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submodule
opencv
Commits
c8cb03fd
Commit
c8cb03fd
authored
May 07, 2015
by
Maksim Shabunin
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Replaced 'corrected' to 'distorted' in camera calibration tutorials
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py_calibration.markdown
...torials/py_calib3d/py_calibration/py_calibration.markdown
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camera_calibration.markdown
...ls/calib3d/camera_calibration/camera_calibration.markdown
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doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown
View file @
c8cb03fd
...
@@ -22,17 +22,17 @@ red line. All the expected straight lines are bulged out. Visit [Distortion
...
@@ -22,17 +22,17 @@ red line. All the expected straight lines are bulged out. Visit [Distortion


This distortion is
solv
ed as follows:
This distortion is
represent
ed as follows:
\f
[
x_{
correc
ted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\\
\f
[
x_{
distor
ted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\\
y_{
correc
ted} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\f
]
y_{
distor
ted} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\f
]
Similarly, another distortion is the tangential distortion which occurs because image taking lense
Similarly, another distortion is the tangential distortion which occurs because image taking lense
is not aligned perfectly parallel to the imaging plane. So some areas in image may look nearer than
is not aligned perfectly parallel to the imaging plane. So some areas in image may look nearer than
expected. It is
solv
ed as below:
expected. It is
represent
ed as below:
\f
[
x_{
correc
ted} = x + [ 2p_1xy + p_2(r^2+2x^2)
]
\\
\f
[
x_{
distor
ted} = x + [ 2p_1xy + p_2(r^2+2x^2)
]
\\
y_{
correc
ted} = y +
[
p_1(r^2+ 2y^2)+ 2p_2xy
]
\f
]
y_{
distor
ted} = y +
[
p_1(r^2+ 2y^2)+ 2p_2xy
]
\f
]
In short, we need to find five parameters, known as distortion coefficients given by:
In short, we need to find five parameters, known as distortion coefficients given by:
...
...
doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown
View file @
c8cb03fd
...
@@ -14,18 +14,18 @@ Theory
...
@@ -14,18 +14,18 @@ Theory
For the distortion OpenCV takes into account the radial and tangential factors. For the radial
For the distortion OpenCV takes into account the radial and tangential factors. For the radial
factor one uses the following formula:
factor one uses the following formula:
\f
[
x_{
correc
ted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\\
\f
[
x_{
distor
ted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\\
y_{
correc
ted} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\f
]
y_{
distor
ted} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)
\f
]
So for an
old pixel point at
\f
$(x,y)
\f
$ coordinates in the input image, its position on the corrected
So for an
undistorted pixel point at
\f
$(x,y)
\f
$ coordinates, its position on the distorted image
output image will be
\f
$(x_{corrected} y_{corrected})
\f
$. The presence of the radial distortion
will be
\f
$(x_{distorted} y_{distorted})
\f
$. The presence of the radial distortion manifests in form
manifests in form
of the "barrel" or "fish-eye" effect.
of the "barrel" or "fish-eye" effect.
Tangential distortion occurs because the image taking lenses are not perfectly parallel to the
Tangential distortion occurs because the image taking lenses are not perfectly parallel to the
imaging plane. It can be
correc
ted via the formulas:
imaging plane. It can be
represen
ted via the formulas:
\f
[
x_{
correc
ted} = x + [ 2p_1xy + p_2(r^2+2x^2)
]
\\
\f
[
x_{
distor
ted} = x + [ 2p_1xy + p_2(r^2+2x^2)
]
\\
y_{
correc
ted} = y +
[
p_1(r^2+ 2y^2)+ 2p_2xy
]
\f
]
y_{
distor
ted} = y +
[
p_1(r^2+ 2y^2)+ 2p_2xy
]
\f
]
So we have five distortion parameters which in OpenCV are presented as one row matrix with 5
So we have five distortion parameters which in OpenCV are presented as one row matrix with 5
columns:
columns:
...
...
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