# -*- coding: utf-8 -*-
"""
:math:`LLAB(l:c)` Colour Appearance Model
=========================================
Defines *:math:`LLAB(l:c)`* colour appearance model objects:
- :class:`colour.appearance.LLAB_InductionFactors`
- :attr:`colour.LLAB_VIEWING_CONDITIONS`
- :class:`colour.LLAB_Specification`
- :func:`colour.XYZ_to_LLAB`
See Also
--------
`LLAB(l:c) Colour Appearance Model Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/appearance/llab.ipynb>`_
References
----------
- :cite:`Fairchild2013x` : Fairchild, M. D. (2013). LLAB Model. In Color
Appearance Models (3rd ed., pp. 6025-6178). Wiley. ISBN:B00DAYO8E2
- :cite:`Luo1996b` : Luo, M. R., Lo, M.-C., & Kuo, W.-G. (1996). The LLAB
(l:c) colour model. Color Research & Application, 21(6), 412-429.
doi:10.1002/(SICI)1520-6378(199612)21:6<412::AID-COL4>3.0.CO;2-Z
- :cite:`Luo1996c` : Luo, M. R., & Morovic, J. (1996). Two Unsolved Issues in
Colour Management - Colour Appearance and Gamut Mapping. In Conference:
5th International Conference on High Technology: Imaging Science and
Technology - Evolution & Promise (pp. 136-147). Retrieved from
http://www.researchgate.net/publication/\236348295_Two_Unsolved_Issues_in\
_Colour_Management__Colour_Appearance_and_Gamut_Mapping
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour.algebra import polar_to_cartesian, spow
from colour.utilities import (CaseInsensitiveMapping, as_float_array,
dot_vector, from_range_degrees, to_domain_100,
tsplit, tstack)
__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__ = [
'LLAB_InductionFactors', 'LLAB_VIEWING_CONDITIONS',
'LLAB_XYZ_TO_RGB_MATRIX', 'LLAB_RGB_TO_XYZ_MATRIX',
'LLAB_ReferenceSpecification', 'LLAB_Specification', 'XYZ_to_LLAB',
'XYZ_to_RGB_LLAB', 'chromatic_adaptation', 'f',
'opponent_colour_dimensions', 'hue_angle', 'chroma_correlate',
'colourfulness_correlate', 'saturation_correlate', 'final_opponent_signals'
]
[docs]class LLAB_InductionFactors(
namedtuple('LLAB_InductionFactors', ('D', 'F_S', 'F_L', 'F_C'))):
"""
*:math:`LLAB(l:c)`* colour appearance model induction factors.
Parameters
----------
D : numeric or array_like
*Discounting-the-Illuminant* factor :math:`D`.
F_S : numeric or array_like
Surround induction factor :math:`F_S`.
F_L : numeric or array_like
*Lightness* induction factor :math:`F_L`.
F_C : numeric or array_like
*Chroma* induction factor :math:`F_C`.
References
----------
:cite:`Fairchild2013x`, :cite:`Luo1996b`, :cite:`Luo1996c`
"""
LLAB_VIEWING_CONDITIONS = CaseInsensitiveMapping({
'Reference Samples & Images, Average Surround, Subtending > 4': (
LLAB_InductionFactors(1, 3, 0, 1)),
'Reference Samples & Images, Average Surround, Subtending < 4': (
LLAB_InductionFactors(1, 3, 1, 1)),
'Television & VDU Displays, Dim Surround': (LLAB_InductionFactors(
0.7, 3.5, 1, 1)),
'Cut Sheet Transparency, Dim Surround': (LLAB_InductionFactors(
1, 5, 1, 1.1)),
'35mm Projection Transparency, Dark Surround': (LLAB_InductionFactors(
0.7, 4, 1, 1))
})
LLAB_VIEWING_CONDITIONS.__doc__ = """
Reference :math:`LLAB(l:c)` colour appearance model viewing conditions.
References
----------
:cite:`Fairchild2013x`, :cite:`Luo1996b`, :cite:`Luo1996c`
LLAB_VIEWING_CONDITIONS : CaseInsensitiveMapping
**{'Reference Samples & Images, Average Surround, Subtending > 4',
'Reference Samples & Images, Average Surround, Subtending < 4',
'Television & VDU Displays, Dim Surround',
'Cut Sheet Transparency, Dim Surround':,
'35mm Projection Transparency, Dark Surround'}**
Aliases:
- 'ref_average_4_plus':
'Reference Samples & Images, Average Surround, Subtending > 4'
- 'ref_average_4_minus':
'Reference Samples & Images, Average Surround, Subtending < 4'
- 'tv_dim': 'Television & VDU Displays, Dim Surround'
- 'sheet_dim': 'Cut Sheet Transparency, Dim Surround'
- 'projected_dark': '35mm Projection Transparency, Dark Surround'
"""
LLAB_VIEWING_CONDITIONS['ref_average_4_plus'] = ( # yapf: disable
LLAB_VIEWING_CONDITIONS['Reference Samples & Images, '
'Average Surround, Subtending > 4'])
LLAB_VIEWING_CONDITIONS['ref_average_4_minus'] = ( # yapf: disable
LLAB_VIEWING_CONDITIONS['Reference Samples & Images, '
'Average Surround, Subtending < 4'])
LLAB_VIEWING_CONDITIONS['tv_dim'] = (
LLAB_VIEWING_CONDITIONS['Television & VDU Displays, Dim Surround'])
LLAB_VIEWING_CONDITIONS['sheet_dim'] = (
LLAB_VIEWING_CONDITIONS['Cut Sheet Transparency, Dim Surround'])
LLAB_VIEWING_CONDITIONS['projected_dark'] = (
LLAB_VIEWING_CONDITIONS['35mm Projection Transparency, Dark Surround'])
LLAB_XYZ_TO_RGB_MATRIX = np.array([
[0.8951, 0.2664, -0.1614],
[-0.7502, 1.7135, 0.0367],
[0.0389, -0.0685, 1.0296],
])
"""
LLAB(l:c) colour appearance model *CIE XYZ* tristimulus values to normalised
cone responses matrix.
LLAB_XYZ_TO_RGB_MATRIX : array_like, (3, 3)
"""
LLAB_RGB_TO_XYZ_MATRIX = np.linalg.inv(LLAB_XYZ_TO_RGB_MATRIX)
"""
LLAB(l:c) colour appearance model normalised cone responses to *CIE XYZ*
tristimulus values matrix.
LLAB_RGB_TO_XYZ_MATRIX : array_like, (3, 3)
"""
class LLAB_ReferenceSpecification(
namedtuple('LLAB_ReferenceSpecification',
('L_L', 'Ch_L', 'h_L', 's_L', 'C_L', 'HC', 'A_L', 'B_L'))):
"""
Defines the *:math:`LLAB(l:c)`* colour appearance model reference
specification.
This specification has field names consistent with *Fairchild (2013)*
reference.
Parameters
----------
L_L : numeric or array_like
Correlate of *Lightness* :math:`L_L`.
Ch_L : numeric or array_like
Correlate of *chroma* :math:`Ch_L`.
h_L : numeric or array_like
*Hue* angle :math:`h_L` in degrees.
s_L : numeric or array_like
Correlate of *saturation* :math:`s_L`.
C_L : numeric or array_like
Correlate of *colourfulness* :math:`C_L`.
HC : numeric or array_like
*Hue* :math:`h` composition :math:`H^C`.
A_L : numeric or array_like
Opponent signal :math:`A_L`.
B_L : numeric or array_like
Opponent signal :math:`B_L`.
References
----------
:cite:`Fairchild2013x`, :cite:`Luo1996b`, :cite:`Luo1996c`
"""
[docs]class LLAB_Specification(
namedtuple('LLAB_Specification',
('J', 'C', 'h', 's', 'M', 'HC', 'a', 'b'))):
"""
Defines the *:math:`LLAB(l:c)`* 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:`L_L`.
C : numeric or array_like
Correlate of *chroma* :math:`Ch_L`.
h : numeric or array_like
*Hue* angle :math:`h_L` in degrees.
s : numeric or array_like
Correlate of *saturation* :math:`s_L`.
M : numeric or array_like
Correlate of *colourfulness* :math:`C_L`.
HC : numeric or array_like
*Hue* :math:`h` composition :math:`H^C`.
a : numeric or array_like
Opponent signal :math:`A_L`.
b : numeric or array_like
Opponent signal :math:`B_L`.
Notes
-----
- This specification is the one used in the current model implementation.
References
----------
:cite:`Fairchild2013x`, :cite:`Luo1996b`, :cite:`Luo1996c`
"""
[docs]def XYZ_to_LLAB(
XYZ,
XYZ_0,
Y_b,
L,
surround=LLAB_VIEWING_CONDITIONS[
'Reference Samples & Images, Average Surround, Subtending < 4']):
"""
Computes the *:math:`LLAB(l:c)`* colour appearance model correlates.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values of test sample / stimulus.
XYZ_0 : array_like
*CIE XYZ* tristimulus values of reference white.
Y_b : numeric or array_like
Luminance factor of the background in :math:`cd/m^2`.
L : numeric or array_like
Absolute luminance :math:`L` of reference white in :math:`cd/m^2`.
surround : LLAB_InductionFactors, optional
Surround viewing conditions induction factors.
Returns
-------
LLAB_Specification
*:math:`LLAB(l:c)`* colour appearance model specification.
Notes
-----
+--------------------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+==========================+=======================+===============+
| ``XYZ`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
| ``XYZ_0`` | [0, 100] | [0, 1] |
+--------------------------+-----------------------+---------------+
+--------------------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+==========================+=======================+===============+
| ``LLAB_Specification.h`` | [0, 360] | [0, 1] |
+--------------------------+-----------------------+---------------+
References
----------
:cite:`Fairchild2013x`, :cite:`Luo1996b`, :cite:`Luo1996c`
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_0 = np.array([95.05, 100.00, 108.88])
>>> Y_b = 20.0
>>> L = 318.31
>>> surround = LLAB_VIEWING_CONDITIONS['ref_average_4_minus']
>>> XYZ_to_LLAB(XYZ, XYZ_0, Y_b, L, surround) # doctest: +ELLIPSIS
LLAB_Specification(J=37.3668650..., C=0.0089496..., h=270..., \
s=0.0002395..., M=0.0190185..., HC=None, a=..., b=-0.0190185...)
"""
_X, Y, _Z = tsplit(to_domain_100(XYZ))
RGB = XYZ_to_RGB_LLAB(to_domain_100(XYZ))
RGB_0 = XYZ_to_RGB_LLAB(to_domain_100(XYZ_0))
# Reference illuminant *CIE Standard Illuminant D Series* *D65*.
XYZ_0r = np.array([95.05, 100.00, 108.88])
RGB_0r = XYZ_to_RGB_LLAB(XYZ_0r)
# Computing chromatic adaptation.
XYZ_r = chromatic_adaptation(RGB, RGB_0, RGB_0r, Y, surround.D)
# -------------------------------------------------------------------------
# Computing the correlate of *Lightness* :math:`L_L`.
# -------------------------------------------------------------------------
# Computing opponent colour dimensions.
L_L, a, b = tsplit(
opponent_colour_dimensions(XYZ_r, Y_b, surround.F_S, surround.F_L))
# Computing perceptual correlates.
# -------------------------------------------------------------------------
# Computing the correlate of *chroma* :math:`Ch_L`.
# -------------------------------------------------------------------------
Ch_L = chroma_correlate(a, b)
# -------------------------------------------------------------------------
# Computing the correlate of *colourfulness* :math:`C_L`.
# -------------------------------------------------------------------------
C_L = colourfulness_correlate(L, L_L, Ch_L, surround.F_C)
# -------------------------------------------------------------------------
# Computing the correlate of *saturation* :math:`s_L`.
# -------------------------------------------------------------------------
s_L = saturation_correlate(Ch_L, L_L)
# -------------------------------------------------------------------------
# Computing the *hue* angle :math:`h_L`.
# -------------------------------------------------------------------------
h_L = hue_angle(a, b)
# TODO: Implement hue composition computation.
# -------------------------------------------------------------------------
# Computing final opponent signals.
# -------------------------------------------------------------------------
A_L, B_L = tsplit(final_opponent_signals(C_L, h_L))
return LLAB_Specification(L_L, Ch_L, from_range_degrees(h_L), s_L, C_L,
None, A_L, B_L)
def XYZ_to_RGB_LLAB(XYZ):
"""
Converts from *CIE XYZ* tristimulus values to normalised cone responses.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Returns
-------
ndarray
Normalised cone responses.
Examples
--------
>>> XYZ = np.array([19.01, 20.00, 21.78])
>>> XYZ_to_RGB_LLAB(XYZ) # doctest: +ELLIPSIS
array([ 0.9414279..., 1.0404012..., 1.0897088...])
"""
_X, Y, _Z = tsplit(XYZ)
Y = tstack([Y, Y, Y])
XYZ_n = XYZ / Y
return dot_vector(LLAB_XYZ_TO_RGB_MATRIX, XYZ_n)
def chromatic_adaptation(RGB, RGB_0, RGB_0r, Y, D=1):
"""
Applies chromatic adaptation to given *RGB* normalised cone responses
array.
Parameters
----------
RGB : array_like
*RGB* normalised cone responses array of test sample / stimulus.
RGB_0 : array_like
*RGB* normalised cone responses array of reference white.
RGB_0r : array_like
*RGB* normalised cone responses array of reference illuminant
*CIE Standard Illuminant D Series* *D65*.
Y : numeric or array_like
Tristimulus values :math:`Y` of the stimulus.
D : numeric or array_like, optional
*Discounting-the-Illuminant* factor normalised to domain [0, 1].
Returns
-------
ndarray
Adapted *CIE XYZ* tristimulus values.
Examples
--------
>>> RGB = np.array([0.94142795, 1.04040120, 1.08970885])
>>> RGB_0 = np.array([0.94146023, 1.04039386, 1.08950293])
>>> RGB_0r = np.array([0.94146023, 1.04039386, 1.08950293])
>>> Y = 20.0
>>> chromatic_adaptation(RGB, RGB_0, RGB_0r, Y) # doctest: +ELLIPSIS
array([ 19.01, 20. , 21.78])
"""
R, G, B = tsplit(RGB)
R_0, G_0, B_0 = tsplit(RGB_0)
R_0r, G_0r, B_0r = tsplit(RGB_0r)
Y = as_float_array(Y)
beta = spow(B_0 / B_0r, 0.0834)
R_r = (D * (R_0r / R_0) + 1 - D) * R
G_r = (D * (G_0r / G_0) + 1 - D) * G
B_r = (D * (B_0r / spow(B_0, beta)) + 1 - D) * spow(B, beta)
RGB_r = tstack([R_r, G_r, B_r])
Y = tstack([Y, Y, Y])
XYZ_r = dot_vector(LLAB_RGB_TO_XYZ_MATRIX, RGB_r * Y)
return XYZ_r
def f(x, F_S):
"""
Defines the nonlinear response function of the *:math:`LLAB(l:c)`* 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`.
F_S : numeric or array_like
Surround induction factor :math:`F_S`.
Returns
-------
numeric or array_like
Modeled visual response variable :math:`x`.
Examples
--------
>>> x = np.array([0.23350512, 0.23351103, 0.23355179])
>>> f(0.200009186234000, 3) # doctest: +ELLIPSIS
array(0.5848125...)
"""
x = as_float_array(x)
F_S = as_float_array(F_S)
x_m = np.where(
x > 0.008856,
spow(x, 1 / F_S),
((spow(0.008856, 1 / F_S) - (16 / 116)) / 0.008856) * x + (16 / 116),
)
return x_m
def opponent_colour_dimensions(XYZ, Y_b, F_S, F_L):
"""
Returns opponent colour dimensions from given adapted *CIE XYZ* tristimulus
values.
The opponent colour dimensions are based on a modified *CIE L\\*a\\*b\\**
colourspace formulae.
Parameters
----------
XYZ : array_like
Adapted *CIE XYZ* tristimulus values.
Y_b : numeric or array_like
Luminance factor of the background in :math:`cd/m^2`.
F_S : numeric or array_like
Surround induction factor :math:`F_S`.
F_L : numeric or array_like
Lightness induction factor :math:`F_L`.
Returns
-------
ndarray
Opponent colour dimensions.
Examples
--------
>>> XYZ = np.array([19.00999572, 20.00091862, 21.77993863])
>>> Y_b = 20.0
>>> F_S = 3.0
>>> F_L = 1.0
>>> opponent_colour_dimensions(XYZ, Y_b, F_S, F_L) # doctest: +ELLIPSIS
array([ 3.7368047...e+01, -4.4986443...e-03, -5.2604647...e-03])
"""
X, Y, Z = tsplit(XYZ)
Y_b = as_float_array(Y_b)
F_S = as_float_array(F_S)
F_L = as_float_array(F_L)
# Account for background lightness contrast.
z = 1 + F_L * spow(Y_b / 100, 0.5)
# Computing modified *CIE L\\*a\\*b\\** colourspace array.
L = 116 * spow(f(Y / 100, F_S), z) - 16
a = 500 * (f(X / 95.05, F_S) - f(Y / 100, F_S))
b = 200 * (f(Y / 100, F_S) - f(Z / 108.88, F_S))
Lab = tstack([L, a, b])
return Lab
def hue_angle(a, b):
"""
Returns the *hue* angle :math:`h_L` in degrees.
Parameters
----------
a : numeric or array_like
Opponent colour dimension :math:`a`.
b : numeric or array_like
Opponent colour dimension :math:`b`.
Returns
-------
numeric or ndarray
*Hue* angle :math:`h_L` in degrees.
Examples
--------
>>> hue_angle(-4.49864756e-03, -5.26046353e-03) # doctest: +ELLIPSIS
229.4635727...
"""
a = as_float_array(a)
b = as_float_array(b)
h_L = np.degrees(np.arctan2(b, a)) % 360
return h_L
def chroma_correlate(a, b):
"""
Returns the correlate of *chroma* :math:`Ch_L`.
Parameters
----------
a : numeric or array_like
Opponent colour dimension :math:`a`.
b : numeric or array_like
Opponent colour dimension :math:`b`.
Returns
-------
numeric or ndarray
Correlate of *chroma* :math:`Ch_L`.
Examples
--------
>>> a = -4.49864756e-03
>>> b = -5.26046353e-03
>>> chroma_correlate(a, b) # doctest: +ELLIPSIS
0.0086506...
"""
a = as_float_array(a)
b = as_float_array(b)
c = spow(a ** 2 + b ** 2, 0.5)
Ch_L = 25 * np.log(1 + 0.05 * c)
return Ch_L
def colourfulness_correlate(L, L_L, Ch_L, F_C):
"""
Returns the correlate of *colourfulness* :math:`C_L`.
Parameters
----------
L : numeric or array_like
Absolute luminance :math:`L` of reference white in :math:`cd/m^2`.
L_L : numeric or array_like
Correlate of *Lightness* :math:`L_L`.
Ch_L : numeric or array_like
Correlate of *chroma* :math:`Ch_L`.
F_C : numeric or array_like
Chroma induction factor :math:`F_C`.
Returns
-------
numeric or ndarray
Correlate of *colourfulness* :math:`C_L`.
Examples
--------
>>> L = 318.31
>>> L_L = 37.368047493928195
>>> Ch_L = 0.008650662051714
>>> F_C = 1.0
>>> colourfulness_correlate(L, L_L, Ch_L, F_C) # doctest: +ELLIPSIS
0.0183832...
"""
L = as_float_array(L)
L_L = as_float_array(L_L)
Ch_L = as_float_array(Ch_L)
F_C = as_float_array(F_C)
S_C = 1 + 0.47 * np.log10(L) - 0.057 * np.log10(L) ** 2
S_M = 0.7 + 0.02 * L_L - 0.0002 * L_L ** 2
C_L = Ch_L * S_M * S_C * F_C
return C_L
def saturation_correlate(Ch_L, L_L):
"""
Returns the correlate of *saturation* :math:`S_L`.
Parameters
----------
Ch_L : numeric or array_like
Correlate of *chroma* :math:`Ch_L`.
L_L : numeric or array_like
Correlate of *Lightness* :math:`L_L`.
Returns
-------
numeric or ndarray
Correlate of *saturation* :math:`S_L`.
Examples
--------
>>> Ch_L = 0.008650662051714
>>> L_L = 37.368047493928195
>>> saturation_correlate(Ch_L, L_L) # doctest: +ELLIPSIS
0.0002314...
"""
Ch_L = as_float_array(Ch_L)
L_L = as_float_array(L_L)
S_L = Ch_L / L_L
return S_L
def final_opponent_signals(C_L, h_L):
"""
Returns the final opponent signals :math:`A_L` and :math:`B_L`.
Parameters
----------
C_L : numeric or array_like
Correlate of *colourfulness* :math:`C_L`.
h_L : numeric or array_like
Correlate of *hue* :math:`h_L` in degrees.
Returns
-------
ndarray
Final opponent signals :math:`A_L` and :math:`B_L`.
Examples
--------
>>> C_L = 0.0183832899143
>>> h_L = 229.46357270858391
>>> final_opponent_signals(C_L, h_L) # doctest: +ELLIPSIS
array([-0.0119478..., -0.0139711...])
"""
AB_L = polar_to_cartesian(tstack([C_L, np.radians(h_L)]))
return AB_L