def xyz_to_cct_ohno(xyzw,
cieobs=_CIEOBS,
out='cct',
wl=None,
accuracy=0.1,
force_out_of_lut=True,
upper_cct_max=10.0**20,
approx_cct_temp=True):
"""
Convert XYZ tristimulus values to correlated color temperature (CCT) and
Duv (distance above (>0) or below (<0) the Planckian locus)
using Ohno's method.
Args:
:xyzw:
| ndarray of tristimulus values
:cieobs:
| luxpy._CIEOBS, optional
| CMF set used to calculated xyzw.
:out:
| 'cct' (or 1), optional
| Determines what to return.
| Other options: 'duv' (or -1), 'cct,duv'(or 2), "[cct,duv]" (or -2)
:wl:
| None, optional
| Wavelengths used when calculating Planckian radiators.
:accuracy:
| float, optional
| Stop brute-force search when cct :accuracy: is reached.
:upper_cct_max:
| 10.0**20, optional
| Limit brute-force search to this cct.
:approx_cct_temp:
| True, optional
| If True: use xyz_to_cct_HA() to get a first estimate of cct
to speed up search.
:force_out_of_lut:
| True, optional
| If True and cct is out of range of the LUT, then switch to
brute-force search method, else return numpy.nan values.
Returns:
:returns:
| ndarray with:
| cct: out == 'cct' (or 1)
| duv: out == 'duv' (or -1)
| cct, duv: out == 'cct,duv' (or 2)
| [cct,duv]: out == "[cct,duv]" (or -2)
Note:
LUTs are stored in ./data/cctluts/
Reference:
1. `Ohno Y. Practical use and calculation of CCT and Duv.
Leukos. 2014 Jan 2;10(1):47-55.
<http://www.tandfonline.com/doi/abs/10.1080/15502724.2014.839020>`_
"""
xyzw = np2d(xyzw)
if len(xyzw.shape) > 2:
raise Exception('xyz_to_cct_ohno(): Input xyzwa.ndim must be <= 2 !')
# get 1960 u,v of test source:
Yuv = xyz_to_Yuv(
xyzw) # remove possible 1-dim + convert xyzw to CIE 1976 u',v'
axis_of_v3 = len(Yuv.shape) - 1 # axis containing color components
u = Yuv[:, 1, None] # get CIE 1960 u
v = (2.0 / 3.0) * Yuv[:, 2, None] # get CIE 1960 v
uv = np2d(np.concatenate((u, v), axis=axis_of_v3))
# load cct & uv from LUT:
if cieobs not in _CCT_LUT:
_CCT_LUT[cieobs] = calculate_lut(ccts=None,
cieobs=cieobs,
add_to_lut=False)
cct_LUT = _CCT_LUT[cieobs][:, 0, None]
uv_LUT = _CCT_LUT[cieobs][:, 1:3]
# calculate CCT of each uv:
CCT = np.ones(uv.shape[0]) * np.nan # initialize with NaN's
Duv = CCT.copy() # initialize with NaN's
idx_m = 0
idx_M = uv_LUT.shape[0] - 1
for i in range(uv.shape[0]):
out_of_lut = False
delta_uv = (((uv_LUT - uv[i])**2.0).sum(
axis=1))**0.5 # calculate distance of uv with uv_LUT
idx_min = delta_uv.argmin() # find index of minimum distance
# find Tm, delta_uv and u,v for 2 points surrounding uv corresponding to idx_min:
if idx_min == idx_m:
idx_min_m1 = idx_min
out_of_lut = True
else:
idx_min_m1 = idx_min - 1
if idx_min == idx_M:
idx_min_p1 = idx_min
out_of_lut = True
else:
idx_min_p1 = idx_min + 1
if (out_of_lut == True) & (force_out_of_lut
== True): # calculate using search-function
cct_i, Duv_i = xyz_to_cct_search(xyzw[i],
cieobs=cieobs,
wl=wl,
accuracy=accuracy,
out='cct,duv',
upper_cct_max=upper_cct_max,
approx_cct_temp=approx_cct_temp)
CCT[i] = cct_i
Duv[i] = Duv_i
continue
elif (out_of_lut == True) & (force_out_of_lut == False):
CCT[i] = np.nan
Duv[i] = np.nan
cct_m1 = cct_LUT[idx_min_m1] # - 2*_EPS
delta_uv_m1 = delta_uv[idx_min_m1]
uv_m1 = uv_LUT[idx_min_m1]
cct_p1 = cct_LUT[idx_min_p1]
delta_uv_p1 = delta_uv[idx_min_p1]
uv_p1 = uv_LUT[idx_min_p1]
cct_0 = cct_LUT[idx_min]
delta_uv_0 = delta_uv[idx_min]
# calculate uv distance between Tm_m1 & Tm_p1:
delta_uv_p1m1 = ((uv_p1[0] - uv_m1[0])**2.0 +
(uv_p1[1] - uv_m1[1])**2.0)**0.5
# Triangular solution:
x = ((delta_uv_m1**2) - (delta_uv_p1**2) +
(delta_uv_p1m1**2)) / (2 * delta_uv_p1m1)
Tx = cct_m1 + ((cct_p1 - cct_m1) * (x / delta_uv_p1m1))
#uBB = uv_m1[0] + (uv_p1[0] - uv_m1[0]) * (x / delta_uv_p1m1)
vBB = uv_m1[1] + (uv_p1[1] - uv_m1[1]) * (x / delta_uv_p1m1)
Tx_corrected_triangular = Tx * 0.99991
signDuv = np.sign(uv[i][1] - vBB)
Duv_triangular = signDuv * np.atleast_1d(
((delta_uv_m1**2.0) - (x**2.0))**0.5)
# Parabolic solution:
a = delta_uv_m1 / (cct_m1 - cct_0 + _EPS) / (cct_m1 - cct_p1 + _EPS)
b = delta_uv_0 / (cct_0 - cct_m1 + _EPS) / (cct_0 - cct_p1 + _EPS)
c = delta_uv_p1 / (cct_p1 - cct_0 + _EPS) / (cct_p1 - cct_m1 + _EPS)
A = a + b + c
B = -(a * (cct_p1 + cct_0) + b * (cct_p1 + cct_m1) + c *
(cct_0 + cct_m1))
C = (a * cct_p1 * cct_0) + (b * cct_p1 * cct_m1) + (c * cct_0 * cct_m1)
Tx = -B / (2 * A + _EPS)
Tx_corrected_parabolic = Tx * 0.99991
Duv_parabolic = signDuv * (A * np.power(Tx_corrected_parabolic, 2) +
B * Tx_corrected_parabolic + C)
Threshold = 0.002
if Duv_triangular < Threshold:
CCT[i] = Tx_corrected_triangular
Duv[i] = Duv_triangular
else:
CCT[i] = Tx_corrected_parabolic
Duv[i] = Duv_parabolic
# Regulate output:
if (out == 'cct') | (out == 1):
return np2dT(CCT)
elif (out == 'duv') | (out == -1):
return np2dT(Duv)
elif (out == 'cct,duv') | (out == 2):
return np2dT(CCT), np2dT(Duv)
elif (out == "[cct,duv]") | (out == -2):
return np.vstack((CCT, Duv)).T
def cct_to_xyz(ccts,
duv=None,
cieobs=_CIEOBS,
wl=None,
mode='lut',
out=None,
accuracy=0.1,
force_out_of_lut=True,
upper_cct_max=10.0 * 20,
approx_cct_temp=True):
"""
Convert correlated color temperature (CCT) and Duv (distance above (>0) or
below (<0) the Planckian locus) to XYZ tristimulus values.
| Finds xyzw_estimated by minimization of:
|
| F = numpy.sqrt(((100.0*(cct_min - cct)/(cct))**2.0)
| + (((duv_min - duv)/(duv))**2.0))
|
| with cct,duv the input values and cct_min, duv_min calculated using
| luxpy.xyz_to_cct(xyzw_estimated,...).
Args:
:ccts:
| ndarray of cct values
:duv:
| None or ndarray of duv values, optional
| Note that duv can be supplied together with cct values in :ccts:
as ndarray with shape (N,2)
:cieobs:
| luxpy._CIEOBS, optional
| CMF set used to calculated xyzw.
:mode:
| 'lut' or 'search', optional
| Determines what method to use.
:out:
| None (or 1), optional
| If not None or 1: output a ndarray that contains estimated
xyz and minimization results:
| (cct_min, duv_min, F_min (objective fcn value))
:wl:
| None, optional
| Wavelengths used when calculating Planckian radiators.
:accuracy:
| float, optional
| Stop brute-force search when cct :accuracy: is reached.
:upper_cct_max:
| 10.0**20, optional
| Limit brute-force search to this cct.
:approx_cct_temp:
| True, optional
| If True: use xyz_to_cct_HA() to get a first estimate of cct to
speed up search.
:force_out_of_lut:
| True, optional
| If True and cct is out of range of the LUT, then switch to
brute-force search method, else return numpy.nan values.
Returns:
:returns:
| ndarray with estimated XYZ tristimulus values
Note:
If duv is not supplied (:ccts:.shape is (N,1) and :duv: is None),
source is assumed to be on the Planckian locus.
"""
# make ccts a min. 2d np.array:
if isinstance(ccts, list):
ccts = np2dT(np.array(ccts))
else:
ccts = np2d(ccts)
if len(ccts.shape) > 2:
raise Exception('cct_to_xyz(): Input ccts.shape must be <= 2 !')
# get cct and duv arrays from :ccts:
cct = np2d(ccts[:, 0, None])
if (duv is None) & (ccts.shape[1] == 2):
duv = np2d(ccts[:, 1, None])
elif duv is not None:
duv = np2d(duv)
#get estimates of approximate xyz values in case duv = None:
BB = cri_ref(ccts=cct, wl3=wl, ref_type=['BB'])
xyz_est = spd_to_xyz(data=BB, cieobs=cieobs, out=1)
results = np.ones([ccts.shape[0], 3]) * np.nan
if duv is not None:
# optimization/minimization setup:
def objfcn(uv_offset,
uv0,
cct,
duv,
out=1): #, cieobs = cieobs, wl = wl, mode = mode):
uv0 = np2d(uv0 + uv_offset)
Yuv0 = np.concatenate((np2d([100.0]), uv0), axis=1)
cct_min, duv_min = xyz_to_cct(Yuv_to_xyz(Yuv0),
cieobs=cieobs,
out='cct,duv',
wl=wl,
mode=mode,
accuracy=accuracy,
force_out_of_lut=force_out_of_lut,
upper_cct_max=upper_cct_max,
approx_cct_temp=approx_cct_temp)
F = np.sqrt(((100.0 * (cct_min[0] - cct[0]) / (cct[0]))**2.0) +
(((duv_min[0] - duv[0]) / (duv[0]))**2.0))
if out == 'F':
return F
else:
return np.concatenate((cct_min, duv_min, np2d(F)), axis=1)
# loop through each xyz_est:
for i in range(xyz_est.shape[0]):
xyz0 = xyz_est[i]
cct_i = cct[i]
duv_i = duv[i]
cct_min, duv_min = xyz_to_cct(xyz0,
cieobs=cieobs,
out='cct,duv',
wl=wl,
mode=mode,
accuracy=accuracy,
force_out_of_lut=force_out_of_lut,
upper_cct_max=upper_cct_max,
approx_cct_temp=approx_cct_temp)
if np.abs(duv[i]) > _EPS:
# find xyz:
Yuv0 = xyz_to_Yuv(xyz0)
uv0 = Yuv0[0][1:3]
OptimizeResult = minimize(fun=objfcn,
x0=np.zeros((1, 2)),
args=(uv0, cct_i, duv_i, 'F'),
method='Nelder-Mead',
options={
"maxiter": np.inf,
"maxfev": np.inf,
'xatol': 0.000001,
'fatol': 0.000001
})
betas = OptimizeResult['x']
#betas = np.zeros(uv0.shape)
if out is not None:
results[i] = objfcn(betas, uv0, cct_i, duv_i, out=3)
uv0 = np2d(uv0 + betas)
Yuv0 = np.concatenate((np2d([100.0]), uv0), axis=1)
xyz_est[i] = Yuv_to_xyz(Yuv0)
else:
xyz_est[i] = xyz0
if (out is None) | (out == 1):
return xyz_est
else:
# Also output results of minimization:
return np.concatenate((xyz_est, results), axis=1)
def cam18sl(data, datab = None, Lb = [100], 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 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,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._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)
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, k, naka, unique_hue_data = [parameters[x] for x in sorted(parameters.keys())]
# precomputations:
Mlms2xyz = np.linalg.inv(_CMF['2006_10']['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 = '2006_10', 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 = '2006_10', 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 = '2006_10', relative = False)
datar = datab.copy()
# 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':
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.nan*np.ones(dshape)
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 = '2006_10', relative = False)
xyzr = spd_to_xyz(np.vstack((datar[0], datar[i+1:i+2,:])), cieobs = '2006_10', relative = False)
else:
xyzb = datab[i:i+1,:]
xyzr = datar[i:i+1,:]
lmsb = np.dot(_CMF['2006_10']['M'],xyzb.T).T # convert to l,m,s
rgbb = (lmsb / _CMF['2006_10']['K']) * k # convert to rho, gamma, beta
#lmsr = np.dot(_CMF['2006_10']['M'],xyzr.T).T # convert to l,m,s
#rgbr = (lmsr / _CMF['2006_10']['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 = '2006_10', relative = False)
elif (inputtype == 'xyz'):
xyz = data[i]
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
# 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
# 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','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 = (((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['2006_10']['K']
xyz = np.dot(Mlms2xyz,lms.T).T
camout[i] = xyz
if camout.shape[0] == 1:
camout = np.squeeze(camout,axis = 0)
return camout