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Extension of the camera distortion model for tilted image sensors (Scheimpflug condition) including test

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This commit is contained in:
Thomas Dunker
2015-10-14 12:07:28 +02:00
parent 5cdf0e3e89
commit 6882c10b45
9 changed files with 1144 additions and 95 deletions
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modules/imgproc/include/opencv2/imgproc.hpp
+28 -8
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@@ -2598,8 +2598,8 @@ the same.
@param dst Output (corrected) image that has the same size and type as src .
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])\f$ of 4, 5, or 8 elements. If the vector is
NULL/empty, the zero distortion coefficients are assumed.
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
@param newCameraMatrix Camera matrix of the distorted image. By default, it is the same as
cameraMatrix but you may additionally scale and shift the result by using a different matrix.
*/
@@ -2625,8 +2625,28 @@ The function actually builds the maps for the inverse mapping algorithm that is
is, for each pixel \f$(u, v)\f$ in the destination (corrected and rectified) image, the function
computes the corresponding coordinates in the source image (that is, in the original image from
camera). The following process is applied:
\f[\begin{array}{l} x \leftarrow (u - {c'}_x)/{f'}_x \\ y \leftarrow (v - {c'}_y)/{f'}_y \\{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\ x' \leftarrow X/W \\ y' \leftarrow Y/W \\ x" \leftarrow x' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + 2p_1 x' y' + p_2(r^2 + 2 x'^2) \\ y" \leftarrow y' (1 + k_1 r^2 + k_2 r^4 + k_3 r^6) + p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' \\ map_x(u,v) \leftarrow x" f_x + c_x \\ map_y(u,v) \leftarrow y" f_y + c_y \end{array}\f]
where \f$(k_1, k_2, p_1, p_2[, k_3])\f$ are the distortion coefficients.
\f[
\begin{array}{l}
x \leftarrow (u - {c'}_x)/{f'}_x \\
y \leftarrow (v - {c'}_y)/{f'}_y \\
{[X\,Y\,W]} ^T \leftarrow R^{-1}*[x \, y \, 1]^T \\
x' \leftarrow X/W \\
y' \leftarrow Y/W \\
r^2 \leftarrow x'^2 + y'^2 \\
x'' \leftarrow x' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
+ 2p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4\\
y'' \leftarrow y' \frac{1 + k_1 r^2 + k_2 r^4 + k_3 r^6}{1 + k_4 r^2 + k_5 r^4 + k_6 r^6}
+ p_1 (r^2 + 2 y'^2) + 2 p_2 x' y' + s_3 r^2 + s_4 r^4 \\
s\vecthree{x'''}{y'''}{1} =
\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
{0}{0}{1} R(\tau_x, \tau_y) \vecthree{x''}{y''}{1}\\
map_x(u,v) \leftarrow x''' f_x + c_x \\
map_y(u,v) \leftarrow y''' f_y + c_y
\end{array}
\f]
where \f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
are the distortion coefficients.
In case of a stereo camera, this function is called twice: once for each camera head, after
stereoRectify, which in its turn is called after cv::stereoCalibrate. But if the stereo camera
@@ -2639,8 +2659,8 @@ where cameraMatrix can be chosen arbitrarily.
@param cameraMatrix Input camera matrix \f$A=\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])\f$ of 4, 5, or 8 elements. If the vector is
NULL/empty, the zero distortion coefficients are assumed.
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
of 4, 5, 8, 12 or 14 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed.
@param R Optional rectification transformation in the object space (3x3 matrix). R1 or R2 ,
computed by stereoRectify can be passed here. If the matrix is empty, the identity transformation
is assumed. In cvInitUndistortMap R assumed to be an identity matrix.
@@ -2715,8 +2735,8 @@ The function can be used for both a stereo camera head or a monocular camera (wh
transformation. If matrix P is identity or omitted, dst will contain normalized point coordinates.
@param cameraMatrix Camera matrix \f$\vecthreethree{f_x}{0}{c_x}{0}{f_y}{c_y}{0}{0}{1}\f$ .
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]])\f$ of 4, 5, or 8 elements. If the vector is
NULL/empty, the zero distortion coefficients are assumed.
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6[, s_1, s_2, s_3, s_4[, \tau_x, \tau_y]]]])\f$
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
modules/imgproc/include/opencv2/imgproc/detail/distortion_model.hpp
+123
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@@ -0,0 +1,123 @@
/*M///////////////////////////////////////////////////////////////////////////////////////
//
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#ifndef __OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP__
#define __OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP__
//! @cond IGNORED
namespace cv { namespace detail {
/**
Computes the matrix for the projection onto a tilted image sensor
\param tauX angular parameter rotation around x-axis
\param tauY angular parameter rotation around y-axis
\param matTilt if not NULL returns the matrix
\f[
\vecthreethree{R_{33}(\tau_x, \tau_y)}{0}{-R_{13}((\tau_x, \tau_y)}
{0}{R_{33}(\tau_x, \tau_y)}{-R_{23}(\tau_x, \tau_y)}
{0}{0}{1} R(\tau_x, \tau_y)
\f]
where
\f[
R(\tau_x, \tau_y) =
\vecthreethree{\cos(\tau_y)}{0}{-\sin(\tau_y)}{0}{1}{0}{\sin(\tau_y)}{0}{\cos(\tau_y)}
\vecthreethree{1}{0}{0}{0}{\cos(\tau_x)}{\sin(\tau_x)}{0}{-\sin(\tau_x)}{\cos(\tau_x)} =
\vecthreethree{\cos(\tau_y)}{\sin(\tau_y)\sin(\tau_x)}{-\sin(\tau_y)\cos(\tau_x)}
{0}{\cos(\tau_x)}{\sin(\tau_x)}
{\sin(\tau_y)}{-\cos(\tau_y)\sin(\tau_x)}{\cos(\tau_y)\cos(\tau_x)}.
\f]
\param dMatTiltdTauX if not NULL it returns the derivative of matTilt with
respect to \f$\tau_x\f$.
\param dMatTiltdTauY if not NULL it returns the derivative of matTilt with
respect to \f$\tau_y\f$.
\param invMatTilt if not NULL it returns the inverse of matTilt
**/
template <typename FLOAT>
void computeTiltProjectionMatrix(FLOAT tauX,
FLOAT tauY,
Matx<FLOAT, 3, 3>* matTilt = 0,
Matx<FLOAT, 3, 3>* dMatTiltdTauX = 0,
Matx<FLOAT, 3, 3>* dMatTiltdTauY = 0,
Matx<FLOAT, 3, 3>* invMatTilt = 0)
{
FLOAT cTauX = cos(tauX);
FLOAT sTauX = sin(tauX);
FLOAT cTauY = cos(tauY);
FLOAT sTauY = sin(tauY);
Matx<FLOAT, 3, 3> matRotX = Matx<FLOAT, 3, 3>(1,0,0,0,cTauX,sTauX,0,-sTauX,cTauX);
Matx<FLOAT, 3, 3> matRotY = Matx<FLOAT, 3, 3>(cTauY,0,-sTauY,0,1,0,sTauY,0,cTauY);
Matx<FLOAT, 3, 3> matRotXY = matRotY * matRotX;
Matx<FLOAT, 3, 3> matProjZ = Matx<FLOAT, 3, 3>(matRotXY(2,2),0,-matRotXY(0,2),0,matRotXY(2,2),-matRotXY(1,2),0,0,1);
if (matTilt)
{
// Matrix for trapezoidal distortion of tilted image sensor
*matTilt = matProjZ * matRotXY;
}
if (dMatTiltdTauX)
{
// Derivative with respect to tauX
Matx<FLOAT, 3, 3> dMatRotXYdTauX = matRotY * Matx<FLOAT, 3, 3>(0,0,0,0,-sTauX,cTauX,0,-cTauX,-sTauX);
Matx<FLOAT, 3, 3> dMatProjZdTauX = Matx<FLOAT, 3, 3>(dMatRotXYdTauX(2,2),0,-dMatRotXYdTauX(0,2),
0,dMatRotXYdTauX(2,2),-dMatRotXYdTauX(1,2),0,0,0);
*dMatTiltdTauX = (matProjZ * dMatRotXYdTauX) + (dMatProjZdTauX * matRotXY);
}
if (dMatTiltdTauY)
{
// Derivative with respect to tauY
Matx<FLOAT, 3, 3> dMatRotXYdTauY = Matx<FLOAT, 3, 3>(-sTauY,0,-cTauY,0,0,0,cTauY,0,-sTauY) * matRotX;
Matx<FLOAT, 3, 3> dMatProjZdTauY = Matx<FLOAT, 3, 3>(dMatRotXYdTauY(2,2),0,-dMatRotXYdTauY(0,2),
0,dMatRotXYdTauY(2,2),-dMatRotXYdTauY(1,2),0,0,0);
*dMatTiltdTauY = (matProjZ * dMatRotXYdTauY) + (dMatProjZdTauY * matRotXY);
}
if (invMatTilt)
{
FLOAT inv = 1./matRotXY(2,2);
Matx<FLOAT, 3, 3> invMatProjZ = Matx<FLOAT, 3, 3>(inv,0,inv*matRotXY(0,2),0,inv,inv*matRotXY(1,2),0,0,1);
*invMatTilt = matRotXY.t()*invMatProjZ;
}
}
}} // namespace detail, cv
//! @endcond
#endif // __OPENCV_IMGPROC_DETAIL_DISTORTION_MODEL_HPP__