Source code for colour.models.cie_luv

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
CIE Luv Colourspace
===================

Defines the *CIE Luv* colourspace transformations:

-   :func:`XYZ_to_Luv`
-   :func:`Luv_to_XYZ`
-   :func:`Luv_to_uv`
-   :func:`Luv_uv_to_xy`
-   :func:`Luv_to_LCHuv`
-   :func:`LCHuv_to_Luv`

See Also
--------
`CIE Luv Colourspace IPython Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/cie_luv.ipynb>`_

References
----------
.. [1]  Wikipedia. (n.d.). CIELUV. Retrieved February 24, 2014, from
        http://en.wikipedia.org/wiki/CIELUV
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.colorimetry import ILLUMINANTS
from colour.constants import CIE_E, CIE_K
from colour.models import xy_to_xyY, xyY_to_XYZ
from colour.utilities import tsplit, tstack

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2016 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'

__all__ = ['XYZ_to_Luv',
           'Luv_to_XYZ',
           'Luv_to_uv',
           'Luv_uv_to_xy',
           'Luv_to_LCHuv',
           'LCHuv_to_Luv']


[docs]def XYZ_to_Luv(XYZ, illuminant=ILLUMINANTS.get( 'CIE 1931 2 Degree Standard Observer').get('D50')): """ Converts from *CIE XYZ* tristimulus values to *CIE Luv* colourspace. Parameters ---------- XYZ : array_like *CIE XYZ* tristimulus values. illuminant : array_like, optional Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array. Returns ------- ndarray *CIE Luv* colourspace array. Notes ----- - Input *CIE XYZ* tristimulus values are in domain [0, 1]. - Input *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array are in domain [0, :math:`\infty`]. - Output :math:`L^*` is in range [0, 100]. References ---------- .. [2] Lindbloom, B. (2003). XYZ to Luv. Retrieved February 24, 2014, from http://brucelindbloom.com/Eqn_XYZ_to_Luv.html Examples -------- >>> XYZ = np.array([0.07049534, 0.10080000, 0.09558313]) >>> XYZ_to_Luv(XYZ) # doctest: +ELLIPSIS array([ 37.9856291..., -28.8021959..., -1.3580070...]) """ X, Y, Z = tsplit(XYZ) X_r, Y_r, Z_r = tsplit(xyY_to_XYZ(xy_to_xyY(illuminant))) y_r = Y / Y_r L = np.where(y_r > CIE_E, 116 * y_r ** (1 / 3) - 16, CIE_K * y_r) u = (13 * L * ((4 * X / (X + 15 * Y + 3 * Z)) - (4 * X_r / (X_r + 15 * Y_r + 3 * Z_r)))) v = (13 * L * ((9 * Y / (X + 15 * Y + 3 * Z)) - (9 * Y_r / (X_r + 15 * Y_r + 3 * Z_r)))) Luv = tstack((L, u, v)) return Luv
[docs]def Luv_to_XYZ(Luv, illuminant=ILLUMINANTS.get( 'CIE 1931 2 Degree Standard Observer').get('D50')): """ Converts from *CIE Luv* colourspace to *CIE XYZ* tristimulus values. Parameters ---------- Luv : array_like *CIE Luv* colourspace array. illuminant : array_like, optional Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array. Returns ------- ndarray *CIE XYZ* tristimulus values. Notes ----- - Input :math:`L^*` is in domain [0, 100]. - Input *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array are in domain [0, :math:`\infty`]. - Output *CIE XYZ* tristimulus values are in range [0, 1]. References ---------- .. [3] Lindbloom, B. (2003). Luv to XYZ. Retrieved February 24, 2014, from http://brucelindbloom.com/Eqn_Luv_to_XYZ.html Examples -------- >>> Luv = np.array([37.9856291 , -28.80219593, -1.35800706]) >>> Luv_to_XYZ(Luv) # doctest: +ELLIPSIS array([ 0.0704953..., 0.1008 , 0.0955831...]) """ L, u, v = tsplit(Luv) X_r, Y_r, Z_r = tsplit(xyY_to_XYZ(xy_to_xyY(illuminant))) Y = np.where(L > CIE_E * CIE_K, ((L + 16) / 116) ** 3, L / CIE_K) a = 1 / 3 * ((52 * L / (u + 13 * L * (4 * X_r / (X_r + 15 * Y_r + 3 * Z_r)))) - 1) b = -5 * Y c = -1 / 3.0 d = Y * (39 * L / (v + 13 * L * (9 * Y_r / (X_r + 15 * Y_r + 3 * Z_r))) - 5) X = (d - b) / (a - c) Z = X * a + b XYZ = tstack((X, Y, Z)) return XYZ
[docs]def Luv_to_uv(Luv, illuminant=ILLUMINANTS.get( 'CIE 1931 2 Degree Standard Observer').get('D50')): """ Returns the :math:`uv^p` chromaticity coordinates from given *CIE Luv* colourspace array. Parameters ---------- Luv : array_like *CIE Luv* colourspace array. illuminant : array_like, optional Reference *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array. Returns ------- ndarray :math:`uv^p` chromaticity coordinates. Notes ----- - Input :math:`L^*` is in domain [0, 100]. - Input *illuminant* *xy* chromaticity coordinates or *CIE xyY* colourspace array are in domain [0, :math:`\infty`]. - Output :math:`uv^p` chromaticity coordinates are in range [0, 1]. References ---------- .. [4] Wikipedia. (n.d.). The forward transformation. Retrieved February 24, 2014, from http://en.wikipedia.org/wiki/CIELUV#The_forward_transformation Examples -------- >>> Luv = np.array([37.9856291 , -28.80219593, -1.35800706]) >>> Luv_to_uv(Luv) # doctest: +ELLIPSIS array([ 0.1508531..., 0.4853297...]) """ X, Y, Z = tsplit(Luv_to_XYZ(Luv, illuminant)) uv = tstack((4 * X / (X + 15 * Y + 3 * Z), 9 * Y / (X + 15 * Y + 3 * Z))) return uv
[docs]def Luv_uv_to_xy(uv): """ Returns the *xy* chromaticity coordinates from given *CIE Luv* colourspace :math:`uv^p` chromaticity coordinates. Parameters ---------- uv : array_like *CIE Luv u"v"* chromaticity coordinates. Returns ------- ndarray *xy* chromaticity coordinates. Notes ----- - Input :math:`uv^p` chromaticity coordinates are in domain [0, 1]. - Output *xy* is in range [0, 1]. References ---------- .. [5] Wikipedia. (n.d.). The reverse transformation. Retrieved from http://en.wikipedia.org/wiki/CIELUV#The_reverse_transformation Examples -------- >>> uv = np.array([0.150853098829857, 0.485329708543180]) >>> Luv_uv_to_xy(uv) # doctest: +ELLIPSIS array([ 0.2641477..., 0.3777000...]) """ u, v = tsplit(uv) xy = tstack((9 * u / (6 * u - 16 * v + 12), 4 * v / (6 * u - 16 * v + 12))) return xy
[docs]def Luv_to_LCHuv(Luv): """ Converts from *CIE Luv* colourspace to *CIE LCHuv* colourspace. Parameters ---------- Luv : array_like *CIE Luv* colourspace array. Returns ------- ndarray *CIE LCHuv* colourspace array. Notes ----- - Input / output :math:`L^*` is in domain / range [0, 100]. References ---------- .. [6] Lindbloom, B. (2003). Luv to LCH(uv). Retrieved February 24, 2014, from http://www.brucelindbloom.com/Eqn_Luv_to_LCH.html Examples -------- >>> Luv = np.array([37.9856291 , -28.80219593, -1.35800706]) >>> Luv_to_LCHuv(Luv) # doctest: +ELLIPSIS array([ 37.9856291..., 28.8341927..., 182.6994640...]) """ L, u, v = tsplit(Luv) H = np.array(180 * np.arctan2(v, u) / np.pi) H[np.array(H < 0)] += 360 LCHuv = tstack((L, np.sqrt(u ** 2 + v ** 2), H)) return LCHuv
[docs]def LCHuv_to_Luv(LCHuv): """ Converts from *CIE LCHuv* colourspace to *CIE Luv* colourspace. Parameters ---------- LCHuv : array_like *CIE LCHuv* colourspace array. Returns ------- ndarray *CIE Luv* colourspace array. Notes ----- - Input / output :math:`L^*` is in domain / range [0, 100]. References ---------- .. [7] Lindbloom, B. (2006). LCH(uv) to Luv. Retrieved February 24, 2014, from http://www.brucelindbloom.com/Eqn_LCH_to_Luv.html Examples -------- >>> LCHuv = np.array([37.98562910, 28.83419279, 182.69946404]) >>> LCHuv_to_Luv(LCHuv) # doctest: +ELLIPSIS array([ 37.9856291..., -28.8021959..., -1.3580070...]) """ L, C, H = tsplit(LCHuv) Luv = tstack((L, C * np.cos(np.radians(H)), C * np.sin(np.radians(H)))) return Luv