diff --git a/doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown b/doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown index 66f578f33..3655400f3 100644 --- a/doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown +++ b/doc/py_tutorials/py_calib3d/py_calibration/py_calibration.markdown @@ -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: diff --git a/doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown b/doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown index a7bd1f059..1a7b90687 100644 --- a/doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown +++ b/doc/tutorials/calib3d/camera_calibration/camera_calibration.markdown @@ -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: