"""
Global Tonemapping Operators
============================
Defines the global tonemapping operators objects:
- :func:`colour_hdri.tonemapping_operator_simple`
- :func:`colour_hdri.tonemapping_operator_normalisation`
- :func:`colour_hdri.tonemapping_operator_gamma`
- :func:`colour_hdri.tonemapping_operator_logarithmic`
- :func:`colour_hdri.tonemapping_operator_exponential`
- :func:`colour_hdri.tonemapping_operator_logarithmic_mapping`
- :func:`colour_hdri.tonemapping_operator_exponentiation_mapping`
- :func:`colour_hdri.tonemapping_operator_Schlick1994`
- :func:`colour_hdri.tonemapping_operator_Tumblin1999`
- :func:`colour_hdri.tonemapping_operator_Reinhard2004`
- :func:`colour_hdri.tonemapping_operator_filmic`
See Also
--------
`Colour - HDRI - Examples: Global Tonemapping Operators Jupyter Notebook
<https://github.com/colour-science/colour-hdri/blob/master/colour_hdri/\
examples/examples_global_tonemapping_operators.ipynb>`__
References
----------
- :cite:`Banterle2011k` : Banterle, F., Artusi, A., Debattista, K., &
Chalmers, A. (2011). 3.2.1 Simple Mapping Methods. In Advanced High
Dynamic Range Imaging (pp. 38-41). A K Peters/CRC Press.
ISBN:978-1-56881-719-4
- :cite:`Habble2010d` : Habble, J. (2010). Filmic Tonemapping Operators.
Retrieved March 15, 2015, from http://filmicgames.com/archives/75
- :cite:`Habble2010e` : Habble, J. (2010). Uncharted 2: HDR Lighting.
Retrieved March 15, 2015, from
http://www.slideshare.net/ozlael/hable-john-uncharted2-hdr-lighting
- :cite:`Reinhard2005c` : Reinhard, E., & Devlin, K. (2005). Dynamic Range
Reduction Inspired by Photoreceptor Physiology. IEEE Transactions on
Visualization and Computer Graphics, 11(01), 13-24. doi:10.1109/TVCG.2005.9
- :cite:`Schlick1994` : Schlick, C. (1994). Quantization Techniques for
Visualization of High Dynamic Range Pictures. Proceedings of the Fifth
Eurographics Workshop on Rendering, Section 5, 7-18. ISSN:0920-5691
- :cite:`Tumblin1999c` : Tumblin, J., Hodgins, J. K., & Guenter, B. K.
(1999). Two methods for display of high contrast images. ACM Transactions
on Graphics, 18(1), 56-94. doi:10.1145/300776.300783
- :cite:`Wikipediabn` : Wikipedia. (n.d.). Tonemapping - Purpose and
methods. Retrieved March 15, 2015, from
http://en.wikipedia.org/wiki/Tone_mapping#Purpose_and_methods
"""
from __future__ import annotations
import numpy as np
from colour.constants import EPSILON
from colour.hints import ArrayLike, NDArrayFloat, cast
from colour.models import RGB_COLOURSPACES, RGB_Colourspace, RGB_luminance
from colour.utilities import as_float_array
__author__ = "Colour Developers"
__copyright__ = "Copyright 2015 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"log_average",
"tonemapping_operator_simple",
"tonemapping_operator_normalisation",
"tonemapping_operator_gamma",
"tonemapping_operator_logarithmic",
"tonemapping_operator_exponential",
"tonemapping_operator_logarithmic_mapping",
"tonemapping_operator_exponentiation_mapping",
"tonemapping_operator_Schlick1994",
"tonemapping_operator_Tumblin1999",
"tonemapping_operator_Reinhard2004",
"tonemapping_operator_filmic",
]
def log_average(a: ArrayLike, epsilon: float = EPSILON) -> NDArrayFloat:
"""
Compute the log average of given array.
Parameters
----------
a
Array to compute the log average.
epsilon
Constant to avoid singularities in computations.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Array log average.
Examples
--------
>>> log_average(np.linspace(0, 10, 10)) # doctest: +ELLIPSIS
0.1...
"""
a = as_float_array(a)
average = np.exp(np.average(np.log(a + epsilon)))
return average
[docs]
def tonemapping_operator_simple(RGB: ArrayLike) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the simple method:
:math:`\\cfrac{RGB}{RGB + 1}`.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Wikipediabn`
Examples
--------
>>> tonemapping_operator_simple(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.3245382..., 0.2601156..., 0.1911532...],
[ 0.5830618..., 0.3567839..., 0.2808993...]],
<BLANKLINE>
[[ 0.8150290..., 0.6831692..., 0.5733340...],
[ 0.8683127..., 0.7746486..., 0.6893211...]]])
"""
RGB = as_float_array(RGB)
return RGB / (RGB + 1)
[docs]
def tonemapping_operator_normalisation(
RGB: ArrayLike, colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"]
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the normalisation method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Banterle2011k`
Examples
--------
>>> tonemapping_operator_normalisation(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.1194997..., 0.0874388..., 0.0587783...],
[ 0.3478122..., 0.1379590..., 0.0971544...]],
<BLANKLINE>
[[ 1.0959009..., 0.5362936..., 0.3342115...],
[ 1.6399638..., 0.8549608..., 0.5518382...]]])
"""
RGB = as_float_array(RGB)
L = RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
L_max = as_float_array(np.max(L))
return RGB / L_max
[docs]
def tonemapping_operator_gamma(
RGB: ArrayLike, gamma: float = 1, EV: float = 0
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the gamma and exposure
correction method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
gamma
:math:`\\gamma` correction value.
EV
Exposure adjustment value.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Banterle2011k`
Examples
--------
>>> tonemapping_operator_gamma(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... ),
... 1.0,
... -3.0,
... ) # doctest: +ELLIPSIS
array([[[ 0.0600585..., 0.0439453..., 0.0295410...],
[ 0.1748046..., 0.0693359..., 0.0488282...]],
<BLANKLINE>
[[ 0.5507817..., 0.2695323..., 0.1679692...],
[ 0.8242187..., 0.4296892..., 0.2773447...]]])
"""
RGB = as_float_array(RGB)
exposure = 2**EV
RGB = (exposure * RGB) ** (1 / gamma)
return RGB
[docs]
def tonemapping_operator_logarithmic(
RGB: ArrayLike,
q: float = 1,
k: float = 1,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the logarithmic method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
q
:math:`q`.
k
:math:`k`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Banterle2011k`
Examples
--------
>>> tonemapping_operator_logarithmic(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... ),
... 1.0,
... 25,
... ) # doctest: +ELLIPSIS
array([[[ 0.0884587..., 0.0647259..., 0.0435102...],
[ 0.2278222..., 0.0903652..., 0.0636376...]],
<BLANKLINE>
[[ 0.4717487..., 0.2308565..., 0.1438669...],
[ 0.5727396..., 0.2985858..., 0.1927235...]]])
"""
RGB = as_float_array(RGB)
q = 1 if q < 1 else q
k = 1 if k < 1 else k
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_max = np.max(L)
L_d = as_float_array(np.log10(1 + L * q) / np.log10(1 + L_max * k))
return RGB * L_d[..., None] / L[..., None]
[docs]
def tonemapping_operator_exponential(
RGB: ArrayLike,
q: float = 1,
k: float = 1,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the exponential method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
q
:math:`q`.
k
:math:`k`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Banterle2011k`
Examples
--------
>>> tonemapping_operator_exponential(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... ),
... 1.0,
... 25,
... ) # doctest: +ELLIPSIS
array([[[ 0.0148082..., 0.0108353..., 0.0072837...],
[ 0.0428669..., 0.0170031..., 0.0119740...]],
<BLANKLINE>
[[ 0.1312736..., 0.0642404..., 0.0400338...],
[ 0.1921684..., 0.1001830..., 0.0646635...]]])
"""
RGB = as_float_array(RGB)
q = 1 if q < 1 else q
k = 1 if k < 1 else k
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_a = log_average(L)
L_d = as_float_array(1 - np.exp(-(L * q) / (L_a * k)))
return RGB * L_d[..., None] / L[..., None]
[docs]
def tonemapping_operator_logarithmic_mapping(
RGB: ArrayLike,
p: float = 1,
q: float = 1,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the logarithmic mapping
method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
p
:math:`p`.
q
:math:`q`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Schlick1994`
Examples
--------
>>> tonemapping_operator_logarithmic_mapping(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.2532899..., 0.1853341..., 0.1245857...],
[ 0.6523387..., 0.2587489..., 0.1822179...]],
<BLANKLINE>
[[ 1.3507897..., 0.6610269..., 0.4119437...],
[ 1.6399638..., 0.8549608..., 0.5518382...]]])
"""
RGB = as_float_array(RGB)
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_max = np.max(L)
L_d = as_float_array((np.log(1 + p * L) / np.log(1 + p * L_max)) ** (1 / q))
return RGB * L_d[..., None] / L[..., None]
[docs]
def tonemapping_operator_exponentiation_mapping(
RGB: ArrayLike,
p: float = 1,
q: float = 1,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using the exponentiation mapping
method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
p
:math:`p`.
q
:math:`q`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Schlick1994`
Examples
--------
>>> tonemapping_operator_exponentiation_mapping(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.1194997..., 0.0874388..., 0.0587783...],
[ 0.3478122..., 0.1379590..., 0.0971544...]],
<BLANKLINE>
[[ 1.0959009..., 0.5362936..., 0.3342115...],
[ 1.6399638..., 0.8549608..., 0.5518382...]]])
"""
RGB = as_float_array(RGB)
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_max = np.max(L)
L_d = as_float_array((L / L_max) ** (p / q))
return RGB * L_d[..., None] / L[..., None]
[docs]
def tonemapping_operator_Schlick1994(
RGB: ArrayLike,
p: float = 1,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using *Schlick (1994)* method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
p
:math:`p`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Banterle2011k`, :cite:`Schlick1994`
Examples
--------
>>> tonemapping_operator_Schlick1994(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.1194997..., 0.0874388..., 0.0587783...],
[ 0.3478122..., 0.1379590..., 0.0971544...]],
<BLANKLINE>
[[ 1.0959009..., 0.5362936..., 0.3342115...],
[ 1.6399638..., 0.8549608..., 0.5518382...]]])
"""
# TODO: Implement automatic *p* and *non-uniform* computations support.
RGB = as_float_array(RGB)
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_max = np.max(L)
L_d = as_float_array((p * L) / (p * L - L + L_max))
return RGB * L_d[..., None] / L[..., None]
[docs]
def tonemapping_operator_Tumblin1999(
RGB: ArrayLike,
L_da: float = 20,
C_max: float = 100,
L_max: float = 100,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using
*Tumblin, Hodgins and Guenter (1999)* method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
L_da
:math:`L_{da}` display adaptation luminance, a mid-range display value.
C_max
:math:`C_{max}` maximum contrast available from the display.
L_max
:math:`L_{max}` maximum display luminance.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Tumblin1999c`
Examples
--------
>>> tonemapping_operator_Tumblin1999(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.0400492..., 0.0293043..., 0.0196990...],
[ 0.1019768..., 0.0404489..., 0.0284852...]],
<BLANKLINE>
[[ 0.2490212..., 0.1218618..., 0.0759427...],
[ 0.3408366..., 0.1776880..., 0.1146895...]]])
"""
RGB = as_float_array(RGB)
L_w = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
def f(x: float | NDArrayFloat) -> NDArrayFloat:
return np.where(x > 100, 2.655, 1.855 + 0.4 * np.log10(x + 2.3 * 10**-5))
L_wa = np.exp(np.mean(np.log(L_w + 2.3 * 10**-5)))
g_d = f(L_da)
g_w = f(L_wa)
g_wd = g_w / (1.855 + 0.4 * np.log(L_da))
mL_wa = np.sqrt(C_max) ** (g_wd - 1)
L_d = mL_wa * L_da * (L_w / L_wa) ** (g_w / g_d)
return (RGB * L_d[..., None] / L_w[..., None]) / L_max
[docs]
def tonemapping_operator_Reinhard2004(
RGB: ArrayLike,
f: float = 0,
m: float = 0.3,
a: float = 0,
c: float = 0,
colourspace: RGB_Colourspace = RGB_COLOURSPACES["sRGB"],
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using *Reinhard and Devlin (2004)*
method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
f
:math:`f`.
m
:math:`m`.
a
:math:`a`.
c
:math:`c`.
colourspace
*RGB* colourspace used for internal *Luminance* computation.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Reinhard2005c`
Examples
--------
>>> tonemapping_operator_Reinhard2004(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... ),
... -10,
... ) # doctest: +ELLIPSIS
array([[[ 0.0216792..., 0.0159556..., 0.0107821...],
[ 0.0605894..., 0.0249445..., 0.0176972...]],
<BLANKLINE>
[[ 0.1688972..., 0.0904532..., 0.0583584...],
[ 0.2331935..., 0.1368456..., 0.0928316...]]])
"""
RGB = as_float_array(RGB)
C_av = np.array(
(
np.average(RGB[..., 0]),
np.average(RGB[..., 1]),
np.average(RGB[..., 2]),
)
)
L = as_float_array(
RGB_luminance(RGB, colourspace.primaries, colourspace.whitepoint)
)
L_lav = log_average(L)
L_min, L_max = np.min(L), np.max(L)
f = np.exp(-f)
m = (
m
if m > 0
else (
0.3
+ 0.7 * ((np.log(L_max) - L_lav) / (np.log(L_max) - np.log(L_min)) ** 1.4)
)
)
I_l = (c * RGB + (1 - c)) * L[..., None]
I_g = c * C_av + (1 - c) * L_lav
I_a = a * I_l + (1 - a) * I_g
return RGB / (RGB + (f * I_a) ** m)
[docs]
def tonemapping_operator_filmic(
RGB: ArrayLike,
shoulder_strength: float = 0.22,
linear_strength: float = 0.3,
linear_angle: float = 0.1,
toe_strength: float = 0.2,
toe_numerator: float = 0.01,
toe_denominator: float = 0.3,
exposure_bias: float = 2,
linear_whitepoint: float = 11.2,
) -> NDArrayFloat:
"""
Perform given *RGB* array tonemapping using *Habble (2010)* method.
Parameters
----------
RGB
*RGB* array to perform tonemapping onto.
shoulder_strength
Shoulder strength.
linear_strength
Linear strength.
linear_angle
Linear angle.
toe_strength
Toe strength.
toe_numerator
Toe numerator.
toe_denominator
Toe denominator.
exposure_bias
Exposure bias.
linear_whitepoint
Linear whitepoint.
Returns
-------
:class:`numpy.ndarray`
Tonemapped *RGB* array.
References
----------
:cite:`Habble2010d`, :cite:`Habble2010e`
Examples
--------
>>> tonemapping_operator_filmic(
... np.array(
... [
... [
... [0.48046875, 0.35156256, 0.23632812],
... [1.39843753, 0.55468757, 0.39062594],
... ],
... [
... [4.40625388, 2.15625895, 1.34375372],
... [6.59375023, 3.43751395, 2.21875829],
... ],
... ]
... )
... ) # doctest: +ELLIPSIS
array([[[ 0.4507954..., 0.3619673..., 0.2617269...],
[ 0.7567191..., 0.4933310..., 0.3911730...]],
<BLANKLINE>
[[ 0.9725554..., 0.8557374..., 0.7465713...],
[ 1.0158782..., 0.9382937..., 0.8615161...]]])
"""
RGB = as_float_array(RGB)
A = shoulder_strength
B = linear_strength
C = linear_angle
D = toe_strength
E = toe_numerator
F = toe_denominator
def f(
x: float | NDArrayFloat,
A: float,
B: float,
C: float,
D: float,
E: float,
F: float,
) -> float | NDArrayFloat:
return ((x * (A * x + C * B) + D * E) / (x * (A * x + B) + D * F)) - E / F
RGB = f(RGB * exposure_bias, A, B, C, D, E, F)
return cast(NDArrayFloat, RGB * (1 / f(linear_whitepoint, A, B, C, D, E, F)))