Source code for colour.models.derivation

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

"""
RGB Colourspace Derivation
==========================

Defines objects related to *RGB* colourspace derivation, essentially
calculating the normalised primary matrix for given *RGB* colourspace primaries
and whitepoint.

See Also
--------
`RGB Colourspaces IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/models/rgb.ipynb>`_  # noqa

References
----------
.. [1]  SMPTE. (1993). Derivation of Basic Television Color Equations. In
        RP 177:1993 (Vol. RP 177:199). doi:10.5594/S9781614821915
"""

from __future__ import division, unicode_literals

import numpy as np

from colour.models import XYZ_to_xy, xy_to_XYZ
from colour.utilities import tsplit

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2015 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'

__all__ = ['xy_to_z',
           'normalised_primary_matrix',
           'primaries_whitepoint',
           'RGB_luminance_equation',
           'RGB_luminance']


[docs]def xy_to_z(xy): """ Returns the *z* coordinate using given *xy* chromaticity coordinates. Parameters ---------- xy : array_like *xy* chromaticity coordinates. Returns ------- numeric *z* coordinate. Examples -------- >>> xy_to_z(np.array([0.25, 0.25])) 0.5 """ x, y = tsplit(xy) z = 1 - x - y return z
[docs]def normalised_primary_matrix(primaries, whitepoint): """ Returns the *normalised primary matrix* using given *primaries* and *whitepoint*. Parameters ---------- primaries : array_like, (3, 2) Primaries chromaticity coordinates. whitepoint : array_like Illuminant / whitepoint chromaticity coordinates. Returns ------- ndarray, (3, 3) *Normalised primary matrix*. Examples -------- >>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700]) >>> whitepoint = np.array([0.32168, 0.33767]) >>> normalised_primary_matrix(pms, whitepoint) # doctest: +ELLIPSIS array([[ 9.5255239...e-01, 0.0000000...e+00, 9.3678631...e-05], [ 3.4396645...e-01, 7.2816609...e-01, -7.2132546...e-02], [ 0.0000000...e+00, 0.0000000...e+00, 1.0088251...e+00]]) """ primaries = np.reshape(primaries, (3, 2)) z = xy_to_z(primaries)[..., np.newaxis] primaries = np.transpose(np.hstack((primaries, z))) whitepoint = xy_to_XYZ(whitepoint) coefficients = np.dot(np.linalg.inv(primaries), whitepoint) coefficients = np.diagflat(coefficients) npm = np.dot(primaries, coefficients) return npm
[docs]def primaries_whitepoint(npm): """ Returns *primaries* and *whitepoint* using given *normalised primary matrix*. Parameters ---------- npm : array_like, (3, 3) *Normalised primary matrix*. Returns ------- tuple *Primaries* and *whitepoint*. References ---------- .. [2] Trieu, T. (2015). Private Discussion with Mansencal, T. Examples -------- >>> npm = np.array([[9.52552396e-01, 0.00000000e+00, 9.36786317e-05], ... [3.43966450e-01, 7.28166097e-01, -7.21325464e-02], ... [0.00000000e+00, 0.00000000e+00, 1.00882518e+00]]) >>> p, w = primaries_whitepoint(npm) >>> p # doctest: +ELLIPSIS array([[ 7.3470000...e-01, 2.6530000...e-01], [ 0.0000000...e+00, 1.0000000...e+00], [ 1.0000000...e-04, -7.7000000...e-02]]) >>> w # doctest: +ELLIPSIS array([ 0.32168, 0.33767]) """ npm = npm.reshape((3, 3)) primaries = XYZ_to_xy( np.transpose(np.dot(npm, np.identity(3)))) whitepoint = np.squeeze(XYZ_to_xy( np.transpose(np.dot(npm, np.ones((3, 1)))))) # TODO: Investigate if we return an ndarray here with primaries and # whitepoint stacked together. return primaries, whitepoint
[docs]def RGB_luminance_equation(primaries, whitepoint): """ Returns the *luminance equation* from given *primaries* and *whitepoint*. Parameters ---------- primaries : array_like, (3, 2) Primaries chromaticity coordinates. whitepoint : array_like Illuminant / whitepoint chromaticity coordinates. Returns ------- unicode *Luminance* equation. Examples -------- >>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700]) >>> whitepoint = np.array([0.32168, 0.33767]) >>> # Doctests skip for Python 2.x compatibility. >>> RGB_luminance_equation(pms, whitepoint) # doctest: +SKIP 'Y = 0.3439664...(R) + 0.7281660...(G) + -0.0721325...(B)' """ return 'Y = {0}(R) + {1}(G) + {2}(B)'.format( *np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6])
[docs]def RGB_luminance(RGB, primaries, whitepoint): """ Returns the *luminance* :math:`Y` of given *RGB* components from given *primaries* and *whitepoint*. Parameters ---------- RGB : array_like *RGB* chromaticity coordinate matrix. primaries : array_like, (3, 2) Primaries chromaticity coordinate matrix. whitepoint : array_like Illuminant / whitepoint chromaticity coordinates. Returns ------- numeric or ndarray *Luminance* :math:`Y`. Examples -------- >>> RGB = np.array([40.6, 4.2, 67.4]) >>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700]) >>> whitepoint = np.array([0.32168, 0.33767]) >>> RGB_luminance(RGB, pms, whitepoint) # doctest: +ELLIPSIS 12.1616018... """ R, G, B = tsplit(RGB) X, Y, Z = np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6] L = X * R + Y * G + Z * B return L