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 _cri_ref_i(cct,
wl3=_WL,
ref_type='iestm30',
mix_range=[4000, 5000],
cieobs='1931_2',
force_daylight_below4000K=False,
n=None,
daylight_locus=None):
"""
Calculates a reference illuminant spectrum based on cct
for color rendering index calculations.
"""
if mix_range is None:
mix_range = _CRI_REF_TYPES[ref_type]
if (cct < mix_range[0]) | (ref_type == 'BB'):
return blackbody(cct, wl3, n=n)
elif (cct > mix_range[0]) | (ref_type == 'DL'):
return daylightphase(
cct,
wl3,
force_daylight_below4000K=force_daylight_below4000K,
cieobs=cieobs,
daylight_locus=daylight_locus)
else:
SrBB = blackbody(cct, wl3, n=n)
SrDL = daylightphase(
cct,
wl3,
verbosity=None,
force_daylight_below4000K=force_daylight_below4000K,
cieobs=cieobs,
daylight_locus=daylight_locus)
cmf = _CMF[cieobs]['bar'] if isinstance(cieobs, str) else cieobs
wl = SrBB[0]
ld = getwld(wl)
SrBB = 100.0 * SrBB[1] / np.array(np.sum(SrBB[1] * cmf[2] * ld))
SrDL = 100.0 * SrDL[1] / np.array(np.sum(SrDL[1] * cmf[2] * ld))
Tb, Te = float(mix_range[0]), float(mix_range[1])
cBB, cDL = (Te - cct) / (Te - Tb), (cct - Tb) / (Te - Tb)
if cBB < 0.0:
cBB = 0.0
elif cBB > 1:
cBB = 1.0
if cDL < 0.0:
cDL = 0.0
elif cDL > 1:
cDL = 1.0
Sr = SrBB * cBB + SrDL * cDL
Sr[Sr == float('NaN')] = 0.0
Sr = np.vstack((wl, (Sr / Sr[_POS_WL560])))
return Sr
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 angle_v1v2(v1,v2,htype = 'deg'):
"""
Calculates angle between two vectors.
Args:
:v1:
| ndarray with vector 1
:v2:
| ndarray with vector 2
:htype:
| 'deg' or 'rad', optional
| Requested angle type.
Returns:
:ang:
| ndarray
"""
denom = magnitude_v(v1)*magnitude_v(v2)
denom[denom==0.] = np.nan
ang = np.arccos(np.sum(v1*v2,axis=1)/denom)
if htype == 'deg':
ang = ang*180/np.pi
return ang
def xyz_to_rfl(xyz, CSF = None, rfl = None, out = 'rfl_est', \
refspd = None, D = None, cieobs = _CIEOBS, \
cspace = 'xyz', cspace_tf = {},\
interp_type = 'nd', k_neighbours = 4, verbosity = 0):
"""
Approximate spectral reflectance of xyz values based on nd-dimensional linear interpolation
or k nearest neighbour interpolation of samples from a standard reflectance set.
Args:
:xyz:
| ndarray with xyz values of target points.
:CSF:
| None, optional
| RGB camera response functions.
| If None: input :xyz: contains raw rgb (float) values. Override :cspace:
| argument and perform estimation directly in raw rgb space!!!
:rfl:
| ndarray, optional
| Reflectance set for color coordinate to rfl mapping.
:out:
| 'rfl_est' or str, optional
:refspd:
| None, optional
| Refer ence spectrum for color coordinate to rfl mapping.
| None defaults to D65.
:cieobs:
| _CIEOBS, optional
| CMF set used for calculation of xyz from spectral data.
:cspace:
| 'xyz', optional
| Color space for color coordinate to rfl mapping.
| Tip: Use linear space (e.g. 'xyz', 'Yuv',...) for (interp_type == 'nd'),
| and perceptually uniform space (e.g. 'ipt') for (interp_type == 'nearest')
:cspace_tf:
| {}, optional
| Dict with parameters for xyz_to_cspace and cspace_to_xyz transform.
:interp_type:
| 'nd', optional
| Options:
| - 'nd': perform n-dimensional linear interpolation using Delaunay triangulation.
| - 'nearest': perform nearest neighbour interpolation.
:k_neighbours:
| 4 or int, optional
| Number of nearest neighbours for reflectance spectrum interpolation.
| Neighbours are found using scipy.spatial.cKDTree
:verbosity:
| 0, optional
| If > 0: make a plot of the color coordinates of original and
| rendered image pixels.
Returns:
:returns:
| :rfl_est:
| ndarrays with estimated reflectance spectra.
"""
# get rfl set:
if rfl is None: # use IESTM30['4880'] set
rfl = _CRI_RFL['ies-tm30']['4880']['5nm']
wlr = rfl[0]
# get Ref spd:
if refspd is None:
refspd = _CIE_ILLUMINANTS['D65'].copy()
refspd = cie_interp(
refspd, wlr,
kind='linear') # force spd to same wavelength range as rfl
# Calculate rgb values of standard rfl set under refspd:
if CSF is None:
# Calculate lab coordinates:
xyz_rr, xyz_wr = spd_to_xyz(refspd,
relative=True,
rfl=rfl,
cieobs=cieobs,
out=2)
cspace_tf_copy = cspace_tf.copy()
cspace_tf_copy[
'xyzw'] = xyz_wr # put correct white point in param. dict
lab_rr = colortf(xyz_rr,
tf=cspace,
fwtf=cspace_tf_copy,
bwtf=cspace_tf_copy)[:, 0, :]
else:
# Calculate rgb coordinates from camera sensitivity functions
rgb_rr = rfl_to_rgb(rfl, spd=refspd, CSF=CSF, wl=None)
lab_rr = rgb_rr
xyz = xyz
lab_rr = np.round(lab_rr, _ROUNDING) # speed up search
# Convert xyz to lab-type values under refspd:
if CSF is None:
lab = colortf(xyz, tf=cspace, fwtf=cspace_tf_copy, bwtf=cspace_tf_copy)
else:
lab = xyz # xyz contained rgb values !!!
rgb = xyz
lab = np.round(lab, _ROUNDING) # speed up search
if interp_type == 'nearest':
# Find rfl (cfr. lab_rr) from rfl set that results in 'near' metameric
# color coordinates for each value in lab_ur (i.e. smallest DE):
# Construct cKDTree:
tree = sp.spatial.cKDTree(lab_rr, copy_data=True)
# Interpolate rfls using k nearest neightbours and inverse distance weigthing:
d, inds = tree.query(lab, k=k_neighbours)
if k_neighbours > 1:
d += _EPS
w = (1.0 / d**2)[:, :, None] # inverse distance weigthing
rfl_est = np.sum(w * rfl[inds + 1, :], axis=1) / np.sum(w, axis=1)
else:
rfl_est = rfl[inds + 1, :].copy()
elif interp_type == 'nd':
rfl_est = math.ndinterp1_scipy(lab_rr, rfl[1:], lab)
_isnan = np.isnan(rfl_est[:, 0])
if (
_isnan.any()
): #do nearest neigbour method for those that fail using Delaunay (i.e. ndinterp1_scipy)
# Find rfl (cfr. lab_rr) from rfl set that results in 'near' metameric
# color coordinates for each value in lab_ur (i.e. smallest DE):
# Construct cKDTree:
tree = sp.spatial.cKDTree(lab_rr, copy_data=True)
# Interpolate rfls using k nearest neightbours and inverse distance weigthing:
d, inds = tree.query(lab[_isnan, ...], k=k_neighbours)
if k_neighbours > 1:
d += _EPS
w = (1.0 / d**2)[:, :, None] # inverse distance weigthing
rfl_est_isnan = np.sum(w * rfl[inds + 1, :], axis=1) / np.sum(
w, axis=1)
else:
rfl_est_isnan = rfl[inds + 1, :].copy()
rfl_est[_isnan, :] = rfl_est_isnan
else:
raise Exception('xyz_to_rfl(): unsupported interp_type!')
rfl_est[
rfl_est <
0] = 0 #can occur for points outside convexhull of standard rfl set.
rfl_est = np.vstack((rfl[0], rfl_est))
if ((verbosity > 0) | ('xyz_est' in out.split(',')) |
('lab_est' in out.split(',')) | ('DEi_ab' in out.split(',')) |
('DEa_ab' in out.split(','))) & (CSF is None):
xyz_est, _ = spd_to_xyz(refspd,
rfl=rfl_est,
relative=True,
cieobs=cieobs,
out=2)
cspace_tf_copy = cspace_tf.copy()
cspace_tf_copy[
'xyzw'] = xyz_wr # put correct white point in param. dict
lab_est = colortf(xyz_est, tf=cspace, fwtf=cspace_tf_copy)[:, 0, :]
DEi_ab = np.sqrt(((lab_est[:, 1:3] - lab[:, 1:3])**2).sum(axis=1))
DEa_ab = DEi_ab.mean()
elif ((verbosity > 0) | ('xyz_est' in out.split(',')) |
('rgb_est' in out.split(',')) | ('DEi_rgb' in out.split(',')) |
('DEa_rgb' in out.split(','))) & (CSF is not None):
rgb_est = rfl_to_rgb(rfl_est[1:], spd=refspd, CSF=CSF, wl=wlr)
xyz_est = rgb_est
DEi_rgb = np.sqrt(((rgb_est - rgb)**2).sum(axis=1))
DEa_rgb = DEi_rgb.mean()
if verbosity > 0:
if CSF is None:
ax = plot_color_data(lab[...,1], lab[...,2], z = lab[...,0], \
show = False, cieobs = cieobs, cspace = cspace, \
formatstr = 'ro', label = 'Original')
plot_color_data(lab_est[...,1], lab_est[...,2], z = lab_est[...,0], \
show = True, axh = ax, cieobs = cieobs, cspace = cspace, \
formatstr = 'bd', label = 'Rendered')
else:
n = 100 #min(rfl.shape[0]-1,rfl_est.shape[0]-1)
s = np.random.permutation(rfl.shape[0] -
1)[:min(n, rfl.shape[0] - 1)]
st = np.random.permutation(rfl_est.shape[0] -
1)[:min(n, rfl_est.shape[0] - 1)]
fig = plt.figure()
ax = np.zeros((3, ), dtype=np.object)
ax[0] = fig.add_subplot(131)
ax[1] = fig.add_subplot(132)
ax[2] = fig.add_subplot(133, projection='3d')
ax[0].plot(rfl[0], rfl[1:][s].T, linestyle='-')
ax[0].set_title('Original RFL set (random selection of all)')
ax[0].set_ylim([0, 1])
ax[1].plot(rfl_est[0], rfl_est[1:][st].T, linestyle='--')
ax[0].set_title('Estimated RFL set (random selection of targets)')
ax[1].set_ylim([0, 1])
ax[2].plot(rgb[st, 0],
rgb[st, 1],
rgb[st, 2],
'ro',
label='Original')
ax[2].plot(rgb_est[st, 0],
rgb_est[st, 1],
rgb_est[st, 2],
'bd',
label='Rendered')
ax[2].legend()
if out == 'rfl_est':
return rfl_est
elif out == 'rfl_est,xyz_est':
return rfl_est, xyz_est
else:
return eval(out)
def VF_colorshift_model(S, cri_type = _VF_CRI_DEFAULT, model_type = _VF_MODEL_TYPE, \
cspace = _VF_CSPACE, sampleset = None, pool = False, \
pcolorshift = {'href': np.arange(np.pi/10,2*np.pi,2*np.pi/10),'Cref' : _VF_MAXR, 'sig' : _VF_SIG}, \
vfcolor = 'k',verbosity = 0):
"""
Applies full vector field model calculations to spectral data.
Args:
:S:
| nump.ndarray with spectral data.
:cri_type:
| _VF_CRI_DEFAULT or str or dict, optional
| Specifies type of color fidelity model to use.
| Controls choice of ref. ill., sample set, averaging, scaling, etc.
| See luxpy.cri.spd_to_cri for more info.
:modeltype:
| _VF_MODEL_TYPE or 'M6' or 'M5', optional
| Specifies degree 5 or degree 6 polynomial model in ab-coordinates.
:cspace:
| _VF_CSPACE or dict, optional
| Specifies color space. See _VF_CSPACE_EXAMPLE for example structure.
:sampleset:
| None or str or ndarray, optional
| Sampleset to be used when calculating vector field model.
:pool:
| False, optional
| If :S: contains multiple spectra, True pools all jab data before
| modeling the vector field, while False models a different field
| for each spectrum.
:pcolorshift:
| default dict (see below) or user defined dict, optional
| Dict containing the specification input
| for apply_poly_model_at_hue_x().
| Default dict = {'href': np.arange(np.pi/10,2*np.pi,2*np.pi/10),
| 'Cref' : _VF_MAXR,
| 'sig' : _VF_SIG,
| 'labels' : '#'}
| 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.
:vfcolor:
| 'k', optional
| For plotting the vector fields.
:verbosity:
| 0, optional
| Report warnings or not.
Returns:
:returns:
| list[dict] (each list element refers to a different test SPD)
| with the following keys:
| - 'Source': dict with ndarrays of the S, cct and duv of source spd.
| - 'metrics': dict with ndarrays for:
| * Rf (color fidelity: base + metameric shift)
| * Rt (metameric uncertainty index)
| * Rfi (specific color fidelity indices)
| * Rti (specific metameric uncertainty indices)
| * cri_type (str with cri_type)
| - 'Jab': dict with with ndarrays for Jabt, Jabr, DEi
| - 'dC/C_dH_x_sig' :
| np.vstack((dCoverC_x,dCoverC_x_sig,dH_x,dH_x_sig)).T
| See get_poly_model() for more info.
| - 'fielddata': dict with dicts containing data on the calculated
| vector-field and circle-fields:
| * 'vectorfield' : {'axt': vfaxt, 'bxt' : vfbxt,
| 'axr' : vfaxr, 'bxr' : vfbxr},
| * 'circlefield' : {'axt': cfaxt, 'bxt' : cfbxt,
| 'axr' : cfaxr, 'bxr' : cfbxr}},
| - 'modeldata' : dict with model info:
| {'pmodel': pmodel,
| 'pcolorshift' : pcolorshift,
| 'dab_model' : dab_model,
| 'dab_res' : dab_res,
| 'dab_std' : dab_std,
| 'modeltype' : modeltype,
| 'fmodel' : poly_model,
| 'Jabtm' : Jabtm,
| 'Jabrm' : Jabrm,
| 'DEim' : DEim},
| - 'vshifts' :dict with various vector shifts:
| * 'Jabshiftvector_r_to_t' : ndarray with difference vectors
| between jabt and jabr.
| * 'vshift_ab_s' : vshift_ab_s: ab-shift vectors of samples
| * 'vshift_ab_s_vf' : vshift_ab_s_vf: ab-shift vectors of
| VF model predictions of samples.
| * 'vshift_ab_vf' : vshift_ab_vf: ab-shift vectors of VF
| model predictions of vector field grid.
"""
if type(cri_type) == str:
cri_type_str = cri_type
else:
cri_type_str = None
# Calculate Rf, Rfi and Jabr, Jabt:
Rf, Rfi, Jabt, Jabr, cct, duv, cri_type = spd_to_cri(
S,
cri_type=cri_type,
out='Rf,Rfi,jabt,jabr,cct,duv,cri_type',
sampleset=sampleset)
# In case of multiple source SPDs, pool:
if (len(Jabr.shape) == 3) & (Jabr.shape[1] > 1) & (pool == True):
#Nsamples = Jabr.shape[0]
Jabr = np.transpose(Jabr, (1, 0, 2)) # set lamps on first dimension
Jabt = np.transpose(Jabt, (1, 0, 2))
Jabr = Jabr.reshape(Jabr.shape[0] * Jabr.shape[1],
3) # put all lamp data one after the other
Jabt = Jabt.reshape(Jabt.shape[0] * Jabt.shape[1], 3)
Jabt = Jabt[:, None, :] # add dim = 1
Jabr = Jabr[:, None, :]
out = [{} for _ in range(Jabr.shape[1])] #initialize empty list of dicts
if pool == False:
N = Jabr.shape[1]
else:
N = 1
for i in range(N):
Jabr_i = Jabr[:, i, :].copy()
Jabr_i = Jabr_i[:, None, :]
Jabt_i = Jabt[:, i, :].copy()
Jabt_i = Jabt_i[:, None, :]
DEi = np.sqrt((Jabr_i[..., 0] - Jabt_i[..., 0])**2 +
(Jabr_i[..., 1] - Jabt_i[..., 1])**2 +
(Jabr_i[..., 2] - Jabt_i[..., 2])**2)
# Determine polynomial model:
poly_model, pmodel, dab_model, dab_res, dCHoverC_res, dab_std, dCHoverC_std = get_poly_model(
Jabt_i, Jabr_i, modeltype=_VF_MODEL_TYPE)
# Apply model at fixed hues:
href = pcolorshift['href']
Cref = pcolorshift['Cref']
sig = pcolorshift['sig']
dCoverC_x, dCoverC_x_sig, dH_x, dH_x_sig = apply_poly_model_at_hue_x(
poly_model, pmodel, dCHoverC_res, hx=href, Cxr=Cref, sig=sig)
# Calculate deshifted a,b values on original samples:
Jt = Jabt_i[..., 0].copy()
at = Jabt_i[..., 1].copy()
bt = Jabt_i[..., 2].copy()
Jr = Jabr_i[..., 0].copy()
ar = Jabr_i[..., 1].copy()
br = Jabr_i[..., 2].copy()
ar = ar + dab_model[:, 0:1] # deshift reference to model prediction
br = br + dab_model[:, 1:2] # deshift reference to model prediction
Jabtm = np.hstack((Jt, at, bt))
Jabrm = np.hstack((Jr, ar, br))
# calculate color differences between test and deshifted ref:
# DEim = np.sqrt((Jr - Jt)**2 + (at - ar)**2 + (bt - br)**2)
DEim = np.sqrt(0 * (Jr - Jt)**2 + (at - ar)**2 +
(bt - br)**2) # J is not used
# Apply scaling function to convert DEim to Rti:
scale_factor = cri_type['scale']['cfactor']
scale_fcn = cri_type['scale']['fcn']
avg = cri_type['avg']
Rfi_deshifted = scale_fcn(DEim, scale_factor)
Rf_deshifted = scale_fcn(avg(DEim, axis=0), scale_factor)
rms = lambda x: np.sqrt(np.sum(x**2, axis=0) / x.shape[0])
Rf_deshifted_rms = scale_fcn(rms(DEim), scale_factor)
# Generate vector field:
vfaxt, vfbxt, vfaxr, vfbxr = generate_vector_field(
poly_model,
pmodel,
axr=np.arange(-_VF_MAXR, _VF_MAXR + _VF_DELTAR, _VF_DELTAR),
bxr=np.arange(-_VF_MAXR, _VF_MAXR + _VF_DELTAR, _VF_DELTAR),
limit_grid_radius=_VF_MAXR,
color=0)
vfaxt, vfbxt, vfaxr, vfbxr = generate_vector_field(
poly_model,
pmodel,
axr=np.arange(-_VF_MAXR, _VF_MAXR + _VF_DELTAR, _VF_DELTAR),
bxr=np.arange(-_VF_MAXR, _VF_MAXR + _VF_DELTAR, _VF_DELTAR),
limit_grid_radius=_VF_MAXR,
color=0)
# Calculate ab-shift vectors of samples and VF model predictions:
vshift_ab_s = calculate_shiftvectors(Jabt_i,
Jabr_i,
average=False,
vtype='ab')[:, 0, 0:3]
vshift_ab_s_vf = calculate_shiftvectors(Jabtm,
Jabrm,
average=False,
vtype='ab')
# Calculate ab-shift vectors using vector field model:
Jabt_vf = np.hstack((np.zeros((vfaxt.shape[0], 1)), vfaxt, vfbxt))
Jabr_vf = np.hstack((np.zeros((vfaxr.shape[0], 1)), vfaxr, vfbxr))
vshift_ab_vf = calculate_shiftvectors(Jabt_vf,
Jabr_vf,
average=False,
vtype='ab')
# Generate circle field:
x, y = plotcircle(radii=np.arange(0, _VF_MAXR + _VF_DELTAR, 10),
angles=np.arange(0, 359, 1),
out='x,y')
cfaxt, cfbxt, cfaxr, cfbxr = generate_vector_field(
poly_model,
pmodel,
make_grid=False,
axr=x[:, None],
bxr=y[:, None],
limit_grid_radius=_VF_MAXR,
color=0)
out[i] = {
'Source': {
'S': S,
'cct': cct[i],
'duv': duv[i]
},
'metrics': {
'Rf': Rf[:, i],
'Rt': Rf_deshifted,
'Rt_rms': Rf_deshifted_rms,
'Rfi': Rfi[:, i],
'Rti': Rfi_deshifted,
'cri_type': cri_type_str
},
'Jab': {
'Jabt': Jabt_i,
'Jabr': Jabr_i,
'DEi': DEi
},
'dC/C_dH_x_sig':
np.vstack((dCoverC_x, dCoverC_x_sig, dH_x, dH_x_sig)).T,
'fielddata': {
'vectorfield': {
'axt': vfaxt,
'bxt': vfbxt,
'axr': vfaxr,
'bxr': vfbxr
},
'circlefield': {
'axt': cfaxt,
'bxt': cfbxt,
'axr': cfaxr,
'bxr': cfbxr
}
},
'modeldata': {
'pmodel': pmodel,
'pcolorshift': pcolorshift,
'dab_model': dab_model,
'dab_res': dab_res,
'dab_std': dab_std,
'model_type': model_type,
'fmodel': poly_model,
'Jabtm': Jabtm,
'Jabrm': Jabrm,
'DEim': DEim
},
'vshifts': {
'Jabshiftvector_r_to_t': np.hstack(
(Jt - Jr, at - ar, bt - br)),
'vshift_ab_s': vshift_ab_s,
'vshift_ab_s_vf': vshift_ab_s_vf,
'vshift_ab_vf': vshift_ab_vf
}
}
return out
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 get_macadam_ellipse(xy = None, k_neighbours = 3, nsteps = 10, average_cik = True):
"""
Estimate n-step MacAdam ellipse at CIE x,y coordinates xy by calculating
average inverse covariance ellipse of the k_neighbours closest ellipses.
Args:
:xy:
| None or ndarray, optional
| If None: output Macadam ellipses, if not None: xy are the
| CIE xy coordinates for which ellipses will be estimated.
:k_neighbours:
| 3, optional
| Number of nearest ellipses to use to calculate ellipse at xy
:nsteps:
| 10, optional
| Set number of MacAdam steps of ellipse.
:average_cik:
| True, optional
| If True: take distance weighted average of inverse
| 'covariance ellipse' elements cik.
| If False: average major & minor axis lengths and
| ellipse orientation angles directly.
Returns:
:v_mac_est:
| estimated MacAdam ellipse(s) in v-format [Rmax,Rmin,xc,yc,theta]
References:
1. MacAdam DL. Visual Sensitivities to Color Differences in Daylight*. J Opt Soc Am. 1942;32(5):247-274.
"""
# list of MacAdam ellipses (x10)
v_mac = np.atleast_2d([
[0.16, 0.057, 0.0085, 0.0035, 62.5],
[0.187, 0.118, 0.022, 0.0055, 77],
[0.253, 0.125, 0.025, 0.005, 55.5],
[0.15, 0.68, 0.096, 0.023, 105],
[0.131, 0.521, 0.047, 0.02, 112.5],
[0.212, 0.55, 0.058, 0.023, 100],
[0.258, 0.45, 0.05, 0.02, 92],
[0.152, 0.365, 0.038, 0.019, 110],
[0.28, 0.385, 0.04, 0.015, 75.5],
[0.38, 0.498, 0.044, 0.012, 70],
[0.16, 0.2, 0.021, 0.0095, 104],
[0.228, 0.25, 0.031, 0.009, 72],
[0.305, 0.323, 0.023, 0.009, 58],
[0.385, 0.393, 0.038, 0.016, 65.5],
[0.472, 0.399, 0.032, 0.014, 51],
[0.527, 0.35, 0.026, 0.013, 20],
[0.475, 0.3, 0.029, 0.011, 28.5],
[0.51, 0.236, 0.024, 0.012, 29.5],
[0.596, 0.283, 0.026, 0.013, 13],
[0.344, 0.284, 0.023, 0.009, 60],
[0.39, 0.237, 0.025, 0.01, 47],
[0.441, 0.198, 0.028, 0.0095, 34.5],
[0.278, 0.223, 0.024, 0.0055, 57.5],
[0.3, 0.163, 0.029, 0.006, 54],
[0.365, 0.153, 0.036, 0.0095, 40]
])
# convert to v-format ([a,b, xc, yc, theta]):
v_mac = v_mac[:,[2,3,0,1,4]]
# convert last column to rad.:
v_mac[:,-1] = v_mac[:,-1]*np.pi/180
# convert to desired number of MacAdam-steps:
v_mac[:,0:2] = v_mac[:,0:2]/10*nsteps
if xy is not None:
#calculate inverse covariance matrices:
cik = math.v_to_cik(v_mac, inverse = True)
if average_cik == True:
cik_long = np.hstack((cik[:,0,:],cik[:,1,:]))
# Calculate k_neighbours closest ellipses to xy:
tree = sp.spatial.cKDTree(v_mac[:,2:4], copy_data = True)
d, inds = tree.query(xy, k = k_neighbours)
if k_neighbours > 1:
pd = 1
w = (1.0 / np.abs(d)**pd)[:,:,None] # inverse distance weigthing
if average_cik == True:
cik_long_est = np.sum(w * cik_long[inds,:], axis=1) / np.sum(w, axis=1)
else:
v_mac_est = np.sum(w * v_mac[inds,:], axis=1) / np.sum(w, axis=1) # for average xyc
else:
v_mac_est = v_mac[inds,:].copy()
# convert cik back to v:
if (average_cik == True) & (k_neighbours >1):
cik_est = np.dstack((cik_long_est[:,0:2],cik_long_est[:,2:4]))
v_mac_est = math.cik_to_v(cik_est, inverse = True)
v_mac_est[:,2:4] = xy
else:
v_mac_est = v_mac
return v_mac_est
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)
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 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_normalize(data, norm_type=None, norm_f=1, wl=True, cieobs=_CIEOBS):
"""
Normalize a spectral power distribution (SPD).
Args:
:data:
| ndarray
:norm_type:
| None, optional
| - 'lambda': make lambda in norm_f equal to 1
| - 'area': area-normalization times norm_f
| - 'max': max-normalization times norm_f
| - 'ru': to :norm_f: radiometric units
| - 'pu': to :norm_f: photometric units
| - 'pusa': to :norm_f: photometric units (with Km corrected
| to standard air, cfr. CIE TN003-2015)
| - 'qu': to :norm_f: quantal energy units
:norm_f:
| 1, optional
| Normalization factor that determines the size of normalization
| for 'max' and 'area'
| or which wavelength is normalized to 1 for 'lambda' option.
:wl:
| True or False, optional
| If True, the first column of data contains wavelengths.
:cieobs:
| _CIEOBS or str, optional
| Type of cmf set to use for normalization using photometric units
| (norm_type == 'pu')
Returns:
:returns:
| ndarray with normalized data.
"""
if norm_type is not None:
if not isinstance(norm_type, list): norm_type = [norm_type]
if norm_f is not None:
if not isinstance(norm_f, list): norm_f = [norm_f]
if ('lambda' in norm_type) | ('qu' in norm_type):
wl = True # for lambda & 'qu' normalization wl MUST be first column
wlr = data[0]
if (('area' in norm_type) | ('ru' in norm_type) | ('pu' in norm_type) |
('pusa' in norm_type)) & (wl == True):
dl = getwld(data[0])
else:
dl = 1 #no wavelengths provided
offset = int(wl)
for i in range(data.shape[0] - offset):
norm_type_ = norm_type[i] if (len(norm_type) > 1) else norm_type[0]
if norm_f is not None:
norm_f_ = norm_f[i] if (len(norm_f) > 1) else norm_f[0]
else:
norm_f_ = 560.0 if (norm_type_ == 'lambda') else 1.0
if norm_type_ == 'max':
data[i + offset] = norm_f_ * data[i + offset] / np.max(
data[i + offset])
elif norm_type_ == 'area':
data[i + offset] = norm_f_ * data[i + offset] / (
np.sum(data[i + offset]) * dl)
elif norm_type_ == 'lambda':
wl_index = np.abs(wlr - norm_f_).argmin()
data[i +
offset] = data[i + offset] / data[i + offset][wl_index]
elif (norm_type_ == 'ru') | (norm_type_ == 'pu') | (
norm_type == 'pusa') | (norm_type_ == 'qu'):
rpq_power = spd_to_power(data[[0, i + offset], :],
cieobs=cieobs,
ptype=norm_type_)
data[i + offset] = (norm_f / rpq_power) * data[i + offset]
else:
data[i + offset] = data[i + offset] / norm_f_
return data
def xyz_to_rfl(xyz, rfl = None, out = 'rfl_est', \
refspd = None, D = None, cieobs = _CIEOBS, \
cspace = 'xyz', cspace_tf = {},\
interp_type = 'nd', k_neighbours = 4, verbosity = 0):
"""
Approximate spectral reflectance of xyz based on nd-dimensional linear interpolation
or k nearest neighbour interpolation of samples from a standard reflectance set.
Args:
:xyz:
| ndarray with tristimulus values of target points.
:rfl:
| ndarray, optional
| Reflectance set for color coordinate to rfl mapping.
:out:
| 'rfl_est' or str, optional
:refspd:
| None, optional
| Refer ence spectrum for color coordinate to rfl mapping.
| None defaults to D65.
:cieobs:
| _CIEOBS, optional
| CMF set used for calculation of xyz from spectral data.
:cspace:
| 'xyz', optional
| Color space for color coordinate to rfl mapping.
| Tip: Use linear space (e.g. 'xyz', 'Yuv',...) for (interp_type == 'nd'),
| and perceptually uniform space (e.g. 'ipt') for (interp_type == 'nearest')
:cspace_tf:
| {}, optional
| Dict with parameters for xyz_to_cspace and cspace_to_xyz transform.
:interp_type:
| 'nd', optional
| Options:
| - 'nd': perform n-dimensional linear interpolation using Delaunay triangulation.
| - 'nearest': perform nearest neighbour interpolation.
:k_neighbours:
| 4 or int, optional
| Number of nearest neighbours for reflectance spectrum interpolation.
| Neighbours are found using scipy.spatial.cKDTree
:verbosity:
| 0, optional
| If > 0: make a plot of the color coordinates of original and
| rendered image pixels.
Returns:
:returns:
| :rfl_est:
| ndarrays with estimated reflectance spectra.
"""
# get rfl set:
if rfl is None: # use IESTM30['4880'] set
rfl = _CRI_RFL['ies-tm30']['4880']['5nm']
# get Ref spd:
if refspd is None:
refspd = _CIE_ILLUMINANTS['D65'].copy()
# Calculate lab-type coordinates of standard rfl set under refspd:
xyz_rr, xyz_wr = spd_to_xyz(refspd,
relative=True,
rfl=rfl,
cieobs=cieobs,
out=2)
cspace_tf_copy = cspace_tf.copy()
cspace_tf_copy['xyzw'] = xyz_wr # put correct white point in param. dict
lab_rr = colortf(xyz_rr,
tf=cspace,
fwtf=cspace_tf_copy,
bwtf=cspace_tf_copy)[:, 0, :]
# Convert xyz to lab-type values under refspd:
lab = colortf(xyz, tf=cspace, fwtf=cspace_tf_copy, bwtf=cspace_tf_copy)
if interp_type == 'nearest':
# Find rfl (cfr. lab_rr) from rfl set that results in 'near' metameric
# color coordinates for each value in lab_ur (i.e. smallest DE):
# Construct cKDTree:
tree = sp.spatial.cKDTree(lab_rr, copy_data=True)
# Interpolate rfls using k nearest neightbours and inverse distance weigthing:
d, inds = tree.query(lab, k=k_neighbours)
if k_neighbours > 1:
d += _EPS
w = (1.0 / d**2)[:, :, None] # inverse distance weigthing
rfl_est = np.sum(w * rfl[inds + 1, :], axis=1) / np.sum(w, axis=1)
else:
rfl_est = rfl[inds + 1, :].copy()
elif interp_type == 'nd':
rfl_est = math.ndinterp1_scipy(lab_rr, rfl[1:], lab)
_isnan = np.isnan(rfl_est[:, 0])
if (
_isnan.any()
): #do nearest neigbour method for those that fail using Delaunay (i.e. ndinterp1_scipy)
# Find rfl (cfr. lab_rr) from rfl set that results in 'near' metameric
# color coordinates for each value in lab_ur (i.e. smallest DE):
# Construct cKDTree:
tree = sp.spatial.cKDTree(lab_rr, copy_data=True)
# Interpolate rfls using k nearest neightbours and inverse distance weigthing:
d, inds = tree.query(lab[_isnan, ...], k=k_neighbours)
if k_neighbours > 1:
d += _EPS
w = (1.0 / d**2)[:, :, None] # inverse distance weigthing
rfl_est_isnan = np.sum(w * rfl[inds + 1, :], axis=1) / np.sum(
w, axis=1)
else:
rfl_est_isnan = rfl[inds + 1, :].copy()
rfl_est[_isnan, :] = rfl_est_isnan
else:
raise Exception('xyz_to_rfl(): unsupported interp_type!')
rfl_est[
rfl_est <
0] = 0 #can occur for points outside convexhull of standard rfl set.
rfl_est = np.vstack((rfl[0], rfl_est))
if (verbosity > 0) | ('xyz_est' in out.split(',')) | (
'lab_est' in out.split(',')) | ('DEi_ab' in out.split(',')) | (
'DEa_ab' in out.split(',')):
xyz_est, _ = spd_to_xyz(refspd,
rfl=rfl_est,
relative=True,
cieobs=cieobs,
out=2)
cspace_tf_copy = cspace_tf.copy()
cspace_tf_copy[
'xyzw'] = xyz_wr # put correct white point in param. dict
lab_est = colortf(xyz_est, tf=cspace, fwtf=cspace_tf_copy)[:, 0, :]
DEi_ab = np.sqrt(((lab_est[:, 1:3] - lab[:, 1:3])**2).sum(axis=1))
DEa_ab = DEi_ab.mean()
if verbosity > 0:
ax = plot_color_data(lab[...,1], lab[...,2], z = lab[...,0], \
show = False, cieobs = cieobs, cspace = cspace, \
formatstr = 'ro', label = 'Original')
plot_color_data(lab_est[...,1], lab_est[...,2], z = lab_est[...,0], \
show = True, axh = ax, cieobs = cieobs, cspace = cspace, \
formatstr = 'bd', label = 'Rendered')
if out == 'rfl_est':
return rfl_est
elif out == 'rfl_est,xyz_est':
return rfl_est, xyz_est
else:
return eval(out)
def cri_ref(ccts, wl3 = None, ref_type = _CRI_REF_TYPE, mix_range = None,
cieobs = None, norm_type = None, norm_f = None,
force_daylight_below4000K = False, n = None,
daylight_locus = None):
"""
Calculates a reference illuminant spectrum based on cct
for color rendering index calculations .
Args:
:ccts:
| list of int/floats or ndarray with ccts.
:wl3:
| None, optional
| New wavelength range for interpolation.
| Defaults to wavelengths specified by luxpy._WL3.
:ref_type:
| str or list[str], optional
| Specifies the type of reference spectrum to be calculated.
| Defaults to luxpy._CRI_REF_TYPE.
| If :ref_type: is list of strings, then for each cct in :ccts:
| a different reference illuminant can be specified.
| If :ref_type: == 'spd', then :ccts: is assumed to be an ndarray
| of reference illuminant spectra.
:mix_range:
| None or ndarray, optional
| Determines the cct range between which the reference illuminant is
| a weigthed mean of a Planckian and Daylight Phase spectrum.
| Weighthing is done as described in IES TM30:
| SPDreference = (Te-T)/(Te-Tb)*Planckian+(T-Tb)/(Te-Tb)*daylight
| with Tb and Te are resp. the starting and end CCTs of the
| mixing range and whereby the Planckian and Daylight SPDs
| have been normalized for equal luminous flux.
| If None: use the default specified for :ref_type:.
| Can be a ndarray with shape[0] > 1, in which different mixing
| ranges will be used for cct in :ccts:.
:cieobs:
| None, optional
| Required for the normalization of the Planckian and Daylight SPDs
| when calculating a 'mixed' reference illuminant.
| Required when calculating daylightphase (adjust locus parameters to cieobs)
| If None: _CIEOBS will be used.
:norm_type:
| None, optional
| - 'lambda': make lambda in norm_f equal to 1
| - 'area': area-normalization times norm_f
| - 'max': max-normalization times norm_f
| - 'ru': to :norm_f: radiometric units
| - 'pu': to :norm_f: photometric units
| - 'pusa': to :norm_f: photometric units (with Km corrected
| to standard air, cfr. CIE TN003-2015)
| - 'qu': to :norm_f: quantal energy units
:norm_f:
| 1, optional
| Normalization factor that determines the size of normalization
| for 'max' and 'area'
| or which wavelength is normalized to 1 for 'lambda' option.
:force_daylight_below4000K:
| False or True, optional
| Daylight locus approximation is not defined below 4000 K,
| but by setting this to True, the calculation can be forced to
| calculate it anyway.
:n:
| None, optional
| Refractive index (for use in calculation of blackbody radiators).
| If None: use the one stored in _BB['n']
:daylight_locus:
| None, optional
| dict with xD(T) and yD(xD) parameters to calculate daylight locus
| for specified cieobs.
| If None: use pre-calculated values.
| If 'calc': calculate them on the fly.
Returns:
:returns:
| ndarray with reference illuminant spectra.
| (:returns:[0] contains wavelengths)
Note:
Future versions will have the ability to take a dict as input
for ref_type. This way other reference illuminants can be specified
than the ones in _CRI_REF_TYPES.
"""
if ref_type == 'spd':
# ccts already contains spectrum of reference:
return spd(ccts, wl = wl3, norm_type = norm_type, norm_f = norm_f)
else:
if mix_range is not None: mix_range = np2d(mix_range)
if not (isinstance(ref_type,list) | isinstance(ref_type,dict)): ref_type = [ref_type]
for i in range(len(ccts)):
cct = ccts[i]
# get ref_type and mix_range:
if isinstance(ref_type,dict):
raise Exception("cri_ref(): dictionary ref_type: Not yet implemented")
else:
ref_type_ = ref_type[i] if (len(ref_type)>1) else ref_type[0]
if mix_range is None:
mix_range_ = _CRI_REF_TYPES[ref_type_]
else:
mix_range_ = mix_range[i] if (mix_range.shape[0]>1) else mix_range[0] #must be np2d !!!
if (mix_range_[0] == mix_range_[1]) | (ref_type_[0:2] == 'BB') | (ref_type_[0:2] == 'DL'):
if ((cct < mix_range_[0]) & (not (ref_type_[0:2] == 'DL'))) | (ref_type_[0:2] == 'BB'):
Sr = blackbody(cct, wl3, n = n)
elif ((cct >= mix_range_[0]) & (not (ref_type_[0:2] == 'BB'))) | (ref_type_[0:2] == 'DL') :
Sr = daylightphase(cct,wl3,force_daylight_below4000K = force_daylight_below4000K, cieobs = cieobs, daylight_locus = daylight_locus)
else:
SrBB = blackbody(cct, wl3, n = n)
SrDL = daylightphase(cct,wl3,verbosity = None,force_daylight_below4000K = force_daylight_below4000K, cieobs = cieobs, daylight_locus = daylight_locus)
cieobs_ = _CIEOBS if cieobs is None else cieobs
cmf = xyzbar(cieobs = cieobs_, scr = 'dict', wl_new = wl3)
wl = SrBB[0]
ld = getwld(wl)
SrBB = 100.0*SrBB[1]/np.array(np.sum(SrBB[1]*cmf[2]*ld))
SrDL = 100.0*SrDL[1]/np.array(np.sum(SrDL[1]*cmf[2]*ld))
Tb, Te = float(mix_range_[0]), float(mix_range_[1])
cBB, cDL = (Te-cct)/(Te-Tb), (cct-Tb)/(Te-Tb)
if cBB < 0.0:
cBB = 0.0
elif cBB > 1:
cBB = 1.0
if cDL < 0.0:
cDL = 0.0
elif cDL > 1:
cDL = 1.0
Sr = SrBB*cBB + SrDL*cDL
Sr[Sr==float('NaN')] = 0.0
Sr560 = Sr[np.where(np.abs(wl - 560.0) == np.min(np.abs(wl - 560.0)))[0]]
Sr = np.vstack((wl,(Sr/Sr560)))
if i == 0:
Srs = Sr[1]
else:
Srs = np.vstack((Srs,Sr[1]))
Srs = np.vstack((Sr[0],Srs))
return spd(Srs, wl = None, norm_type = norm_type, norm_f = norm_f)