# -*- coding: utf-8 -*-
"""
Tristimulus Values
==================
Defines objects for tristimulus values computation from spectral data:
- :func:`colour.colorimetry.tristimulus_weighting_factors_ASTME2022`
- :func:`colour.colorimetry.sd_to_XYZ_integration`
- :func:`colour.colorimetry.\
sd_to_XYZ_tristimulus_weighting_factors_ASTME308`
- :func:`colour.colorimetry.sd_to_XYZ_ASTME308`
- :attr:`colour.SD_TO_XYZ_METHODS`
- :func:`colour.sd_to_XYZ`
- :func:`colour.colorimetry.multi_sds_to_XYZ_integration`
- :func:`colour.colorimetry.multi_sds_to_XYZ_ASTME308`
- :attr:`colour.MULTI_SD_TO_XYZ_METHODS`
- :func:`colour.multi_sds_to_XYZ`
- :func:`colour.wavelength_to_XYZ`
The default implementation is based on practise *ASTM E308-15* method.
References
----------
- :cite:`ASTMInternational2011a` : ASTM International. (2011). ASTM E2022-11
- Standard Practice for Calculation of Weighting Factors for Tristimulus
Integration. doi:10.1520/E2022-11
- :cite:`ASTMInternational2015b` : ASTM International. (2015). ASTM E308-15 -
Standard Practice for Computing the Colors of Objects by Using the CIE
System. doi:10.1520/E0308-15
- :cite:`Wyszecki2000bf` : Wyszecki, G., & Stiles, W. S. (2000). Integration
Replaced by Summation. In Color Science: Concepts and Methods, Quantitative
Data and Formulae (pp. 158-163). Wiley. ISBN:978-0471399186
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import lagrange_coefficients
from colour.colorimetry import (DEFAULT_SPECTRAL_SHAPE,
MultiSpectralDistributions, SpectralShape,
STANDARD_OBSERVERS_CMFS, sd_ones)
from colour.constants import DEFAULT_INT_DTYPE
from colour.utilities import (CaseInsensitiveMapping, as_float_array,
filter_kwargs, from_range_100, runtime_warning,
tsplit)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - https://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'ASTME308_PRACTISE_SHAPE', 'lagrange_coefficients_ASTME2022',
'tristimulus_weighting_factors_ASTME2022',
'adjust_tristimulus_weighting_factors_ASTME308', 'sd_to_XYZ_integration',
'sd_to_XYZ_tristimulus_weighting_factors_ASTME308', 'sd_to_XYZ_ASTME308',
'SD_TO_XYZ_METHODS', 'sd_to_XYZ', 'multi_sds_to_XYZ_integration',
'multi_sds_to_XYZ_ASTME308', 'MULTI_SD_TO_XYZ_METHODS', 'multi_sds_to_XYZ',
'wavelength_to_XYZ'
]
ASTME308_PRACTISE_SHAPE = DEFAULT_SPECTRAL_SHAPE
ASTME308_PRACTISE_SHAPE.__doc__ = """
Shape for *ASTM E308-15* practise: (360, 780, 1).
References
----------
:cite:`ASTMInternational2015b`
ASTME308_PRACTISE_SHAPE : SpectralShape
"""
_LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE = None
_TRISTIMULUS_WEIGHTING_FACTORS_CACHE = None
[docs]def lagrange_coefficients_ASTME2022(interval=10, interval_type='inner'):
"""
Computes the *Lagrange Coefficients* for given interval size using practise
*ASTM E2022-11* method.
Parameters
----------
interval : int
Interval size in nm.
interval_type : unicode, optional
**{'inner', 'boundary'}**,
If the interval is an *inner* interval *Lagrange Coefficients* are
computed for degree 4. Degree 3 is used for a *boundary* interval.
Returns
-------
ndarray
*Lagrange Coefficients*.
References
----------
:cite:`ASTMInternational2011a`
Examples
--------
>>> lagrange_coefficients_ASTME2022(10, 'inner')
... # doctest: +ELLIPSIS
array([[-0.028..., 0.940..., 0.104..., -0.016...],
[-0.048..., 0.864..., 0.216..., -0.032...],
[-0.059..., 0.773..., 0.331..., -0.045...],
[-0.064..., 0.672..., 0.448..., -0.056...],
[-0.062..., 0.562..., 0.562..., -0.062...],
[-0.056..., 0.448..., 0.672..., -0.064...],
[-0.045..., 0.331..., 0.773..., -0.059...],
[-0.032..., 0.216..., 0.864..., -0.048...],
[-0.016..., 0.104..., 0.940..., -0.028...]])
>>> lagrange_coefficients_ASTME2022(10, 'boundary')
... # doctest: +ELLIPSIS
array([[ 0.85..., 0.19..., -0.04...],
[ 0.72..., 0.36..., -0.08...],
[ 0.59..., 0.51..., -0.10...],
[ 0.48..., 0.64..., -0.12...],
[ 0.37..., 0.75..., -0.12...],
[ 0.28..., 0.84..., -0.12...],
[ 0.19..., 0.91..., -0.10...],
[ 0.12..., 0.96..., -0.08...],
[ 0.05..., 0.99..., -0.04...]])
"""
global _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE
if _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE is None:
_LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE = CaseInsensitiveMapping()
name_lica = ', '.join((str(interval), interval_type))
if name_lica in _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE:
return _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE[name_lica]
r_n = np.linspace(1 / interval, 1 - (1 / interval), interval - 1)
d = 3
if interval_type.lower() == 'inner':
r_n += 1
d = 4
lica = _LAGRANGE_INTERPOLATING_COEFFICIENTS_CACHE[name_lica] = (
as_float_array([lagrange_coefficients(r, d) for r in r_n]))
return lica
[docs]def tristimulus_weighting_factors_ASTME2022(cmfs, illuminant, shape, k=None):
"""
Returns a table of tristimulus weighting factors for given colour matching
functions and illuminant using practise *ASTM E2022-11* method.
The computed table of tristimulus weighting factors should be used with
spectral data that has been corrected for spectral bandpass dependence.
Parameters
----------
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution
Illuminant spectral distribution.
shape : SpectralShape
Shape used to build the table, only the interval is needed.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
Returns
-------
ndarray
Tristimulus weighting factors table.
Raises
------
ValueError
If the colour matching functions or illuminant intervals are not equal
to 1 nm.
Warning
-------
- The tables of tristimulus weighting factors are cached in
:attr:`colour.colorimetry.tristimulus.\
_TRISTIMULUS_WEIGHTING_FACTORS_CACHE` attribute. Their identifier key is
defined by the colour matching functions and illuminant names along
with the current shape and normalisation constant :math:`k` such as:
`CIE 1964 10 Degree Standard Observer, A, (360.0, 830.0, 10.0), None`
Considering the above, one should be mindful that using similar colour
matching functions and illuminant names but with different spectral
data will lead to unexpected behaviour.
Notes
-----
- Input colour matching functions and illuminant intervals are expected
to be equal to 1 nm. If the illuminant data is not available at 1 nm
interval, it needs to be interpolated using *CIE* recommendations:
The method developed by *Sprague (1880)* should be used for
interpolating functions having a uniformly spaced independent variable
and a *Cubic Spline* method for non-uniformly spaced independent
variable.
References
----------
:cite:`ASTMInternational2011a`
Examples
--------
>>> from colour import (CMFS, sd_CIE_standard_illuminant_A,
... SpectralDistribution, SpectralShape)
>>> from colour.utilities import numpy_print_options
>>> cmfs = CMFS['CIE 1964 10 Degree Standard Observer']
>>> A = sd_CIE_standard_illuminant_A(cmfs.shape)
>>> with numpy_print_options(suppress=True):
... tristimulus_weighting_factors_ASTME2022(
... cmfs, A, SpectralShape(360, 830, 20))
... # doctest: +ELLIPSIS
array([[ -0.0002981..., -0.0000317..., -0.0013301...],
[ -0.0087155..., -0.0008915..., -0.0407436...],
[ 0.0599679..., 0.0050203..., 0.2565018...],
[ 0.7734225..., 0.0779839..., 3.6965732...],
[ 1.9000905..., 0.3037005..., 9.7554195...],
[ 1.9707727..., 0.8552809..., 11.4867325...],
[ 0.7183623..., 2.1457000..., 6.7845806...],
[ 0.0426667..., 4.8985328..., 2.3208000...],
[ 1.5223302..., 9.6471138..., 0.7430671...],
[ 5.6770329..., 14.4609708..., 0.1958194...],
[ 12.4451744..., 17.4742541..., 0.0051827...],
[ 20.5535772..., 17.5838219..., -0.0026512...],
[ 25.3315384..., 14.8957035..., 0. ...],
[ 21.5711570..., 10.0796619..., 0. ...],
[ 12.1785817..., 5.0680655..., 0. ...],
[ 4.6675746..., 1.8303239..., 0. ...],
[ 1.3236117..., 0.5129694..., 0. ...],
[ 0.3175325..., 0.1230084..., 0. ...],
[ 0.0746341..., 0.0290243..., 0. ...],
[ 0.0182990..., 0.0071606..., 0. ...],
[ 0.0047942..., 0.0018888..., 0. ...],
[ 0.0013293..., 0.0005277..., 0. ...],
[ 0.0004254..., 0.0001704..., 0. ...],
[ 0.0000962..., 0.0000389..., 0. ...]])
"""
if cmfs.shape.interval != 1:
raise ValueError('"{0}" shape "interval" must be 1!'.format(cmfs))
if illuminant.shape.interval != 1:
raise ValueError(
'"{0}" shape "interval" must be 1!'.format(illuminant))
global _TRISTIMULUS_WEIGHTING_FACTORS_CACHE
if _TRISTIMULUS_WEIGHTING_FACTORS_CACHE is None:
_TRISTIMULUS_WEIGHTING_FACTORS_CACHE = CaseInsensitiveMapping()
name_twf = ', '.join((cmfs.name, illuminant.name, str(shape), str(k)))
if name_twf in _TRISTIMULUS_WEIGHTING_FACTORS_CACHE:
return _TRISTIMULUS_WEIGHTING_FACTORS_CACHE[name_twf]
Y = cmfs.values
S = illuminant.values
interval_i = DEFAULT_INT_DTYPE(shape.interval)
W = S[::interval_i, np.newaxis] * Y[::interval_i, :]
# First and last measurement intervals *Lagrange Coefficients*.
c_c = lagrange_coefficients_ASTME2022(interval_i, 'boundary')
# Intermediate measurement intervals *Lagrange Coefficients*.
c_b = lagrange_coefficients_ASTME2022(interval_i, 'inner')
# Total wavelengths count.
w_c = len(Y)
# Measurement interval interpolated values count.
r_c = c_b.shape[0]
# Last interval first interpolated wavelength.
w_lif = w_c - (w_c - 1) % interval_i - 1 - r_c
# Intervals count.
i_c = W.shape[0]
i_cm = i_c - 1
# "k" is used as index in the nested loop.
k_n = k
for i in range(3):
# First interval.
for j in range(r_c):
for k in range(3):
W[k, i] = W[k, i] + c_c[j, k] * S[j + 1] * Y[j + 1, i]
# Last interval.
for j in range(r_c):
for k in range(i_cm, i_cm - 3, -1):
W[k, i] = (W[k, i] + c_c[r_c - j - 1, i_cm - k] * S[j + w_lif]
* Y[j + w_lif, i])
# Intermediate intervals.
for j in range(i_c - 3):
for k in range(r_c):
w_i = (r_c + 1) * (j + 1) + 1 + k
W[j, i] = W[j, i] + c_b[k, 0] * S[w_i] * Y[w_i, i]
W[j + 1, i] = W[j + 1, i] + c_b[k, 1] * S[w_i] * Y[w_i, i]
W[j + 2, i] = W[j + 2, i] + c_b[k, 2] * S[w_i] * Y[w_i, i]
W[j + 3, i] = W[j + 3, i] + c_b[k, 3] * S[w_i] * Y[w_i, i]
# Extrapolation of potential incomplete interval.
for j in range(
DEFAULT_INT_DTYPE(w_c - ((w_c - 1) % interval_i)), w_c, 1):
W[i_cm, i] = W[i_cm, i] + S[j] * Y[j, i]
W *= 100 / np.sum(W, axis=0)[1] if k_n is None else k_n
_TRISTIMULUS_WEIGHTING_FACTORS_CACHE[name_twf] = W
return W
[docs]def adjust_tristimulus_weighting_factors_ASTME308(W, shape_r, shape_t):
"""
Adjusts given table of tristimulus weighting factors to account for a
shorter wavelengths range of the test spectral shape compared to the
reference spectral shape using practise *ASTM E308-15* method:
Weights at the wavelengths for which data are not available are added to
the weights at the shortest and longest wavelength for which spectral data
are available.
Parameters
----------
W : array_like
Tristimulus weighting factors table.
shape_r : SpectralShape
Reference spectral shape.
shape_t : SpectralShape
Test spectral shape.
Returns
-------
ndarray
Adjusted tristimulus weighting factors.
References
----------
:cite:`ASTMInternational2015b`
Examples
--------
>>> from colour import (CMFS, sd_CIE_standard_illuminant_A,
... SpectralDistribution, SpectralShape)
>>> from colour.utilities import numpy_print_options
>>> cmfs = CMFS['CIE 1964 10 Degree Standard Observer']
>>> A = sd_CIE_standard_illuminant_A(cmfs.shape)
>>> W = tristimulus_weighting_factors_ASTME2022(
... cmfs, A, SpectralShape(360, 830, 20))
>>> with numpy_print_options(suppress=True):
... adjust_tristimulus_weighting_factors_ASTME308(
... W, SpectralShape(360, 830, 20), SpectralShape(400, 700, 20))
... # doctest: +ELLIPSIS
array([[ 0.0509543..., 0.0040971..., 0.2144280...],
[ 0.7734225..., 0.0779839..., 3.6965732...],
[ 1.9000905..., 0.3037005..., 9.7554195...],
[ 1.9707727..., 0.8552809..., 11.4867325...],
[ 0.7183623..., 2.1457000..., 6.7845806...],
[ 0.0426667..., 4.8985328..., 2.3208000...],
[ 1.5223302..., 9.6471138..., 0.7430671...],
[ 5.6770329..., 14.4609708..., 0.1958194...],
[ 12.4451744..., 17.4742541..., 0.0051827...],
[ 20.5535772..., 17.5838219..., -0.0026512...],
[ 25.3315384..., 14.8957035..., 0. ...],
[ 21.5711570..., 10.0796619..., 0. ...],
[ 12.1785817..., 5.0680655..., 0. ...],
[ 4.6675746..., 1.8303239..., 0. ...],
[ 1.3236117..., 0.5129694..., 0. ...],
[ 0.4171109..., 0.1618194..., 0. ...]])
"""
W = np.copy(W)
start_index = DEFAULT_INT_DTYPE(
(shape_t.start - shape_r.start) / shape_r.interval)
for i in range(start_index):
W[start_index] += W[i]
end_index = DEFAULT_INT_DTYPE(
(shape_r.end - shape_t.end) / shape_r.interval)
for i in range(end_index):
W[-end_index - 1] += W[-i - 1]
return W[start_index:-end_index or None, ...]
[docs]def sd_to_XYZ_integration(
sd,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(DEFAULT_SPECTRAL_SHAPE),
illuminant=sd_ones(),
k=None):
"""
Converts given spectral distribution to *CIE XYZ* tristimulus values
using given colour matching functions and illuminant according to classical
integration method.
Parameters
----------
sd : SpectralDistribution
Spectral distribution.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
Returns
-------
ndarray, (3,)
*CIE XYZ* tristimulus values.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`Wyszecki2000bf`
Examples
--------
>>> from colour import (
... CMFS, ILLUMINANTS_SDS, SpectralDistribution)
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> data = {
... 400: 0.0641,
... 420: 0.0645,
... 440: 0.0562,
... 460: 0.0537,
... 480: 0.0559,
... 500: 0.0651,
... 520: 0.0705,
... 540: 0.0772,
... 560: 0.0870,
... 580: 0.1128,
... 600: 0.1360,
... 620: 0.1511,
... 640: 0.1688,
... 660: 0.1996,
... 680: 0.2397,
... 700: 0.2852
... }
>>> sd = SpectralDistribution(data)
>>> illuminant = ILLUMINANTS_SDS['D65']
>>> sd_to_XYZ_integration(sd, cmfs, illuminant)
... # doctest: +ELLIPSIS
array([ 10.8401846..., 9.6837311..., 6.2120912...])
"""
if illuminant.shape != cmfs.shape:
runtime_warning(
'Aligning "{0}" illuminant shape to "{1}" colour matching '
'functions shape.'.format(illuminant.name, cmfs.name))
illuminant = illuminant.copy().align(cmfs.shape)
if sd.shape != cmfs.shape:
runtime_warning('Aligning "{0}" spectral distribution shape to "{1}" '
'colour matching functions shape.'.format(
sd.name, cmfs.name))
sd = sd.copy().align(cmfs.shape)
S = illuminant.values
x_bar, y_bar, z_bar = tsplit(cmfs.values)
R = sd.values
dw = cmfs.shape.interval
k = 100 / (np.sum(y_bar * S) * dw) if k is None else k
X_p = R * x_bar * S * dw
Y_p = R * y_bar * S * dw
Z_p = R * z_bar * S * dw
XYZ = k * np.sum(np.array([X_p, Y_p, Z_p]), axis=-1)
return from_range_100(XYZ)
[docs]def sd_to_XYZ_tristimulus_weighting_factors_ASTME308(
sd,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(ASTME308_PRACTISE_SHAPE),
illuminant=sd_ones(ASTME308_PRACTISE_SHAPE),
k=None):
"""
Converts given spectral distribution to *CIE XYZ* tristimulus values
using given colour matching functions and illuminant using a table of
tristimulus weighting factors according to practise *ASTM E308-15* method.
Parameters
----------
sd : SpectralDistribution
Spectral distribution.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
Returns
-------
ndarray, (3,)
*CIE XYZ* tristimulus values.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`ASTMInternational2015b`
Examples
--------
>>> from colour import (
... CMFS, ILLUMINANTS_SDS, SpectralDistribution)
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> data = {
... 400: 0.0641,
... 420: 0.0645,
... 440: 0.0562,
... 460: 0.0537,
... 480: 0.0559,
... 500: 0.0651,
... 520: 0.0705,
... 540: 0.0772,
... 560: 0.0870,
... 580: 0.1128,
... 600: 0.1360,
... 620: 0.1511,
... 640: 0.1688,
... 660: 0.1996,
... 680: 0.2397,
... 700: 0.2852
... }
>>> sd = SpectralDistribution(data)
>>> illuminant = ILLUMINANTS_SDS['D65']
>>> sd_to_XYZ_tristimulus_weighting_factors_ASTME308(
... sd, cmfs, illuminant) # doctest: +ELLIPSIS
array([ 10.8402899..., 9.6843539..., 6.2160858...])
"""
if illuminant.shape != cmfs.shape:
runtime_warning(
'Aligning "{0}" illuminant shape to "{1}" colour matching '
'functions shape.'.format(illuminant.name, cmfs.name))
illuminant = illuminant.copy().align(cmfs.shape)
if sd.shape.boundaries != cmfs.shape.boundaries:
runtime_warning('Trimming "{0}" spectral distribution shape to "{1}" '
'colour matching functions shape.'.format(
illuminant.name, cmfs.name))
sd = sd.copy().trim(cmfs.shape)
W = tristimulus_weighting_factors_ASTME2022(
cmfs, illuminant,
SpectralShape(cmfs.shape.start, cmfs.shape.end, sd.shape.interval), k)
start_w = cmfs.shape.start
end_w = cmfs.shape.start + sd.shape.interval * (W.shape[0] - 1)
W = adjust_tristimulus_weighting_factors_ASTME308(
W, SpectralShape(start_w, end_w, sd.shape.interval), sd.shape)
R = sd.values
XYZ = np.sum(W * R[..., np.newaxis], axis=0)
return from_range_100(XYZ)
[docs]def sd_to_XYZ_ASTME308(
sd,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(ASTME308_PRACTISE_SHAPE),
illuminant=sd_ones(ASTME308_PRACTISE_SHAPE),
use_practice_range=True,
mi_5nm_omission_method=True,
mi_20nm_interpolation_method=True,
k=None):
"""
Converts given spectral distribution to *CIE XYZ* tristimulus values using
given colour matching functions and illuminant according to practise
*ASTM E308-15* method.
Parameters
----------
sd : SpectralDistribution
Spectral distribution.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
use_practice_range : bool, optional
Practise *ASTM E308-15* working wavelengths range is [360, 780],
if *True* this argument will trim the colour matching functions
appropriately.
mi_5nm_omission_method : bool, optional
5 nm measurement intervals spectral distribution conversion to
tristimulus values will use a 5 nm version of the colour matching
functions instead of a table of tristimulus weighting factors.
mi_20nm_interpolation_method : bool, optional
20 nm measurement intervals spectral distribution conversion to
tristimulus values will use a dedicated interpolation method instead
of a table of tristimulus weighting factors.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
Returns
-------
ndarray, (3,)
*CIE XYZ* tristimulus values.
Warning
-------
- The tables of tristimulus weighting factors are cached in
:attr:`colour.colorimetry.tristimulus.\
_TRISTIMULUS_WEIGHTING_FACTORS_CACHE` attribute. Their identifier key is
defined by the colour matching functions and illuminant names along
with the current shape and normalisation constant :math:`k` such as:
`CIE 1964 10 Degree Standard Observer, A, (360.0, 830.0, 10.0), None`
Considering the above, one should be mindful that using similar colour
matching functions and illuminant names but with different spectral
data will lead to unexpected behaviour.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`ASTMInternational2015b`
Examples
--------
>>> from colour import (
... CMFS, ILLUMINANTS_SDS, SpectralDistribution)
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> data = {
... 400: 0.0641,
... 420: 0.0645,
... 440: 0.0562,
... 460: 0.0537,
... 480: 0.0559,
... 500: 0.0651,
... 520: 0.0705,
... 540: 0.0772,
... 560: 0.0870,
... 580: 0.1128,
... 600: 0.1360,
... 620: 0.1511,
... 640: 0.1688,
... 660: 0.1996,
... 680: 0.2397,
... 700: 0.2852
... }
>>> sd = SpectralDistribution(data)
>>> illuminant = ILLUMINANTS_SDS['D65']
>>> sd_to_XYZ_ASTME308(sd, cmfs, illuminant)
... # doctest: +ELLIPSIS
array([ 10.8399031..., 9.6840375..., 6.2164159...])
"""
if sd.shape.interval not in (1, 5, 10, 20):
raise ValueError(
'Tristimulus values conversion from spectral data according to '
'practise "ASTM E308-15" should be performed on spectral data '
'with measurement interval of 1, 5, 10 or 20nm!')
if use_practice_range:
cmfs = cmfs.copy().trim(ASTME308_PRACTISE_SHAPE)
method = sd_to_XYZ_tristimulus_weighting_factors_ASTME308
if sd.shape.interval == 1:
method = sd_to_XYZ_integration
elif sd.shape.interval == 5 and mi_5nm_omission_method:
if cmfs.shape.interval != 5:
cmfs = cmfs.copy().interpolate(SpectralShape(interval=5))
method = sd_to_XYZ_integration
elif sd.shape.interval == 20 and mi_20nm_interpolation_method:
sd = sd.copy()
if sd.shape.boundaries != cmfs.shape.boundaries:
runtime_warning(
'Trimming "{0}" spectral distribution shape to "{1}" '
'colour matching functions shape.'.format(
illuminant.name, cmfs.name))
sd.trim(cmfs.shape)
# Extrapolation of additional 20nm padding intervals.
sd.align(SpectralShape(sd.shape.start - 20, sd.shape.end + 20, 10))
for i in range(2):
sd[sd.wavelengths[i]] = (
3 * sd.values[i + 2] -
3 * sd.values[i + 4] + sd.values[i + 6]) # yapf: disable
i_e = len(sd.domain) - 1 - i
sd[sd.wavelengths[i_e]] = (
sd.values[i_e - 6] - 3 * sd.values[i_e - 4] +
3 * sd.values[i_e - 2])
# Interpolating every odd numbered values.
# TODO: Investigate code vectorisation.
for i in range(3, len(sd.domain) - 3, 2):
sd[sd.wavelengths[i]] = (
-0.0625 * sd.values[i - 3] + 0.5625 * sd.values[i - 1] +
0.5625 * sd.values[i + 1] - 0.0625 * sd.values[i + 3])
# Discarding the additional 20nm padding intervals.
sd.trim(SpectralShape(sd.shape.start + 20, sd.shape.end - 20, 10))
XYZ = method(sd, cmfs, illuminant, k=k)
return XYZ
SD_TO_XYZ_METHODS = CaseInsensitiveMapping({
'ASTM E308': sd_to_XYZ_ASTME308,
'Integration': sd_to_XYZ_integration
})
SD_TO_XYZ_METHODS.__doc__ = """
Supported spectral distribution to *CIE XYZ* tristimulus values conversion
methods.
References
----------
:cite:`ASTMInternational2011a`, :cite:`ASTMInternational2015b`,
:cite:`Wyszecki2000bf`
SD_TO_XYZ_METHODS : CaseInsensitiveMapping
**{'ASTM E308', 'Integration'}**
Aliases:
- 'astm2015': 'ASTM E308'
"""
SD_TO_XYZ_METHODS['astm2015'] = SD_TO_XYZ_METHODS['ASTM E308']
[docs]def sd_to_XYZ(
sd,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(DEFAULT_SPECTRAL_SHAPE),
illuminant=sd_ones(),
k=None,
method='ASTM E308',
**kwargs):
"""
Converts given spectral distribution to *CIE XYZ* tristimulus values using
given colour matching functions, illuminant and method.
Parameters
----------
sd : SpectralDistribution
Spectral distribution.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
method : unicode, optional
**{'ASTM E308', 'Integration'}**,
Computation method.
Other Parameters
----------------
mi_5nm_omission_method : bool, optional
{:func:`colour.colorimetry.sd_to_XYZ_ASTME308`},
5 nm measurement intervals spectral distribution conversion to
tristimulus values will use a 5 nm version of the colour matching
functions instead of a table of tristimulus weighting factors.
mi_20nm_interpolation_method : bool, optional
{:func:`colour.colorimetry.sd_to_XYZ_ASTME308`},
20 nm measurement intervals spectral distribution conversion to
tristimulus values will use a dedicated interpolation method instead
of a table of tristimulus weighting factors.
use_practice_range : bool, optional
{:func:`colour.colorimetry.sd_to_XYZ_ASTME308`},
Practise *ASTM E308-15* working wavelengths range is [360, 780],
if *True* this argument will trim the colour matching functions
appropriately.
Returns
-------
ndarray, (3,)
*CIE XYZ* tristimulus values.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
References
----------
:cite:`ASTMInternational2011a`, :cite:`ASTMInternational2015b`,
:cite:`Wyszecki2000bf`
Examples
--------
>>> from colour import (
... CMFS, ILLUMINANTS_SDS, SpectralDistribution)
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> data = {
... 400: 0.0641,
... 420: 0.0645,
... 440: 0.0562,
... 460: 0.0537,
... 480: 0.0559,
... 500: 0.0651,
... 520: 0.0705,
... 540: 0.0772,
... 560: 0.0870,
... 580: 0.1128,
... 600: 0.1360,
... 620: 0.1511,
... 640: 0.1688,
... 660: 0.1996,
... 680: 0.2397,
... 700: 0.2852
... }
>>> sd = SpectralDistribution(data)
>>> illuminant = ILLUMINANTS_SDS['D65']
>>> sd_to_XYZ(sd, cmfs, illuminant)
... # doctest: +ELLIPSIS
array([ 10.8399031..., 9.6840375..., 6.2164159...])
>>> sd_to_XYZ(sd, cmfs, illuminant, use_practice_range=False)
... # doctest: +ELLIPSIS
array([ 10.8399852..., 9.6840602..., 6.2164085...])
>>> sd_to_XYZ(sd, cmfs, illuminant, method='Integration')
... # doctest: +ELLIPSIS
array([ 10.8401846..., 9.6837311..., 6.2120912...])
"""
function = SD_TO_XYZ_METHODS[method]
return function(
sd, cmfs, illuminant, k=k, **filter_kwargs(function, **kwargs))
[docs]def multi_sds_to_XYZ_integration(
msds,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(DEFAULT_SPECTRAL_SHAPE),
illuminant=sd_ones(),
k=None,
shape=DEFAULT_SPECTRAL_SHAPE):
"""
Converts given multi-spectral distributions to *CIE XYZ* tristimulus values
using given colour matching functions and illuminant. The multi-spectral
distribution can be either a :class:`colour.MultiSpectralDistributions`
class instance or an *array_like* in which case the ``shape`` must be
passed.
Parameters
----------
msds : MultiSpectralDistributions or array_like
Multi-spectral distributions, if an *array_like* the wavelengths are
expected to be in the last axis, e.g. for a 512x384 multi-spectral
image with 77 bins, ``msds`` shape should be (384, 512, 77).
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
shape : SpectralShape, optional
Spectral shape of the multi-spectral distributions, ``cmfs`` and
``illuminant`` will be aligned to it.
Returns
-------
array_like
*CIE XYZ* tristimulus values, for a 512x384 multi-spectral image with
77 bins, the output shape will be (384, 512, 3).
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
- The code path using the *array_like* multi-spectral distributions
produces results different to the code path using a
:class:`colour.MultiSpectralDistributions` class instance: the former
favours execution speed by aligning the colour matching functions and
illuminant to the given spectral shape while the latter favours
precision by aligning the multi-spectral distributions to the colour
matching functions.
References
----------
:cite:`Wyszecki2000bf`
Examples
--------
>>> from colour import ILLUMINANTS_SDS
>>> shape = SpectralShape(400, 700, 60)
>>> D65 = ILLUMINANTS_SDS['D65']
>>> data = np.array([
... [0.0137, 0.0159, 0.0096, 0.0111, 0.0179, 0.1057, 0.0433,
... 0.0258, 0.0248, 0.0186, 0.0310, 0.0473],
... [0.0913, 0.3145, 0.2582, 0.0709, 0.2971, 0.4620, 0.2683,
... 0.0831, 0.1203, 0.1292, 0.1682, 0.3221],
... [0.0152, 0.0842, 0.4139, 0.0220, 0.5630, 0.1918, 0.2373,
... 0.0430, 0.0054, 0.0079, 0.3719, 0.2268],
... [0.0281, 0.0907, 0.2228, 0.1249, 0.2375, 0.5625, 0.0518,
... 0.3230, 0.0065, 0.4006, 0.0861, 0.3161],
... [0.1918, 0.7103, 0.0041, 0.1817, 0.0024, 0.4209, 0.0118,
... 0.2302, 0.1860, 0.9404, 0.0041, 0.1124],
... [0.0430, 0.0437, 0.3744, 0.0020, 0.5819, 0.0027, 0.0823,
... 0.0081, 0.3625, 0.3213, 0.7849, 0.0024],
... ])
>>> msds = MultiSpectralDistributions(data, shape.range())
>>> multi_sds_to_XYZ_integration(msds, illuminant=D65, shape=shape)
... # doctest: +ELLIPSIS
array([[ 7.5031039..., 3.9486887..., 8.4053425...],
[ 26.9265732..., 15.0721676..., 28.7125195...],
[ 16.7039284..., 28.2175962..., 25.6515081...],
[ 11.5765075..., 8.6399161..., 6.5783111...],
[ 18.7324243..., 35.0755847..., 30.1525320...],
[ 45.1654991..., 39.6132308..., 43.6877410...],
[ 8.1765955..., 13.0937369..., 25.9477816...],
[ 22.4668631..., 19.3095206..., 7.9654068...],
[ 6.5782666..., 2.5254216..., 11.0954901...],
[ 43.9134487..., 27.9794809..., 11.731893 ...],
[ 8.5371481..., 19.7034075..., 17.7088101...],
[ 23.9092001..., 26.2129391..., 30.6831630...]])
>>> msds = np.array([
... [
... [0.0137, 0.0913, 0.0152, 0.0281, 0.1918, 0.0430],
... [0.0159, 0.3145, 0.0842, 0.0907, 0.7103, 0.0437],
... [0.0096, 0.2582, 0.4139, 0.2228, 0.0041, 0.3744],
... [0.0111, 0.0709, 0.0220, 0.1249, 0.1817, 0.0020],
... [0.0179, 0.2971, 0.5630, 0.2375, 0.0024, 0.5819],
... [0.1057, 0.4620, 0.1918, 0.5625, 0.4209, 0.0027],
... ],
... [
... [0.0433, 0.2683, 0.2373, 0.0518, 0.0118, 0.0823],
... [0.0258, 0.0831, 0.0430, 0.3230, 0.2302, 0.0081],
... [0.0248, 0.1203, 0.0054, 0.0065, 0.1860, 0.3625],
... [0.0186, 0.1292, 0.0079, 0.4006, 0.9404, 0.3213],
... [0.0310, 0.1682, 0.3719, 0.0861, 0.0041, 0.7849],
... [0.0473, 0.3221, 0.2268, 0.3161, 0.1124, 0.0024],
... ],
... ])
>>> multi_sds_to_XYZ_integration(msds, illuminant=D65, shape=shape)
... # doctest: +ELLIPSIS
array([[[ 7.1958378..., 3.8605390..., 10.1016398...],
[ 25.5738615..., 14.7200581..., 34.8440007...],
[ 17.5854414..., 28.5668344..., 30.1806687...],
[ 11.3271912..., 8.4598177..., 7.9015758...],
[ 19.6581831..., 35.5918480..., 35.1430220...],
[ 45.8212491..., 39.2600939..., 51.7907710...]],
<BLANKLINE>
[[ 8.8287837..., 13.3870357..., 30.5702050...],
[ 22.3324362..., 18.9560919..., 9.3952305...],
[ 6.6887212..., 2.5728891..., 13.2618778...],
[ 41.8166227..., 27.1191979..., 14.2627944...],
[ 9.2414098..., 20.2056200..., 20.1992502...],
[ 24.7830551..., 26.2221584..., 36.4430633...]]])
"""
if isinstance(msds, MultiSpectralDistributions):
return as_float_array([
sd_to_XYZ_integration(sd, cmfs, illuminant, k)
for sd in msds.to_sds()
])
else:
msds = as_float_array(msds)
msd_shape_m_1, shape_wl_count = msds.shape[-1], len(shape.range())
assert msd_shape_m_1 == shape_wl_count, (
'Multi-spectral distributions array with {0} wavelengths '
'is not compatible with spectral shape with {1} wavelengths!'.
format(msd_shape_m_1, shape_wl_count))
if cmfs.shape != shape:
runtime_warning('Aligning "{0}" cmfs shape to "{1}".'.format(
cmfs.name, shape))
cmfs = cmfs.copy().align(shape)
if illuminant.shape != shape:
runtime_warning('Aligning "{0}" illuminant shape to "{1}".'.format(
illuminant.name, shape))
illuminant = illuminant.copy().align(shape)
S = illuminant.values
x_bar, y_bar, z_bar = tsplit(cmfs.values)
dw = cmfs.shape.interval
k = 100 / (np.sum(y_bar * S) * dw) if k is None else k
X_p = msds * x_bar * S * dw
Y_p = msds * y_bar * S * dw
Z_p = msds * z_bar * S * dw
XYZ = k * np.sum(np.array([X_p, Y_p, Z_p]), axis=-1)
return from_range_100(np.rollaxis(XYZ, 0, msds.ndim))
[docs]def multi_sds_to_XYZ_ASTME308(
msds,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(ASTME308_PRACTISE_SHAPE),
illuminant=sd_ones(ASTME308_PRACTISE_SHAPE),
use_practice_range=True,
mi_5nm_omission_method=True,
mi_20nm_interpolation_method=True,
k=None):
"""
Converts given multi-spectral distributions to *CIE XYZ* tristimulus values
using given colour matching functions and illuminant according to practise
*ASTM E308-15* method.
Parameters
----------
msds : MultiSpectralDistributions or array_like
Multi-spectral distributions.
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
use_practice_range : bool, optional
Practise *ASTM E308-15* working wavelengths range is [360, 780],
if *True* this argument will trim the colour matching functions
appropriately.
mi_5nm_omission_method : bool, optional
5 nm measurement intervals multi-spectral distributions conversion to
tristimulus values will use a 5 nm version of the colour matching
functions instead of a table of tristimulus weighting factors.
mi_20nm_interpolation_method : bool, optional
20 nm measurement intervals multi-spectral distributions conversion to
tristimulus values will use a dedicated interpolation method instead
of a table of tristimulus weighting factors.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
shape : SpectralShape, optional
Spectral shape of the multi-spectral distributions, ``cmfs`` and
``illuminant`` will be aligned to it.
Returns
-------
array_like
*CIE XYZ* tristimulus values.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
- The code path using the *array_like* multi-spectral distributions
produces results different to the code path using a
:class:`colour.MultiSpectralDistributions` class instance: the former
favours execution speed by aligning the colour matching functions and
illuminant to the given spectral shape while the latter favours
precision by aligning the multi-spectral distributions to the colour
matching functions.
References
----------
:cite:`Wyszecki2000bf`
Examples
--------
>>> from colour import ILLUMINANTS_SDS
>>> shape = SpectralShape(400, 700, 60)
>>> D65 = ILLUMINANTS_SDS['D65']
>>> data = np.array([
... [0.0137, 0.0159, 0.0096, 0.0111, 0.0179, 0.1057, 0.0433,
... 0.0258, 0.0248, 0.0186, 0.0310, 0.0473],
... [0.0913, 0.3145, 0.2582, 0.0709, 0.2971, 0.4620, 0.2683,
... 0.0831, 0.1203, 0.1292, 0.1682, 0.3221],
... [0.0152, 0.0842, 0.4139, 0.0220, 0.5630, 0.1918, 0.2373,
... 0.0430, 0.0054, 0.0079, 0.3719, 0.2268],
... [0.0281, 0.0907, 0.2228, 0.1249, 0.2375, 0.5625, 0.0518,
... 0.3230, 0.0065, 0.4006, 0.0861, 0.3161],
... [0.1918, 0.7103, 0.0041, 0.1817, 0.0024, 0.4209, 0.0118,
... 0.2302, 0.1860, 0.9404, 0.0041, 0.1124],
... [0.0430, 0.0437, 0.3744, 0.0020, 0.5819, 0.0027, 0.0823,
... 0.0081, 0.3625, 0.3213, 0.7849, 0.0024],
... ])
>>> msds = MultiSpectralDistributions(data, shape.range())
>>> msds = msds.align(SpectralShape(400, 700, 20))
>>> multi_sds_to_XYZ_ASTME308(msds, illuminant=D65)
... # doctest: +ELLIPSIS
array([[ 7.5054003..., 3.9556401..., 8.3911571...],
[ 26.9413788..., 15.0983954..., 28.6698509...],
[ 16.7055672..., 28.2093633..., 25.6615580...],
[ 11.570967 ..., 8.6443158..., 6.5602307...],
[ 18.7440223..., 35.0632090..., 30.1846483...],
[ 45.1222564..., 39.6234504..., 43.5905694...],
[ 8.1797385..., 13.0953249..., 25.9383064...],
[ 22.4455034..., 19.311139 ..., 7.9320266...],
[ 6.5766847..., 2.5305175..., 11.0749224...],
[ 43.9100652..., 27.9994198..., 11.6878495...],
[ 8.5504477..., 19.6918148..., 17.7437346...],
[ 23.8870261..., 26.2147602..., 30.6365272...]])
"""
if isinstance(msds, MultiSpectralDistributions):
return as_float_array([
sd_to_XYZ_ASTME308(sd, cmfs, illuminant, use_practice_range,
mi_5nm_omission_method,
mi_20nm_interpolation_method, k)
for sd in msds.to_sds()
])
else:
raise ValueError('"ASTM E308-15" method does not support "array_like" '
'multi-spectral distributions!')
MULTI_SD_TO_XYZ_METHODS = CaseInsensitiveMapping({
'ASTM E308': multi_sds_to_XYZ_ASTME308,
'Integration': multi_sds_to_XYZ_integration
})
MULTI_SD_TO_XYZ_METHODS.__doc__ = """
Supported multi-spectral array to *CIE XYZ* tristimulus values conversion
methods.
References
----------
:cite:`ASTMInternational2011a`, :cite:`ASTMInternational2015b`,
:cite:`Wyszecki2000bf`
MULTI_SD_TO_XYZ_METHODS : CaseInsensitiveMapping
**{'ASTM E308', 'Integration'}**
Aliases:
- 'astm2015': 'ASTM E308'
"""
MULTI_SD_TO_XYZ_METHODS['astm2015'] = MULTI_SD_TO_XYZ_METHODS['ASTM E308']
[docs]def multi_sds_to_XYZ(
msds,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
.copy().trim(DEFAULT_SPECTRAL_SHAPE),
illuminant=sd_ones(),
k=None,
method='ASTM E308',
**kwargs):
"""
Converts given multi-spectral distributions to *CIE XYZ* tristimulus values
using given colour matching functions and illuminant. For the *Integration*
method, the multi-spectral distributions can be either a
:class:`colour.MultiSpectralDistributions` class instance or an
*array_like* in which case the ``shape`` must be passed.
Parameters
----------
msds : MultiSpectralDistributions or array_like
Multi-spectral distributions, if an *array_like* the wavelengths are
expected to be in the last axis, e.g. for a 512x384 multi-spectral
image with 77 bins, ``msds`` shape should be (384, 512, 77).
cmfs : XYZ_ColourMatchingFunctions
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
k : numeric, optional
Normalisation constant :math:`k`. For reflecting or transmitting object
colours, :math:`k` is chosen so that :math:`Y = 100` for objects for
which the spectral reflectance factor :math:`R(\\lambda)` of the object
colour or the spectral transmittance factor :math:`\\tau(\\lambda)` of
the object is equal to unity for all wavelengths. For self-luminous
objects and illuminants, the constants :math:`k` is usually chosen on
the grounds of convenience. If, however, in the CIE 1931 standard
colorimetric system, the :math:`Y` value is required to be numerically
equal to the absolute value of a photometric quantity, the constant,
:math:`k`, must be put equal to the numerical value of :math:`K_m`, the
maximum spectral luminous efficacy (which is equal to
683 :math:`lm\\cdot W^{-1}`) and :math:`\\Phi_\\lambda(\\lambda)` must
be the spectral concentration of the radiometric quantity corresponding
to the photometric quantity required.
method : unicode, optional
**{'ASTM E308', 'Integration'}**,
Computation method.
Other Parameters
----------------
use_practice_range : bool, optional
{:func:`colour.colorimetry.multi_sds_to_XYZ_ASTME308`},
Practise *ASTM E308-15* working wavelengths range is [360, 780],
if *True* this argument will trim the colour matching functions
appropriately.
mi_5nm_omission_method : bool, optional
{:func:`colour.colorimetry.multi_sds_to_XYZ_ASTME308`},
5 nm measurement intervals multi-spectral distributions conversion to
tristimulus values will use a 5 nm version of the colour matching
functions instead of a table of tristimulus weighting factors.
mi_20nm_interpolation_method : bool, optional
{:func:`colour.colorimetry.multi_sds_to_XYZ_ASTME308`},
20 nm measurement intervals multi-spectral distributions conversion to
tristimulus values will use a dedicated interpolation method instead
of a table of tristimulus weighting factors.
shape : SpectralShape, optional
{:func:`colour.colorimetry.multi_sds_to_XYZ_integration`},
Spectral shape of the multi-spectral distributions array :math:`msds`,
``cmfs`` and ``illuminant`` will be aligned to it.
Returns
-------
array_like
*CIE XYZ* tristimulus values, for a 512x384 multi-spectral image with
77 wavelengths, the output shape will be (384, 512, 3).
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+-----------+-----------------------+---------------+
- The code path using the *array_like* multi-spectral distributions
produces results different to the code path using a
:class:`colour.MultiSpectralDistributions` class instance: the former
favours execution speed by aligning the colour matching functions and
illuminant to the given spectral shape while the latter favours
precision by aligning the multi-spectral distributions to the colour
matching functions.
References
----------
:cite:`ASTMInternational2011a`, :cite:`ASTMInternational2015b`,
:cite:`Wyszecki2000bf`
Examples
--------
>>> shape = SpectralShape(400, 700, 60)
>>> data = np.array([
... [0.0137, 0.0159, 0.0096, 0.0111, 0.0179, 0.1057, 0.0433,
... 0.0258, 0.0248, 0.0186, 0.0310, 0.0473],
... [0.0913, 0.3145, 0.2582, 0.0709, 0.2971, 0.4620, 0.2683,
... 0.0831, 0.1203, 0.1292, 0.1682, 0.3221],
... [0.0152, 0.0842, 0.4139, 0.0220, 0.5630, 0.1918, 0.2373,
... 0.0430, 0.0054, 0.0079, 0.3719, 0.2268],
... [0.0281, 0.0907, 0.2228, 0.1249, 0.2375, 0.5625, 0.0518,
... 0.3230, 0.0065, 0.4006, 0.0861, 0.3161],
... [0.1918, 0.7103, 0.0041, 0.1817, 0.0024, 0.4209, 0.0118,
... 0.2302, 0.1860, 0.9404, 0.0041, 0.1124],
... [0.0430, 0.0437, 0.3744, 0.0020, 0.5819, 0.0027, 0.0823,
... 0.0081, 0.3625, 0.3213, 0.7849, 0.0024],
... ])
>>> msds = MultiSpectralDistributions(data, shape.range())
>>> multi_sds_to_XYZ(msds, method='Integration', shape=shape)
... # doctest: +ELLIPSIS
array([[ 8.2415862..., 4.2543993..., 7.6100842...],
[ 29.6144619..., 16.1158465..., 25.9015472...],
[ 16.6799560..., 27.2350547..., 22.9413337...],
[ 12.5597688..., 9.0667136..., 5.9670327...],
[ 18.5804689..., 33.6618109..., 26.9249733...],
[ 47.7113308..., 40.4573249..., 39.6439145...],
[ 7.830207 ..., 12.3689624..., 23.3742655...],
[ 24.1695370..., 20.0629815..., 7.2718670...],
[ 7.2333751..., 2.7982097..., 10.0688374...],
[ 48.7358074..., 30.2417164..., 10.6753233...],
[ 8.3231013..., 18.6791507..., 15.8228184...],
[ 24.6452277..., 26.0809382..., 27.7106399...]])
>>> msds = np.array([
... [
... [0.0137, 0.0913, 0.0152, 0.0281, 0.1918, 0.0430],
... [0.0159, 0.3145, 0.0842, 0.0907, 0.7103, 0.0437],
... [0.0096, 0.2582, 0.4139, 0.2228, 0.0041, 0.3744],
... [0.0111, 0.0709, 0.0220, 0.1249, 0.1817, 0.0020],
... [0.0179, 0.2971, 0.5630, 0.2375, 0.0024, 0.5819],
... [0.1057, 0.4620, 0.1918, 0.5625, 0.4209, 0.0027],
... ],
... [
... [0.0433, 0.2683, 0.2373, 0.0518, 0.0118, 0.0823],
... [0.0258, 0.0831, 0.0430, 0.3230, 0.2302, 0.0081],
... [0.0248, 0.1203, 0.0054, 0.0065, 0.1860, 0.3625],
... [0.0186, 0.1292, 0.0079, 0.4006, 0.9404, 0.3213],
... [0.0310, 0.1682, 0.3719, 0.0861, 0.0041, 0.7849],
... [0.0473, 0.3221, 0.2268, 0.3161, 0.1124, 0.0024],
... ],
... ])
>>> multi_sds_to_XYZ(msds, method='Integration', shape=shape)
... # doctest: +ELLIPSIS
array([[[ 7.6862675..., 4.0925470..., 8.4950412...],
[ 27.4119366..., 15.5014764..., 29.2825122...],
[ 17.1283666..., 27.7798651..., 25.5232032...],
[ 11.9824544..., 8.8127109..., 6.6518695...],
[ 19.1030682..., 34.4597818..., 29.7653804...],
[ 46.8243374..., 39.9551652..., 43.6541858...]],
<BLANKLINE>
[[ 8.0978189..., 12.7544378..., 25.8004512...],
[ 23.4360673..., 19.6127966..., 7.9342408...],
[ 7.0933208..., 2.7894394..., 11.1527704...],
[ 45.6313772..., 29.0068105..., 11.9934522...],
[ 8.9327884..., 19.4008147..., 17.1534186...],
[ 24.6610235..., 26.1093760..., 30.7298791...]]])
"""
function = MULTI_SD_TO_XYZ_METHODS[method]
return function(msds, cmfs, illuminant, k,
**filter_kwargs(function, **kwargs))
[docs]def wavelength_to_XYZ(
wavelength,
cmfs=STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']):
"""
Converts given wavelength :math:`\\lambda` to *CIE XYZ* tristimulus values
using given colour matching functions.
If the wavelength :math:`\\lambda` is not available in the colour matching
function, its value will be calculated according to *CIE 15:2004*
recommendation: the method developed by *Sprague (1880)* will be used for
interpolating functions having a uniformly spaced independent variable and
the *Cubic Spline* method for non-uniformly spaced independent variable.
Parameters
----------
wavelength : numeric or array_like
Wavelength :math:`\\lambda` in nm.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Raises
------
ValueError
If wavelength :math:`\\lambda` is not contained in the colour matching
functions domain.
Notes
-----
+-----------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+===========+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+-----------+-----------------------+---------------+
Examples
--------
>>> from colour import CMFS
>>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer']
>>> wavelength_to_XYZ(480, cmfs) # doctest: +ELLIPSIS
array([ 0.09564 , 0.13902 , 0.8129501...])
>>> wavelength_to_XYZ(480.5, cmfs) # doctest: +ELLIPSIS
array([ 0.0914287..., 0.1418350..., 0.7915726...])
"""
cmfs_shape = cmfs.shape
if (np.min(wavelength) < cmfs_shape.start or
np.max(wavelength) > cmfs_shape.end):
raise ValueError(
'"{0}nm" wavelength is not in "[{1}, {2}]" domain!'.format(
wavelength, cmfs_shape.start, cmfs_shape.end))
XYZ = np.reshape(cmfs[np.ravel(wavelength)],
as_float_array(wavelength).shape + (3, ))
return XYZ