Source code for colour.appearance.llab

# -*- 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`

References
----------
-   :cite:`Fairchild2013x` : Fairchild, M. D. (2013). LLAB Model. In Color
    Appearance Models (3rd ed., pp. 6025-6178). Wiley. ISBN:B00DAYO8E2
-   :cite:`Luo1996b` : Luo, Ming Ronnier, 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, Ming Ronnier, & Morovic, J. (1996). Two Unsolved
    Issues in Colour Management - Colour Appearance and Gamut Mapping.
    Conference: 5th International Conference on High Technology: Imaging
    Science and Technology - Evolution & Promise, 136-147.
    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) 2013-2020 - Colour Developers'
__license__ = 'New BSD License - https://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-developers@colour-science.org'
__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