Source code for colour.colorimetry.uniformity
"""
Spectral Uniformity
===================
Defines the objects to compute the *spectral uniformity*
(or *spectral flatness*) of spectral distributions.
References
----------
- :cite:`David2015a` : David, A., Fini, P. T., Houser, K. W., Ohno, Y.,
Royer, M. P., Smet, K. A. G., Wei, M., & Whitehead, L. (2015). Development
of the IES method for evaluating the color rendition of light sources.
Optics Express, 23(12), 15888. doi:10.1364/OE.23.015888
"""
from __future__ import annotations
import numpy as np
from colour.colorimetry import (
MultiSpectralDistributions,
SpectralDistribution,
sds_and_msds_to_msds,
)
from colour.hints import Boolean, List, NDArray, Union
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 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__ = [
"spectral_uniformity",
]
[docs]def spectral_uniformity(
sds: Union[
List[Union[SpectralDistribution, MultiSpectralDistributions]],
MultiSpectralDistributions,
],
use_second_order_derivatives: Boolean = False,
) -> NDArray:
"""
Compute the *spectral uniformity* (or *spectral flatness*) of given
spectral distributions.
Spectral uniformity :math:`(r')^2` is computed as follows:
:math:`mean((r'_1)^2, (r'_2)^2, ..., (r'_n)^2)`
where :math:`(r'_i)^2` is the first-order derivative, squared, of the
reflectance :math:`r_i` of a test sample.
Parameters
----------
sds
Spectral distributions or multi-spectral distributions to
compute the spectral uniformity of. `sds` can be a single
:class:`colour.MultiSpectralDistributions` class instance, a list
of :class:`colour.MultiSpectralDistributions` class instances or a
list of :class:`colour.SpectralDistribution` class instances.
use_second_order_derivatives
Whether to use the second-order derivatives in the computations.
Returns
-------
:class:`numpy.ndarray`
Spectral uniformity.
Warnings
--------
The spectral distributions must have the same spectral shape.
References
----------
:cite:`David2015a`
Examples
--------
>>> from colour.quality.datasets import SDS_TCS
>>> spectral_uniformity(SDS_TCS.values()) # doctest: +ELLIPSIS
array([ 9.5514285...e-06, 1.1482142...e-05, 1.8784285...e-05,
2.8711428...e-05, 3.1971428...e-05, 3.2342857...e-05,
3.3850000...e-05, 3.9925714...e-05, 4.1333571...e-05,
2.4002142...e-05, 5.7621428...e-06, 1.4757142...e-06,
9.7928571...e-07, 2.0057142...e-06, 3.7157142...e-06,
5.7678571...e-06, 7.5557142...e-06, 7.4635714...e-06,
5.7492857...e-06, 3.8692857...e-06, 3.5407142...e-06,
4.4742857...e-06, 5.6435714...e-06, 7.6371428...e-06,
1.0171428...e-05, 1.2254285...e-05, 1.4810000...e-05,
1.6517142...e-05, 1.5430714...e-05, 1.4536428...e-05,
1.4037857...e-05, 1.1587857...e-05, 1.0743571...e-05,
1.0979285...e-05, 1.0398571...e-05, 8.2971428...e-06,
6.3057142...e-06, 5.0942857...e-06, 4.8500000...e-06,
5.5371428...e-06, 6.4128571...e-06, 7.2592857...e-06,
7.7750000...e-06, 7.1607142...e-06, 6.6635714...e-06,
6.7328571...e-06, 7.5307142...e-06, 1.0733571...e-05,
1.6234285...e-05, 2.2570714...e-05, 2.7056428...e-05,
2.7781428...e-05, 2.5025714...e-05, 1.7966428...e-05,
1.0505000...e-05, 5.9657142...e-06, 3.6421428...e-06,
2.1664285...e-06, 1.2935714...e-06, 8.3642857...e-07,
7.2500000...e-07, 6.3928571...e-07, 6.6285714...e-07,
8.5571428...e-07, 1.4507142...e-06, 2.2542857...e-06,
3.4142857...e-06, 4.9864285...e-06, 6.4907142...e-06,
7.8928571...e-06, 9.1664285...e-06, 9.9521428...e-06,
9.7664285...e-06, 9.3150000...e-06, 8.9092857...e-06,
8.1578571...e-06, 6.8935714...e-06, 5.5721428...e-06,
4.4592857...e-06, 3.4778571...e-06, 2.7650000...e-06,
2.3114285...e-06, 1.7092857...e-06, 1.1771428...e-06,
9.8428571...e-07, 8.8285714...e-07, 7.4142857...e-07,
7.0142857...e-07, 7.0857142...e-07, 6.6642857...e-07,
7.5928571...e-07, 8.7000000...e-07, 8.2714285...e-07,
7.1714285...e-07, 6.6000000...e-07])
"""
msds = sds_and_msds_to_msds(sds)
interval = msds.shape.interval
r_i = np.gradient(np.transpose(msds.values), axis=1) / interval
if use_second_order_derivatives:
r_i = np.gradient(r_i, axis=1) / interval
return np.mean(r_i**2, axis=0)