#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Whiteness Index :math:`W`
=========================
Defines *whiteness* index :math:`W` computation objects:
- :func:`whiteness_Berger1959`
- :func:`whiteness_Taube1960`
- :func:`whiteness_Stensby1968`
- :func:`whiteness_ASTM313`
- :func:`whiteness_Ganz1979`
- :func:`whiteness_CIE2004`
See Also
--------
`Whiteness IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/whiteness.ipynb>`_ # noqa
References
----------
.. [1] Wikipedia. (n.d.). Whiteness. Retrieved September 17, 2014, from
http://en.wikipedia.org/wiki/Whiteness
.. [2] X-Rite, & Pantone. (2012). Color iQC and Color iMatch Color
Calculations Guide. Retrieved from
http://www.xrite.com/documents/literature/en/09_Color_Calculations_en.pdf # noqa
.. [3] Wyszecki, G., & Stiles, W. S. (2000). Table I(6.5.3) Whiteness
Formulae (Whiteness Measure Denoted by W). In Color Science: Concepts
and Methods, Quantitative Data and Formulae (pp. 837–839). Wiley.
ISBN:978-0471399186
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.utilities import CaseInsensitiveMapping, tsplit, tstack
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['whiteness_Berger1959',
'whiteness_Taube1960',
'whiteness_Stensby1968',
'whiteness_ASTM313',
'whiteness_Ganz1979',
'whiteness_CIE2004',
'WHITENESS_METHODS',
'whiteness']
[docs]def whiteness_Berger1959(XYZ, XYZ_0):
"""
Returns the *whiteness* index :math:`WI` of given sample *CIE XYZ*
tristimulus values using Berger (1959) method. [2]_
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of sample.
XYZ_0 : array_like
*CIE XYZ* tristimulus values of reference white.
Returns
-------
numeric or ndarray
*Whiteness* :math:`WI`.
Notes
-----
- Input *CIE XYZ* and *CIE XYZ_0* tristimulus values are in domain
[0, 100].
- *Whiteness* :math:`WI` values larger than 33.33 indicate a bluish
white, and values smaller than 33.33 indicate a yellowish white.
Warning
-------
The input domain of that definition is non standard!
Examples
--------
>>> XYZ = np.array([95.00000000, 100.00000000, 105.00000000])
>>> XYZ_0 = np.array([94.80966767, 100.00000000, 107.30513595])
>>> whiteness_Berger1959(XYZ, XYZ_0) # doctest: +ELLIPSIS
30.3638017...
"""
X, Y, Z = tsplit(XYZ)
X_0, Y_0, Z_0 = tsplit(XYZ_0)
WI = 0.333 * Y + 125 * (Z / Z_0) - 125 * (X / X_0)
return WI
[docs]def whiteness_Taube1960(XYZ, XYZ_0):
"""
Returns the *whiteness* index :math:`WI` of given sample *CIE XYZ*
tristimulus values using Taube (1960) method. [2]_
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of sample.
XYZ_0 : array_like
*CIE XYZ* tristimulus values of reference white.
Returns
-------
numeric or ndarray
*Whiteness* :math:`WI`.
Notes
-----
- Input *CIE XYZ* and *CIE XYZ_0* tristimulus values are in domain
[0, 100].
- *Whiteness* :math:`WI` values larger than 100 indicate a bluish
white, and values smaller than 100 indicate a yellowish white.
Examples
--------
>>> XYZ = np.array([95.00000000, 100.00000000, 105.00000000])
>>> XYZ_0 = np.array([94.80966767, 100.00000000, 107.30513595])
>>> whiteness_Taube1960(XYZ, XYZ_0) # doctest: +ELLIPSIS
91.4071738...
"""
X, Y, Z = tsplit(XYZ)
X_0, Y_0, Z_0 = tsplit(XYZ_0)
WI = 400 * (Z / Z_0) - 3 * Y
return WI
[docs]def whiteness_Stensby1968(Lab):
"""
Returns the *whiteness* index :math:`WI` of given sample *CIE Lab*
colourspace array using Stensby (1968) method. [2]_
Parameters
----------
Lab : array_like
*CIE Lab* colourspace array of sample.
Returns
-------
numeric or ndarray
*Whiteness* :math:`WI`.
Notes
-----
- Input *CIE Lab* colourspace array is in domain [0, 100].
- *Whiteness* :math:`WI` values larger than 100 indicate a bluish
white, and values smaller than 100 indicate a yellowish white.
Examples
--------
>>> Lab = np.array([100.00000000, -2.46875131, -16.72486654])
>>> whiteness_Stensby1968(Lab) # doctest: +ELLIPSIS
142.7683456...
"""
L, a, b = tsplit(Lab)
WI = L - 3 * b + 3 * a
return WI
[docs]def whiteness_ASTM313(XYZ):
"""
Returns the *whiteness* index :math:`WI` of given sample *CIE XYZ*
tristimulus values using ASTM 313 method. [2]_
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of sample.
Returns
-------
numeric or ndarray
*Whiteness* :math:`WI`.
Notes
-----
- Input *CIE XYZ* tristimulus values are in domain [0, 100].
Warning
-------
The input domain of that definition is non standard!
Examples
--------
>>> XYZ = np.array([95.00000000, 100.00000000, 105.00000000])
>>> whiteness_ASTM313(XYZ) # doctest: +ELLIPSIS
55.7400000...
"""
X, Y, Z = tsplit(XYZ)
WI = 3.388 * Z - 3 * Y
return WI
[docs]def whiteness_Ganz1979(xy, Y):
"""
Returns the *whiteness* index :math:`W` and *tint* :math:`T` of given
sample *xy* chromaticity coordinates using Ganz and Griesser (1979)
method. [2]_
Parameters
----------
xy : array_like
Chromaticity coordinates *xy* of sample.
Y : numeric or array_like
Tristimulus :math:`Y` value of sample.
Returns
-------
ndarray
*Whiteness* :math:`W` and *tint* :math:`T`.
Notes
-----
- Input tristimulus :math:`Y` value is in domain [0, 100].
- The formula coefficients are valid for
*CIE Standard Illuminant D Series* *D65* and
*CIE 1964 10 Degree Standard Observer*.
- Positive output *tint* :math:`T` values indicate a greener tint while
negative values indicate a redder tint.
- Whiteness differences of less than 5 Ganz units appear to be
indistinguishable to the human eye.
- Tint differences of less than 0.5 Ganz units appear to be
indistinguishable to the human eye.
Warning
-------
The input domain of that definition is non standard!
Examples
--------
>>> xy = np.array([0.3167, 0.3334])
>>> whiteness_Ganz1979(xy, 100) # doctest: +ELLIPSIS
array([ 85.6003766..., 0.6789003...])
"""
x, y = tsplit(xy)
Y = np.asarray(Y)
W = Y - 1868.322 * x - 3695.690 * y + 1809.441
T = -1001.223 * x + 748.366 * y + 68.261
WT = tstack((W, T))
return WT
[docs]def whiteness_CIE2004(xy,
Y,
xy_n,
observer='CIE 1931 2 Degree Standard Observer'):
"""
Returns the *whiteness* :math:`W` or :math:`W_{10}` and *tint* :math:`T`
or :math:`T_{10}` of given sample *xy* chromaticity coordinates using
CIE 2004 method.
Parameters
----------
xy : array_like
Chromaticity coordinates *xy* of sample.
Y : numeric or array_like
Tristimulus :math:`Y` value of sample.
xy_n : array_like
Chromaticity coordinates *xy_n* of perfect diffuser.
observer : unicode, optional
{'CIE 1931 2 Degree Standard Observer',
'CIE 1964 10 Degree Standard Observer'}
*CIE Standard Observer* used for computations, *tint* :math:`T` or
:math:`T_{10}` value is dependent on viewing field angular subtense.
Returns
-------
ndarray
*Whiteness* :math:`W` or :math:`W_{10}` and *tint* :math:`T` or
:math:`T_{10}` of given sample.
Notes
-----
- Input tristimulus :math:`Y` value is in domain [0, 100].
- This method may be used only for samples whose values of :math:`W` or
:math:`W_{10}` lie within the following limits: greater than 40 and
less than 5Y - 280, or 5Y10 - 280.
- This method may be used only for samples whose values of :math:`T` or
:math:`T_{10}` lie within the following limits: greater than -4 and
less than +2.
- Output *whiteness* :math:`W` or :math:`W_{10}` values larger than 100
indicate a bluish white while values smaller than 100 indicate a
yellowish white. [2]_
- Positive output *tint* :math:`T` or :math:`T_{10}` values indicate a
greener tint while negative values indicate a redder tint.
Warning
-------
The input domain of that definition is non standard!
References
----------
.. [4] CIE TC 1-48. (2004). The evaluation of whiteness. In CIE 015:2004
Colorimetry, 3rd Edition (p. 24). ISBN:978-3-901-90633-6
Examples
--------
>>> xy = np.array([0.3167, 0.3334])
>>> xy_n = np.array([0.3139, 0.3311])
>>> whiteness_CIE2004(xy, 100, xy_n) # doctest: +ELLIPSIS
array([ 93.85..., -1.305...])
"""
x, y = tsplit(xy)
Y = np.asarray(Y)
x_n, y_n = tsplit(xy_n)
W = Y + 800 * (x_n - x) + 1700 * (y_n - y)
T = (1000 if '1931' in observer else 900) * (x_n - x) - 650 * (y_n - y)
WT = tstack((W, T))
return WT
WHITENESS_METHODS = CaseInsensitiveMapping(
{'Berger 1959': whiteness_Berger1959,
'Taube 1960': whiteness_Taube1960,
'Stensby 1968': whiteness_Stensby1968,
'ASTM 313': whiteness_ASTM313,
'Ganz 1979': whiteness_Ganz1979,
'CIE 2004': whiteness_CIE2004})
"""
Supported *whiteness* computations methods.
WHITENESS_METHODS : CaseInsensitiveMapping
{'CIE 2004', 'Berger 1959', 'Taube 1960', 'Stensby 1968', 'ASTM 313',
'Ganz 1979', 'CIE 2004'}
Aliases:
- 'cie2004': 'CIE 2004'
"""
WHITENESS_METHODS['cie2004'] = WHITENESS_METHODS['CIE 2004']
[docs]def whiteness(method='CIE 2004', **kwargs):
"""
Returns the *whiteness* :math:`W` using given method.
Parameters
----------
method : unicode, optional
{'CIE 2004', 'Berger 1959', 'Taube 1960', 'Stensby 1968', 'ASTM 313',
'Ganz 1979', 'CIE 2004'}
Computation method.
\*\*kwargs : \*\*
Keywords arguments.
Returns
-------
numeric or ndarray
*whiteness* :math:`W`.
Examples
--------
>>> xy = np.array([0.3167, 0.3334])
>>> Y = 100
>>> xy_n = np.array([0.3139, 0.3311])
>>> whiteness(xy=xy, Y=Y, xy_n=xy_n) # doctest: +ELLIPSIS
array([ 93.85..., -1.305...])
>>> XYZ = np.array([95.00000000, 100.00000000, 105.00000000])
>>> XYZ_0 = np.array([94.80966767, 100.00000000, 107.30513595])
>>> method = 'Taube 1960'
>>> whiteness(XYZ=XYZ, XYZ_0=XYZ_0, method=method) # doctest: +ELLIPSIS
91.4071738...
"""
return WHITENESS_METHODS.get(method)(**kwargs)
Colour 0.3