def add_to_cmf_dict(bar=None, cieobs='indv', K=683, M=np.eye(3)):
"""
Add set of cmfs to _CMF dict.
Args:
:bar:
| None, optional
| Set of CMFs. None: initializes to empty ndarray.
:cieobs:
| 'indv' or str, optional
| Name of CMF set.
:K:
| 683 (lm/W), optional
| Conversion factor from radiometric to photometric quantity.
:M:
| np.eye, optional
| Matrix for lms to xyz conversion.
"""
if bar is None:
wl3 = getwlr(_WL3)
bar = np.vstack((wl3, np.empty((3, wl3.shape[0]))))
_CMF['types'].append(cieobs)
_CMF[cieobs] = {'bar': bar}
_CMF[cieobs]['K'] = K
_CMF[cieobs]['M'] = M
def Vrb_mb_to_xyz(Vrb,
cieobs=_CIEOBS,
scaling=[1, 1],
M=None,
Minverted=False,
**kwargs):
"""
Convert V,r,b (Macleod-Boynton) color coordinates to XYZ tristimulus values.
| Macleod Boynton: V = R+G, r = R/V, b = B/V
| Note that R,G,B ~ L,M,S
Args:
:Vrb:
| ndarray with V,r,b (Macleod-Boynton) color coordinates
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when getting the default M, which is
the xyz to lms conversion matrix.
:scaling:
| list of scaling factors for r and b dimensions.
:M:
| None, optional
| Conversion matrix for going from XYZ to RGB (LMS)
| If None, :cieobs: determines the M (function does inversion)
:Minverted:
| False, optional
| Bool that determines whether M should be inverted.
Returns:
:xyz:
| ndarray with tristimulus values
Reference:
1. `MacLeod DI, and Boynton RM (1979).
Chromaticity diagram showing cone excitation by stimuli of equal luminance.
J. Opt. Soc. Am. 69, 1183–1186.
<https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-8-1183>`_
"""
Vrb = np2d(Vrb)
RGB = np.empty(Vrb.shape)
RGB[..., 0] = Vrb[..., 1] * Vrb[..., 0] / scaling[0]
RGB[..., 2] = Vrb[..., 2] * Vrb[..., 0] / scaling[1]
RGB[..., 1] = Vrb[..., 0] - RGB[..., 0]
if M is None:
M = _CMF[cieobs]['M']
if Minverted == False:
M = np.linalg.inv(M)
if len(RGB.shape) == 3:
return np.einsum('ij,klj->kli', M, RGB)
else:
return np.einsum('ij,lj->li', M, RGB)
def xyz_to_Vrb_mb(xyz, cieobs=_CIEOBS, scaling=[1, 1], M=None, **kwargs):
"""
Convert XYZ tristimulus values to V,r,b (Macleod-Boynton) color coordinates.
| Macleod Boynton: V = R+G, r = R/V, b = B/V
| Note that R,G,B ~ L,M,S
Args:
:xyz:
| ndarray with tristimulus values
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when getting the default M, which is
the xyz to lms conversion matrix.
:scaling:
| list of scaling factors for r and b dimensions.
:M:
| None, optional
| Conversion matrix for going from XYZ to RGB (LMS)
| If None, :cieobs: determines the M (function does inversion)
Returns:
:Vrb:
| ndarray with V,r,b (Macleod-Boynton) color coordinates
Reference:
1. `MacLeod DI, and Boynton RM (1979).
Chromaticity diagram showing cone excitation by stimuli of equal luminance.
J. Opt. Soc. Am. 69, 1183–1186.
<https://www.osapublishing.org/josa/abstract.cfm?uri=josa-69-8-1183>`_
"""
xyz = np2d(xyz)
if M is None:
M = _CMF[cieobs]['M']
if len(xyz.shape) == 3:
RGB = np.einsum('ij,klj->kli', M, xyz)
else:
RGB = np.einsum('ij,lj->li', M, xyz)
Vrb = np.empty(xyz.shape)
Vrb[..., 0] = RGB[..., 0] + RGB[..., 1]
Vrb[..., 1] = RGB[..., 0] / Vrb[..., 0] * scaling[0]
Vrb[..., 2] = RGB[..., 2] / Vrb[..., 0] * scaling[1]
return Vrb
def Yxy_to_xyz(Yxy, **kwargs):
"""
Convert CIE Yxy chromaticity values to XYZ tristimulus values.
Args:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yxy = np2d(Yxy)
xyz = np.empty(Yxy.shape)
xyz[..., 1] = Yxy[..., 0]
xyz[..., 0] = Yxy[..., 0] * Yxy[..., 1] / Yxy[..., 2]
xyz[..., 2] = Yxy[..., 0] * (1.0 - Yxy[..., 1] - Yxy[..., 2]) / Yxy[..., 2]
return xyz
def xyz_to_lab(xyz, xyzw=None, cieobs=_CIEOBS, **kwargs):
"""
Convert XYZ tristimulus values to CIE 1976 L*a*b* (CIELAB) coordinates.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:lab:
| ndarray with CIE 1976 L*a*b* (CIELAB) color coordinates
"""
xyz = np2d(xyz)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs)
# get and normalize (X,Y,Z) to white point:
XYZr = xyz / xyzw
# Apply cube-root compression:
fXYZr = XYZr**(1.0 / 3.0)
# Check for T/Tn <= 0.008856: (Note (24/116)**3 = 0.008856)
pqr = XYZr <= (24 / 116)**3
# calculate f(T) for T/Tn <= 0.008856: (Note:(1/3)*((116/24)**2) = 841/108 = 7.787)
fXYZr[pqr] = ((841 / 108) * XYZr[pqr] + 16.0 / 116.0)
# calculate L*, a*, b*:
Lab = np.empty(xyz.shape)
Lab[..., 0] = 116.0 * (fXYZr[..., 1]) - 16.0
Lab[pqr[..., 1], 0] = 903.3 * XYZr[pqr[..., 1], 1]
Lab[..., 1] = 500.0 * (fXYZr[..., 0] - fXYZr[..., 1])
Lab[..., 2] = 200.0 * (fXYZr[..., 1] - fXYZr[..., 2])
return Lab
def Yuv_to_xyz(Yuv, **kwargs):
"""
Convert CIE 1976 Yu'v' chromaticity values to XYZ tristimulus values.
Args:
:Yuv:
| ndarray with CIE 1976 Yu'v' chromaticity values
(Y value refers to luminance or luminance factor)
Returns:
:xyz:
| ndarray with tristimulus values
"""
Yuv = np2d(Yuv)
xyz = np.empty(Yuv.shape)
xyz[..., 1] = Yuv[..., 0]
xyz[..., 0] = Yuv[..., 0] * (9.0 * Yuv[..., 1]) / (4.0 * Yuv[..., 2])
xyz[..., 2] = Yuv[..., 0] * (12.0 - 3.0 * Yuv[..., 1] -
20.0 * Yuv[..., 2]) / (4.0 * Yuv[..., 2])
return xyz
def xyz_to_Yuv(xyz, **kwargs):
"""
Convert XYZ tristimulus values CIE 1976 Yu'v' chromaticity values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:Yuv:
| ndarray with CIE 1976 Yu'v' chromaticity values
(Y value refers to luminance or luminance factor)
"""
xyz = np2d(xyz)
Yuv = np.empty(xyz.shape)
denom = xyz[..., 0] + 15.0 * xyz[..., 1] + 3.0 * xyz[..., 2]
Yuv[..., 0] = xyz[..., 1]
Yuv[..., 1] = 4.0 * xyz[..., 0] / denom
Yuv[..., 2] = 9.0 * xyz[..., 1] / denom
return Yuv
def xyz_to_Yxy(xyz, **kwargs):
"""
Convert XYZ tristimulus values CIE Yxy chromaticity values.
Args:
:xyz:
| ndarray with tristimulus values
Returns:
:Yxy:
| ndarray with Yxy chromaticity values
(Y value refers to luminance or luminance factor)
"""
xyz = np2d(xyz)
Yxy = np.empty(xyz.shape)
sumxyz = xyz[..., 0] + xyz[..., 1] + xyz[..., 2]
Yxy[..., 0] = xyz[..., 1]
Yxy[..., 1] = xyz[..., 0] / sumxyz
Yxy[..., 2] = xyz[..., 1] / sumxyz
return Yxy
def lab_to_xyz(lab, xyzw=None, cieobs=_CIEOBS, **kwargs):
"""
Convert CIE 1976 L*a*b* (CIELAB) color coordinates to XYZ tristimulus values.
Args:
:lab:
| ndarray with CIE 1976 L*a*b* (CIELAB) color coordinates
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:xyz:
| ndarray with tristimulus values
"""
lab = np2d(lab)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs)
# make xyzw same shape as data:
xyzw = xyzw * np.ones(lab.shape)
# get L*, a*, b* and Xw, Yw, Zw:
fXYZ = np.empty(lab.shape)
fXYZ[..., 1] = (lab[..., 0] + 16.0) / 116.0
fXYZ[..., 0] = lab[..., 1] / 500.0 + fXYZ[..., 1]
fXYZ[..., 2] = fXYZ[..., 1] - lab[..., 2] / 200.0
# apply 3rd power:
xyz = (fXYZ**3.0) * xyzw
# Now calculate T where T/Tn is below the knee point:
pqr = fXYZ <= (24 / 116) #(24/116)**3**(1/3)
xyz[pqr] = np.squeeze(xyzw[pqr] * ((fXYZ[pqr] - 16.0 / 116.0) /
(841 / 108)))
return xyz
def dtlz2(x, M):
"""
DTLZ2 multi-objective function
This function represents a hyper-sphere.
Using k = 10, the number of dimensions must be n = (M - 1) + k.
The Pareto optimal solutions are obtained when the last k variables of x
are equal to 0.5.
Args:
:x:
| a n x mu ndarray with mu points and n dimensions
:M:
| a scalar with the number of objectives
Returns:
f:
| a m x mu ndarray with mu points and their m objectives computed at
| the input
"""
k = 10
# Error check: the number of dimensions must be M-1+k
n = (M - 1) + k
#this is the default
if x.shape[0] != n:
raise Exception(
'Using k = 10, it is required that the number of dimensions be n = (M - 1) + k = {:1.0f} in this case.'
.format(n))
xm = x[(n - k):, :].copy() #xm contains the last k variables
g = ((xm - 0.5)**2).sum(axis=0)
# Computes the functions:
f = np.empty((M, x.shape[1]))
f[0, :] = (1 + g) * np.prod(np.cos(np.pi / 2 * x[:(M - 1), :]), axis=0)
for ii in range(1, M - 1):
f[ii, :] = (1 + g) * np.prod(np.cos(np.pi / 2 * x[:(M - ii - 1), :]),
axis=0) * np.sin(
np.pi / 2 * x[M - ii - 1, :])
f[M - 1, :] = (1 + g) * np.sin(np.pi / 2 * x[0, :])
return f
def xyz_to_wuv(xyz, xyzw=_COLORTF_DEFAULT_WHITE_POINT, **kwargs):
"""
Convert XYZ tristimulus values CIE 1964 U*V*W* color space.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| ndarray with tristimulus values of white point, optional
(Defaults to luxpy._COLORTF_DEFAULT_WHITE_POINT)
Returns:
:wuv:
| ndarray with W*U*V* values
"""
Yuv = xyz_to_Yuv(np2d(xyz)) # convert to cie 1976 u'v'
Yuvw = xyz_to_Yuv(np2d(xyzw))
wuv = np.empty(xyz.shape)
wuv[..., 0] = 25.0 * (Yuv[..., 0]**(1 / 3)) - 17.0
wuv[..., 1] = 13.0 * wuv[..., 0] * (Yuv[..., 1] - Yuvw[..., 1])
wuv[..., 2] = 13.0 * wuv[..., 0] * (Yuv[..., 2] - Yuvw[..., 2]) * (
2.0 / 3.0) #*(2/3) to convert to cie 1960 u, v
return wuv
def wuv_to_xyz(wuv, xyzw=_COLORTF_DEFAULT_WHITE_POINT, **kwargs):
"""
Convert CIE 1964 U*V*W* color space coordinates to XYZ tristimulus values.
Args:
:wuv:
| ndarray with W*U*V* values
:xyzw:
| ndarray with tristimulus values of white point, optional
(Defaults to luxpy._COLORTF_DEFAULT_WHITE_POINT)
Returns:
:xyz:
| ndarray with tristimulus values
"""
wuv = np2d(wuv)
Yuvw = xyz_to_Yuv(xyzw) # convert to cie 1976 u'v'
Yuv = np.empty(wuv.shape)
Yuv[..., 0] = ((wuv[..., 0] + 17.0) / 25.0)**3.0
Yuv[..., 1] = Yuvw[..., 1] + wuv[..., 1] / (13.0 * wuv[..., 0])
Yuv[..., 2] = Yuvw[..., 2] + wuv[..., 2] / (13.0 * wuv[..., 0]) * (
3.0 / 2.0) # convert to cie 1960 u, v
return Yuv_to_xyz(Yuv)
def xyz_to_luv(xyz, xyzw=None, cieobs=_CIEOBS, **kwargs):
"""
Convert XYZ tristimulus values to CIE 1976 L*u*v* (CIELUV) coordinates.
Args:
:xyz:
| ndarray with tristimulus values
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:luv:
| ndarray with CIE 1976 L*u*v* (CIELUV) color coordinates
"""
xyz = np2d(xyz)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs)
# Calculate u',v' of test and white:
Yuv = xyz_to_Yuv(xyz)
Yuvw = xyz_to_Yuv(todim(xyzw,
xyz.shape)) # todim: make xyzw same shape as xyz
#uv1976 to CIELUV
luv = np.empty(xyz.shape)
YdivYw = Yuv[..., 0] / Yuvw[..., 0]
luv[..., 0] = 116.0 * YdivYw**(1.0 / 3.0) - 16.0
p = np.where(YdivYw <= (6.0 / 29.0)**3.0)
luv[..., 0][p] = ((29.0 / 3.0)**3.0) * YdivYw[p]
luv[..., 1] = 13.0 * luv[..., 0] * (Yuv[..., 1] - Yuvw[..., 1])
luv[..., 2] = 13.0 * luv[..., 0] * (Yuv[..., 2] - Yuvw[..., 2])
return luv
def luv_to_xyz(luv, xyzw=None, cieobs=_CIEOBS, **kwargs):
"""
Convert CIE 1976 L*u*v* (CIELUVB) coordinates to XYZ tristimulus values.
Args:
:luv:
| ndarray with CIE 1976 L*u*v* (CIELUV) color coordinates
:xyzw:
| None or ndarray with tristimulus values of white point, optional
| None defaults to xyz of CIE D65 using the :cieobs: observer.
:cieobs:
| luxpy._CIEOBS, optional
| CMF set to use when calculating xyzw.
Returns:
:xyz:
| ndarray with tristimulus values
"""
luv = np2d(luv)
if xyzw is None:
xyzw = spd_to_xyz(_CIE_ILLUMINANTS['D65'], cieobs=cieobs)
# Make xyzw same shape as luv and convert to Yuv:
Yuvw = todim(xyz_to_Yuv(xyzw), luv.shape, equal_shape=True)
# calculate u'v' from u*,v*:
Yuv = np.empty(luv.shape)
Yuv[..., 1:3] = (luv[..., 1:3] / (13 * luv[..., 0])) + Yuvw[..., 1:3]
Yuv[Yuv[..., 0] == 0, 1:3] = 0
Yuv[..., 0] = Yuvw[..., 0] * (((luv[..., 0] + 16.0) / 116.0)**3.0)
p = np.where((Yuv[..., 0] / Yuvw[..., 0]) < ((6.0 / 29.0)**3.0))
Yuv[..., 0][p] = Yuvw[..., 0][p] * (luv[..., 0][p] / ((29.0 / 3.0)**3.0))
return Yuv_to_xyz(Yuv)
def cie2006cmfsEx(age = 32,fieldsize = 10, wl = None,\
var_od_lens = 0, var_od_macula = 0, \
var_od_L = 0, var_od_M = 0, var_od_S = 0,\
var_shft_L = 0, var_shft_M = 0, var_shft_S = 0,\
out = 'LMS', allow_negative_values = False):
"""
Generate Individual Observer CMFs (cone fundamentals)
based on CIE2006 cone fundamentals and published literature
on observer variability in color matching and in physiological parameters.
Args:
:age:
| 32 or float or int, optional
| Observer age
:fieldsize:
| 10, optional
| Field size of stimulus in degrees (between 2° and 10°).
:wl:
| None, optional
| Interpolation/extraplation of :LMS: output to specified wavelengths.
| None: output original _WL = np.array([390,780,5])
:var_od_lens:
| 0, optional
| Std Dev. in peak optical density [%] of lens.
:var_od_macula:
| 0, optional
| Std Dev. in peak optical density [%] of macula.
:var_od_L:
| 0, optional
| Std Dev. in peak optical density [%] of L-cone.
:var_od_M:
| 0, optional
| Std Dev. in peak optical density [%] of M-cone.
:var_od_S:
| 0, optional
| Std Dev. in peak optical density [%] of S-cone.
:var_shft_L:
| 0, optional
| Std Dev. in peak wavelength shift [nm] of L-cone.
:var_shft_L:
| 0, optional
| Std Dev. in peak wavelength shift [nm] of M-cone.
:var_shft_S:
| 0, optional
| Std Dev. in peak wavelength shift [nm] of S-cone.
:out:
| 'LMS' or , optional
| Determines output.
:allow_negative_values:
| False, optional
| Cone fundamentals or color matching functions
should not have negative values.
| If False: X[X<0] = 0.
Returns:
:returns:
| - 'LMS' : ndarray with individual observer area-normalized
| cone fundamentals. Wavelength have been added.
| [- 'trans_lens': ndarray with lens transmission
| (no wavelengths added, no interpolation)
| - 'trans_macula': ndarray with macula transmission
| (no wavelengths added, no interpolation)
| - 'sens_photopig' : ndarray with photopigment sens.
| (no wavelengths added, no interpolation)]
References:
1. `Asano Y, Fairchild MD, and Blondé L (2016).
Individual Colorimetric Observer Model.
PLoS One 11, 1–19.
<http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0145671>`_
2. `Asano Y, Fairchild MD, Blondé L, and Morvan P (2016).
Color matching experiment for highlighting interobserver variability.
Color Res. Appl. 41, 530–539.
<https://onlinelibrary.wiley.com/doi/abs/10.1002/col.21975>`_
3. `CIE, and CIE (2006).
Fundamental Chromaticity Diagram with Physiological Axes - Part I
(Vienna: CIE).
<http://www.cie.co.at/publications/fundamental-chromaticity-diagram-physiological-axes-part-1>`_
4. `Asano's Individual Colorimetric Observer Model
<https://www.rit.edu/cos/colorscience/re_AsanoObserverFunctions.php>`_
"""
fs = fieldsize
rmd = _INDVCMF_DATA['rmd'].copy()
LMSa = _INDVCMF_DATA['LMSa'].copy()
docul = _INDVCMF_DATA['docul'].copy()
# field size corrected macular density:
pkOd_Macula = 0.485 * np.exp(-fs / 6.132) * (
1 + var_od_macula / 100) # varied peak optical density of macula
corrected_rmd = rmd * pkOd_Macula
# age corrected lens/ocular media density:
if (age <= 60):
correct_lomd = docul[:1] * (1 + 0.02 * (age - 32)) + docul[1:2]
else:
correct_lomd = docul[:1] * (1.56 + 0.0667 * (age - 60)) + docul[1:2]
correct_lomd = correct_lomd * (1 + var_od_lens / 100
) # varied overall optical density of lens
# Peak Wavelength Shift:
wl_shifted = np.empty(LMSa.shape)
wl_shifted[0] = _WL + var_shft_L
wl_shifted[1] = _WL + var_shft_M
wl_shifted[2] = _WL + var_shft_S
LMSa_shft = np.empty(LMSa.shape)
kind = 'cubic'
LMSa_shft[0] = interpolate.interp1d(wl_shifted[0],
LMSa[0],
kind=kind,
bounds_error=False,
fill_value="extrapolate")(_WL)
LMSa_shft[1] = interpolate.interp1d(wl_shifted[1],
LMSa[1],
kind=kind,
bounds_error=False,
fill_value="extrapolate")(_WL)
LMSa_shft[2] = interpolate.interp1d(wl_shifted[2],
LMSa[2],
kind=kind,
bounds_error=False,
fill_value="extrapolate")(_WL)
# LMSa[2,np.where(_WL >= _WL_CRIT)] = 0 #np.nan # Not defined above 620nm
# LMSa_shft[2,np.where(_WL >= _WL_CRIT)] = 0
ssw = np.hstack(
(0, np.sign(np.diff(LMSa_shft[2, :]))
)) #detect poor interpolation (sign switch due to instability)
LMSa_shft[2, np.where((ssw >= 0) & (_WL > 560))] = np.nan
# corrected LMS (no age correction):
pkOd_L = (0.38 + 0.54 * np.exp(-fs / 1.333)) * (
1 + var_od_L / 100) # varied peak optical density of L-cone
pkOd_M = (0.38 + 0.54 * np.exp(-fs / 1.333)) * (
1 + var_od_M / 100) # varied peak optical density of M-cone
pkOd_S = (0.30 + 0.45 * np.exp(-fs / 1.333)) * (
1 + var_od_S / 100) # varied peak optical density of S-cone
alpha_lms = 0. * LMSa_shft
alpha_lms[0] = 1 - 10**(-pkOd_L * (10**LMSa_shft[0]))
alpha_lms[1] = 1 - 10**(-pkOd_M * (10**LMSa_shft[1]))
alpha_lms[2] = 1 - 10**(-pkOd_S * (10**LMSa_shft[2]))
# this fix is required because the above math fails for alpha_lms[2,:]==0
alpha_lms[2, np.where(_WL >= _WL_CRIT)] = 0
# Corrected to Corneal Incidence:
lms_barq = alpha_lms * (10**(-corrected_rmd - correct_lomd)) * np.ones(
alpha_lms.shape)
# Corrected to Energy Terms:
lms_bar = lms_barq * _WL
# Set NaN values to zero:
lms_bar[np.isnan(lms_bar)] = 0
# normalized:
LMS = 100 * lms_bar / np.nansum(lms_bar, axis=1, keepdims=True)
# Output extra:
trans_lens = 10**(-correct_lomd)
trans_macula = 10**(-corrected_rmd)
sens_photopig = alpha_lms * _WL
# Add wavelengths:
LMS = np.vstack((_WL, LMS))
if ('xyz' in out.lower().split(',')):
LMS = lmsb_to_xyzb(LMS,
fieldsize,
out='xyz',
allow_negative_values=allow_negative_values)
out = out.replace('xyz', 'LMS').replace('XYZ', 'LMS')
if ('lms' in out.lower().split(',')):
out = out.replace('lms', 'LMS')
# Interpolate/extrapolate:
if wl is None:
interpolation = None
else:
interpolation = 'cubic'
LMS = spd(LMS, wl=wl, interpolation=interpolation, norm_type='area')
if (out == 'LMS'):
return LMS
elif (out == 'LMS,trans_lens,trans_macula,sens_photopig'):
return LMS, trans_lens, trans_macula, sens_photopig
elif (out == 'LMS,trans_lens,trans_macula,sens_photopig,LMSa'):
return LMS, trans_lens, trans_macula, sens_photopig, LMSa
else:
return eval(out)
def Ydlep_to_xyz(Ydlep,
cieobs=_CIEOBS,
xyzw=_COLORTF_DEFAULT_WHITE_POINT,
flip_axes=False,
**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!)
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']
wlsl = SL[0, None].T
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# 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 = np.abs(wlslb - wlib)
q1 = dwl.argmin(axis=0) # index of closest wl
dwl[q1] = 10000.0
q2 = dwl.argmin(axis=0) # index of second closest 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 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']
wlsl = SL[0]
Yxysl = xyz_to_Yxy(SL[1:4].T)[:, None]
# 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
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 + 360.0)
) # 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 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] = 1000.0
q2 = dh.argmin(axis=0) # index of second closest hue
dominantwavelength[:, i] = wlsl[q1] + np.divide(
np.multiply((wlsl[q2] - wlsl[q1]),
(h[:, i] - hsl[q1, 0])), (hsl[q2, 0] - hsl[q1, 0])
) # calculate wl corresponding to h: y = y1 + (y2-y1)*(x-x1)/(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)
def spd_to_ies_tm30_metrics(SPD, cri_type = None, \
hbins = 16, start_hue = 0.0,\
scalef = 100, \
vf_model_type = _VF_MODEL_TYPE, \
vf_pcolorshift = _VF_PCOLORSHIFT,\
scale_vf_chroma_to_sample_chroma = False):
"""
Calculates IES TM30 metrics from spectral data.
Args:
:data:
| numpy.ndarray with spectral data
:cri_type:
| None, optional
| If None: defaults to cri_type = 'iesrf'.
| Not none values of :hbins:, :start_hue: and :scalef: overwrite
input in cri_type['rg_pars']
:hbins:
| None or numpy.ndarray with sorted hue bin centers (°), optional
:start_hue:
| None, optional
:scalef:
| None, optional
| Scale factor for reference circle.
:vf_pcolorshift:
| _VF_PCOLORSHIFT or user defined dict, optional
| The polynomial models of degree 5 and 6 can be fully specified or
summarized by the model parameters themselved OR by calculating the
dCoverC and dH at resp. 5 and 6 hues. :VF_pcolorshift: specifies
these hues and chroma level.
:scale_vf_chroma_to_sample_chroma:
| False, optional
| Scale chroma of reference and test vf fields such that average of
binned reference chroma equals that of the binned sample chroma
before calculating hue bin metrics.
Returns:
:data:
| dict with color rendering data:
| - 'SPD' : ndarray test SPDs
| - 'bjabt': ndarray with binned jab data under test SPDs
| - 'bjabr': ndarray with binned jab data under reference SPDs
| - 'cct' : ndarray with CCT of test SPD
| - 'duv' : ndarray with distance to blackbody locus of test SPD
| - 'Rf' : ndarray with general color fidelity indices
| - 'Rg' : ndarray with gamut area indices
| - 'Rfi' : ndarray with specific color fidelity indices
| - 'Rfhi' : ndarray with local (hue binned) fidelity indices
| - 'Rcshi': ndarray with local chroma shifts indices
| - 'Rhshi': ndarray with local hue shifts indices
| - 'Rt' : ndarray with general metameric uncertainty index Rt
| - 'Rti' : ndarray with specific metameric uncertainty indices Rti
| - 'Rfhi_vf' : ndarray with local (hue binned) fidelity indices
| obtained from VF model predictions at color space
| pixel coordinates
| - 'Rcshi_vf': ndarray with local chroma shifts indices
| (same as above)
| - 'Rhshi_vf': ndarray with local hue shifts indices
| (same as above)
"""
if cri_type is None:
cri_type = 'iesrf'
#Calculate color rendering measures for SPDs in data:
out = 'Rf,Rg,cct,duv,Rfi,jabt,jabr,Rfhi,Rcshi,Rhshi,cri_type'
if isinstance(cri_type, str): # get dict
cri_type = _CRI_DEFAULTS[cri_type].copy()
if hbins is not None:
cri_type['rg_pars']['nhbins'] = hbins
if start_hue is not None:
cri_type['rg_pars']['start_hue'] = start_hue
if scalef is not None:
cri_type['rg_pars']['normalized_chroma_ref'] = scalef
Rf, Rg, cct, duv, Rfi, jabt, jabr, Rfhi, Rcshi, Rhshi, cri_type = spd_to_cri(
SPD, cri_type=cri_type, out=out)
rg_pars = cri_type['rg_pars']
#Calculate Metameric uncertainty and base color shifts:
dataVF = VF_colorshift_model(SPD,
cri_type=cri_type,
model_type=vf_model_type,
cspace=cri_type['cspace'],
sampleset=eval(cri_type['sampleset']),
pool=False,
pcolorshift=vf_pcolorshift,
vfcolor=0)
Rf_ = np.array([dataVF[i]['metrics']['Rf'] for i in range(len(dataVF))]).T
Rt = np.array([dataVF[i]['metrics']['Rt'] for i in range(len(dataVF))]).T
Rti = np.array([dataVF[i]['metrics']['Rti']
for i in range(len(dataVF))][0])
# Get normalized and sliced sample data for plotting:
rg_pars = cri_type['rg_pars']
nhbins, normalize_gamut, normalized_chroma_ref, start_hue = [
rg_pars[x] for x in sorted(rg_pars.keys())
]
normalized_chroma_ref = scalef
# np.sqrt((jabr[...,1]**2 + jabr[...,2]**2)).mean(axis = 0).mean()
if scale_vf_chroma_to_sample_chroma == True:
normalize_gamut = False
bjabt, bjabr = gamut_slicer(
jabt,
jabr,
out='jabt,jabr',
nhbins=nhbins,
start_hue=start_hue,
normalize_gamut=normalize_gamut,
normalized_chroma_ref=normalized_chroma_ref,
close_gamut=True)
Cr_s = (np.sqrt(bjabr[:-1, ..., 1]**2 + bjabr[:-1, ..., 2]**2)).mean(
axis=0) # for rescaling vector field average reference chroma
normalize_gamut = True #(for plotting)
bjabt, bjabr = gamut_slicer(jabt,
jabr,
out='jabt,jabr',
nhbins=nhbins,
start_hue=start_hue,
normalize_gamut=normalize_gamut,
normalized_chroma_ref=normalized_chroma_ref,
close_gamut=True)
Rfhi_vf = np.empty(Rfhi.shape)
Rcshi_vf = np.empty(Rcshi.shape)
Rhshi_vf = np.empty(Rhshi.shape)
for i in range(cct.shape[0]):
# Get normalized and sliced VF data for hue specific metrics:
vfjabt = np.hstack(
(np.ones(dataVF[i]['fielddata']['vectorfield']['axt'].shape),
dataVF[i]['fielddata']['vectorfield']['axt'],
dataVF[i]['fielddata']['vectorfield']['bxt']))
vfjabr = np.hstack(
(np.ones(dataVF[i]['fielddata']['vectorfield']['axr'].shape),
dataVF[i]['fielddata']['vectorfield']['axr'],
dataVF[i]['fielddata']['vectorfield']['bxr']))
nhbins, normalize_gamut, normalized_chroma_ref, start_hue = [
rg_pars[x] for x in sorted(rg_pars.keys())
]
vfbjabt, vfbjabr, vfbDEi = gamut_slicer(
vfjabt,
vfjabr,
out='jabt,jabr,DEi',
nhbins=nhbins,
start_hue=start_hue,
normalize_gamut=normalize_gamut,
normalized_chroma_ref=normalized_chroma_ref,
close_gamut=False)
if scale_vf_chroma_to_sample_chroma == True:
#rescale vfbjabt and vfbjabr to same chroma level as bjabr.
Cr_vfb = np.sqrt(vfbjabr[..., 1]**2 + vfbjabr[..., 2]**2)
Cr_vf = np.sqrt(vfjabr[..., 1]**2 + vfjabr[..., 2]**2)
hr_vf = np.arctan2(vfjabr[..., 2], vfjabr[..., 1])
Ct_vf = np.sqrt(vfjabt[..., 1]**2 + vfjabt[..., 2]**2)
ht_vf = np.arctan2(vfjabt[..., 2], vfjabt[..., 1])
fC = Cr_s.mean() / Cr_vfb.mean()
vfjabr[..., 1] = fC * Cr_vf * np.cos(hr_vf)
vfjabr[..., 2] = fC * Cr_vf * np.sin(hr_vf)
vfjabt[..., 1] = fC * Ct_vf * np.cos(ht_vf)
vfjabt[..., 2] = fC * Ct_vf * np.sin(ht_vf)
vfbjabt, vfbjabr, vfbDEi = gamut_slicer(
vfjabt,
vfjabr,
out='jabt,jabr,DEi',
nhbins=nhbins,
start_hue=start_hue,
normalize_gamut=normalize_gamut,
normalized_chroma_ref=normalized_chroma_ref,
close_gamut=False)
scale_factor = cri_type['scale']['cfactor']
scale_fcn = cri_type['scale']['fcn']
vfRfhi, vfRcshi, vfRhshi = jab_to_rhi(
jabt=vfbjabt,
jabr=vfbjabr,
DEi=vfbDEi,
cri_type=cri_type,
scale_factor=scale_factor,
scale_fcn=scale_fcn,
use_bin_avg_DEi=True
) # [:-1,...] removes last row from jab as this was added to close the gamut.
Rfhi_vf[:, i:i + 1] = vfRfhi
Rhshi_vf[:, i:i + 1] = vfRhshi
Rcshi_vf[:, i:i + 1] = vfRcshi
# Create dict with CRI info:
data = {'SPD' : SPD, 'cct' : cct, 'duv' : duv, 'bjabt' : bjabt, 'bjabr' : bjabr,\
'Rf' : Rf, 'Rg' : Rg, 'Rfi': Rfi, 'Rfhi' : Rfhi, 'Rchhi' : Rcshi, 'Rhshi' : Rhshi, \
'Rt' : Rt, 'Rti' : Rti, 'Rfhi_vf' : Rfhi_vf, 'Rfcshi_vf' : Rcshi_vf, 'Rfhshi_vf' : Rhshi_vf, \
'dataVF' : dataVF,'cri_type' : cri_type}
return data
