#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
LLAB(l:c) Colour Appearance Model
=================================
Defines *LLAB(l:c)* colour appearance model objects:
- :class:`LLAB_InductionFactors`
- :attr:`LLAB_VIEWING_CONDITIONS`
- :class:`LLAB_Specification`
- :func:`XYZ_to_LLAB`
See Also
--------
`LLAB(l:c) Colour Appearance Model IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/appearance/llab.ipynb>`_ # noqa
References
----------
.. [1] **Mark D. Fairchild**, *Color Appearance Models, 3nd Edition*,
The Wiley-IS&T Series in Imaging Science and Technology,
published June 2013, ASIN: B00DAYO8E2,
locations 6019-6178.
.. [2] **Luo, M. R., & Morovic, J.**,
*Two Unsolved Issues in Colour Management – Colour Appearance and
Gamut Mapping*,
*5th International Conference on High Technology: Imaging Science and
Technology – Evolution & Promise*
published 1996, pp. 136–147.
.. [3] **Luo, M. R., Lo, M. C., & Kuo, W. G.**,
*The LLAB (l:c) colour model*,
*Color Research & Application, Volume 21, Issue 6, pages 412–429,
December 1996*
"""
from __future__ import division, unicode_literals
import math
import numpy as np
from collections import namedtuple
from colour.utilities import CaseInsensitiveMapping
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'GPL V3.0 - http://www.gnu.org/licenses/'
__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'))):
"""
*LLAB(l:c)* colour appearance model induction factors.
Parameters
----------
D : numeric
*Discounting-the-Illuminant* factor :math:`D` in domain [0, 1].
F_S : numeric
Surround induction factor :math:`F_S`.
F_L : numeric
*Lightness* induction factor :math:`F_L`.
F_C : numeric
*Chroma* induction factor :math:`F_C`.
"""
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))})
"""
Reference *LLAB(l:c)* colour appearance model viewing conditions.
LLAB_VIEWING_CONDITIONS : dict
('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'] = (
LLAB_VIEWING_CONDITIONS[
'Reference Samples & Images, Average Surround, Subtending > 4'])
LLAB_VIEWING_CONDITIONS['ref_average_4_minus'] = (
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* colourspace matrix to normalised
cone responses matrix.
LLAB_XYZ_TO_RGB_MATRIX : array_like, (3, 3)
"""
LLAB_RGB_TO_XYZ_MATRIX = np.around(
np.linalg.inv(LLAB_XYZ_TO_RGB_MATRIX),
decimals=4)
"""
*LLAB(l:c)* colour appearance model normalised cone responses to *CIE XYZ*
colourspace matrix.
Notes
-----
- This matrix has been rounded on purpose to 4 decimals so that we keep
consistency with **Mark D. Fairchild** implementation results.
LLAB_RGB_TO_XYZ_MATRIX : array_like, (3, 3)
"""
[docs]class LLAB_ReferenceSpecification(
namedtuple('LLAB_ReferenceSpecification',
('L_L', 'Ch_L', 'h_L', 's_L', 'C_L', 'HC', 'A_L', 'B_L'))):
"""
Defines the *LLAB(l:c)* colour appearance model reference specification.
This specification has field names consistent with **Mark D. Fairchild**
reference.
Parameters
----------
L_L : numeric
Correlate of *Lightness* :math:`L_L`.
Ch_L : numeric
Correlate of *chroma* :math:`Ch_L`.
h_L : numeric
*Hue* angle :math:`h_L` in degrees.
s_L : numeric
Correlate of *saturation* :math:`s_L`.
C_L : numeric
Correlate of *colourfulness* :math:`C_L`.
HC : numeric
*Hue* :math:`h` composition :math:`H^C`.
A_L : numeric
Opponent signal :math:`A_L`.
B_L : numeric
Opponent signal :math:`B_L`.
"""
[docs]class LLAB_Specification(
namedtuple('LLAB_Specification',
('J', 'C', 'h', 's', 'M', 'HC', 'a', 'b'))):
"""
Defines the *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
**Mark D. Fairchild** reference.
Parameters
----------
J : numeric
Correlate of *Lightness* :math:`L_L`.
C : numeric
Correlate of *chroma* :math:`Ch_L`.
h : numeric
*Hue* angle :math:`h_L` in degrees.
s : numeric
Correlate of *saturation* :math:`s_L`.
M : numeric
Correlate of *colourfulness* :math:`C_L`.
HC : numeric
*Hue* :math:`h` composition :math:`H^C`.
a : numeric
Opponent signal :math:`A_L`.
b : numeric
Opponent signal :math:`B_L`.
"""
[docs]def XYZ_to_LLAB(
XYZ,
XYZ_0,
Y_b,
L,
surround=LLAB_VIEWING_CONDITIONS.get(
'Reference Samples & Images, Average Surround, Subtending < 4')):
"""
Computes the *LLAB(L:c)* colour appearance model correlates.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix of test sample / stimulus in domain
[0, 100].
XYZ_0 : array_like, (3,)
*CIE XYZ* colourspace matrix of reference white in domain [0, 100].
Y_b : numeric
Luminance factor of the background in :math:`cd/m^2`.
L : numeric
Absolute luminance :math:`L` of reference white in :math:`cd/m^2`.
surround : LLAB_InductionFactors, optional
Surround viewing conditions induction factors.
Returns
-------
LLAB_Specification
*LLAB(L:c)* colour appearance model specification.
Warning
-------
The output domain of that definition is non standard!
Notes
-----
- Input *CIE XYZ* colourspace matrix is in domain [0, 100].
- Input *CIE XYZ_0* colourspace matrix is in domain [0, 100].
Examples
--------
>>> XYZ = np.array([19.01, 20, 21.78])
>>> XYZ_0 = np.array([95.05, 100, 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=37.3680474..., C=0.0086506..., h=229.4635727..., s=0.0002314..., M=0.0183832..., HC=None, a=-0.0119478..., b=-0.0139711...)
"""
X, Y, Z = np.ravel(XYZ)
RGB = XYZ_to_RGB_LLAB(XYZ)
RGB_0 = XYZ_to_RGB_LLAB(XYZ_0)
# Reference illuminant *CIE Standard Illuminant D Series* *D65*.
XYZ_0r = np.array([95.05, 100, 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 = 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)
h_Lr = math.radians(h_L)
# TODO: Implement hue composition computation.
# -------------------------------------------------------------------------
# Computing final opponent signals.
# -------------------------------------------------------------------------
A_L, B_L = final_opponent_signals(C_L, h_Lr)
return LLAB_Specification(L_L, Ch_L, h_L, s_L, C_L, None, A_L, B_L)
[docs]def XYZ_to_RGB_LLAB(XYZ):
"""
Converts from *CIE XYZ* colourspace to normalised cone responses.
Parameters
----------
XYZ : array_like, (3,)
*CIE XYZ* colourspace matrix.
Returns
-------
ndarray, (3,)
Normalised cone responses.
Examples
--------
>>> XYZ = np.array([19.01, 20, 21.78])
>>> XYZ_to_RGB_LLAB(XYZ) # doctest: +ELLIPSIS
array([ 0.9414279..., 1.0404012..., 1.0897088...])
"""
return LLAB_XYZ_TO_RGB_MATRIX.dot(XYZ / XYZ[1])
[docs]def chromatic_adaptation(RGB, RGB_0, RGB_0r, Y, D=1):
"""
Applies chromatic adaptation to given *RGB* normalised cone responses
matrix.
Parameters
----------
RGB : array_like, (3,)
*RGB* normalised cone responses matrix of test sample / stimulus.
RGB_0 : array_like, (3,)
*RGB* normalised cone responses matrix of reference white.
RGB_0r : array_like, (3,)
*RGB* normalised cone responses matrix of reference illuminant
*CIE Standard Illuminant D Series* *D65*.
Y : numeric
Tristimulus values :math:`Y` of the stimulus.
D : numeric, optional
*Discounting-the-Illuminant* factor in domain [0, 1].
Returns
-------
ndarray, (3,)
Adapted *CIE XYZ* colourspace matrix.
Examples
--------
>>> RGB = np.array([0.94142795, 1.0404012, 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([ 19.0099957..., 20.0009186..., 21.7799386...])
"""
R, G, B = np.ravel(RGB)
R_0, G_0, B_0 = np.ravel(RGB_0)
R_0r, G_0r, B_0r = np.ravel(RGB_0r)
beta = (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 / (B_0 ** beta)) + 1 - D) * (abs(B) ** beta)
RGB_r = np.array([R_r, G_r, B_r])
X_r, Y_r, Z_r = LLAB_RGB_TO_XYZ_MATRIX.dot(RGB_r * Y)
return np.array([X_r, Y_r, Z_r])
[docs]def f(x, F_S):
"""
Defines the nonlinear response function of the *LLAB(L:c)* colour
appearance model used to model the nonlinear behavior of various visual
responses.
Parameters
----------
x : numeric or array_like
Visual response variable :math:`x`.
F_S : numeric
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(0.20000918623399996, 3) # doctest: +ELLIPSIS
array(0.5848125...)
"""
x_m = np.where(x > 0.008856,
x ** (1 / F_S),
((((0.008856 ** (1 / F_S)) -
(16 / 116)) / 0.008856) * x + (16 / 116)))
return x_m
[docs]def opponent_colour_dimensions(XYZ, Y_b, F_S, F_L):
"""
Returns opponent colour dimensions from given adapted *CIE XYZ* colourspace
matrix.
The opponent colour dimensions are based on a modified *CIE Lab*
colourspace formulae.
Parameters
----------
XYZ : array_like, (3,)
Adapted *CIE XYZ* colourspace matrix.
Y_b : numeric
Luminance factor of the background in :math:`cd/m^2`.
F_S : numeric
Surround induction factor :math:`F_S`.
F_L : numeric
Lightness induction factor :math:`F_L`.
Returns
-------
ndarray, (3,)
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 = np.ravel(XYZ)
# Account for background lightness contrast.
z = 1 + F_L * ((Y_b / 100) ** 0.5)
# Computing modified *CIE Lab* colourspace matrix.
L = 116 * (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))
return np.array([L, a, b])
[docs]def hue_angle(a, b):
"""
Returns the *hue* angle :math:`h_L` in degrees.
Parameters
----------
a : numeric
Opponent colour dimension :math:`a`.
b : numeric
Opponent colour dimension :math:`b`.
Returns
-------
numeric
*Hue* angle :math:`h_L` in degrees.
Examples
--------
>>> hue_angle(-4.49864756e-03, -5.26046353e-03) # doctest: +ELLIPSIS
229.4635727...
"""
h_L = math.degrees(np.arctan2(b, a)) % 360
return h_L
[docs]def chroma_correlate(a, b):
"""
Returns the correlate of *chroma* :math:`Ch_L`.
Parameters
----------
a : numeric
Opponent colour dimension :math:`a`.
b : numeric
Opponent colour dimension :math:`b`.
Returns
-------
numeric
Correlate of *chroma* :math:`Ch_L`.
Examples
--------
>>> a = -4.49864756e-03
>>> b = -5.26046353e-03
>>> chroma_correlate(a, b) # doctest: +ELLIPSIS
0.0086506...
"""
c = (a ** 2 + b ** 2) ** 0.5
Ch_L = 25 * np.log(1 + 0.05 * c)
return Ch_L
[docs]def colourfulness_correlate(L, L_L, Ch_L, F_C):
"""
Returns the correlate of *colourfulness* :math:`C_L`.
Parameters
----------
L : numeric
Absolute luminance :math:`L` of reference white in :math:`cd/m^2`.
L_L : numeric
Correlate of *Lightness* :math:`L_L`.
Ch_L : numeric
Correlate of *chroma* :math:`Ch_L`.
F_C : numeric
Chroma induction factor :math:`F_C`.
Returns
-------
numeric
Correlate of *colourfulness* :math:`C_L`.
Examples
--------
>>> L = 318.31
>>> L_L = 37.368047493928195
>>> Ch_L = 0.0086506620517144972
>>> F_C = 1.0
>>> colourfulness_correlate(L, L_L, Ch_L, F_C) # doctest: +ELLIPSIS
0.0183832...
"""
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
[docs]def saturation_correlate(Ch_L, L_L):
"""
Returns the correlate of *saturation* :math:`S_L`.
Parameters
----------
Ch_L : numeric
Correlate of *chroma* :math:`Ch_L`.
L_L : numeric
Correlate of *Lightness* :math:`L_L`.
Returns
-------
numeric
Correlate of *saturation* :math:`S_L`.
Examples
--------
>>> Ch_L = 0.0086506620517144972
>>> L_L = 37.368047493928195
>>> saturation_correlate(Ch_L, L_L) # doctest: +ELLIPSIS
0.0002314...
"""
S_L = Ch_L / L_L
return S_L
[docs]def final_opponent_signals(C_L, h_L):
"""
Returns the final opponent signals :math:`A_L` and :math:`B_L`.
Parameters
----------
C_L : numeric
Correlate of *colourfulness* :math:`C_L`.
h_L : numeric
Correlate of *hue* :math:`h_L` in radians.
Returns
-------
tuple
Final opponent signals :math:`A_L` and :math:`B_L`.
Examples
--------
>>> C_L = 0.0183832899143
>>> h_L = 4.004894857014253
>>> final_opponent_signals(C_L, h_L) # doctest: +ELLIPSIS
(-0.0119478..., -0.0139711...)
"""
A_L = C_L * np.cos(h_L)
B_L = C_L * np.sin(h_L)
return A_L, B_L
Colour 0.3