def histogram(a, bins=10, bin_center = False, range=None, normed=False, weights=None, density=None):
"""
Histogram function that can take as bins either
the center (cfr. matlab hist) or bin-edges.
Args:
:bin_center:
| False, optional
| False: if :bins: int, str or sequence of scalars:
| default to numpy.histogram (uses bin edges).
| True: if :bins: is a sequence of scalars:
| bins (containing centers) are transformed to edges
| and nump.histogram is run.
| Mimicks matlab hist (uses bin centers).
Note:
For other armuments and output, see ?numpy.histogram
Returns:
:returns:
| ndarray with histogram
"""
if (isinstance(bins, list) | isinstance(bins, np.ndarray)) & (bin_center == True):
if len(bins) == 1:
edges = np.hstack((bins[0],np.inf))
else:
centers = bins
d = np.diff(centers)/2
edges = np.hstack((centers[0]-d[0], centers[:-1] + d, centers[-1] + d[-1]))
edges[1:] = edges[1:] + np.finfo(float).eps
return np.histogram(a, bins=edges, range=range, normed=normed, weights=weights, density=density)
else:
return np.histogram(a, bins=bins, range=range, normed=normed, weights=weights, density=density)
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)