vienna, Austria, 2018. <https://doi.org/10.25039/TR.015.2018>`_
"""
data = getdata(data,
kind='np') if isinstance(data, pd.DataFrame) else np2d(
data) # convert to np format and ensure 2D-array
# get wl spacing:
dl = getwld(data[0])
# get cmf,k for cieobs:
if isinstance(cieobs, str):
if K is None: K = _CMF[cieobs]['K']
scr = 'dict'
else:
scr = 'cieobs'
if (K is None) & (relative == False): K = 1
# Interpolate to wl of data:
cmf = xyzbar(cieobs=cieobs, scr=scr, wl_new=data[0], kind='np')
# Add CIE standard deviate observer function to cmf if requested:
if cie_std_dev_obs is not None:
cmf_cie_std_dev_obs = xyzbar(cieobs='cie_std_dev_obs_' +
cie_std_dev_obs.lower(),
scr=scr,
wl_new=data[0],
kind='np')
cmf[1:] = cmf[1:] + cmf_cie_std_dev_obs[1:]
# Rescale xyz using k or 100/Yw:
if relative == True: K = 100.0 / np.dot(data[1:], cmf[2, :] * dl)
# Interpolate rfls to lambda range of spd and calculate xyz:
if rfl is not None:
rfl = cie_interp(data=np2d(rfl), wl_new=data[0], kind='rfl')
rfl = np.concatenate((np.ones((1, data.shape[1])),
rfl[1:])) #add rfl = 1 for light source spectrum
xyz = K * np.array(
[np.dot(rfl, (data[1:] * cmf[i + 1, :] * dl).T)
for i in range(3)]) #calculate tristimulus values
rflwasnotnone = 1
else:
rfl = np.ones((1, data.shape[1]))
xyz = (K * (np.dot((cmf[1:] * dl), data[1:].T))[:, None, :])
rflwasnotnone = 0
xyz = np.transpose(xyz, [1, 2, 0]) #order [rfl,spd,xyz]
# Setup output:
if out == 2:
xyzw = xyz[0, ...]
xyz = xyz[rflwasnotnone:, ...]
if rflwasnotnone == 0: xyz = np.squeeze(xyz, axis=0)
return xyz, xyzw
elif out == 1:
if rflwasnotnone == 0: xyz = np.squeeze(xyz, axis=0)
return xyz
else:
xyz = xyz[rflwasnotnone:, ...]
if rflwasnotnone == 0: xyz = np.squeeze(xyz, axis=0)
return xyz
def get_poly_model(jabt, jabr, modeltype=_VF_MODEL_TYPE):
"""
Setup base color shift model (delta_a, delta_b),
determine model parameters and accuracy.
| Calculates a base color shift (delta) from the ref. chromaticity ar, br.
Args:
:jabt:
| ndarray with jab color coordinates under the test SPD.
:jabr:
| ndarray with jab color coordinates under the reference SPD.
:modeltype:
| _VF_MODEL_TYPE or 'M6' or 'M5', optional
| Specifies degree 5 or degree 6 polynomial model in ab-coordinates.
| (see notes below)
Returns:
:returns:
| (poly_model,
| pmodel,
| dab_model,
| dab_res,
| dCHoverC_res,
| dab_std,
| dCHoverC_std)
|
| :poly_model: function handle to model
| :pmodel: ndarray with model parameters
| :dab_model: ndarray with ab model predictions from ar, br.
| :dab_res: ndarray with residuals between 'da,db' of samples and
| 'da,db' predicted by the model.
| :dCHoverC_res: ndarray with residuals between 'dCoverC,dH'
| of samples and 'dCoverC,dH' predicted by the model.
| Note: dCoverC = (Ct - Cr)/Cr and dH = ht - hr
| (predicted from model, see notes below)
| :dab_std: ndarray with std of :dab_res:
| :dCHoverC_std: ndarray with std of :dCHoverC_res:
Notes:
1. Model types:
| poly5_model = lambda a,b,p: p[0]*a + p[1]*b + p[2]*(a**2) + p[3]*a*b + p[4]*(b**2)
| poly6_model = lambda a,b,p: p[0] + p[1]*a + p[2]*b + p[3]*(a**2) + p[4]*a*b + p[5]*(b**2)
2. Calculation of dCoverC and dH:
| dCoverC = (np.cos(hr)*da + np.sin(hr)*db)/Cr
| dHoverC = (np.cos(hr)*db - np.sin(hr)*da)/Cr
"""
at = jabt[..., 1]
bt = jabt[..., 2]
ar = jabr[..., 1]
br = jabr[..., 2]
# A. Calculate da, db:
da = at - ar
db = bt - br
# B.1 Calculate model matrix:
# 5-parameter model:
M5 = np.array([[
np.sum(ar * ar),
np.sum(ar * br),
np.sum(ar * ar**2),
np.sum(ar * ar * br),
np.sum(ar * br**2)
],
[
np.sum(br * ar),
np.sum(br * br),
np.sum(br * ar**2),
np.sum(br * ar * br),
np.sum(br * br**2)
],
[
np.sum((ar**2) * ar),
np.sum((ar**2) * br),
np.sum((ar**2) * ar**2),
np.sum((ar**2) * ar * br),
np.sum((ar**2) * br**2)
],
[
np.sum(ar * br * ar),
np.sum(ar * br * br),
np.sum(ar * br * ar**2),
np.sum(ar * br * ar * br),
np.sum(ar * br * br**2)
],
[
np.sum((br**2) * ar),
np.sum((br**2) * br),
np.sum((br**2) * ar**2),
np.sum((br**2) * ar * br),
np.sum((br**2) * br**2)
]])
#6-parameters model
M6 = np.array([[
ar.size,
np.sum(1.0 * ar),
np.sum(1.0 * br),
np.sum(1.0 * ar**2),
np.sum(1.0 * ar * br),
np.sum(1.0 * br**2)
],
[
np.sum(ar * 1.0),
np.sum(ar * ar),
np.sum(ar * br),
np.sum(ar * ar**2),
np.sum(ar * ar * br),
np.sum(ar * br**2)
],
[
np.sum(br * 1.0),
np.sum(br * ar),
np.sum(br * br),
np.sum(br * ar**2),
np.sum(br * ar * br),
np.sum(br * br**2)
],
[
np.sum((ar**2) * 1.0),
np.sum((ar**2) * ar),
np.sum((ar**2) * br),
np.sum((ar**2) * ar**2),
np.sum((ar**2) * ar * br),
np.sum((ar**2) * br**2)
],
[
np.sum(ar * br * 1.0),
np.sum(ar * br * ar),
np.sum(ar * br * br),
np.sum(ar * br * ar**2),
np.sum(ar * br * ar * br),
np.sum(ar * br * br**2)
],
[
np.sum((br**2) * 1.0),
np.sum((br**2) * ar),
np.sum((br**2) * br),
np.sum((br**2) * ar**2),
np.sum((br**2) * ar * br),
np.sum((br**2) * br**2)
]])
# B.2 Define model function:
poly5_model = lambda a, b, p: p[0] * a + p[1] * b + p[2] * (a**2) + p[
3] * a * b + p[4] * (b**2)
poly6_model = lambda a, b, p: p[0] + p[1] * a + p[2] * b + p[3] * (
a**2) + p[4] * a * b + p[5] * (b**2)
if modeltype == 'M5':
M = M5
poly_model = poly5_model
else:
M = M6
poly_model = poly6_model
M = np.linalg.inv(M)
# C.1 Data a,b analysis output:
if modeltype == 'M5':
da_model_parameters = np.dot(
M,
np.array([
np.sum(da * ar),
np.sum(da * br),
np.sum(da * ar**2),
np.sum(da * ar * br),
np.sum(da * br**2)
]))
db_model_parameters = np.dot(
M,
np.array([
np.sum(db * ar),
np.sum(db * br),
np.sum(db * ar**2),
np.sum(db * ar * br),
np.sum(db * br**2)
]))
else:
da_model_parameters = np.dot(
M,
np.array([
np.sum(da * 1.0),
np.sum(da * ar),
np.sum(da * br),
np.sum(da * ar**2),
np.sum(da * ar * br),
np.sum(da * br**2)
]))
db_model_parameters = np.dot(
M,
np.array([
np.sum(db * 1.0),
np.sum(db * ar),
np.sum(db * br),
np.sum(db * ar**2),
np.sum(db * ar * br),
np.sum(db * br**2)
]))
pmodel = np.vstack((da_model_parameters, db_model_parameters))
# D.1 Calculate model da, db:
da_model = poly_model(ar, br, pmodel[0])
db_model = poly_model(ar, br, pmodel[1])
dab_model = np.hstack((da_model, db_model))
# D.2 Calculate residuals for da & db:
da_res = da - da_model
db_res = db - db_model
dab_res = np.hstack((da_res, db_res))
dab_std = np.vstack((np.std(da_res, axis=0), np.std(db_res, axis=0)))
# E Calculate href, Cref:
href = np.arctan2(br, ar)
Cref = (ar**2 + br**2)**0.5
# F Calculate dC/C, dH/C for data and model and calculate residuals:
dCoverC = (np.cos(href) * da + np.sin(href) * db) / Cref
dHoverC = (np.cos(href) * db - np.sin(href) * da) / Cref
dCoverC_model = (np.cos(href) * da_model + np.sin(href) * db_model) / Cref
dHoverC_model = (np.cos(href) * db_model - np.sin(href) * da_model) / Cref
dCoverC_res = dCoverC - dCoverC_model
dHoverC_res = dHoverC - dHoverC_model
dCHoverC_std = np.vstack((np.std(dCoverC_res,
axis=0), np.std(dHoverC_res, axis=0)))
dCHoverC_res = np.hstack((href, dCoverC_res, dHoverC_res))
return poly_model, pmodel, dab_model, dab_res, dCHoverC_res, dab_std, dCHoverC_std
def xyz_to_Ydlep_(xyz,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
**kwargs):
"""
Convert XYZ tristimulus values to Y, dominant (complementary) wavelength
and excitation purity.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
Returns:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
| and excitation purity
"""
xyz3 = np3d(xyz).copy().astype(np.float)
# flip axis so that shortest dim is on axis0 (save time in looping):
if (xyz3.shape[0] < xyz3.shape[1]) & (flip_axes == True):
axes12flipped = True
xyz3 = xyz3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyz to Yxy:
Yxy = xyz_to_Yxy(xyz3)
Yxyw = xyz_to_Yxy(xyzw)
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0]
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
pmaxlambda = Yxysl[..., 1].argmax()
maxlambda = wlsl[pmaxlambda]
maxlambda = 700
print(np.where(wlsl == maxlambda))
pmaxlambda = np.where(wlsl == maxlambda)[0][0]
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1)]
# center on xyzw:
Yxy = Yxy - Yxyw
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, x, y = asplit(Yxy)
Yw, xw, yw = asplit(Yxyw)
Ysl, xsl, ysl = asplit(Yxysl)
# calculate hue:
h = math.positive_arctan(x, y, htype='deg')
print(h)
print('rh', h[0, 0] - h[0, 1])
print(wlsl[0], wlsl[-1])
hsl = math.positive_arctan(xsl, ysl, htype='deg')
hsl_max = hsl[0] # max hue angle at min wavelength
hsl_min = hsl[-1] # min hue angle at max wavelength
if hsl_min < hsl_max: hsl_min += 360
dominantwavelength = np.empty(Y.shape)
purity = np.empty(Y.shape)
print('xyz:', xyz)
for i in range(xyz3.shape[1]):
print('\ni:', i, h[:, i], hsl_max, hsl_min)
print(h)
# find index of complementary wavelengths/hues:
pc = np.where(
(h[:, i] > hsl_max) & (h[:, i] < hsl_min)
) # hue's requiring complementary wavelength (purple line)
print('pc', (h[:, i] > hsl_max) & (h[:, i] < hsl_min))
h[:, i][pc] = h[:, i][pc] - np.sign(
h[:, i][pc] - 180.0
) * 180.0 # add/subtract 180° to get positive complementary wavelength
# find 2 closest hues in sl:
#hslb,hib = meshblock(hsl,h[:,i:i+1])
hib, hslb = np.meshgrid(h[:, i:i + 1], hsl)
dh = np.abs(hslb - hib)
q1 = dh.argmin(axis=0) # index of closest hue
dh[q1] = 1000000.0
q2 = dh.argmin(axis=0) # index of second closest hue
print('q1q2', q2, q1)
print('wls:', h[:, i], wlsl[q1], wlsl[q2])
print('hsls:', hsl[q2, 0], hsl[q1, 0])
print('d', (wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]),
(wlsl[q2] - wlsl[q1]) / (hsl[q2, 0] - hsl[q1, 0]))
print('(h[:,i] - hsl[q1,0])', (h[:, i] - hsl[q1, 0]))
print('div', np.divide((wlsl[q2] - wlsl[q1]),
(hsl[q2, 0] - hsl[q1, 0])))
print(
'mult(...)',
np.multiply((h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]),
(hsl[q2, 0] - hsl[q1, 0]))))
dominantwavelength[:, i] = wlsl[q1] + np.multiply(
(h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]))
) # calculate wl corresponding to h: y = y1 + (x-x1)*(y2-y1)/(x2-x1)
print('dom', dominantwavelength[:, i])
dominantwavelength[(dominantwavelength[:,
i] > max(wlsl[q1], wlsl[q2])),
i] = max(wlsl[q1], wlsl[q2])
dominantwavelength[(dominantwavelength[:,
i] < min(wlsl[q1], wlsl[q2])),
i] = min(wlsl[q1], wlsl[q2])
dominantwavelength[:, i][pc] = -dominantwavelength[:, i][
pc] #complementary wavelengths are specified by '-' sign
# calculate excitation purity:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate y of dom. wl
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to sl
d = (x[:, i]**2.0 +
y[:, i]**2.0)**0.5 # distance from white point to test point
purity[:, i] = d / d_wl
# correct for those test points that have a complementary wavelength
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x[:, i], y[:, i])).T
xyw = np.hstack((xw, yw))
xypl1 = np.hstack((xsl[0, None], ysl[0, None]))
xypl2 = np.hstack((xsl[-1, None], ysl[-1, None]))
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T #[0]
purity[:, i][pc] = d[pc] / d_linecross[pc][:, 0]
Ydlep = np.dstack((xyz3[:, :, 1], dominantwavelength, purity))
if axes12flipped == True:
Ydlep = Ydlep.transpose((1, 0, 2))
else:
Ydlep = Ydlep.transpose((0, 1, 2))
return Ydlep.reshape(xyz.shape)
def cam_sww16(data,
dataw=None,
Yb=20.0,
Lw=400.0,
Ccwb=None,
relative=True,
inputtype='xyz',
direction='forward',
parameters=None,
cieobs='2006_10',
match_to_conversionmatrix_to_cieobs=True):
"""
A simple principled color appearance model based on a mapping of
the Munsell color system.
| This function implements the JOSA A (parameters = 'JOSA') published model.
Args:
:data:
| ndarray with input tristimulus values
| or spectral data
| or input color appearance correlates
| Can be of shape: (N [, xM], x 3), whereby:
| N refers to samples and M refers to light sources.
| Note that for spectral input shape is (N x (M+1) x wl)
:dataw:
| None or ndarray, optional
| Input tristimulus values or spectral data of white point.
| None defaults to the use of CIE illuminant C.
:Yb:
| 20.0, optional
| Luminance factor of background (perfect white diffuser, Yw = 100)
:Lw:
| 400.0, optional
| Luminance (cd/m²) of white point.
:Ccwb:
| None, optional
| Degree of cognitive adaptation (white point balancing)
| If None: use [..,..] from parameters dict.
:relative:
| True or False, optional
| True: xyz tristimulus values are relative (Yw = 100)
:parameters:
| None or str or dict, optional
| Dict with model parameters.
| - None: defaults to luxpy.cam._CAM_SWW_2016_PARAMETERS['JOSA']
| - str: 'best-fit-JOSA' or 'best-fit-all-Munsell'
| - dict: user defined model parameters
| (dict should have same structure)
:inputtype:
| 'xyz' or 'spd', optional
| Specifies the type of input:
| tristimulus values or spectral data for the forward mode.
:direction:
| 'forward' or 'inverse', optional
| -'forward': xyz -> cam_sww_2016
| -'inverse': cam_sww_2016 -> xyz
:cieobs:
| '2006_10', optional
| CMF set to use to perform calculations where spectral data
| is involved (inputtype == 'spd'; dataw = None)
| Other options: see luxpy._CMF['types']
:match_to_conversionmatrix_to_cieobs:
| When channging to a different CIE observer, change the xyz-to_lms
| matrix to the one corresponding to that observer. If False: use
| the one set in parameters or _CAM_SWW16_PARAMETERS
Returns:
:returns:
| ndarray with color appearance correlates (:direction: == 'forward')
| or
| XYZ tristimulus values (:direction: == 'inverse')
Notes:
| This function implements the JOSA A (parameters = 'JOSA')
| published model.
| With:
| 1. A correction for the parameter
| in Eq.4 of Fig. 11: 0.952 --> -0.952
|
| 2. The delta_ac and delta_bc white-balance shifts in Eq. 5e & 5f
| should be: -0.028 & 0.821
|
| (cfr. Ccwb = 0.66 in:
| ab_test_out = ab_test_int - Ccwb*ab_gray_adaptation_field_int))
References:
1. `Smet, K. A. G., Webster, M. A., & Whitehead, L. A. (2016).
A simple principled approach for modeling and understanding uniform color metrics.
Journal of the Optical Society of America A, 33(3), A319–A331.
<https://doi.org/10.1364/JOSAA.33.00A319>`_
"""
#--------------------------------------------------------------------------
# Get model parameters:
#--------------------------------------------------------------------------
args = locals().copy()
parameters = _update_parameter_dict(
args,
parameters=parameters,
match_to_conversionmatrix_to_cieobs=match_to_conversionmatrix_to_cieobs
)
#unpack model parameters:
Cc, Ccwb, Cf, Mxyz2lms, cLMS, cab_int, cab_out, calpha, cbeta, cga1, cga2, cgb1, cgb2, cl_int, clambda, lms0 = [
parameters[x] for x in sorted(parameters.keys())
]
#--------------------------------------------------------------------------
# Setup default adaptation field:
#--------------------------------------------------------------------------
dataw = _setup_default_adaptation_field(dataw=dataw,
Lw=Lw,
inputtype=inputtype,
relative=relative,
cieobs=cieobs)
#--------------------------------------------------------------------------
# Redimension input data to ensure most appropriate sizes
# for easy and efficient looping and initialize output array:
#--------------------------------------------------------------------------
data, dataw, camout, originalshape = _massage_input_and_init_output(
data, dataw, inputtype=inputtype, direction=direction)
#--------------------------------------------------------------------------
# Do precomputations needed for both the forward and inverse model,
# and which do not depend on sample or light source data:
#--------------------------------------------------------------------------
Mxyz2lms = np.dot(
np.diag(cLMS), Mxyz2lms
) # weight the xyz-to-lms conversion matrix with cLMS (cfr. stage 1 calculations)
invMxyz2lms = np.linalg.inv(
Mxyz2lms) # Calculate the inverse lms-to-xyz conversion matrix
MAab = np.array(
[clambda, calpha, cbeta]
) # Create matrix with scale factors for L, M, S for quick matrix multiplications
invMAab = np.linalg.inv(
MAab) # Pre-calculate its inverse to avoid repeat in loop.
#--------------------------------------------------------------------------
# Apply forward/inverse model by looping over each row (=light source dim.)
# in data:
#--------------------------------------------------------------------------
N = data.shape[0]
for i in range(N):
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# START FORWARD MODE and common part of inverse mode
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#-----------------------------------------------------------------------------
# Get absolute tristimulus values for stimulus field and white point for row i:
#-----------------------------------------------------------------------------
xyzt, xyzw, xyzw_abs = _get_absolute_xyz_xyzw(data,
dataw,
i=i,
Lw=Lw,
direction=direction,
cieobs=cieobs,
inputtype=inputtype,
relative=relative)
#-----------------------------------------------------------------------------
# stage 1: calculate photon rates of stimulus and white white, and
# adapting field: i.e. lmst, lmsw and lmsf
#-----------------------------------------------------------------------------
# Convert to white point l,m,s:
lmsw = 683.0 * np.dot(Mxyz2lms, xyzw.T).T / _CMF[cieobs]['K']
# Calculate adaptation field and convert to l,m,s:
lmsf = (Yb / 100.0) * lmsw
# Calculate lms of stimulus
# or put adaptation lmsf in test field lmst for later use in inverse-mode (no xyz in 'inverse' mode!!!):
lmst = (683.0 * np.dot(Mxyz2lms, xyzt.T).T /
_CMF[cieobs]['K']) if (direction == 'forward') else lmsf
#-----------------------------------------------------------------------------
# stage 2: calculate cone outputs of stimulus lmstp
#-----------------------------------------------------------------------------
lmstp = math.erf(Cc *
(np.log(lmst / lms0) +
Cf * np.log(lmsf / lms0))) # stimulus test field
lmsfp = math.erf(Cc * (np.log(lmsf / lms0) +
Cf * np.log(lmsf / lms0))) # adaptation field
# add adaptation field lms temporarily to lmstp for quick calculation
lmstp = np.vstack((lmsfp, lmstp))
#-----------------------------------------------------------------------------
# stage 3: calculate optic nerve signals, lam*, alphp, betp:
#-----------------------------------------------------------------------------
lstar, alph, bet = asplit(np.dot(MAab, lmstp.T).T)
alphp = cga1[0] * alph
alphp[alph < 0] = cga1[1] * alph[alph < 0]
betp = cgb1[0] * bet
betp[bet < 0] = cgb1[1] * bet[bet < 0]
#-----------------------------------------------------------------------------
# stage 4: calculate recoded nerve signals, alphapp, betapp:
#-----------------------------------------------------------------------------
alphpp = cga2[0] * (alphp + betp)
betpp = cgb2[0] * (alphp - betp)
#-----------------------------------------------------------------------------
# stage 5: calculate conscious color perception:
#-----------------------------------------------------------------------------
lstar_int = cl_int[0] * (lstar + cl_int[1])
alph_int = cab_int[0] * (np.cos(cab_int[1] * np.pi / 180.0) * alphpp -
np.sin(cab_int[1] * np.pi / 180.0) * betpp)
bet_int = cab_int[0] * (np.sin(cab_int[1] * np.pi / 180.0) * alphpp +
np.cos(cab_int[1] * np.pi / 180.0) * betpp)
lstar_out = lstar_int
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# stage 5 continued but SPLIT IN FORWARD AND INVERSE MODES:
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#--------------------------------------
# FORWARD MODE TO PERCEPTUAL SIGNALS:
#--------------------------------------
if direction == 'forward':
if Ccwb is None:
alph_out = alph_int - cab_out[0]
bet_out = bet_int - cab_out[1]
else:
Ccwb = Ccwb * np.ones((2))
Ccwb[Ccwb < 0.0] = 0.0
Ccwb[Ccwb > 1.0] = 1.0
# white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation:
alph_out = alph_int - Ccwb[0] * alph_int[0]
bet_out = bet_int - Ccwb[1] * bet_int[0]
# stack together and remove adaptation field from vertical stack
# camout is an ndarray with perceptual signals:
camout[i] = np.vstack((lstar_out[1:], alph_out[1:], bet_out[1:])).T
#--------------------------------------
# INVERSE MODE FROM PERCEPTUAL SIGNALS:
#--------------------------------------
elif direction == 'inverse':
# stack cognitive pre-adapted adaptation field signals (first on stack) together:
#labf_int = np.hstack((lstar_int[0],alph_int[0],bet_int[0]))
# get lstar_out, alph_out & bet_out for data
#(contains model perceptual signals in inverse mode!!!):
lstar_out, alph_out, bet_out = asplit(data[i])
#------------------------------------------------------------------------
# Inverse stage 5: undo cortical white-balance:
#------------------------------------------------------------------------
if Ccwb is None:
alph_int = alph_out + cab_out[0]
bet_int = bet_out + cab_out[1]
else:
Ccwb = Ccwb * np.ones((2))
Ccwb[Ccwb < 0.0] = 0.0
Ccwb[Ccwb > 1.0] = 1.0
# inverse white balance shift using adaptation gray background (Yb=20%), with Ccw: degree of adaptation
alph_int = alph_out + Ccwb[0] * alph_int[0]
bet_int = bet_out + Ccwb[1] * bet_int[0]
alphpp = (1.0 / cab_int[0]) * (
np.cos(-cab_int[1] * np.pi / 180.0) * alph_int -
np.sin(-cab_int[1] * np.pi / 180.0) * bet_int)
betpp = (1.0 / cab_int[0]) * (
np.sin(-cab_int[1] * np.pi / 180.0) * alph_int +
np.cos(-cab_int[1] * np.pi / 180.0) * bet_int)
lstar_int = lstar_out
lstar = (lstar_int / cl_int[0]) - cl_int[1]
#---------------------------------------------------------------------------
# Inverse stage 4: pre-adapted perceptual signals to recoded nerve signals:
#---------------------------------------------------------------------------
alphp = 0.5 * (alphpp / cga2[0] + betpp / cgb2[0]
) # <-- alphpp = (Cga2.*(alphp+betp));
betp = 0.5 * (alphpp / cga2[0] - betpp / cgb2[0]
) # <-- betpp = (Cgb2.*(alphp-betp));
#---------------------------------------------------------------------------
# Inverse stage 3: recoded nerve signals to optic nerve signals:
#---------------------------------------------------------------------------
alph = alphp / cga1[0]
bet = betp / cgb1[0]
sa = np.sign(cga1[1])
sb = np.sign(cgb1[1])
alph[(sa * alphp) < 0.0] = alphp[(sa * alphp) < 0] / cga1[1]
bet[(sb * betp) < 0.0] = betp[(sb * betp) < 0] / cgb1[1]
lab = ajoin((lstar, alph, bet))
#---------------------------------------------------------------------------
# Inverse stage 2: optic nerve signals to cone outputs:
#---------------------------------------------------------------------------
lmstp = np.dot(invMAab, lab.T).T
lmstp[lmstp < -1.0] = -1.0
lmstp[lmstp > 1.0] = 1.0
#---------------------------------------------------------------------------
# Inverse stage 1: cone outputs to photon rates:
#---------------------------------------------------------------------------
lmstp = math.erfinv(lmstp) / Cc - Cf * np.log(lmsf / lms0)
lmst = np.exp(lmstp) * lms0
#---------------------------------------------------------------------------
# Photon rates to absolute or relative tristimulus values:
#---------------------------------------------------------------------------
xyzt = np.dot(invMxyz2lms, lmst.T).T * (_CMF[cieobs]['K'] / 683.0)
if relative == True:
xyzt = (100 / Lw) * xyzt
# store in same named variable as forward mode:
camout[i] = xyzt
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# END inverse mode
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
return _massage_output_data_to_original_shape(camout, originalshape)
def Ydlep_to_xyz(Ydlep,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
SL_max_lambda=None,
**kwargs):
"""
Convert Y, dominant (complementary) wavelength and excitation purity to XYZ
tristimulus values.
Args:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
and excitation purity
:xyzw:
| None or narray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
:SL_max_lambda:
| None or float, optional
| Maximum wavelength of spectrum locus before it turns back on itelf in the high wavelength range (~700 nm)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Ydlep3 = np3d(Ydlep).copy().astype(np.float)
# flip axis so that longest dim is on first axis (save time in looping):
if (Ydlep3.shape[0] < Ydlep3.shape[1]) & (flip_axes == True):
axes12flipped = True
Ydlep3 = Ydlep3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyzw to Yxyw:
Yxyw = xyz_to_Yxy(xyzw)
Yxywo = Yxyw.copy()
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0, None].T
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# Get maximum wavelength of spectrum locus (before it turns back on itself)
if SL_max_lambda is None:
pmaxlambda = Yxysl[..., 1].argmax() # lambda with largest x value
dwl = np.diff(
Yxysl[:, 0,
1]) # spectrumlocus in that range should have increasing x
dwl[wlsl[:-1, 0] < 600] = 10000
pmaxlambda = np.where(
dwl <= 0)[0][0] # Take first element with zero or <zero slope
else:
pmaxlambda = np.abs(wlsl - SL_max_lambda).argmin()
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1), :1]
# center on xyzw:
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, dom, pur = asplit(Ydlep3)
Yw, xw, yw = asplit(Yxyw)
Ywo, xwo, ywo = asplit(Yxywo)
Ysl, xsl, ysl = asplit(Yxysl)
# loop over longest dim:
x = np.empty(Y.shape)
y = np.empty(Y.shape)
for i in range(Ydlep3.shape[1]):
# find closest wl's to dom:
#wlslb,wlib = meshblock(wlsl,np.abs(dom[i,:])) #abs because dom<0--> complemtary wl
wlib, wlslb = np.meshgrid(np.abs(dom[:, i]), wlsl)
dwl = wlslb - wlib
q1 = np.abs(dwl).argmin(axis=0) # index of closest wl
sign_q1 = np.sign(dwl[q1])
dwl[np.sign(dwl) ==
sign_q1] = 1000000 # set all dwl on the same side as q1 to a very large value
q2 = np.abs(dwl).argmin(
axis=0) # index of second closest (enclosing) wl
# calculate x,y of dom:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (
np.abs(dom[:, i]) - wlsl[q1, 0]) / (wlsl[q2, 0] - wlsl[q1, 0]
) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (
np.abs(dom[:, i]) - wlsl[q1, 0]) / (wlsl[q2, 0] - wlsl[q1, 0]
) # calculate y of dom. wl
# calculate x,y of test:
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to dom
d = pur[:, i] * d_wl
hdom = math.positive_arctan(x_dom_wl, y_dom_wl, htype='deg')
x[:, i] = d * np.cos(hdom * np.pi / 180.0)
y[:, i] = d * np.sin(hdom * np.pi / 180.0)
# complementary:
pc = np.where(dom[:, i] < 0.0)
hdom[pc] = hdom[pc] - np.sign(dom[:, i][pc] -
180.0) * 180.0 # get positive hue angle
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x_dom_wl, y_dom_wl)).T
xyw = np.vstack((xw, yw)).T
xypl1 = np.vstack((xsl[0, None], ysl[0, None])).T
xypl2 = np.vstack((xsl[-1, None], ysl[-1, None])).T
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T[:, 0]
x[:, i][pc] = pur[:, i][pc] * d_linecross[pc] * np.cos(
hdom[pc] * np.pi / 180)
y[:, i][pc] = pur[:, i][pc] * d_linecross[pc] * np.sin(
hdom[pc] * np.pi / 180)
Yxy = np.dstack((Ydlep3[:, :, 0], x + xwo, y + ywo))
if axes12flipped == True:
Yxy = Yxy.transpose((1, 0, 2))
else:
Yxy = Yxy.transpose((0, 1, 2))
return Yxy_to_xyz(Yxy).reshape(Ydlep.shape)
def spd_to_aopicE(sid,
Ee=None,
E=None,
Q=None,
cieobs=_CIEOBS,
sid_units='W/m2',
out='Eeas,Eas'):
"""
Calculate alpha-opic irradiance (Ee,α) and equivalent luminance (Eα) values
for the l-cone, m-cone, s-cone, rod and iprgc (α) photoreceptor cells
following CIE technical note TN 003:2015.
Args:
:sid:
| numpy.ndarray with retinal spectral irradiance in :sid_units:
| (if 'uW/cm2', sid will be converted to SI units 'W/m2')
:Ee:
| None, optional
| If not None: normalize :sid: to an irradiance of :Ee:
:E:
| None, optional
| If not None: normalize :sid: to an illuminance of :E:
| Note that E is calculate using a Km factor corrected to standard air.
:Q:
| None, optional
| If not None: nNormalize :sid: to a quantal energy of :Q:
:cieobs:
| _CIEOBS or str, optional
| Type of cmf set to use for photometric units.
:sid_units:
| 'W/m2', optional
| Other option 'uW/m2', input units of :sid:
:out:
| 'Eeas, Eas' or str, optional
| Determines values to return.
Returns:
:returns:
| (Eeas, Eas) with Eeas and Eas resp. numpy.ndarrays with the
| α-opic irradiance and equivalent illuminance values
| of all spectra in :sid: in SI-units.
|
| (other choice can be set using :out:)
"""
outlist = out.split(',')
# Convert to Watt/m²:
if sid_units == 'uW/cm2':
sid[1:] = sid[1:] / 100
elif sid_units == 'W/m2':
pass
else:
raise Exception(
"spd_to_aopicE(): {} unsupported units for SID.".format(sid_units))
# Normalize sid to Ee:
if Ee is not None:
sid = spd_normalize(sid, norm_type='ru', norm_f=Ee)
elif E is not None:
sid = spd_normalize(sid, norm_type='pusa', norm_f=E)
elif Q is not None:
sid = spd_normalize(sid, norm_type='qu', norm_f=Q)
# Get sid irradiance (W/m²):
if 'Ee' in outlist:
Ee = spd_to_power(sid, cieobs=cieobs, ptype='ru')
# Get sid illuminance (lx):
if 'E' in outlist:
E = spd_to_power(
sid, cieobs=cieobs,
ptype='pusa') #photometric units (Km corrected to standard air)
# Get sid quantal energy (photons/m²/s):
if 'Q' in outlist:
Q = spd_to_power(sid, cieobs=cieobs, ptype='qu')
# get SI actinic action spectra, sa:
sa = spd(_ACTIONSPECTRA, wl=sid[0], interpolation='cmf', norm_type='max')
# get wavelength spacing:
dl = getwld(sid[0])
# Calculate all alpha-opics Ee's:
Eeas = (np.dot((sa[1:] * dl), sid[1:].T)).T
# Calculate equivalent alpha-opic E's:
Vl, Km = vlbar(cieobs=cieobs, wl_new=sid[0], out=2)
Eas = Km * Km_correction_factor * Eeas * (Vl[1].sum() / sa[1:].sum(axis=1))
#Prepare output:
if out == 'Eeas,Eas':
return Eeas, Eas
elif out == 'Eeas':
return Eeas
elif out == 'Eas':
return Eas
else:
eval(out)
def apply(data, n_step = 2, catmode = None, cattype = 'vonkries', xyzw1 = None, xyzw2 = None, xyzw0 = None,\
D = None, mcat = [_MCAT_DEFAULT], normxyz0 = None, outtype = 'xyz', La = None, F = None, Dtype = None):
"""
Calculate corresponding colors by applying a von Kries chromatic adaptation
transform (CAT), i.e. independent rescaling of 'sensor sensitivity' to data
to adapt from current adaptation conditions (1) to the new conditions (2).
Args:
:data:
| ndarray of tristimulus values (can be NxMx3)
:n_step:
| 2, optional
| Number of step in CAT (1: 1-step, 2: 2-step)
:catmode:
| None, optional
| - None: use :n_step: to set mode: 1 = '1>2', 2:'1>0>2'
| -'1>0>2': Two-step CAT
| from illuminant 1 to baseline illuminant 0 to illuminant 2.
| -'1>2': One-step CAT
| from illuminant 1 to illuminant 2.
| -'1>0': One-step CAT
| from illuminant 1 to baseline illuminant 0.
| -'0>2': One-step CAT
| from baseline illuminant 0 to illuminant 2.
:cattype:
| 'vonkries' (others: 'rlab', see Farchild 1990), optional
:xyzw1:
| None, depending on :catmode: optional (can be Mx3)
:xyzw2:
| None, depending on :catmode: optional (can be Mx3)
:xyzw0:
| None, depending on :catmode: optional (can be Mx3)
:D:
| None, optional
| Degrees of adaptation. Defaults to [1.0, 1.0].
:La:
| None, optional
| Adapting luminances.
| If None: xyz values are absolute or relative.
| If not None: xyz are relative.
:F:
| None, optional
| Surround parameter(s) for CAT02/CAT16 calculations
| (:Dtype: == 'cat02' or 'cat16')
| Defaults to [1.0, 1.0].
:Dtype:
| None, optional
| Type of degree of adaptation function from literature
| See luxpy.cat.get_degree_of_adaptation()
:mcat:
| [_MCAT_DEFAULT], optional
| List[str] or List[ndarray] of sensor space matrices for each
| condition pair. If len(:mcat:) == 1, the same matrix is used.
:normxyz0:
| None, optional
| Set of xyz tristimulus values to normalize the sensor space matrix to.
:outtype:
| 'xyz' or 'lms', optional
| - 'xyz': return corresponding tristimulus values
| - 'lms': return corresponding sensor space excitation values
| (e.g. for further calculations)
Returns:
:returns:
| ndarray with corresponding colors
Reference:
1. `Smet, K. A. G., & Ma, S. (2020).
Some concerns regarding the CAT16 chromatic adaptation transform.
Color Research & Application, 45(1), 172–177.
<https://doi.org/10.1002/col.22457>`_
"""
if (xyzw1 is None) & (xyzw2 is None):
return data # do nothing
else:
# Set catmode:
if catmode is None:
if n_step == 2:
catmode = '1>0>2'
elif n_step == 1:
catmode = '1>2'
else:
raise Exception(
'cat.apply(n_step = {:1.0f}, catmode = None): Unknown requested n-step CAT mode !'
.format(n_step))
# Make data 2d:
data = np2d(data)
data_original_shape = data.shape
if data.ndim < 3:
target_shape = np.hstack((1, data.shape))
data = data * np.ones(target_shape)
else:
target_shape = data.shape
target_shape = data.shape
# initialize xyzw0:
if (xyzw0 is None): # set to iLL.E
xyzw0 = np2d([100.0, 100.0, 100.0])
xyzw0 = np.ones(target_shape) * xyzw0
La0 = xyzw0[..., 1, None]
# Determine cat-type (1-step or 2-step) + make input same shape as data for block calculations:
expansion_axis = np.abs(1 * (len(data_original_shape) == 2) - 1)
if ((xyzw1 is not None) & (xyzw2 is not None)):
xyzw1 = xyzw1 * np.ones(target_shape)
xyzw2 = xyzw2 * np.ones(target_shape)
default_La12 = [xyzw1[..., 1, None], xyzw2[..., 1, None]]
elif (xyzw2 is None) & (xyzw1
is not None): # apply one-step CAT: 1-->0
catmode = '1>0' #override catmode input
xyzw1 = xyzw1 * np.ones(target_shape)
default_La12 = [xyzw1[..., 1, None], La0]
elif (xyzw1 is None) & (xyzw2 is not None):
raise Exception(
"von_kries(): cat transformation '0>2' not supported, use '1>0' !"
)
# Get or set La (La == None: xyz are absolute or relative, La != None: xyz are relative):
target_shape_1 = tuple(np.hstack((target_shape[:-1], 1)))
La1, La2 = parse_x1x2_parameters(La,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis,
default=default_La12)
# Set degrees of adaptation, D10, D20: (note D20 is degree of adaptation for 2-->0!!)
D10, D20 = parse_x1x2_parameters(D,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis)
# Set F surround in case of Dtype == 'cat02':
F1, F2 = parse_x1x2_parameters(F,
target_shape=target_shape_1,
catmode=catmode,
expand_2d_to_3d=expansion_axis)
# Make xyz relative to go to relative xyz0:
if La is None:
data = 100 * data / La1
xyzw1 = 100 * xyzw1 / La1
xyzw0 = 100 * xyzw0 / La0
if (catmode == '1>0>2') | (catmode == '1>2'):
xyzw2 = 100 * xyzw2 / La2
# transform data (xyz) to sensor space (lms) and perform cat:
xyzc = np.zeros(data.shape)
xyzc.fill(np.nan)
mcat = np.array(mcat)
if (mcat.shape[0] != data.shape[1]) & (mcat.shape[0] == 1):
mcat = np.repeat(mcat, data.shape[1], axis=0)
elif (mcat.shape[0] != data.shape[1]) & (mcat.shape[0] > 1):
raise Exception(
'von_kries(): mcat.shape[0] > 1 and does not match data.shape[0]!'
)
for i in range(xyzc.shape[1]):
# get cat sensor matrix:
if mcat[i].dtype == np.float64:
mcati = mcat[i]
else:
mcati = _MCATS[mcat[i]]
# normalize sensor matrix:
if normxyz0 is not None:
mcati = math.normalize_3x3_matrix(mcati, xyz0=normxyz0)
# convert from xyz to lms:
lms = np.dot(mcati, data[:, i].T).T
lmsw0 = np.dot(mcati, xyzw0[:, i].T).T
if (catmode == '1>0>2') | (catmode == '1>0'):
lmsw1 = np.dot(mcati, xyzw1[:, i].T).T
Dpar1 = dict(D=D10[:, i],
F=F1[:, i],
La=La1[:, i],
La0=La0[:, i],
order='1>0')
D10[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar1) #get degree of adaptation depending on Dtype
lmsw2 = None # in case of '1>0'
if (catmode == '1>0>2'):
lmsw2 = np.dot(mcati, xyzw2[:, i].T).T
Dpar2 = dict(D=D20[:, i],
F=F2[:, i],
La=La2[:, i],
La0=La0[:, i],
order='0>2')
D20[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar2) #get degree of adaptation depending on Dtype
if (catmode == '1>2'):
lmsw1 = np.dot(mcati, xyzw1[:, i].T).T
lmsw2 = np.dot(mcati, xyzw2[:, i].T).T
Dpar12 = dict(D=D10[:, i],
F=F1[:, i],
La=La1[:, i],
La2=La2[:, i],
order='1>2')
D10[:, i] = get_degree_of_adaptation(
Dtype=Dtype,
**Dpar12) #get degree of adaptation depending on Dtype
# Determine transfer function Dt:
Dt = get_transfer_function(cattype=cattype,
catmode=catmode,
lmsw1=lmsw1,
lmsw2=lmsw2,
lmsw0=lmsw0,
D10=D10[:, i],
D20=D20[:, i],
La1=La1[:, i],
La2=La2[:, i])
# Perform cat:
lms = np.dot(np.diagflat(Dt[0]), lms.T).T
# Make xyz, lms 'absolute' again:
if (catmode == '1>0>2'):
lms = (La2[:, i] / La1[:, i]) * lms
elif (catmode == '1>0'):
lms = (La0[:, i] / La1[:, i]) * lms
elif (catmode == '1>2'):
lms = (La2[:, i] / La1[:, i]) * lms
# transform back from sensor space to xyz (or not):
if outtype == 'xyz':
xyzci = np.dot(np.linalg.inv(mcati), lms.T).T
xyzci[np.where(xyzci < 0)] = _EPS
xyzc[:, i] = xyzci
else:
xyzc[:, i] = lms
# return data to original shape:
if len(data_original_shape) == 2:
xyzc = xyzc[0]
return xyzc
def cam18sl(data,
datab=None,
Lb=[100],
fov=10.0,
inputtype='xyz',
direction='forward',
outin='Q,aS,bS',
parameters=None):
"""
Convert between CIE 2006 10° XYZ tristimulus values (or spectral data)
and CAM18sl color appearance correlates.
Args:
:data:
| ndarray of CIE 2006 10° absolute XYZ tristimulus values or spectral data
| or color appearance attributes of stimulus
:datab:
| ndarray of CIE 2006 10° absolute XYZ tristimulus values or spectral data
| of stimulus background
:Lb:
| [100], optional
| Luminance (cd/m²) value(s) of background(s) calculated using the CIE 2006 10° CMFs
| (only used in case datab == None and the background is assumed to be an Equal-Energy-White)
:fov:
| 10.0, optional
| Field-of-view of stimulus (for size effect on brightness)
:inputtpe:
| 'xyz' or 'spd', optional
| Specifies the type of input:
| tristimulus values or spectral data for the forward mode.
:direction:
| 'forward' or 'inverse', optional
| -'forward': xyz -> cam18sl
| -'inverse': cam18sl -> xyz
:outin:
| 'Q,aS,bS' or str, optional
| 'Q,aS,bS' (brightness and opponent signals for saturation)
| other options: 'Q,aM,bM' (colorfulness)
| (Note that 'Q,aW,bW' would lead to a Cartesian
| a,b-coordinate system centered at (1,0))
| Str specifying the type of
| input (:direction: == 'inverse') and
| output (:direction: == 'forward')
:parameters:
| None or dict, optional
| Set of model parameters.
| - None: defaults to luxpy.cam._CAM18SL_PARAMETERS
| (see references below)
Returns:
:returns:
| ndarray with color appearance correlates (:direction: == 'forward')
| or
| XYZ tristimulus values (:direction: == 'inverse')
Notes:
| * Instead of using the CIE 1964 10° CMFs in some places of the model,
| the CIE 2006 10° CMFs are used througout, making it more self_consistent.
| This has an effect on the k scaling factors (now different those in CAM15u)
| and the illuminant E normalization for use in the chromatic adaptation transform.
| (see future erratum to Hermans et al., 2018)
| * The paper also used an equation for the amount of white W, which is
| based on a Q value not expressed in 'bright' ('cA' = 0.937 instead of 123).
| This has been corrected for in the luxpy version of the model, i.e.
| _CAM18SL_PARAMETERS['cW'][0] has been changed from 2.29 to 1/11672.
| (see future erratum to Hermans et al., 2018)
| * Default output was 'Q,aW,bW' prior to March 2020, but since this
| is an a,b Cartesian system centered on (1,0), the default output
| has been changed to 'Q,aS,bS'.
References:
1. `Hermans, S., Smet, K. A. G., & Hanselaer, P. (2018).
"Color appearance model for self-luminous stimuli."
Journal of the Optical Society of America A, 35(12), 2000–2009.
<https://doi.org/10.1364/JOSAA.35.002000>`_
"""
if parameters is None:
parameters = _CAM18SL_PARAMETERS
outin = outin.split(',')
#unpack model parameters:
cA, cAlms, cHK, cM, cW, ca, calms, cb, cblms, cfov, cieobs, k, naka, unique_hue_data = [
parameters[x] for x in sorted(parameters.keys())
]
# precomputations:
Mlms2xyz = np.linalg.inv(_CMF[cieobs]['M'])
MAab = np.array([cAlms, calms, cblms])
invMAab = np.linalg.inv(MAab)
#-------------------------------------------------
# setup EEW reference field and default background field (Lr should be equal to Lb):
# Get Lb values:
if datab is not None:
if inputtype != 'xyz':
Lb = spd_to_xyz(datab, cieobs=cieobs, relative=False)[..., 1:2]
else:
Lb = datab[..., 1:2]
else:
if isinstance(Lb, list):
Lb = np2dT(Lb)
# Setup EEW ref of same luminance as datab:
if inputtype == 'xyz':
wlr = getwlr(_CAM18SL_WL3)
else:
if datab is None:
wlr = data[0] # use wlr of stimulus data
else:
wlr = datab[0] # use wlr of background data
datar = np.vstack((wlr, np.ones(
(Lb.shape[0], wlr.shape[0])))) # create eew
xyzr = spd_to_xyz(datar, cieobs=cieobs,
relative=False) # get abs. tristimulus values
datar[1:] = datar[1:] / xyzr[..., 1:2] * Lb
# Create datab if None:
if (datab is None):
if inputtype != 'xyz':
datab = datar.copy()
else:
datab = spd_to_xyz(datar, cieobs=cieobs, relative=False)
# prepare data and datab for loop over backgrounds:
# make axis 1 of datab have 'same' dimensions as data:
if (data.ndim == 2):
data = np.expand_dims(data, axis=1) # add light source axis 1
if inputtype == 'xyz':
datar = spd_to_xyz(datar, cieobs=cieobs,
relative=False) # convert to xyz!!
if datab.shape[
0] == 1: #make datab and datar have same lights source dimension (used to store different backgrounds) size as data
datab = np.repeat(datab, data.shape[1], axis=0)
datar = np.repeat(datar, data.shape[1], axis=0)
else:
if datab.shape[0] == 2:
datab = np.vstack(
(datab[0], np.repeat(datab[1:], data.shape[1], axis=0)))
if datar.shape[0] == 2:
datar = np.vstack(
(datar[0], np.repeat(datar[1:], data.shape[1], axis=0)))
# Flip light source/ background dim to axis 0:
data = np.transpose(data, axes=(1, 0, 2))
#-------------------------------------------------
#initialize camout:
dshape = list(data.shape)
dshape[-1] = len(outin) # requested number of correlates
if (inputtype != 'xyz') & (direction == 'forward'):
dshape[-2] = dshape[
-2] - 1 # wavelength row doesn't count & only with forward can the input data be spectral
camout = np.zeros(dshape)
camout.fill(np.nan)
for i in range(data.shape[0]):
# get rho, gamma, beta of background and reference white:
if (inputtype != 'xyz'):
xyzb = spd_to_xyz(np.vstack((datab[0], datab[i + 1:i + 2, :])),
cieobs=cieobs,
relative=False)
xyzr = spd_to_xyz(np.vstack((datar[0], datar[i + 1:i + 2, :])),
cieobs=cieobs,
relative=False)
else:
xyzb = datab[i:i + 1, :]
xyzr = datar[i:i + 1, :]
lmsb = np.dot(_CMF[cieobs]['M'], xyzb.T).T # convert to l,m,s
rgbb = (lmsb / _CMF[cieobs]['K']) * k # convert to rho, gamma, beta
#lmsr = np.dot(_CMF[cieobs]['M'],xyzr.T).T # convert to l,m,s
#rgbr = (lmsr / _CMF[cieobs]['K']) * k # convert to rho, gamma, beta
#rgbr = rgbr/rgbr[...,1:2]*Lb[i] # calculated EEW cone excitations at same luminance values as background
rgbr = np.ones(xyzr.shape) * Lb[
i] # explicitely equal EEW cone excitations at same luminance values as background
if direction == 'forward':
# get rho, gamma, beta of stimulus:
if (inputtype != 'xyz'):
xyz = spd_to_xyz(data[i], cieobs=cieobs, relative=False)
elif (inputtype == 'xyz'):
xyz = data[i]
lms = np.dot(_CMF[cieobs]['M'], xyz.T).T # convert to l,m,s
rgb = (lms / _CMF[cieobs]['K']) * k # convert to rho, gamma, beta
# apply von-kries cat with D = 1:
if (rgbb == 0).any():
Mcat = np.eye(3)
else:
Mcat = np.diag((rgbr / rgbb)[0])
rgba = np.dot(Mcat, rgb.T).T
# apply naka-rushton compression:
rgbc = naka_rushton(rgba,
n=naka['n'],
sig=naka['sig'](rgbr.mean()),
noise=naka['noise'],
scaling=naka['scaling'])
#rgbc = np.ones(rgbc.shape)*rgbc.mean() # test if eew ends up at origin
# calculate achromatic and color difference signals, A, a, b:
Aab = np.dot(MAab, rgbc.T).T
A, a, b = asplit(Aab)
a = ca * a
b = cb * b
# calculate colorfullness like signal M:
M = cM * ((a**2.0 + b**2.0)**0.5)
# calculate brightness Q:
Q = cA * (
A + cHK[0] * M**cHK[1]
) # last term is contribution of Helmholtz-Kohlrausch effect on brightness
# calculate saturation, s:
s = M / Q
S = s # make extra variable, jsut in case 'S' is called
# calculate amount of white, W:
W = 1 / (1.0 + cW[0] * (s**cW[1]))
# adjust Q for size (fov) of stimulus (matter of debate whether to do this before or after calculation of s or W, there was no data on s, M or W for different sized stimuli: after)
Q = Q * (fov / 10.0)**cfov
# calculate hue, h and Hue quadrature, H:
h = hue_angle(a, b, htype='deg')
if 'H' in outin:
H = hue_quadrature(h, unique_hue_data=unique_hue_data)
else:
H = None
# calculate cart. co.:
if 'aM' in outin:
aM = M * np.cos(h * np.pi / 180.0)
bM = M * np.sin(h * np.pi / 180.0)
if 'aS' in outin:
aS = s * np.cos(h * np.pi / 180.0)
bS = s * np.sin(h * np.pi / 180.0)
if 'aW' in outin:
aW = W * np.cos(h * np.pi / 180.0)
bW = W * np.sin(h * np.pi / 180.0)
if (outin != ['Q', 'as', 'bs']):
camout[i] = eval('ajoin((' + ','.join(outin) + '))')
else:
camout[i] = ajoin((Q, aS, bS))
elif direction == 'inverse':
# get Q, M and a, b depending on input type:
if 'aW' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
W = (a**2.0 + b**2.0)**0.5
s = (((1.0 / W) - 1.0) / cW[0])**(1.0 / cW[1])
M = s * Q
if 'aM' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
M = (a**2.0 + b**2.0)**0.5
if 'aS' in outin:
Q, a, b = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
s = (a**2.0 + b**2.0)**0.5
M = s * Q
if 'h' in outin:
Q, WsM, h = asplit(data[i])
Q = Q / (
(fov / 10.0)**cfov
) #adjust Q for size (fov) of stimulus back to that 10° ref
if 'W' in outin:
s = (((1.0 / WsM) - 1.0) / cW[0])**(1.0 / cW[1])
M = s * Q
elif 's' in outin:
M = WsM * Q
elif 'M' in outin:
M = WsM
# calculate achromatic signal, A from Q and M:
A = Q / cA - cHK[0] * M**cHK[1]
# calculate hue angle:
h = hue_angle(a, b, htype='rad')
# calculate a,b from M and h:
a = (M / cM) * np.cos(h)
b = (M / cM) * np.sin(h)
a = a / ca
b = b / cb
# create Aab:
Aab = ajoin((A, a, b))
# calculate rgbc:
rgbc = np.dot(invMAab, Aab.T).T
# decompress rgbc to (adapted) rgba :
rgba = naka_rushton(rgbc,
n=naka['n'],
sig=naka['sig'](rgbr.mean()),
noise=naka['noise'],
scaling=naka['scaling'],
direction='inverse')
# apply inverse von-kries cat with D = 1:
rgb = np.dot(np.diag((rgbb / rgbr)[0]), rgba.T).T
# convert rgb to lms to xyz:
lms = rgb / k * _CMF[cieobs]['K']
xyz = np.dot(Mlms2xyz, lms.T).T
camout[i] = xyz
camout = np.transpose(camout, axes=(1, 0, 2))
if camout.shape[1] == 1:
camout = np.squeeze(camout, axis=1)
return camout
def xyz_to_Ydlep(xyz,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
SL_max_lambda=None,
**kwargs):
"""
Convert XYZ tristimulus values to Y, dominant (complementary) wavelength
and excitation purity.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of a single (!) native white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating spectrum locus coordinates.
:flip_axes:
| False, optional
| If True: flip axis 0 and axis 1 in Ydelep to increase speed of loop in function.
| (single xyzw with is not flipped!)
:SL_max_lambda:
| None or float, optional
| Maximum wavelength of spectrum locus before it turns back on itelf in the high wavelength range (~700 nm)
Returns:
:Ydlep:
| ndarray with Y, dominant (complementary) wavelength
| and excitation purity
"""
xyz3 = np3d(xyz).copy().astype(np.float)
# flip axis so that shortest dim is on axis0 (save time in looping):
if (xyz3.shape[0] < xyz3.shape[1]) & (flip_axes == True):
axes12flipped = True
xyz3 = xyz3.transpose((1, 0, 2))
else:
axes12flipped = False
# convert xyz to Yxy:
Yxy = xyz_to_Yxy(xyz3)
Yxyw = xyz_to_Yxy(xyzw)
# get spectrum locus Y,x,y and wavelengths:
SL = _CMF[cieobs]['bar']
SL = SL[:, SL[1:].sum(axis=0) >
0] # avoid div by zero in xyz-to-Yxy conversion
wlsl = SL[0]
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# Get maximum wavelength of spectrum locus (before it turns back on itself)
if SL_max_lambda is None:
pmaxlambda = Yxysl[..., 1].argmax() # lambda with largest x value
dwl = np.diff(
Yxysl[:, 0,
1]) # spectrumlocus in that range should have increasing x
dwl[wlsl[:-1] < 600] = 10000
pmaxlambda = np.where(
dwl <= 0)[0][0] # Take first element with zero or <zero slope
else:
pmaxlambda = np.abs(wlsl - SL_max_lambda).argmin()
Yxysl = Yxysl[:(pmaxlambda + 1), :]
wlsl = wlsl[:(pmaxlambda + 1)]
# center on xyzw:
Yxy = Yxy - Yxyw
Yxysl = Yxysl - Yxyw
Yxyw = Yxyw - Yxyw
#split:
Y, x, y = asplit(Yxy)
Yw, xw, yw = asplit(Yxyw)
Ysl, xsl, ysl = asplit(Yxysl)
# calculate hue:
h = math.positive_arctan(x, y, htype='deg')
hsl = math.positive_arctan(xsl, ysl, htype='deg')
hsl_max = hsl[0] # max hue angle at min wavelength
hsl_min = hsl[-1] # min hue angle at max wavelength
if hsl_min < hsl_max: hsl_min += 360
dominantwavelength = np.empty(Y.shape)
purity = np.empty(Y.shape)
for i in range(xyz3.shape[1]):
# find index of complementary wavelengths/hues:
pc = np.where(
(h[:, i] > hsl_max) & (h[:, i] < hsl_min)
) # hue's requiring complementary wavelength (purple line)
h[:, i][pc] = h[:, i][pc] - np.sign(
h[:, i][pc] - 180.0
) * 180.0 # add/subtract 180° to get positive complementary wavelength
# find 2 closest enclosing hues in sl:
#hslb,hib = meshblock(hsl,h[:,i:i+1])
hib, hslb = np.meshgrid(h[:, i:i + 1], hsl)
dh = (hslb - hib)
q1 = np.abs(dh).argmin(axis=0) # index of closest hue
sign_q1 = np.sign(dh[q1])[0]
dh[np.sign(dh) ==
sign_q1] = 1000000 # set all dh on the same side as q1 to a very large value
q2 = np.abs(dh).argmin(
axis=0) # index of second closest (enclosing) hue
# # Test changes to code:
# print('wls',i, wlsl[q1],wlsl[q2])
# import matplotlib.pyplot as plt
# plt.figure()
# plt.plot(wlsl[:-1],np.diff(xsl[:,0]),'k.-')
# plt.figure()
# plt.plot(x[0,i],y[0,i],'k.'); plt.plot(xsl,ysl,'r.-');plt.plot(xsl[q1],ysl[q1],'b.');plt.plot(xsl[q2],ysl[q2],'g.');plt.plot(xsl[-1],ysl[-1],'c+')
dominantwavelength[:, i] = wlsl[q1] + np.multiply(
(h[:, i] - hsl[q1, 0]),
np.divide((wlsl[q2] - wlsl[q1]), (hsl[q2, 0] - hsl[q1, 0]))
) # calculate wl corresponding to h: y = y1 + (x-x1)*(y2-y1)/(x2-x1)
dominantwavelength[:, i][pc] = -dominantwavelength[:, i][
pc] #complementary wavelengths are specified by '-' sign
# calculate excitation purity:
x_dom_wl = xsl[q1, 0] + (xsl[q2, 0] - xsl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate x of dom. wl
y_dom_wl = ysl[q1, 0] + (ysl[q2, 0] - ysl[q1, 0]) * (h[:, i] - hsl[
q1, 0]) / (hsl[q2, 0] - hsl[q1, 0]) # calculate y of dom. wl
d_wl = (x_dom_wl**2.0 +
y_dom_wl**2.0)**0.5 # distance from white point to sl
d = (x[:, i]**2.0 +
y[:, i]**2.0)**0.5 # distance from white point to test point
purity[:, i] = d / d_wl
# correct for those test points that have a complementary wavelength
# calculate intersection of line through white point and test point and purple line:
xy = np.vstack((x[:, i], y[:, i])).T
xyw = np.hstack((xw, yw))
xypl1 = np.hstack((xsl[0, None], ysl[0, None]))
xypl2 = np.hstack((xsl[-1, None], ysl[-1, None]))
da = (xy - xyw)
db = (xypl2 - xypl1)
dp = (xyw - xypl1)
T = np.array([[0.0, -1.0], [1.0, 0.0]])
dap = np.dot(da, T)
denom = np.sum(dap * db, axis=1, keepdims=True)
num = np.sum(dap * dp, axis=1, keepdims=True)
xy_linecross = (num / denom) * db + xypl1
d_linecross = np.atleast_2d(
(xy_linecross[:, 0]**2.0 + xy_linecross[:, 1]**2.0)**0.5).T #[0]
purity[:, i][pc] = d[pc] / d_linecross[pc][:, 0]
Ydlep = np.dstack((xyz3[:, :, 1], dominantwavelength, purity))
if axes12flipped == True:
Ydlep = Ydlep.transpose((1, 0, 2))
else:
Ydlep = Ydlep.transpose((0, 1, 2))
return Ydlep.reshape(xyz.shape)
