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doxygen: undistortPoints - replace matlab code by latex forumlae

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This commit is contained in:
Pavel Rojtberg 2016-09-02 12:20:32 +02:00
parent 4e8f8922e2
commit 62cabb58a9
1 changed files with 18 additions and 15 deletions
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33
modules/imgproc/include/opencv2/imgproc.hpp
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@ -2953,20 +2953,23 @@ The function is similar to cv::undistort and cv::initUndistortRectifyMap but it
sparse set of points instead of a raster image. Also the function performs a reverse transformation
to projectPoints. In case of a 3D object, it does not reconstruct its 3D coordinates, but for a
planar object, it does, up to a translation vector, if the proper R is specified.
@code
// (u,v) is the input point, (u', v') is the output point
// camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1]
// P=[fx' 0 cx' tx; 0 fy' cy' ty; 0 0 1 tz]
x" = (u - cx)/fx
y" = (v - cy)/fy
(x',y') = undistort(x",y",dist_coeffs)
[X,Y,W]T = R*[x' y' 1]T
x = X/W, y = Y/W
// only performed if P=[fx' 0 cx' [tx]; 0 fy' cy' [ty]; 0 0 1 [tz]] is specified
u' = x*fx' + cx'
v' = y*fy' + cy',
@endcode
where cv::undistort is an approximate iterative algorithm that estimates the normalized original
For each observed point coordinate \f$(u, v)\f$ the function computes:
\f[
\begin{array}{l}
x^{"} \leftarrow (u - c_x)/f_x \\
y^{"} \leftarrow (v - c_y)/f_y \\
(x',y') = undistort(x^{"},y^{"}, \texttt{distCoeffs}) \\
{[X\,Y\,W]} ^T \leftarrow R*[x' \, y' \, 1]^T \\
x \leftarrow X/W \\
y \leftarrow Y/W \\
\text{only performed if P is specified:} \\
u' \leftarrow x {f'}_x + {c'}_x \\
v' \leftarrow y {f'}_y + {c'}_y
\end{array}
\f]
where *undistort* is an approximate iterative algorithm that estimates the normalized original
point coordinates out of the normalized distorted point coordinates ("normalized" means that the
coordinates do not depend on the camera matrix).
@ -2981,7 +2984,7 @@ transformation. If matrix P is identity or omitted, dst will contain normalized
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
@param R Rectification transformation in the object space (3x3 matrix). R1 or R2 computed by
cv::stereoRectify can be passed here. If the matrix is empty, the identity transformation is used.
@param P New camera matrix (3x3) or new projection matrix (3x4). P1 or P2 computed by
@param P New camera matrix (3x3) or new projection matrix (3x4) \f$\begin{bmatrix} {f'}_x & 0 & {c'}_x & t_x \\ 0 & {f'}_y & {c'}_y & t_y \\ 0 & 0 & 1 & t_z \end{bmatrix}\f$. P1 or P2 computed by
cv::stereoRectify can be passed here. If the matrix is empty, the identity new camera matrix is used.
*/
CV_EXPORTS_W void undistortPoints( InputArray src, OutputArray dst,