"""
Adobe DNG SDK Colour Processing
===============================
Defines various objects implementing *Adobe DNG SDK* colour processing:
- :func:`colour_hdri.xy_to_camera_neutral`
- :func:`colour_hdri.camera_neutral_to_xy`
- :func:`colour_hdri.matrix_XYZ_to_camera_space`
- :func:`colour_hdri.matrix_camera_space_to_XYZ`
The *Adobe DNG SDK* defines the following tags relevant for the current
implementation:
- *CalibrationIlluminant1* : The illuminant used for the first set of colour
calibration tags.
- *CalibrationIlluminant2* : The illuminant used for an optional second set
of colour calibration tags.
- *ColorMatrix1* : *ColorMatrix1* defines a transformation matrix that
converts XYZ values to reference camera native colour space values, under
the first calibration illuminant.
- *ColorMatrix2* : *ColorMatrix2* defines a transformation matrix that
converts XYZ values to reference camera native colour space values, under
the second calibration illuminant.
- *CameraCalibration1* : *CameraCalibration1* defines a calibration matrix
that transforms reference camera native space values to individual camera
native space values under the first calibration illuminant. This matrix is
stored separately from the matrix specified by the *ColorMatrix1* tag to
allow raw converters to swap in replacement colour matrices based on
*UniqueCameraModel* tag, while still taking advantage of any per-individual
camera calibration performed by the camera manufacturer.
- *CameraCalibration2* : *CameraCalibration2* defines a calibration matrix
that transforms reference camera native space values to individual camera
native space values under the second calibration illuminant. This matrix is
stored separately from the matrix specified by the *ColorMatrix2* tag to
allow raw converters to swap in replacement colour matrices based on
*UniqueCameraModel* tag, while still taking advantage of any per-individual
camera calibration performed by the camera manufacturer.
- *ReductionMatrix1* : *ReductionMatrix1* defines a dimensionality reduction
matrix for use as the first stage in converting colour camera native space
values to XYZ values, under the first calibration illuminant. This tag may
only be used if *ColorPlanes* is greater than 3.
- *ReductionMatrix2* : *ReductionMatrix2* defines a dimensionality reduction
matrix for use as the first stage in converting colour camera native space
values to XYZ values, under the second calibration illuminant. This tag may
only be used if *ColorPlanes* is greater than 3.
- *AnalogBalance* : Normally the stored raw values are not white balanced,
since any digital white balancing will reduce the dynamic range of the
final image if the user decides to later adjust the white balance; however,
if camera hardware is capable of white balancing the colour channels before
the signal is digitized, it can improve the dynamic range of the final
image. *AnalogBalance* defines the gain, either analog (recommended) or
digital (not recommended) that has been applied the stored raw values.
- *AsShotNeutral* : *AsShotNeutral* specifies the selected white balance at
time of capture, encoded as the coordinates of a perfectly neutral colour
in linear reference space values. The inclusion of this tag precludes the
inclusion of the *AsShotWhiteXY* tag.
- *AsShotWhiteXY* : *AsShotWhiteXY* specifies the selected white balance at
time of capture, encoded as x-y chromaticity coordinates. The inclusion of
this tag precludes the inclusion of the *AsShotNeutral* tag.
- *ForwardMatrix1* : This tag defines a matrix that maps white balanced
camera colours to XYZ D50 colours.
- *ForwardMatrix2* : This tag defines a matrix that maps white balanced
camera colours to XYZ D50 colours.
Notes
-----
- At least one of the *ColorMatrix1* or *ColorMatrix2* tags must be included
in the camera profile, the current implementation expects them to be passed
as identity matrices if not included.
- If the *ForwardMatrix1* or *ForwardMatrix2* tags are not included in the
camera profile, the current implementation expects them to be passed as
identity matrices.
- The *ReductionMatrix1* and *ReductionMatrix2* tags are ignored by the
current implementation which expects cameras with 3 colour planes.
- *DNG 1.2.0.0* and later supports different companies creating the camera
calibration tags using different reference cameras. When rendering a *DNG*
file using a camera profile, it is important to know if the selected camera
profile was designed using the same reference camera used to create the
camera calibration tags. If so, then the camera calibration tags should be
used. If not, then it is preferable to ignore the camera calibration tags
and use identity matrices instead in order to minimize the worse case
calibration mismatch error. This matching is done by comparing the
*CameraCalibrationSignature* tag and the *ProfileCalibrationSignature* tag
for the selected camera profile. If they match, then use the camera
calibration tags. If not, then use identity matrices.
- The Hue/Saturation/Value Mapping Table is ignored by the current
implementation because deemed unsuitable :cite:`McGuffog2012a`.
- The various matrices used in this module are extracted from a *Canon EOS 5D
Mark II* camera.
References
----------
- :cite:`AdobeSystems2012d` : Adobe Systems. (2012). Translating White
Balance xy Coordinates to Camera Neutral Coordinates. In Digital Negative
(DNG) Specification (p. 80).
- :cite:`AdobeSystems2012e` : Adobe Systems. (2012). Translating Camera
Neutral Coordinates to White Balance xy Coordinates. In Digital Negative
(DNG) Specification (pp. 80-81).
- :cite:`AdobeSystems2012f` : Adobe Systems. (2012). Digital Negative (DNG)
Specification (pp. 1-101).
- :cite:`AdobeSystems2012g` : Adobe Systems. (2012). Camera to XYZ (D50)
Transform. In Digital Negative (DNG) Specification (p. 81).
- :cite:`AdobeSystems2015d` : Adobe Systems. (2015). Adobe DNG SDK 1.4.
http://download.adobe.com/pub/adobe/dng/dng_sdk_1_4.zip
- :cite:`McGuffog2012a` : McGuffog, S. (2012). Hue Twists in DNG Camera
Profiles. Retrieved October 29, 2016, from
http://dcptool.sourceforge.net/Hue%20Twists.html
"""
from __future__ import annotations
import numpy as np
from colour.adaptation import matrix_chromatic_adaptation_VonKries
from colour.algebra import (
is_identity,
linear_conversion,
matrix_dot,
vector_dot,
)
from colour.constants import EPSILON
from colour.hints import ArrayLike, Literal, NDArrayFloat
from colour.models import UCS_to_uv, XYZ_to_UCS, XYZ_to_xy, xy_to_XYZ
from colour.temperature import uv_to_CCT_Robertson1968
from colour.utilities import as_float_array, tstack
from colour_hdri.models import CCS_ILLUMINANT_ADOBEDNG
__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__ = [
"matrix_interpolated",
"xy_to_camera_neutral",
"camera_neutral_to_xy",
"matrix_XYZ_to_camera_space",
"matrix_camera_space_to_XYZ",
]
def matrix_interpolated(
CCT: float,
CCT_1: float,
CCT_2: float,
M_1: ArrayLike,
M_2: ArrayLike,
) -> NDArrayFloat:
"""
Compute the matrix interpolated from :math:`CCT_1` and :math:`CCT_2`
correlated colour temperatures to respectively :math:`M_T` and :math:`M_R`
colour matrices using given correlated colour temperature :math:`CCT`
interpolation value.
Parameters
----------
CCT
Correlated colour temperature :math:`CCT`.
CCT_1
Correlated colour temperature :math:`CCT_1`.
CCT_2
Correlated colour temperature :math:`CCT_2`.
M_1
:math:`M_T` colour matrix.
M_2
:math:`M_R` colour matrix.
Returns
-------
:class:`numpy.ndarray`
Interpolated colour matrix :math:`M_i`.
Notes
-----
- The computation is performed in mired (MIcro REciprocal Degree,
reciprocal megakelvin) :math:`MK^{-1}`.
Examples
--------
>>> CCT = 5000
>>> CCT_1 = 2850
>>> CCT_2 = 6500
>>> M_T = np.array(
... [
... [0.5309, -0.0229, -0.0336],
... [-0.6241, 1.3265, 0.3337],
... [-0.0817, 0.1215, 0.6664],
... ]
... )
>>> M_R = np.array(
... [
... [0.4716, 0.0603, -0.0830],
... [-0.7798, 1.5474, 0.2480],
... [-0.1496, 0.1937, 0.6651],
... ]
... )
>>> matrix_interpolated(CCT, CCT_1, CCT_2, M_T, M_R) # doctest: +ELLIPSIS
array([[ 0.4854908..., 0.0408106..., -0.0714282...],
[-0.7433278..., 1.4956549..., 0.2680749...],
[-0.1336946..., 0.1767874..., 0.6654045...]])
"""
M_1 = as_float_array(M_1)
M_2 = as_float_array(M_2)
if CCT <= CCT_1:
return M_1
elif CCT >= CCT_2:
return M_2
else:
return linear_conversion(
1e6 / CCT, (1e6 / CCT_1, 1e6 / CCT_2), tstack([M_1, M_2])
)
[docs]
def xy_to_camera_neutral(
xy: ArrayLike,
CCT_calibration_illuminant_1: float,
CCT_calibration_illuminant_2: float,
M_color_matrix_1: ArrayLike,
M_color_matrix_2: ArrayLike,
M_camera_calibration_1: ArrayLike,
M_camera_calibration_2: ArrayLike,
analog_balance: ArrayLike,
) -> NDArrayFloat:
"""
Convert given *xy* white balance chromaticity coordinates to
*Camera Neutral* coordinates.
Parameters
----------
xy
*xy* white balance chromaticity coordinates.
CCT_calibration_illuminant_1
Correlated colour temperature of *CalibrationIlluminant1*.
CCT_calibration_illuminant_2
Correlated colour temperature of *CalibrationIlluminant2*.
M_color_matrix_1
*ColorMatrix1* tag matrix.
M_color_matrix_2
*ColorMatrix2* tag matrix.
M_camera_calibration_1
*CameraCalibration1* tag matrix.
M_camera_calibration_2
*CameraCalibration2* tag matrix.
analog_balance
*AnalogBalance* tag vector.
Returns
-------
:class:`numpy.ndarray`
*Camera Neutral* coordinates.
References
----------
:cite:`AdobeSystems2012d`, :cite:`AdobeSystems2012f`,
:cite:`AdobeSystems2015d`, :cite:`McGuffog2012a`
Examples
--------
>>> M_color_matrix_1 = np.array(
... [
... [0.5309, -0.0229, -0.0336],
... [-0.6241, 1.3265, 0.3337],
... [-0.0817, 0.1215, 0.6664],
... ]
... )
>>> M_color_matrix_2 = np.array(
... [
... [0.4716, 0.0603, -0.0830],
... [-0.7798, 1.5474, 0.2480],
... [-0.1496, 0.1937, 0.6651],
... ]
... )
>>> M_camera_calibration_1 = np.identity(3)
>>> M_camera_calibration_2 = np.identity(3)
>>> analog_balance = np.ones(3)
>>> xy_to_camera_neutral( # doctest: +ELLIPSIS
... np.array([0.32816244, 0.34698169]),
... 2850,
... 6500,
... M_color_matrix_1,
... M_color_matrix_2,
... M_camera_calibration_1,
... M_camera_calibration_2,
... analog_balance,
... )
array([ 0.4130699..., 1... , 0.646465...])
"""
M_XYZ_to_camera = matrix_XYZ_to_camera_space(
xy,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_color_matrix_1,
M_color_matrix_2,
M_camera_calibration_1,
M_camera_calibration_2,
analog_balance,
)
camera_neutral = vector_dot(M_XYZ_to_camera, xy_to_XYZ(xy))
camera_neutral /= camera_neutral[1]
return camera_neutral
[docs]
def camera_neutral_to_xy(
camera_neutral: ArrayLike,
CCT_calibration_illuminant_1: float,
CCT_calibration_illuminant_2: float,
M_color_matrix_1: ArrayLike,
M_color_matrix_2: ArrayLike,
M_camera_calibration_1: ArrayLike,
M_camera_calibration_2: ArrayLike,
analog_balance: ArrayLike,
epsilon: float = EPSILON,
) -> NDArrayFloat:
"""
Convert given *Camera Neutral* coordinates to *xy* white balance
chromaticity coordinates.
Parameters
----------
camera_neutral
*Camera Neutral* coordinates.
CCT_calibration_illuminant_1
Correlated colour temperature of *CalibrationIlluminant1*.
CCT_calibration_illuminant_2
Correlated colour temperature of *CalibrationIlluminant2*.
M_color_matrix_1
*ColorMatrix1* tag matrix.
M_color_matrix_2
*ColorMatrix2* tag matrix.
M_camera_calibration_1
*CameraCalibration1* tag matrix.
M_camera_calibration_2
*CameraCalibration2* tag matrix.
analog_balance
*AnalogBalance* tag vector.
epsilon
Threshold value for computation convergence.
Returns
-------
:class:`numpy.ndarray`
*xy* white balance chromaticity coordinates.
Raises
------
RuntimeError
If the given *Camera Neutral* coordinates did not converge to *xy*
white balance chromaticity coordinates.
References
----------
:cite:`AdobeSystems2012e`, :cite:`AdobeSystems2012f`,
:cite:`AdobeSystems2015d`, :cite:`McGuffog2012a`
Examples
--------
>>> M_color_matrix_1 = np.array(
... [
... [0.5309, -0.0229, -0.0336],
... [-0.6241, 1.3265, 0.3337],
... [-0.0817, 0.1215, 0.6664],
... ]
... )
>>> M_color_matrix_2 = np.array(
... [
... [0.4716, 0.0603, -0.0830],
... [-0.7798, 1.5474, 0.2480],
... [-0.1496, 0.1937, 0.6651],
... ]
... )
>>> M_camera_calibration_1 = np.identity(3)
>>> M_camera_calibration_2 = np.identity(3)
>>> analog_balance = np.ones(3)
>>> camera_neutral_to_xy( # doctest: +ELLIPSIS
... np.array([0.413070, 1.000000, 0.646465]),
... 2850,
... 6500,
... M_color_matrix_1,
... M_color_matrix_2,
... M_camera_calibration_1,
... M_camera_calibration_2,
... analog_balance,
... )
array([ 0.3281624..., 0.3469816...])
"""
# Initial *xy* chromaticity coordinates guess.
xy = np.array((1 / 3, 1 / 3))
while True:
xy_p = np.copy(xy)
M_XYZ_to_camera = matrix_XYZ_to_camera_space(
xy,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_color_matrix_1,
M_color_matrix_2,
M_camera_calibration_1,
M_camera_calibration_2,
analog_balance,
)
XYZ = vector_dot(np.linalg.inv(M_XYZ_to_camera), camera_neutral)
xy = XYZ_to_xy(XYZ)
if np.abs(np.sum(xy_p - xy)) <= epsilon:
return xy
raise RuntimeError(
f'"Camera Neutral" coordinates "{xy}" did not converge to "xy" white '
f"balance chromaticity coordinates!"
)
[docs]
def matrix_XYZ_to_camera_space(
xy: ArrayLike,
CCT_calibration_illuminant_1: float,
CCT_calibration_illuminant_2: float,
M_color_matrix_1: ArrayLike,
M_color_matrix_2: ArrayLike,
M_camera_calibration_1: ArrayLike,
M_camera_calibration_2: ArrayLike,
analog_balance: ArrayLike,
) -> NDArrayFloat:
"""
Return the *CIE XYZ* to *Camera Space* matrix for given *xy* white balance
chromaticity coordinates.
Parameters
----------
xy
*xy* white balance chromaticity coordinates.
CCT_calibration_illuminant_1
Correlated colour temperature of *CalibrationIlluminant1*.
CCT_calibration_illuminant_2
Correlated colour temperature of *CalibrationIlluminant2*.
M_color_matrix_1
*ColorMatrix1* tag matrix.
M_color_matrix_2
*ColorMatrix2* tag matrix.
M_camera_calibration_1
*CameraCalibration1* tag matrix.
M_camera_calibration_2
*CameraCalibration2* tag matrix.
analog_balance
*AnalogBalance* tag vector.
Returns
-------
:class:`numpy.ndarray`
*CIE XYZ* to *Camera Space* matrix.
Notes
-----
- The reference illuminant is D50 as defined per
:attr:`colour_hdri.models.datasets.dng.CCS_ILLUMINANT_ADOBEDNG`
attribute.
References
----------
:cite:`AdobeSystems2012f`, :cite:`AdobeSystems2015d`, :cite:`McGuffog2012a`
Examples
--------
>>> M_color_matrix_1 = np.array(
... [
... [0.5309, -0.0229, -0.0336],
... [-0.6241, 1.3265, 0.3337],
... [-0.0817, 0.1215, 0.6664],
... ]
... )
>>> M_color_matrix_2 = np.array(
... [
... [0.4716, 0.0603, -0.0830],
... [-0.7798, 1.5474, 0.2480],
... [-0.1496, 0.1937, 0.6651],
... ]
... )
>>> M_camera_calibration_1 = np.identity(3)
>>> M_camera_calibration_2 = np.identity(3)
>>> analog_balance = np.ones(3)
>>> matrix_XYZ_to_camera_space( # doctest: +ELLIPSIS
... np.array([0.34510414, 0.35162252]),
... 2850,
... 6500,
... M_color_matrix_1,
... M_color_matrix_2,
... M_camera_calibration_1,
... M_camera_calibration_2,
... analog_balance,
... )
array([[ 0.4854908..., 0.0408106..., -0.0714282...],
[-0.7433278..., 1.4956549..., 0.2680749...],
[-0.1336946..., 0.1767874..., 0.6654045...]])
"""
M_AB = np.diagflat(analog_balance)
uv = UCS_to_uv(XYZ_to_UCS(xy_to_XYZ(xy)))
CCT, _D_uv = uv_to_CCT_Robertson1968(uv)
if is_identity(M_color_matrix_1) or is_identity(M_color_matrix_2):
M_CM = M_color_matrix_1 if is_identity(M_color_matrix_2) else M_color_matrix_2
else:
M_CM = matrix_interpolated(
CCT,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_color_matrix_1,
M_color_matrix_2,
)
M_CC = matrix_interpolated(
CCT,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_camera_calibration_1,
M_camera_calibration_2,
)
M_XYZ_to_camera_space = matrix_dot(matrix_dot(M_AB, M_CC), M_CM)
return M_XYZ_to_camera_space
[docs]
def matrix_camera_space_to_XYZ(
xy: ArrayLike,
CCT_calibration_illuminant_1: float,
CCT_calibration_illuminant_2: float,
M_color_matrix_1: ArrayLike,
M_color_matrix_2: ArrayLike,
M_camera_calibration_1: ArrayLike,
M_camera_calibration_2: ArrayLike,
analog_balance: ArrayLike,
M_forward_matrix_1: ArrayLike,
M_forward_matrix_2: ArrayLike,
chromatic_adaptation_transform: (
Literal[
"Bianco 2010",
"Bianco PC 2010",
"Bradford",
"CAT02 Brill 2008",
"CAT02",
"CAT16",
"CMCCAT2000",
"CMCCAT97",
"Fairchild",
"Sharp",
"Von Kries",
"XYZ Scaling",
]
| str
) = "Bradford",
) -> NDArrayFloat:
"""
Return the *Camera Space* to *CIE XYZ* matrix for given *xy* white
balance chromaticity coordinates.
Parameters
----------
xy
*xy* white balance chromaticity coordinates.
CCT_calibration_illuminant_1
Correlated colour temperature of *CalibrationIlluminant1*.
CCT_calibration_illuminant_2
Correlated colour temperature of *CalibrationIlluminant2*.
M_color_matrix_1
*ColorMatrix1* tag matrix.
M_color_matrix_2
*ColorMatrix2* tag matrix.
M_camera_calibration_1
*CameraCalibration1* tag matrix.
M_camera_calibration_2
*CameraCalibration2* tag matrix.
analog_balance
*AnalogBalance* tag vector.
M_forward_matrix_1
*ForwardMatrix1* tag matrix.
M_forward_matrix_2
*ForwardMatrix2* tag matrix.
chromatic_adaptation_transform
Chromatic adaptation transform.
Returns
-------
:class:`numpy.ndarray`
*Camera Space* to *CIE XYZ* matrix.
Notes
-----
- The reference illuminant is D50 as defined per
:attr:`colour_hdri.models.datasets.dng.CCS_ILLUMINANT_ADOBEDNG`
attribute.
References
----------
:cite:`AdobeSystems2012f`, :cite:`AdobeSystems2012g`,
:cite:`AdobeSystems2015d`, :cite:`McGuffog2012a`
Examples
--------
>>> M_color_matrix_1 = np.array(
... [
... [0.5309, -0.0229, -0.0336],
... [-0.6241, 1.3265, 0.3337],
... [-0.0817, 0.1215, 0.6664],
... ]
... )
>>> M_color_matrix_2 = np.array(
... [
... [0.4716, 0.0603, -0.0830],
... [-0.7798, 1.5474, 0.2480],
... [-0.1496, 0.1937, 0.6651],
... ]
... )
>>> M_camera_calibration_1 = np.identity(3)
>>> M_camera_calibration_2 = np.identity(3)
>>> analog_balance = np.ones(3)
>>> M_forward_matrix_1 = np.array(
... [
... [0.8924, -0.1041, 0.1760],
... [0.4351, 0.6621, -0.0972],
... [0.0505, -0.1562, 0.9308],
... ]
... )
>>> M_forward_matrix_2 = np.array(
... [
... [0.8924, -0.1041, 0.1760],
... [0.4351, 0.6621, -0.0972],
... [0.0505, -0.1562, 0.9308],
... ]
... )
>>> matrix_camera_space_to_XYZ( # doctest: +ELLIPSIS
... np.array([0.32816244, 0.34698169]),
... 2850,
... 6500,
... M_color_matrix_1,
... M_color_matrix_2,
... M_camera_calibration_1,
... M_camera_calibration_2,
... analog_balance,
... M_forward_matrix_1,
... M_forward_matrix_2,
... )
array([[ 2.1604087..., -0.1041... , 0.2722498...],
[ 1.0533324..., 0.6621... , -0.1503561...],
[ 0.1222553..., -0.1562... , 1.4398304...]])
"""
# *ForwardMatrix1* and *ForwardMatrix2* are not included in the camera
# profile.
if is_identity(M_forward_matrix_1) and is_identity(M_forward_matrix_2):
M_camera_to_XYZ = np.linalg.inv(
matrix_XYZ_to_camera_space(
xy,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_color_matrix_1,
M_color_matrix_2,
M_camera_calibration_1,
M_camera_calibration_2,
analog_balance,
)
)
M_CAT = matrix_chromatic_adaptation_VonKries(
xy_to_XYZ(xy),
xy_to_XYZ(CCS_ILLUMINANT_ADOBEDNG),
chromatic_adaptation_transform,
)
M_camera_space_to_XYZ = matrix_dot(M_CAT, M_camera_to_XYZ)
else:
uv = UCS_to_uv(XYZ_to_UCS(xy_to_XYZ(xy)))
CCT, _D_uv = uv_to_CCT_Robertson1968(uv)
M_CC = matrix_interpolated(
CCT,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_camera_calibration_1,
M_camera_calibration_2,
)
# The reference implementation :cite:`AdobeSystems2015d` diverges from
# the white-paper :cite:`AdobeSystems2012f`:
# The reference implementation directly computes the camera neutral by
# multiplying directly the interpolated colour matrix :math:`CM` with
# the tristimulus values of the *xy* white balance chromaticity
# coordinates.
# The current implementation is based on the white-paper so that the
# interpolated camera calibration matrix :math:`CC` and the
# analog balance matrix :math:`AB` are accounted for.
camera_neutral = xy_to_camera_neutral(
xy,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_color_matrix_1,
M_color_matrix_2,
M_camera_calibration_1,
M_camera_calibration_2,
analog_balance,
)
M_AB = np.diagflat(analog_balance)
M_reference_neutral = vector_dot(
np.linalg.inv(matrix_dot(M_AB, M_CC)), camera_neutral
)
M_D = np.linalg.inv(np.diagflat(M_reference_neutral))
M_FM = matrix_interpolated(
CCT,
CCT_calibration_illuminant_1,
CCT_calibration_illuminant_2,
M_forward_matrix_1,
M_forward_matrix_2,
)
M_camera_space_to_XYZ = matrix_dot(
matrix_dot(M_FM, M_D), np.linalg.inv(matrix_dot(M_AB, M_CC))
)
return M_camera_space_to_XYZ