"""
Common Log Encodings
====================
Define the common log encodings.
- :func:`colour.models.logarithmic_function_basic`
- :func:`colour.models.logarithmic_function_quasilog`
- :func:`colour.models.logarithmic_function_camera`
- :func:`colour.models.log_encoding_Log2`
- :func:`colour.models.log_decoding_Log2`
References
----------
- :cite:`TheAcademyofMotionPictureArtsandSciencesa` :
The Academy of Motion Picture Arts and Sciences,
Science and Technology Council,
& Academy Color Encoding System (ACES) Project Subcommittee.(n.d.).
ACESutil.Lin_to_Log2_param.ctl. Retrieved June 14, 2020,
from https://github.com/ampas/aces-dev/blob/\
518c27f577e99cdecfddf2ebcfaa53444b1f9343/transforms/ctl/utilities/\
ACESutil.Lin_to_Log2_param.ctl
- :cite:`TheAcademyofMotionPictureArtsandSciencesb` :
The Academy of Motion Picture Arts and Sciences,
Science and Technology Council,
& Academy Color Encoding System (ACES) Project Subcommittee.(n.d.).
ACESutil.Log2_to_Lin_param.ctl. Retrieved June 14, 2020,
from https://github.com/ampas/aces-dev/blob/\
518c27f577e99cdecfddf2ebcfaa53444b1f9343/transforms/ctl/utilities/\
ACESutil.Log2_to_Lin_param.ctl
: cite: `TheAcademyofMotionPictureArtsandSciences2020` : The Academy of
Motion Picture Arts and Sciences, Science and Technology Council, & Academy
Color Encoding System (ACES) Project Subcommittee. (2020). Specification
S-2014-006 - Common LUT Format (CLF) - A Common File Format for Look-Up
Tables. Retrieved June 24, 2020, from http://j.mp/S-2014-006
"""
from __future__ import annotations
import typing
import numpy as np
from colour.algebra import sdiv, sdiv_mode
if typing.TYPE_CHECKING:
from colour.hints import (
ArrayLike,
Literal,
NDArrayFloat,
)
from colour.hints import cast
from colour.utilities import (
as_float,
as_float_array,
optional,
validate_method,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 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__ = [
"logarithmic_function_basic",
"logarithmic_function_quasilog",
"logarithmic_function_camera",
"log_encoding_Log2",
"log_decoding_Log2",
]
FLT_MIN = 1.175494e-38
[docs]
def logarithmic_function_basic(
x: ArrayLike,
style: (
Literal["log10", "antiLog10", "log2", "antiLog2", "logB", "antiLogB"] | str
) = "log2",
base: int = 2,
) -> NDArrayFloat:
"""
Apply a logarithmic or anti-logarithmic transformation to the specified array.
Parameters
----------
x
Logarithmically encoded data :math:`x`.
style
Specifies the behaviour for the logarithmic function to operate:
- *log10*: Applies a base 10 logarithm to the passed value.
- *antiLog10*: Applies a base 10 anti-logarithm to the passed value.
- *log2*: Applies a base 2 logarithm to the passed value.
- *antiLog2*: Applies a base 2 anti-logarithm to the passed value.
- *logB*: Applies an arbitrary base logarithm to the passed value.
- *antiLogB*: Applies an arbitrary base anti-logarithm to the passed
value.
base
Logarithmic base used for the conversion.
Returns
-------
:class:`numpy.ndarray`
Logarithmically transformed data.
Examples
--------
The basic logarithmic function *styles* operate as follows:
>>> logarithmic_function_basic(0.18) # doctest: +ELLIPSIS
np.float64(-2.4739311...)
>>> logarithmic_function_basic(0.18, "log10") # doctest: +ELLIPSIS
np.float64(-0.7447274...)
>>> logarithmic_function_basic(0.18, "logB", 3) # doctest: +ELLIPSIS
np.float64(-1.5608767...)
>>> logarithmic_function_basic( # doctest: +ELLIPSIS
... -2.473931188332412, "antiLog2"
... )
np.float64(0.18000000...)
>>> logarithmic_function_basic( # doctest: +ELLIPSIS
... -0.7447274948966939, "antiLog10"
... )
np.float64(0.18000000...)
>>> logarithmic_function_basic( # doctest: +ELLIPSIS
... -1.5608767950073117, "antiLogB", 3
... )
np.float64(0.18000000...)
"""
x = as_float_array(x)
style = validate_method(
style,
("log10", "antiLog10", "log2", "antiLog2", "logB", "antiLogB"),
'"{0}" style is invalid, it must be one of {1}!',
)
if style == "log10":
return as_float(np.where(x >= FLT_MIN, np.log10(x), np.log10(FLT_MIN)))
if style == "antilog10":
return as_float(10**x)
if style == "log2":
return as_float(np.where(x >= FLT_MIN, np.log2(x), np.log2(FLT_MIN)))
if style == "antilog2":
return as_float(2**x)
if style == "logb":
return as_float(np.log(x) / np.log(base))
# style == 'antilogb'
return as_float(base**x)
[docs]
def logarithmic_function_quasilog(
x: ArrayLike,
style: Literal["linToLog", "logToLin"] | str = "linToLog",
base: int = 2,
log_side_slope: float = 1,
lin_side_slope: float = 1,
log_side_offset: float = 0,
lin_side_offset: float = 0,
) -> NDArrayFloat:
"""
Apply the *Quasilog* logarithmic function for encoding and decoding.
This function implements a logarithmic transformation with configurable
slopes and offsets for both linear and logarithmic sides.
Parameters
----------
x
Logarithmically encoded data :math:`x`.
style
Specifies the behaviour for the logarithmic function to operate:
- *linToLog*: Apply a logarithm to convert linear data to
logarithmic data.
- *logToLin*: Apply an anti-logarithm to convert logarithmic
data to linear data.
base
Logarithmic base used for the conversion.
log_side_slope
Slope (or gain) applied to the log side of the logarithmic function.
The default value is 1.
lin_side_slope
Slope of the linear side of the logarithmic function. The default
value is 1.
log_side_offset
Offset applied to the log side of the logarithmic function. The
default value is 0.
lin_side_offset
Offset applied to the linear side of the logarithmic function. The
default value is 0.
Returns
-------
:class:`numpy.ndarray`
Encoded/Decoded data.
Examples
--------
>>> logarithmic_function_quasilog(0.18, "linToLog") # doctest: +ELLIPSIS
np.float64(-2.4739311...)
>>> logarithmic_function_quasilog( # doctest: +ELLIPSIS
... -2.473931188332412, "logToLin"
... )
np.float64(0.18000000...)
"""
x = as_float_array(x)
style = validate_method(
style,
("lintolog", "logtolin"),
'"{0}" style is invalid, it must be one of {1}!',
)
if style == "lintolog":
y = (
log_side_slope
* (
np.log(np.maximum(lin_side_slope * x + lin_side_offset, FLT_MIN))
/ np.log(base)
)
+ log_side_offset
)
else: # style == 'logtolin'
with sdiv_mode():
y = sdiv(
base ** sdiv(x - log_side_offset, log_side_slope) - lin_side_offset,
lin_side_slope,
)
return as_float(y)
[docs]
def logarithmic_function_camera(
x: ArrayLike,
style: (Literal["cameraLinToLog", "cameraLogToLin"] | str) = "cameraLinToLog",
base: int = 2,
log_side_slope: float = 1,
lin_side_slope: float = 1,
log_side_offset: float = 0,
lin_side_offset: float = 0,
lin_side_break: float = 0.005,
linear_slope: float | None = None,
) -> NDArrayFloat:
"""
Apply a camera logarithmic function to the specified array.
Apply a piece-wise function with logarithmic and linear segments
for encoding or decoding camera data.
Parameters
----------
x
Logarithmically encoded data :math:`x`.
style
Specifies the behaviour for the logarithmic function to operate:
- *cameraLinToLog*: Applies a piece-wise function with logarithmic
and linear segments on linear values, converting them to non-linear
values.
- *cameraLogToLin*: Applies a piece-wise function with logarithmic
and linear segments on non-linear values, converting them to linear
values.
base
Logarithmic base used for the conversion.
log_side_slope
Slope (or gain) applied to the log side of the logarithmic function.
The default value is 1.
lin_side_slope
Slope of the linear side of the logarithmic function. The
default value is 1.
log_side_offset
Offset applied to the log side of the logarithmic function. The
default value is 0.
lin_side_offset
Offset applied to the linear side of the logarithmic function.
The default value is 0.
lin_side_break
Break-point, defined in linear space, at which the piece-wise
function transitions between the logarithmic and linear
segments.
linear_slope
Slope of the linear portion of the curve. The default value is
*None*.
Returns
-------
:class:`numpy.ndarray`
Encoded/Decoded data.
Examples
--------
>>> logarithmic_function_camera( # doctest: +ELLIPSIS
... 0.18, "cameraLinToLog"
... )
np.float64(-2.4739311...)
>>> logarithmic_function_camera( # doctest: +ELLIPSIS
... -2.4739311883324122, "cameraLogToLin"
... )
np.float64(0.1800000...)
"""
x = as_float_array(x)
style = validate_method(
style,
("cameraLinToLog", "cameraLogToLin"),
'"{0}" style is invalid, it must be one of {1}!',
)
log_side_break = (
log_side_slope
* (np.log(lin_side_slope * lin_side_break + lin_side_offset) / np.log(base))
+ log_side_offset
)
with sdiv_mode():
linear_slope = cast(
"float",
optional(
linear_slope,
(
log_side_slope
* (
sdiv(
lin_side_slope,
(lin_side_slope * lin_side_break + lin_side_offset)
* np.log(base),
)
)
),
),
)
linear_offset = log_side_break - linear_slope * lin_side_break
if style == "cameralintolog":
m_x = x <= lin_side_break
y = np.where(
m_x,
linear_slope * x + linear_offset,
logarithmic_function_quasilog(
x,
"linToLog",
base,
log_side_slope,
lin_side_slope,
log_side_offset,
lin_side_offset,
),
)
else: # style == 'cameralogtolin'
with sdiv_mode():
m_x = x <= log_side_break
y = np.where(
m_x,
sdiv(x - linear_offset, linear_slope),
logarithmic_function_quasilog(
x,
"logToLin",
base,
log_side_slope,
lin_side_slope,
log_side_offset,
lin_side_offset,
),
)
return as_float(y)
[docs]
def log_encoding_Log2(
lin: ArrayLike,
middle_grey: float = 0.18,
min_exposure: float = -6.5,
max_exposure: float = 6.5,
) -> NDArrayFloat:
"""
Apply the common *Log2* log encoding opto-electronic transfer function (OETF).
Parameters
----------
lin
Linear *Log2* decoded data.
middle_grey
*Middle Grey* exposure value.
min_exposure
Minimum exposure level.
max_exposure
Maximum exposure level.
Returns
-------
:class:`numpy.ndarray`
Non-linear *Log2* encoded data.
Notes
-----
+--------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+==============+=======================+===============+
| ``lin`` | 1 | 1 |
+--------------+-----------------------+---------------+
+--------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+==============+=======================+===============+
| ``log_norm`` | 1 | 1 |
+--------------+-----------------------+---------------+
- The common *Log2* encoding function can be used to build linear to
logarithmic shapers in the *ACES OCIO configuration*.
- A (48-nits OCIO) shaper having values in a linear domain, can be
encoded to a logarithmic domain:
+-------------------+-------------------+
| **Shaper Domain** | **Shaper Range** |
+===================+===================+
| [0.002, 16.291] | [0, 1] |
+-------------------+-------------------+
References
----------
:cite:`TheAcademyofMotionPictureArtsandSciencesa`
Examples
--------
>>> log_encoding_Log2(0.18)
np.float64(0.5)
"""
lin = as_float_array(lin)
lg2 = np.log2(lin / middle_grey)
log_norm = (lg2 - min_exposure) / (max_exposure - min_exposure)
return as_float(log_norm)
[docs]
def log_decoding_Log2(
log_norm: ArrayLike,
middle_grey: float = 0.18,
min_exposure: float = -6.5,
max_exposure: float = 6.5,
) -> NDArrayFloat:
"""
Apply the common *Log2* log decoding inverse opto-electronic transfer
function (OETF).
Parameters
----------
log_norm
Non-linear *Log2* encoded data.
middle_grey
*Middle Grey* exposure value.
min_exposure
Minimum exposure level.
max_exposure
Maximum exposure level.
Returns
-------
:class:`numpy.ndarray`
Linear *Log2* decoded data.
Notes
-----
+--------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+==============+=======================+===============+
| ``log_norm`` | 1 | 1 |
+--------------+-----------------------+---------------+
+--------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+==============+=======================+===============+
| ``lin`` | 1 | 1 |
+--------------+-----------------------+---------------+
- The common *Log2* decoding function can be used to build logarithmic
to linear shapers in the *ACES OCIO configuration*.
- The shaper with logarithmic encoded values can be decoded back to
linear domain:
+-------------------+-------------------+
| **Shaper Range** | **Shaper Domain** |
+===================+===================+
| [0, 1] | [0.002, 16.291] |
+-------------------+-------------------+
References
----------
:cite:`TheAcademyofMotionPictureArtsandSciencesb`
Examples
--------
>>> log_decoding_Log2(0.5) # doctest: +ELLIPSIS
np.float64(0.18)
"""
log_norm = as_float_array(log_norm)
lg2 = log_norm * (max_exposure - min_exposure) + min_exposure
lin = (2**lg2) * middle_grey
return as_float(lin)
