#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Variance Minimization Light Probe Sampling - Viriyothai (2009)
==============================================================
Defines Viriyothai (2009) variance minimization light probe sampling objects:
- :func:`light_probe_sampling_variance_minimization`
References
----------
.. [1] Viriyothai, K., & Debevec, P. (2009). Variance minimization light probe
sampling. SIGGRAPH’09: Posters, (Egsr), 60558.
doi:10.1145/1599301.1599393
"""
from __future__ import division, unicode_literals
import numpy as np
from collections import namedtuple
from colour import centroid, warning
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2015-2016 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['DEFAULT_LUMINANCE_FACTORS',
'Light_Specification',
'luminance_variance',
'find_regions_variance_minimization',
'highlight_regions_variance_minimization',
'light_probe_sampling_variance_minimization']
DEFAULT_LUMINANCE_FACTORS = np.array([0.2126, 0.7152, 0.0722])
"""
Default weighting factors for Luminance conversion, i.e., *Rec. 709*.
DEFAULT_LUMINANCE_FACTORS : array_like
"""
[docs]class Light_Specification(
namedtuple('Light_Specification', ('uv', 'colour', 'index'))):
"""
Defines a light probe sampling resulting light specification.
Parameters
----------
uv : array_like
:math:`uv` coordinates of the sampled light.
colour : array_like
Sampled light colour.
index : array_like
Sampled light location index in its original array.
"""
[docs]def luminance_variance(a):
"""
Computes the Luminance variance of given :math:`a` 2-D array.
Parameters
----------
a : array_like
:math:`a` 2-D array to compute the Luminance variation.
Returns
-------
numeric
:math:`a` 2-D array Luminance variance.
Examples
--------
>>> a = np.tile(np.arange(5), (5, 1))
>>> luminance_variance(a) # doctest: +ELLIPSIS
12.2474487...
"""
x, y = np.mgrid[0:np.shape(a)[0], 0:np.shape(a)[1]]
x_centroid, y_centroid = centroid(a)
variance = np.sqrt(np.sum(
a * ((y - y_centroid) ** 2 + (x - x_centroid) ** 2)))
return variance
[docs]def find_regions_variance_minimization(a, n=4):
"""
Finds the :math:`2^n` regions using Viriyothai (2009) variance minimization
light probe sampling algorithm on given :math:`a` 2-D array.
Parameters
----------
a : array_like
:math:`a` 2-D array to find the regions.
n : int
Iterations count, the total regions count is :math:`2^n`.
Returns
-------
list
Regions with variance minimized.
"""
a = np.asarray(a)
regions = [(0, a.shape[0], 0, a.shape[1])]
for i in range(n):
sub_regions = []
for region in regions:
variance = np.inf
horizontal = False
location = -1
y_min, y_max, x_min, x_max = region
# Vertical cut on image width.
for j in range(x_min, x_max):
variance_c = max(
luminance_variance(a[y_min:y_max, x_min:j]),
luminance_variance(a[y_min:y_max, j:x_max]))
if variance_c < variance:
variance = variance_c
horizontal = False
location = j
# Horizontal cut on image height.
for j in range(y_min, y_max):
variance_c = max(
luminance_variance(a[y_min:j, x_min:x_max]),
luminance_variance(a[j:y_max, x_min:x_max]))
if variance_c < variance:
variance = variance_c
horizontal = True
location = j
if horizontal:
sub_regions.append((y_min, location, x_min, x_max))
sub_regions.append((location, y_max, x_min, x_max))
else:
sub_regions.append((y_min, y_max, x_min, location))
sub_regions.append((y_min, y_max, location, x_max))
regions = sub_regions
return regions
[docs]def highlight_regions_variance_minimization(
a,
regions,
highlight_colour=np.array([0, 1, 0])):
"""
Highlights regions using with variance minimized on given :math:`a`
3-D array.
Parameters
----------
a : array_like
:math:`a` 3-D array to highlight the regions.
regions : array_like
Regions with variance minimized.
highlight_colour : array_like
Highlight colour.
Returns
-------
ndarray
:math:`a` 3-D array with highlighted regions.
"""
a = np.copy(a)
for region in regions:
y_min, y_max, x_min, x_max = region
a[y_min:y_max, x_min] = highlight_colour
a[y_min:y_max, x_max - 1] = highlight_colour
a[y_min, x_min:x_max] = highlight_colour
a[y_max - 1, x_min:x_max] = highlight_colour
return a
[docs]def light_probe_sampling_variance_minimization(
light_probe,
lights_count=16,
luminance_factors=DEFAULT_LUMINANCE_FACTORS):
"""
Sample given light probe to find lights using Viriyothai (2009) variance
minimization light probe sampling algorithm.
Parameters
----------
light_probe : array_like
Array to sample for lights.
lights_count : int
Amount of lights to generate.
luminance_factors : array_like
Weighting factors for Luminance conversion.
Returns
-------
list
list of :class:`Light_Specification` lights.
"""
light_probe = np.asarray(light_probe)
iterations = np.sqrt(lights_count).astype(np.int_)
if iterations ** 2 != lights_count:
warning(
'{0} lights requested, {1} will be effectively computed!'.format(
lights_count, iterations ** 2))
Y = np.dot(light_probe, luminance_factors)
regions = find_regions_variance_minimization(Y, iterations)
lights = []
for region in regions:
y_min, y_max, x_min, x_max = region
c = centroid(Y[y_min:y_max, x_min:x_max])
c = (c + np.array([y_min, x_min]))
lights.append(
Light_Specification(
(c / np.array(Y.shape))[::-1],
np.sum(np.sum(light_probe[y_min:y_max, x_min:x_max], 0), 0),
c))
return lights