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

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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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86
modules/calib3d/include/opencv2/calib3d.hpp
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@@ -99,14 +99,50 @@ v = f_y*y' + c_y
Real lenses usually have some distortion, mostly radial distortion and slight tangential distortion.
So, the above model is extended as:
\f[\begin{array}{l} \vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\ x' = x/z \\ y' = y/z \\ x'' = 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} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\ y'' = 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 \\ \text{where} \quad r^2 = x'^2 + y'^2 \\ u = f_x*x'' + c_x \\ v = f_y*y'' + c_y \end{array}\f]
\f[\begin{array}{l}
\vecthree{x}{y}{z} = R \vecthree{X}{Y}{Z} + t \\
x' = x/z \\
y' = y/z \\
x'' = 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} + 2 p_1 x' y' + p_2(r^2 + 2 x'^2) + s_1 r^2 + s_2 r^4 \\
y'' = 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 \\
\text{where} \quad r^2 = x'^2 + y'^2 \\
u = f_x*x'' + c_x \\
v = f_y*y'' + c_y
\end{array}\f]
\f$k_1\f$, \f$k_2\f$, \f$k_3\f$, \f$k_4\f$, \f$k_5\f$, and \f$k_6\f$ are radial distortion coefficients. \f$p_1\f$ and \f$p_2\f$ are
tangential distortion coefficients. \f$s_1\f$, \f$s_2\f$, \f$s_3\f$, and \f$s_4\f$, are the thin prism distortion
coefficients. Higher-order coefficients are not considered in OpenCV. In the functions below the
coefficients are passed or returned as
coefficients. Higher-order coefficients are not considered in OpenCV.
\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]])\f]
In some cases the image sensor may be tilted in order to focus an oblique plane in front of the
camera (Scheimpfug condition). This can be useful for particle image velocimetry (PIV) or
triangulation with a laser fan. The tilt causes a perspective distortion of \f$x''\f$ and
\f$y''\f$. This distortion can be modelled in the following way, see e.g. @cite Louhichi07.
\f[\begin{array}{l}
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}\\
u = f_x*x''' + c_x \\
v = f_y*y''' + c_y
\end{array}\f]
where the matrix \f$R(\tau_x, \tau_y)\f$ is defined by two rotations with angular parameter \f$\tau_x\f$
and \f$\tau_y\f$, respectively,
\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]
In the functions below the coefficients are passed or returned as
\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]
vector. That is, if the vector contains four elements, it means that \f$k_3=0\f$ . The distortion
coefficients do not depend on the scene viewed. Thus, they also belong to the intrinsic camera
@@ -221,6 +257,8 @@ enum { CALIB_USE_INTRINSIC_GUESS = 0x00001,
CALIB_RATIONAL_MODEL = 0x04000,
CALIB_THIN_PRISM_MODEL = 0x08000,
CALIB_FIX_S1_S2_S3_S4 = 0x10000,
CALIB_TILTED_MODEL = 0x40000,
CALIB_FIX_TAUX_TAUY = 0x80000,
// only for stereo
CALIB_FIX_INTRINSIC = 0x00100,
CALIB_SAME_FOCAL_LENGTH = 0x00200,
@@ -444,8 +482,8 @@ vector\<Point3f\> ), where N is the number of points in the view.
@param tvec Translation vector.
@param cameraMatrix 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$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 elements. If
the vector is 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 empty, the zero distortion coefficients are assumed.
@param imagePoints Output array of image points, 2xN/Nx2 1-channel or 1xN/Nx1 2-channel, or
vector\<Point2f\> .
@param jacobian Optional output 2Nx(10+\<numDistCoeffs\>) jacobian matrix of derivatives of image
@@ -483,8 +521,9 @@ CV_EXPORTS_W void projectPoints( InputArray objectPoints,
where N is the number of points. vector\<Point2f\> can be also passed here.
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}\f$ .
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 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 rvec Output rotation vector (see Rodrigues ) that, together with tvec , brings points from
the model coordinate system to the camera coordinate system.
@param tvec Output translation vector.
@@ -539,8 +578,9 @@ CV_EXPORTS_W bool solvePnP( InputArray objectPoints, InputArray imagePoints,
where N is the number of points. vector\<Point2f\> can be also passed here.
@param cameraMatrix Input camera matrix \f$A = \vecthreethree{fx}{0}{cx}{0}{fy}{cy}{0}{0}{1}\f$ .
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 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 rvec Output rotation vector (see Rodrigues ) that, together with tvec , brings points from
the model coordinate system to the camera coordinate system.
@param tvec Output translation vector.
@@ -719,7 +759,8 @@ together.
and/or CV_CALIB_FIX_ASPECT_RATIO are specified, some or all of fx, fy, cx, cy must be
initialized before calling the function.
@param distCoeffs Output vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 elements.
\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.
@param rvecs Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view
(e.g. std::vector<cv::Mat>>). That is, each k-th rotation vector together with the corresponding
k-th translation vector (see the next output parameter description) brings the calibration pattern
@@ -755,6 +796,13 @@ set, the function computes and returns only 5 distortion coefficients.
- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
- **CALIB_TILTED_MODEL** Coefficients tauX and tauY are enabled. To provide the
backward compatibility, this extra flag should be explicitly specified to make the
calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
set, the function computes and returns only 5 distortion coefficients.
- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
@param criteria Termination criteria for the iterative optimization algorithm.
The function estimates the intrinsic camera parameters and extrinsic parameters for each of the
@@ -839,8 +887,8 @@ any of CV_CALIB_USE_INTRINSIC_GUESS , CV_CALIB_FIX_ASPECT_RATIO ,
CV_CALIB_FIX_INTRINSIC , or CV_CALIB_FIX_FOCAL_LENGTH are specified, some or all of the
matrix components must be initialized. See the flags description for details.
@param distCoeffs1 Input/output vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 ot 12 elements. The
output vector length depends on the flags.
\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. The output vector length depends on the flags.
@param cameraMatrix2 Input/output second camera matrix. The parameter is similar to cameraMatrix1
@param distCoeffs2 Input/output lens distortion coefficients for the second camera. The parameter
is similar to distCoeffs1 .
@@ -875,6 +923,13 @@ set, the function computes and returns only 5 distortion coefficients.
- **CALIB_FIX_S1_S2_S3_S4** The thin prism distortion coefficients are not changed during
the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
- **CALIB_TILTED_MODEL** Coefficients tauX and tauY are enabled. To provide the
backward compatibility, this extra flag should be explicitly specified to make the
calibration function use the tilted sensor model and return 14 coefficients. If the flag is not
set, the function computes and returns only 5 distortion coefficients.
- **CALIB_FIX_TAUX_TAUY** The coefficients of the tilted sensor model are not changed during
the optimization. If CV_CALIB_USE_INTRINSIC_GUESS is set, the coefficient from the
supplied distCoeffs matrix is used. Otherwise, it is set to 0.
@param criteria Termination criteria for the iterative optimization algorithm.
The function estimates transformation between two cameras making a stereo pair. If you have a stereo
@@ -1058,8 +1113,9 @@ CV_EXPORTS_W float rectify3Collinear( InputArray cameraMatrix1, InputArray distC
@param cameraMatrix Input camera matrix.
@param distCoeffs Input vector of distortion coefficients
\f$(k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6],[s_1, s_2, s_3, s_4]])\f$ of 4, 5, 8 or 12 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 imageSize Original image size.
@param alpha Free scaling parameter between 0 (when all the pixels in the undistorted image are
valid) and 1 (when all the source image pixels are retained in the undistorted image). See

2
modules/calib3d/include/opencv2/calib3d/calib3d_c.h
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@@ -243,6 +243,8 @@ CVAPI(void) cvDrawChessboardCorners( CvArr* image, CvSize pattern_size,
#define CV_CALIB_RATIONAL_MODEL 16384
#define CV_CALIB_THIN_PRISM_MODEL 32768
#define CV_CALIB_FIX_S1_S2_S3_S4 65536
#define CV_CALIB_TILTED_MODEL 262144
#define CV_CALIB_FIX_TAUX_TAUY 524288
/* Finds intrinsic and extrinsic camera parameters