generic-library/opencv
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Replaced 'corrected' to 'distorted' in camera calibration tutorials

Browse Source
This commit is contained in:
Maksim Shabunin 2015-05-07 18:00:11 +03:00
parent 4743184078
commit c8cb03fd8f
2 changed files with 14 additions and 14 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

12
doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown
View File

@ -22,17 +22,17 @@ red line. All the expected straight lines are bulged out. Visit [Distortion
![image](images/calib_radial.jpg)
This distortion is solved as follows:
This distortion is represented as follows:
\f[x_{corrected} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6) \\
y_{corrected} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)\f]
\f[x_{distorted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6) \\
y_{distorted} = 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
is not aligned perfectly parallel to the imaging plane. So some areas in image may look nearer than
expected. It is solved as below:
expected. It is represented as below:
\f[x_{corrected} = x + [ 2p_1xy + p_2(r^2+2x^2)] \\
y_{corrected} = y + [ p_1(r^2+ 2y^2)+ 2p_2xy]\f]
\f[x_{distorted} = x + [ 2p_1xy + p_2(r^2+2x^2)] \\
y_{distorted} = y + [ p_1(r^2+ 2y^2)+ 2p_2xy]\f]
In short, we need to find five parameters, known as distortion coefficients given by:

16
doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown
View File

@ -14,18 +14,18 @@ Theory
For the distortion OpenCV takes into account the radial and tangential factors. For the radial
factor one uses the following formula:
\f[x_{corrected} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6) \\
y_{corrected} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)\f]
\f[x_{distorted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6) \\
y_{distorted} = 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
output image will be \f$(x_{corrected} y_{corrected})\f$. The presence of the radial distortion
manifests in form of the "barrel" or "fish-eye" effect.
So for an undistorted pixel point at \f$(x,y)\f$ coordinates, its position on the distorted image
will be \f$(x_{distorted} y_{distorted})\f$. The presence of the radial distortion manifests in form
of the "barrel" or "fish-eye" effect.
Tangential distortion occurs because the image taking lenses are not perfectly parallel to the
imaging plane. It can be corrected via the formulas:
imaging plane. It can be represented via the formulas:
\f[x_{corrected} = x + [ 2p_1xy + p_2(r^2+2x^2)] \\
y_{corrected} = y + [ p_1(r^2+ 2y^2)+ 2p_2xy]\f]
\f[x_{distorted} = x + [ 2p_1xy + p_2(r^2+2x^2)] \\
y_{distorted} = 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
columns: