# -*- coding: utf-8 -*-
"""
Hunt Colour Appearance Model
============================
Defines *Hunt* colour appearance model objects:
- :class:`colour.appearance.Hunt_InductionFactors`
- :attr:`colour.HUNT_VIEWING_CONDITIONS`
- :class:`colour.Hunt_Specification`
- :func:`colour.XYZ_to_Hunt`
See Also
--------
`Hunt Colour Appearance Model Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/
blob/master/notebooks/appearance/hunt.ipynb>`_
References
----------
- :cite:`Fairchild2013u` : Fairchild, M. D. (2013). The Hunt Model. In Color
Appearance Models (3rd ed., pp. 5094-5556). Wiley. ISBN:B00DAYO8E2
- :cite:`Hunt2004b` : Hunt, R. W. G. (2004). The Reproduction of Colour
(6th ed.). Chichester, UK: John Wiley & Sons, Ltd. doi:10.1002/0470024275
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.algebra import spow
from colour.utilities import (CaseInsensitiveMapping, as_float_array,
dot_vector, from_range_degrees, to_domain_100,
tsplit, tstack, usage_warning)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2019 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = [
'Hunt_InductionFactors', 'HUNT_VIEWING_CONDITIONS',
'HUE_DATA_FOR_HUE_QUADRATURE', 'XYZ_TO_HPE_MATRIX', 'HPE_TO_XYZ_MATRIX',
'Hunt_ReferenceSpecification', 'Hunt_Specification', 'XYZ_to_Hunt',
'luminance_level_adaptation_factor', 'illuminant_scotopic_luminance',
'XYZ_to_rgb', 'f_n', 'chromatic_adaptation',
'adjusted_reference_white_signals', 'achromatic_post_adaptation_signal',
'colour_difference_signals', 'hue_angle', 'eccentricity_factor',
'low_luminance_tritanopia_factor', 'yellowness_blueness_response',
'redness_greenness_response', 'overall_chromatic_response',
'saturation_correlate', 'achromatic_signal', 'brightness_correlate',
'lightness_correlate', 'chroma_correlate', 'colourfulness_correlate'
]
class Hunt_InductionFactors(
namedtuple('Hunt_InductionFactors', ('N_c', 'N_b', 'N_cb', 'N_bb'))):
"""
*Hunt* colour appearance model induction factors.
Parameters
----------
N_c : numeric or array_like
Chromatic surround induction factor :math:`N_c`.
N_b : numeric or array_like
*Brightness* surround induction factor :math:`N_b`.
N_cb : numeric or array_like, optional
Chromatic background induction factor :math:`N_{cb}`, approximated
using tristimulus values :math:`Y_w` and :math:`Y_b` of
respectively the reference white and the background if not specified.
N_bb : numeric or array_like, optional
*Brightness* background induction factor :math:`N_{bb}`, approximated
using tristimulus values :math:`Y_w` and :math:`Y_b` of
respectively the reference white and the background if not specified.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
def __new__(cls, N_c, N_b, N_cb=None, N_bb=None):
"""
Returns a new instance of the
:class:`colour.appearance.Hunt_InductionFactors` class.
"""
return super(Hunt_InductionFactors, cls).__new__(
cls, N_c, N_b, N_cb, N_bb)
HUNT_VIEWING_CONDITIONS = CaseInsensitiveMapping({
'Small Areas, Uniform Background & Surrounds':
Hunt_InductionFactors(1, 300),
'Normal Scenes':
Hunt_InductionFactors(1, 75),
'Television & CRT, Dim Surrounds':
Hunt_InductionFactors(1, 25),
'Large Transparencies On Light Boxes':
Hunt_InductionFactors(0.7, 25),
'Projected Transparencies, Dark Surrounds':
Hunt_InductionFactors(0.7, 10)
})
HUNT_VIEWING_CONDITIONS.__doc__ = """
Reference *Hunt* colour appearance model viewing conditions.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
HUNT_VIEWING_CONDITIONS : CaseInsensitiveMapping
**{'Small Areas, Uniform Background & Surrounds',
'Normal Scenes',
'Television & CRT, Dim Surrounds',
'Large Transparencies On Light Boxes',
'Projected Transparencies, Dark Surrounds'}**
Aliases:
- 'small_uniform': 'Small Areas, Uniform Background & Surrounds'
- 'normal': 'Normal Scenes'
- 'tv_dim': 'Television & CRT, Dim Surrounds'
- 'light_boxes': 'Large Transparencies On Light Boxes'
- 'projected_dark': 'Projected Transparencies, Dark Surrounds'
"""
HUNT_VIEWING_CONDITIONS['small_uniform'] = (
HUNT_VIEWING_CONDITIONS['Small Areas, Uniform Background & Surrounds'])
HUNT_VIEWING_CONDITIONS['normal'] = (HUNT_VIEWING_CONDITIONS['Normal Scenes'])
HUNT_VIEWING_CONDITIONS['tv_dim'] = (
HUNT_VIEWING_CONDITIONS['Television & CRT, Dim Surrounds'])
HUNT_VIEWING_CONDITIONS['light_boxes'] = (
HUNT_VIEWING_CONDITIONS['Large Transparencies On Light Boxes'])
HUNT_VIEWING_CONDITIONS['projected_dark'] = (
HUNT_VIEWING_CONDITIONS['Projected Transparencies, Dark Surrounds'])
HUE_DATA_FOR_HUE_QUADRATURE = {
'h_s': np.array([20.14, 90.00, 164.25, 237.53]),
'e_s': np.array([0.8, 0.7, 1.0, 1.2])
}
XYZ_TO_HPE_MATRIX = np.array([
[0.38971, 0.68898, -0.07868],
[-0.22981, 1.18340, 0.04641],
[0.00000, 0.00000, 1.00000],
])
"""
*Hunt* colour appearance model *CIE XYZ* tristimulus values to
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace matrix.
XYZ_TO_HPE_MATRIX : array_like, (3, 3)
"""
HPE_TO_XYZ_MATRIX = np.linalg.inv(XYZ_TO_HPE_MATRIX)
"""
*Hunt* colour appearance model *Hunt-Pointer-Estevez*
:math:`\\rho\\gamma\\beta` colourspace to *CIE XYZ* tristimulus values matrix.
HPE_TO_XYZ_MATRIX : array_like, (3, 3)
"""
class Hunt_ReferenceSpecification(
namedtuple('Hunt_ReferenceSpecification',
('J', 'C_94', 'h_S', 's', 'Q', 'M_94', 'H', 'H_C'))):
"""
Defines the *Hunt* colour appearance model reference specification.
This specification has field names consistent with *Fairchild (2013)*
reference.
Parameters
----------
J : numeric or array_like
Correlate of *Lightness* :math:`J`.
C_94 : numeric or array_like
Correlate of *chroma* :math:`C_94`.
h_S : numeric or array_like
*Hue* angle :math:`h_S` in degrees.
s : numeric or array_like
Correlate of *saturation* :math:`s`.
Q : numeric or array_like
Correlate of *brightness* :math:`Q`.
M_94 : numeric or array_like
Correlate of *colourfulness* :math:`M_94`.
H : numeric or array_like
*Hue* :math:`h` quadrature :math:`H`.
H_C : numeric or array_like
*Hue* :math:`h` composition :math:`H_C`.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
[docs]class Hunt_Specification(
namedtuple('Hunt_Specification',
('J', 'C', 'h', 's', 'Q', 'M', 'H', 'HC'))):
"""
Defines the *Hunt* colour appearance model specification.
This specification has field names consistent with the remaining colour
appearance models in :mod:`colour.appearance` but diverge from
*Fairchild (2013)* reference.
Parameters
----------
J : numeric or array_like
Correlate of *Lightness* :math:`J`.
C : numeric or array_like
Correlate of *chroma* :math:`C_94`.
h : numeric or array_like
*Hue* angle :math:`h_S` in degrees.
s : numeric or array_like
Correlate of *saturation* :math:`s`.
Q : numeric or array_like
Correlate of *brightness* :math:`Q`.
M : numeric or array_like
Correlate of *colourfulness* :math:`M_94`.
H : numeric or array_like
*Hue* :math:`h` quadrature :math:`H`.
HC : numeric or array_like
*Hue* :math:`h` composition :math:`H_C`.
Notes
-----
- This specification is the one used in the current model implementation.
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
"""
[docs]def XYZ_to_Hunt(XYZ,
XYZ_w,
XYZ_b,
L_A,
surround=HUNT_VIEWING_CONDITIONS['Normal Scenes'],
L_AS=None,
CCT_w=None,
XYZ_p=None,
p=None,
S=None,
S_w=None,
helson_judd_effect=False,
discount_illuminant=True):
"""
Computes the *Hunt* colour appearance model correlates.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
XYZ_b : array_like
*CIE XYZ* tristimulus values of background.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
surround : Hunt_InductionFactors, optional
Surround viewing conditions induction factors.
L_AS : numeric or array_like, optional
Scotopic luminance :math:`L_{AS}` of the illuminant, approximated if
not specified.
CCT_w : numeric or array_like, optional
Correlated color temperature :math:`T_{cp}`: of the illuminant, needed
to approximate :math:`L_{AS}`.
XYZ_p : array_like, optional
*CIE XYZ* tristimulus values of proximal field, assumed to be equal to
background if not specified.
p : numeric or array_like, optional
Simultaneous contrast / assimilation factor :math:`p` with value
normalised to domain [-1, 0] when simultaneous contrast occurs and
normalised to domain [0, 1] when assimilation occurs.
S : numeric or array_like, optional
Scotopic response :math:`S` to the stimulus, approximated using
tristimulus values :math:`Y` of the stimulus if not specified.
S_w : numeric or array_like, optional
Scotopic response :math:`S_w` for the reference white, approximated
using the tristimulus values :math:`Y_w` of the reference white if not
specified.
helson_judd_effect : bool, optional
Truth value indicating whether the *Helson-Judd* effect should be
accounted for.
discount_illuminant : bool, optional
Truth value indicating if the illuminant should be discounted.
Returns
-------
Hunt_Specification
*Hunt* colour appearance model specification.
Raises
------
ValueError
If an illegal arguments combination is specified.
Notes
-----
+--------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+==========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
| ``XYZ_w`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
| ``XYZ_b`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
| ``XYZ_p`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
+--------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+==========================+=======================+===============+
| ``Hunt_Specification.h`` | [0, 360] | [0, 1] |
+--------------------------+-----------------------+---------------+
References
----------
:cite:`Fairchild2013u`, :cite:`Hunt2004b`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> XYZ_b = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> surround = HUNT_VIEWING_CONDITIONS['Normal Scenes']
>>> CCT_w = 6504.0
>>> XYZ_to_Hunt(XYZ, XYZ_w, XYZ_b, L_A, surround, CCT_w=CCT_w)
... # doctest: +ELLIPSIS
Hunt_Specification(J=30.0462678..., C=0.1210508..., h=269.2737594..., \
s=0.0199093..., Q=22.2097654..., M=0.1238964..., H=None, HC=None)
"""
XYZ = to_domain_100(XYZ)
XYZ_w = to_domain_100(XYZ_w)
XYZ_b = to_domain_100(XYZ_b)
_X, Y, _Z = tsplit(XYZ)
_X_w, Y_w, _Z_w = tsplit(XYZ_w)
X_b, Y_b, _Z_b = tsplit(XYZ_b)
# Arguments handling.
if XYZ_p is not None:
X_p, Y_p, Z_p = tsplit(to_domain_100(XYZ_p))
else:
X_p = X_b
Y_p = Y_b
Z_p = Y_b
usage_warning('Unspecified proximal field "XYZ_p" argument, using '
'background "XYZ_b" as approximation!')
if surround.N_cb is None:
N_cb = 0.725 * spow(Y_w / Y_b, 0.2)
usage_warning('Unspecified "N_cb" argument, using approximation: '
'"{0}"'.format(N_cb))
if surround.N_bb is None:
N_bb = 0.725 * spow(Y_w / Y_b, 0.2)
usage_warning('Unspecified "N_bb" argument, using approximation: '
'"{0}"'.format(N_bb))
if L_AS is None and CCT_w is None:
raise ValueError('Either the scotopic luminance "L_AS" of the '
'illuminant or its correlated colour temperature '
'"CCT_w" must be specified!')
if L_AS is None:
L_AS = illuminant_scotopic_luminance(L_A, CCT_w)
usage_warning(
'Unspecified "L_AS" argument, using approximation from "CCT": '
'"{0}"'.format(L_AS))
if (S is None and S_w is not None) or (S is not None and S_w is None):
raise ValueError('Either both stimulus scotopic response "S" and '
'reference white scotopic response "S_w" arguments '
'need to be specified or none of them!')
elif S is None and S_w is None:
S = Y
S_w = Y_w
usage_warning(
'Unspecified stimulus scotopic response "S" and reference '
'white scotopic response "S_w" arguments, using '
'approximation: "{0}", "{1}"'.format(S, S_w))
if p is None:
usage_warning(
'Unspecified simultaneous contrast / assimilation "p" '
'argument, model will not account for simultaneous chromatic '
'contrast!')
XYZ_p = tstack([X_p, Y_p, Z_p])
# Computing luminance level adaptation factor :math:`F_L`.
F_L = luminance_level_adaptation_factor(L_A)
# Computing test sample chromatic adaptation.
rgb_a = chromatic_adaptation(XYZ, XYZ_w, XYZ_b, L_A, F_L, XYZ_p, p,
helson_judd_effect, discount_illuminant)
# Computing reference white chromatic adaptation.
rgb_aw = chromatic_adaptation(XYZ_w, XYZ_w, XYZ_b, L_A, F_L, XYZ_p, p,
helson_judd_effect, discount_illuminant)
# Computing opponent colour dimensions.
# Computing achromatic post adaptation signals.
A_a = achromatic_post_adaptation_signal(rgb_a)
A_aw = achromatic_post_adaptation_signal(rgb_aw)
# Computing colour difference signals.
C = colour_difference_signals(rgb_a)
C_w = colour_difference_signals(rgb_aw)
# -------------------------------------------------------------------------
# Computing the *hue* angle :math:`h_s`.
# -------------------------------------------------------------------------
h = hue_angle(C)
# hue_w = hue_angle(C_w)
# TODO: Implement hue quadrature & composition computation.
# -------------------------------------------------------------------------
# Computing the correlate of *saturation* :math:`s`.
# -------------------------------------------------------------------------
# Computing eccentricity factors.
e_s = eccentricity_factor(h)
# Computing low luminance tritanopia factor :math:`F_t`.
F_t = low_luminance_tritanopia_factor(L_A)
M_yb = yellowness_blueness_response(C, e_s, surround.N_c, N_cb, F_t)
M_rg = redness_greenness_response(C, e_s, surround.N_c, N_cb)
M_yb_w = yellowness_blueness_response(C_w, e_s, surround.N_c, N_cb, F_t)
M_rg_w = redness_greenness_response(C_w, e_s, surround.N_c, N_cb)
# Computing overall chromatic response.
M = overall_chromatic_response(M_yb, M_rg)
M_w = overall_chromatic_response(M_yb_w, M_rg_w)
s = saturation_correlate(M, rgb_a)
# -------------------------------------------------------------------------
# Computing the correlate of *brightness* :math:`Q`.
# -------------------------------------------------------------------------
# Computing achromatic signal :math:`A`.
A = achromatic_signal(L_AS, S, S_w, N_bb, A_a)
A_w = achromatic_signal(L_AS, S_w, S_w, N_bb, A_aw)
Q = brightness_correlate(A, A_w, M, surround.N_b)
brightness_w = brightness_correlate(A_w, A_w, M_w, surround.N_b)
# TODO: Implement whiteness-blackness :math:`Q_{wb}` computation.
# -------------------------------------------------------------------------
# Computing the correlate of *Lightness* :math:`J`.
# -------------------------------------------------------------------------
J = lightness_correlate(Y_b, Y_w, Q, brightness_w)
# -------------------------------------------------------------------------
# Computing the correlate of *chroma* :math:`C_{94}`.
# -------------------------------------------------------------------------
C_94 = chroma_correlate(s, Y_b, Y_w, Q, brightness_w)
# -------------------------------------------------------------------------
# Computing the correlate of *colourfulness* :math:`M_{94}`.
# -------------------------------------------------------------------------
M_94 = colourfulness_correlate(F_L, C_94)
return Hunt_Specification(J, C_94, from_range_degrees(h), s, Q, M_94, None,
None)
def luminance_level_adaptation_factor(L_A):
"""
Returns the *luminance* level adaptation factor :math:`F_L`.
Parameters
----------
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
Returns
-------
numeric or ndarray
*Luminance* level adaptation factor :math:`F_L`
Examples
--------
>>> luminance_level_adaptation_factor(318.31) # doctest: +ELLIPSIS
1.1675444...
"""
L_A = as_float_array(L_A)
k = 1 / (5 * L_A + 1)
k4 = k ** 4
F_L = 0.2 * k4 * (5 * L_A) + 0.1 * (1 - k4) ** 2 * spow(5 * L_A, 1 / 3)
return F_L
def illuminant_scotopic_luminance(L_A, CCT):
"""
Returns the approximate scotopic luminance :math:`L_{AS}` of the
illuminant.
Parameters
----------
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
CCT : numeric or array_like
Correlated color temperature :math:`T_{cp}` of the illuminant.
Returns
-------
numeric or ndarray
Approximate scotopic luminance :math:`L_{AS}`.
Examples
--------
>>> illuminant_scotopic_luminance(318.31, 6504.0) # doctest: +ELLIPSIS
769.9376286...
"""
L_A = as_float_array(L_A)
CCT = as_float_array(CCT)
CCT = 2.26 * L_A * spow((CCT / 4000) - 0.4, 1 / 3)
return CCT
def XYZ_to_rgb(XYZ):
"""
Converts from *CIE XYZ* tristimulus values to *Hunt-Pointer-Estevez*
:math:`\\rho\\gamma\\beta` colourspace.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Returns
-------
ndarray
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_to_rgb(XYZ) # doctest: +ELLIPSIS
array([ 19.4743367..., 20.3101217..., 21.78 ])
"""
return dot_vector(XYZ_TO_HPE_MATRIX, XYZ)
def f_n(x):
"""
Defines the nonlinear response function of the *Hunt* colour appearance
model used to model the nonlinear behaviour of various visual responses.
Parameters
----------
x : numeric or array_like or array_like
Visual response variable :math:`x`.
Returns
-------
numeric or array_like
Modeled visual response variable :math:`x`.
Examples
--------
>>> x = np.array([0.23350512, 0.23351103, 0.23355179])
>>> f_n(x) # doctest: +ELLIPSIS
array([ 5.8968592..., 5.8969521..., 5.8975927...])
"""
x = as_float_array(x)
x_p = spow(x, 0.73)
x_m = 40 * (x_p / (x_p + 2))
return x_m
def chromatic_adaptation(XYZ,
XYZ_w,
XYZ_b,
L_A,
F_L,
XYZ_p=None,
p=None,
helson_judd_effect=False,
discount_illuminant=True):
"""
Applies chromatic adaptation to given *CIE XYZ* tristimulus values.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample.
XYZ_b : array_like
*CIE XYZ* tristimulus values of background.
XYZ_w : array_like
*CIE XYZ* tristimulus values of reference white.
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
F_L : numeric or array_like
Luminance adaptation factor :math:`F_L`.
XYZ_p : array_like, optional
*CIE XYZ* tristimulus values of proximal field, assumed to be equal to
background if not specified.
p : numeric or array_like, optional
Simultaneous contrast / assimilation factor :math:`p` with value
normalised to domain [-1, 0] when simultaneous contrast occurs and
normalised to domain [0, 1] when assimilation occurs.
helson_judd_effect : bool, optional
Truth value indicating whether the *Helson-Judd* effect should be
accounted for.
discount_illuminant : bool, optional
Truth value indicating if the illuminant should be discounted.
Returns
-------
ndarray
Adapted *CIE XYZ* tristimulus values.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_b = np.array([95.05, 100.00, 108.88])
>>> XYZ_w = np.array([95.05, 100.00, 108.88])
>>> L_A = 318.31
>>> F_L = 1.16754446415
>>> chromatic_adaptation(XYZ, XYZ_w, XYZ_b, L_A, F_L) # doctest: +ELLIPSIS
array([ 6.8959454..., 6.8959991..., 6.8965708...])
"""
XYZ_w = as_float_array(XYZ_w)
XYZ_b = as_float_array(XYZ_b)
L_A = as_float_array(L_A)
F_L = as_float_array(F_L)
rgb = XYZ_to_rgb(XYZ)
rgb_w = XYZ_to_rgb(XYZ_w)
Y_w = XYZ_w[..., 1]
Y_b = XYZ_b[..., 1]
h_rgb = 3 * rgb_w / np.sum(rgb_w, axis=-1)[..., np.newaxis]
# Computing chromatic adaptation factors.
if not discount_illuminant:
L_A_p = spow(L_A, 1 / 3)
F_rgb = ((1 + L_A_p + h_rgb) / (1 + L_A_p + (1 / h_rgb)))
else:
F_rgb = np.ones(h_rgb.shape)
# Computing Helson-Judd effect parameters.
if helson_judd_effect:
D_rgb = (f_n((Y_b / Y_w) * F_L * F_rgb[..., 1]) - f_n(
(Y_b / Y_w) * F_L * F_rgb))
else:
D_rgb = np.zeros(F_rgb.shape)
# Computing cone bleach factors.
B_rgb = (10 ** 7) / ((10 ** 7) + 5 * L_A[..., np.newaxis] * (rgb_w / 100))
# Computing adjusted reference white signals.
if XYZ_p is not None and p is not None:
rgb_p = XYZ_to_rgb(XYZ_p)
rgb_w = adjusted_reference_white_signals(rgb_p, B_rgb, rgb_w, p)
# Computing adapted cone responses.
rgb_a = 1
rgb_a += B_rgb * (f_n(F_L[..., np.newaxis] * F_rgb * rgb / rgb_w) + D_rgb)
return rgb_a
def adjusted_reference_white_signals(rgb_p, rgb_b, rgb_w, p):
"""
Adjusts the white point for simultaneous chromatic contrast.
Parameters
----------
rgb_p : array_like
Cone signals *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta`
colourspace array of the proximal field.
rgb_b : array_like
Cone signals *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta`
colourspace array of the background.
rgb_w : array_like
Cone signals array *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta`
colourspace array of the reference white.
p : numeric or array_like
Simultaneous contrast / assimilation factor :math:`p` with value
normalised to domain [-1, 0] when simultaneous contrast occurs and
normalised to domain [0, 1] when assimilation occurs.
Returns
-------
ndarray
Adjusted cone signals *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta`
colourspace array of the reference white.
Examples
--------
>>> rgb_p = np.array([98.07193550, 101.13755950, 100.00000000])
>>> rgb_b = np.array([0.99984505, 0.99983840, 0.99982674])
>>> rgb_w = np.array([97.37325710, 101.54968030, 108.88000000])
>>> p = 0.1
>>> adjusted_reference_white_signals(rgb_p, rgb_b, rgb_w, p)
... # doctest: +ELLIPSIS
array([ 88.0792742..., 91.8569553..., 98.4876543...])
"""
rgb_p = as_float_array(rgb_p)
rgb_b = as_float_array(rgb_b)
rgb_w = as_float_array(rgb_w)
p = as_float_array(p)
p_rgb = rgb_p / rgb_b
rgb_w = (rgb_w * (spow((1 - p) * p_rgb + (1 + p) / p_rgb, 0.5)) / (spow(
(1 + p) * p_rgb + (1 - p) / p_rgb, 0.5)))
return rgb_w
def achromatic_post_adaptation_signal(rgb):
"""
Returns the achromatic post adaptation signal :math:`A` from given
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace array.
Parameters
----------
rgb : array_like
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace array.
Returns
-------
numeric or ndarray
Achromatic post adaptation signal :math:`A`.
Examples
--------
>>> rgb = np.array([6.89594549, 6.89599915, 6.89657085])
>>> achromatic_post_adaptation_signal(rgb) # doctest: +ELLIPSIS
18.9827186...
"""
r, g, b = tsplit(rgb)
A = 2 * r + g + (1 / 20) * b - 3.05 + 1
return A
def colour_difference_signals(rgb):
"""
Returns the colour difference signals :math:`C_1`, :math:`C_2` and
:math:`C_3` from given *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta`
colourspace array.
Parameters
----------
rgb : array_like
*Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace array.
Returns
-------
ndarray
Colour difference signals :math:`C_1`, :math:`C_2` and :math:`C_3`.
Examples
--------
>>> rgb = np.array([6.89594549, 6.89599915, 6.89657085])
>>> colour_difference_signals(rgb) # doctest: +ELLIPSIS
array([ -5.3660000...e-05, -5.7170000...e-04, 6.2536000...e-04])
"""
r, g, b = tsplit(rgb)
C_1 = r - g
C_2 = g - b
C_3 = b - r
C = tstack([C_1, C_2, C_3])
return C
def hue_angle(C):
"""
Returns the *hue* angle :math:`h` in degrees from given colour difference
signals :math:`C`.
Parameters
----------
C : array_like
Colour difference signals :math:`C`.
Returns
-------
numeric or ndarray
*Hue* angle :math:`h` in degrees.
Examples
--------
>>> C = np.array([
... -5.365865581996587e-05,
... -0.000571699383647,
... 0.000625358039467
... ])
>>> hue_angle(C) # doctest: +ELLIPSIS
269.2737594...
"""
C_1, C_2, C_3 = tsplit(C)
hue = (180 * np.arctan2(0.5 * (C_2 - C_3) / 4.5, C_1 -
(C_2 / 11)) / np.pi) % 360
return hue
def eccentricity_factor(hue):
"""
Returns eccentricity factor :math:`e_s` from given hue angle :math:`h`
in degrees.
Parameters
----------
hue : numeric or array_like
Hue angle :math:`h` in degrees.
Returns
-------
numeric or ndarray
Eccentricity factor :math:`e_s`.
Examples
--------
>>> eccentricity_factor(269.273759) # doctest: +ELLIPSIS
array(1.1108365...)
"""
hue = as_float_array(hue)
h_s = HUE_DATA_FOR_HUE_QUADRATURE['h_s']
e_s = HUE_DATA_FOR_HUE_QUADRATURE['e_s']
x = np.interp(hue, h_s, e_s)
x = np.where(hue < 20.14, 0.856 - (hue / 20.14) * 0.056, x)
x = np.where(hue > 237.53, 0.856 + 0.344 * (360 - hue) / (360 - 237.53), x)
return x
def low_luminance_tritanopia_factor(L_A):
"""
Returns the low luminance tritanopia factor :math:`F_t` from given adapting
field *luminance* :math:`L_A` in :math:`cd/m^2`.
Parameters
----------
L_A : numeric or array_like
Adapting field *luminance* :math:`L_A` in :math:`cd/m^2`.
Returns
-------
numeric or ndarray
Low luminance tritanopia factor :math:`F_t`.
Examples
--------
>>> low_luminance_tritanopia_factor(318.31) # doctest: +ELLIPSIS
0.9996859...
"""
L_A = as_float_array(L_A)
F_t = L_A / (L_A + 0.1)
return F_t
def yellowness_blueness_response(C, e_s, N_c, N_cb, F_t):
"""
Returns the yellowness / blueness response :math:`M_{yb}`.
Parameters
----------
C : array_like
Colour difference signals :math:`C`.
e_s : numeric or array_like
Eccentricity factor :math:`e_s`.
N_c : numeric or array_like
Chromatic surround induction factor :math:`N_c`.
N_cb : numeric or array_like
Chromatic background induction factor :math:`N_{cb}`.
F_t : numeric or array_like
Low luminance tritanopia factor :math:`F_t`.
Returns
-------
numeric or ndarray
Yellowness / blueness response :math:`M_{yb}`.
Examples
--------
>>> C = np.array([
... -5.365865581996587e-05,
... -0.000571699383647,
... 0.000625358039467
... ])
>>> e_s = 1.110836504862630
>>> N_c = 1.0
>>> N_cb = 0.725000000000000
>>> F_t = 0.99968593951195
>>> yellowness_blueness_response(C, e_s, N_c, N_cb, F_t)
... # doctest: +ELLIPSIS
-0.0082372...
"""
_C_1, C_2, C_3 = tsplit(C)
e_s = as_float_array(e_s)
N_c = as_float_array(N_c)
N_cb = as_float_array(N_cb)
F_t = as_float_array(F_t)
M_yb = (
100 * (0.5 * (C_2 - C_3) / 4.5) * (e_s * (10 / 13) * N_c * N_cb * F_t))
return M_yb
def redness_greenness_response(C, e_s, N_c, N_cb):
"""
Returns the redness / greenness response :math:`M_{yb}`.
Parameters
----------
C : array_like
Colour difference signals :math:`C`.
e_s : numeric or array_like
Eccentricity factor :math:`e_s`.
N_c : numeric or array_like
Chromatic surround induction factor :math:`N_c`.
N_cb : numeric or array_like
Chromatic background induction factor :math:`N_{cb}`.
Returns
-------
numeric or ndarray
Redness / greenness response :math:`M_{rg}`.
Examples
--------
>>> C = np.array([
... -5.365865581996587e-05,
... -0.000571699383647,
... 0.000625358039467
... ])
>>> e_s = 1.110836504862630
>>> N_c = 1.0
>>> N_cb = 0.725000000000000
>>> redness_greenness_response(C, e_s, N_c, N_cb) # doctest: +ELLIPSIS
-0.0001044...
"""
C_1, C_2, _C_3 = tsplit(C)
e_s = as_float_array(e_s)
N_c = as_float_array(N_c)
N_cb = as_float_array(N_cb)
M_rg = 100 * (C_1 - (C_2 / 11)) * (e_s * (10 / 13) * N_c * N_cb)
return M_rg
def overall_chromatic_response(M_yb, M_rg):
"""
Returns the overall chromatic response :math:`M`.
Parameters
----------
M_yb : numeric or array_like
Yellowness / blueness response :math:`M_{yb}`.
M_rg : numeric or array_like
Redness / greenness response :math:`M_{rg}`.
Returns
-------
numeric or ndarray
Overall chromatic response :math:`M`.
Examples
--------
>>> M_yb = -0.008237223618825
>>> M_rg = -0.000104447583276
>>> overall_chromatic_response(M_yb, M_rg) # doctest: +ELLIPSIS
0.0082378...
"""
M_yb = as_float_array(M_yb)
M_rg = as_float_array(M_rg)
M = spow((M_yb ** 2) + (M_rg ** 2), 0.5)
return M
def saturation_correlate(M, rgb_a):
"""
Returns the *saturation* correlate :math:`s`.
Parameters
----------
M : numeric or array_like
Overall chromatic response :math:`M`.
rgb_a : array_like
Adapted *Hunt-Pointer-Estevez* :math:`\\rho\\gamma\\beta` colourspace
array.
Returns
-------
numeric or ndarray
*Saturation* correlate :math:`s`.
Examples
--------
>>> M = 0.008237885787274
>>> rgb_a = np.array([6.89594549, 6.89599915, 6.89657085])
>>> saturation_correlate(M, rgb_a) # doctest: +ELLIPSIS
0.0199093...
"""
M = as_float_array(M)
rgb_a = as_float_array(rgb_a)
s = 50 * M / np.sum(rgb_a, axis=-1)
return s
def achromatic_signal(L_AS, S, S_w, N_bb, A_a):
"""
Returns the achromatic signal :math:`A`.
Parameters
----------
L_AS : numeric or array_like
Scotopic luminance :math:`L_{AS}` of the illuminant.
S : numeric or array_like
Scotopic response :math:`S` to the stimulus.
S_w : numeric or array_like
Scotopic response :math:`S_w` for the reference white.
N_bb : numeric or array_like
Brightness background induction factor :math:`N_{bb}`.
A_a: numeric or array_like
Achromatic post adaptation signal of the stimulus :math:`A_a`.
Returns
-------
numeric or ndarray
Achromatic signal :math:`A`.
Examples
--------
>>> L_AS = 769.9376286541402
>>> S = 20.0
>>> S_w = 100.0
>>> N_bb = 0.725000000000000
>>> A_a = 18.982718664838487
>>> achromatic_signal(L_AS, S, S_w, N_bb, A_a) # doctest: +ELLIPSIS
15.5068546...
"""
L_AS = as_float_array(L_AS)
S = as_float_array(S)
S_w = as_float_array(S_w)
N_bb = as_float_array(N_bb)
A_a = as_float_array(A_a)
j = 0.00001 / ((5 * L_AS / 2.26) + 0.00001)
# Computing scotopic luminance level adaptation factor :math:`F_{LS}`.
F_LS = 3800 * (j ** 2) * (5 * L_AS / 2.26)
F_LS += 0.2 * (spow(1 - (j ** 2), 0.4)) * (spow(5 * L_AS / 2.26, 1 / 6))
# Computing cone bleach factors :math:`B_S`.
B_S = 0.5 / (1 + 0.3 * spow((5 * L_AS / 2.26) * (S / S_w), 0.3))
B_S += 0.5 / (1 + 5 * (5 * L_AS / 2.26))
# Computing adapted scotopic signal :math:`A_S`.
A_S = (f_n(F_LS * S / S_w) * 3.05 * B_S) + 0.3
# Computing achromatic signal :math:`A`.
A = N_bb * (A_a - 1 + A_S - 0.3 + np.sqrt((1 + (0.3 ** 2))))
return A
def brightness_correlate(A, A_w, M, N_b):
"""
Returns the *brightness* correlate :math:`Q`.
Parameters
----------
A : numeric or array_like
Achromatic signal :math:`A`.
A_w: numeric or array_like
Achromatic post adaptation signal of the reference white :math:`A_w`.
M : numeric or array_like
Overall chromatic response :math:`M`.
N_b : numeric or array_like
Brightness surround induction factor :math:`N_b`.
Returns
-------
numeric or ndarray
*Brightness* correlate :math:`Q`.
Examples
--------
>>> A = 15.506854623621885
>>> A_w = 35.718916676317086
>>> M = 0.008237885787274
>>> N_b = 75.0
>>> brightness_correlate(A, A_w, M, N_b) # doctest: +ELLIPSIS
22.2097654...
"""
A = as_float_array(A)
A_w = as_float_array(A_w)
M = as_float_array(M)
N_b = as_float_array(N_b)
N_1 = (spow(7 * A_w, 0.5)) / (5.33 * spow(N_b, 0.13))
N_2 = (7 * A_w * spow(N_b, 0.362)) / 200
Q = spow(7 * (A + (M / 100)), 0.6) * N_1 - N_2
return Q
def lightness_correlate(Y_b, Y_w, Q, Q_w):
"""
Returns the *Lightness* correlate :math:`J`.
Parameters
----------
Y_b : numeric or array_like
Tristimulus values :math:`Y_b` the background.
Y_w : numeric or array_like
Tristimulus values :math:`Y_b` the reference white.
Q : numeric or array_like
*Brightness* correlate :math:`Q` of the stimulus.
Q_w : numeric or array_like
*Brightness* correlate :math:`Q` of the reference white.
Returns
-------
numeric or ndarray
*Lightness* correlate :math:`J`.
Examples
--------
>>> Y_b = 100.0
>>> Y_w = 100.0
>>> Q = 22.209765491265024
>>> Q_w = 40.518065821226081
>>> lightness_correlate(Y_b, Y_w, Q, Q_w) # doctest: +ELLIPSIS
30.0462678...
"""
Y_b = as_float_array(Y_b)
Y_w = as_float_array(Y_w)
Q = as_float_array(Q)
Q_w = as_float_array(Q_w)
Z = 1 + spow(Y_b / Y_w, 0.5)
J = 100 * spow(Q / Q_w, Z)
return J
def chroma_correlate(s, Y_b, Y_w, Q, Q_w):
"""
Returns the *chroma* correlate :math:`C_94`.
Parameters
----------
s : numeric or array_like
*Saturation* correlate :math:`s`.
Y_b : numeric or array_like
Tristimulus values :math:`Y_b` the background.
Y_w : numeric or array_like
Tristimulus values :math:`Y_b` the reference white.
Q : numeric or array_like
*Brightness* correlate :math:`Q` of the stimulus.
Q_w : numeric or array_like
*Brightness* correlate :math:`Q` of the reference white.
Returns
-------
numeric or ndarray
*Chroma* correlate :math:`C_94`.
Examples
--------
>>> s = 0.0199093206929
>>> Y_b = 100.0
>>> Y_w = 100.0
>>> Q = 22.209765491265024
>>> Q_w = 40.518065821226081
>>> chroma_correlate(s, Y_b, Y_w, Q, Q_w) # doctest: +ELLIPSIS
0.1210508...
"""
s = as_float_array(s)
Y_b = as_float_array(Y_b)
Y_w = as_float_array(Y_w)
Q = as_float_array(Q)
Q_w = as_float_array(Q_w)
C_94 = (2.44 * spow(s, 0.69) * (spow(Q / Q_w, Y_b / Y_w)) *
(1.64 - spow(0.29, Y_b / Y_w)))
return C_94
def colourfulness_correlate(F_L, C_94):
"""
Returns the *colourfulness* correlate :math:`M_94`.
Parameters
----------
F_L : numeric or array_like
Luminance adaptation factor :math:`F_L`.
C_94 : numeric
*Chroma* correlate :math:`C_94`.
Returns
-------
numeric
*Colourfulness* correlate :math:`M_94`.
Examples
--------
>>> F_L = 1.16754446414718
>>> C_94 = 0.121050839936176
>>> colourfulness_correlate(F_L, C_94) # doctest: +ELLIPSIS
0.1238964...
"""
F_L = as_float_array(F_L)
C_94 = as_float_array(C_94)
M_94 = spow(F_L, 0.15) * C_94
return M_94