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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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10
doc/opencv.bib
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@ -415,6 +415,16 @@
pages = {2548--2555},
organization = {IEEE}
}
@ARTICLE{Louhichi07,
author = {Louhichi, H. and Fournel, T. and Lavest, J. M. and Ben Aissia, H.},
title = {Self-calibration of Scheimpflug cameras: an easy protocol},
year = {2007},
pages = {2616–2622},
journal = {Meas. Sci. Technol.},
volume = {18},
number = {8},
publisher = {IOP Publishing Ltd}
}
@ARTICLE{LibSVM,
author = {Chang, Chih-Chung and Lin, Chih-Jen},
title = {LIBSVM: a library for support vector machines},

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

210
modules/calib3d/src/calibration.cpp
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@ -42,6 +42,7 @@
#include "precomp.hpp"
#include "opencv2/imgproc/imgproc_c.h"
#include "opencv2/imgproc/detail/distortion_model.hpp"
#include "opencv2/calib3d/calib3d_c.h"
#include <stdio.h>
#include <iterator>
@ -523,7 +524,7 @@ CV_IMPL int cvRodrigues2( const CvMat* src, CvMat* dst, CvMat* jacobian )
}
static const char* cvDistCoeffErr = "Distortion coefficients must be 1x4, 4x1, 1x5, 5x1, 1x8, 8x1, 1x12 or 12x1 floating-point vector";
static const char* cvDistCoeffErr = "Distortion coefficients must be 1x4, 4x1, 1x5, 5x1, 1x8, 8x1, 1x12, 12x1, 1x14 or 14x1 floating-point vector";
CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
const CvMat* r_vec,
@ -542,7 +543,10 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
int calc_derivatives;
const CvPoint3D64f* M;
CvPoint2D64f* m;
double r[3], R[9], dRdr[27], t[3], a[9], k[12] = {0,0,0,0,0,0,0,0,0,0,0,0}, fx, fy, cx, cy;
double r[3], R[9], dRdr[27], t[3], a[9], k[14] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0}, fx, fy, cx, cy;
Matx33d matTilt = Matx33d::eye();
Matx33d dMatTiltdTauX(0,0,0,0,0,0,0,-1,0);
Matx33d dMatTiltdTauY(0,0,0,0,0,0,1,0,0);
CvMat _r, _t, _a = cvMat( 3, 3, CV_64F, a ), _k;
CvMat matR = cvMat( 3, 3, CV_64F, R ), _dRdr = cvMat( 3, 9, CV_64F, dRdr );
double *dpdr_p = 0, *dpdt_p = 0, *dpdk_p = 0, *dpdf_p = 0, *dpdc_p = 0;
@ -646,12 +650,18 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
(distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 4 &&
distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 5 &&
distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 8 &&
distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 12) )
distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 12 &&
distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 14) )
CV_Error( CV_StsBadArg, cvDistCoeffErr );
_k = cvMat( distCoeffs->rows, distCoeffs->cols,
CV_MAKETYPE(CV_64F,CV_MAT_CN(distCoeffs->type)), k );
cvConvert( distCoeffs, &_k );
if(k[12] != 0 || k[13] != 0)
{
detail::computeTiltProjectionMatrix(k[12], k[13],
&matTilt, &dMatTiltdTauX, &dMatTiltdTauY);
}
}
if( dpdr )
@ -728,8 +738,8 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
{
if( !CV_IS_MAT(dpdk) ||
(CV_MAT_TYPE(dpdk->type) != CV_32FC1 && CV_MAT_TYPE(dpdk->type) != CV_64FC1) ||
dpdk->rows != count*2 || (dpdk->cols != 12 && dpdk->cols != 8 && dpdk->cols != 5 && dpdk->cols != 4 && dpdk->cols != 2) )
CV_Error( CV_StsBadArg, "dp/df must be 2Nx12, 2Nx8, 2Nx5, 2Nx4 or 2Nx2 floating-point matrix" );
dpdk->rows != count*2 || (dpdk->cols != 14 && dpdk->cols != 12 && dpdk->cols != 8 && dpdk->cols != 5 && dpdk->cols != 4 && dpdk->cols != 2) )
CV_Error( CV_StsBadArg, "dp/df must be 2Nx14, 2Nx12, 2Nx8, 2Nx5, 2Nx4 or 2Nx2 floating-point matrix" );
if( !distCoeffs )
CV_Error( CV_StsNullPtr, "distCoeffs is NULL while dpdk is not" );
@ -753,7 +763,11 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
double y = R[3]*X + R[4]*Y + R[5]*Z + t[1];
double z = R[6]*X + R[7]*Y + R[8]*Z + t[2];
double r2, r4, r6, a1, a2, a3, cdist, icdist2;
double xd, yd;
double xd, yd, xd0, yd0, invProj;
Vec3d vecTilt;
Vec3d dVecTilt;
Matx22d dMatTilt;
Vec2d dXdYd;
z = z ? 1./z : 1;
x *= z; y *= z;
@ -766,8 +780,14 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
a3 = r2 + 2*y*y;
cdist = 1 + k[0]*r2 + k[1]*r4 + k[4]*r6;
icdist2 = 1./(1 + k[5]*r2 + k[6]*r4 + k[7]*r6);
xd = x*cdist*icdist2 + k[2]*a1 + k[3]*a2 + k[8]*r2+k[9]*r4;
yd = y*cdist*icdist2 + k[2]*a3 + k[3]*a1 + k[10]*r2+k[11]*r4;
xd0 = x*cdist*icdist2 + k[2]*a1 + k[3]*a2 + k[8]*r2+k[9]*r4;
yd0 = y*cdist*icdist2 + k[2]*a3 + k[3]*a1 + k[10]*r2+k[11]*r4;
// additional distortion by projecting onto a tilt plane
vecTilt = matTilt*Vec3d(xd0, yd0, 1);
invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
xd = invProj * vecTilt(0);
yd = invProj * vecTilt(1);
m[i].x = xd*fx + cx;
m[i].y = yd*fy + cy;
@ -798,42 +818,75 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
}
dpdf_p += dpdf_step*2;
}
for (int row = 0; row < 2; ++row)
for (int col = 0; col < 2; ++col)
dMatTilt(row,col) = matTilt(row,col)*vecTilt(2)
- matTilt(2,col)*vecTilt(row);
double invProjSquare = (invProj*invProj);
dMatTilt *= invProjSquare;
if( dpdk_p )
{
dpdk_p[0] = fx*x*icdist2*r2;
dpdk_p[1] = fx*x*icdist2*r4;
dpdk_p[dpdk_step] = fy*y*icdist2*r2;
dpdk_p[dpdk_step+1] = fy*y*icdist2*r4;
dXdYd = dMatTilt*Vec2d(x*icdist2*r2, y*icdist2*r2);
dpdk_p[0] = fx*dXdYd(0);
dpdk_p[dpdk_step] = fy*dXdYd(1);
dXdYd = dMatTilt*Vec2d(x*icdist2*r4, y*icdist2*r4);
dpdk_p[1] = fx*dXdYd(0);
dpdk_p[dpdk_step+1] = fy*dXdYd(1);
if( _dpdk->cols > 2 )
{
dpdk_p[2] = fx*a1;
dpdk_p[3] = fx*a2;
dpdk_p[dpdk_step+2] = fy*a3;
dpdk_p[dpdk_step+3] = fy*a1;
dXdYd = dMatTilt*Vec2d(a1, a3);
dpdk_p[2] = fx*dXdYd(0);
dpdk_p[dpdk_step+2] = fy*dXdYd(1);
dXdYd = dMatTilt*Vec2d(a2, a1);
dpdk_p[3] = fx*dXdYd(0);
dpdk_p[dpdk_step+3] = fy*dXdYd(1);
if( _dpdk->cols > 4 )
{
dpdk_p[4] = fx*x*icdist2*r6;
dpdk_p[dpdk_step+4] = fy*y*icdist2*r6;
dXdYd = dMatTilt*Vec2d(x*icdist2*r6, y*icdist2*r6);
dpdk_p[4] = fx*dXdYd(0);
dpdk_p[dpdk_step+4] = fy*dXdYd(1);
if( _dpdk->cols > 5 )
{
dpdk_p[5] = fx*x*cdist*(-icdist2)*icdist2*r2;
dpdk_p[dpdk_step+5] = fy*y*cdist*(-icdist2)*icdist2*r2;
dpdk_p[6] = fx*x*cdist*(-icdist2)*icdist2*r4;
dpdk_p[dpdk_step+6] = fy*y*cdist*(-icdist2)*icdist2*r4;
dpdk_p[7] = fx*x*cdist*(-icdist2)*icdist2*r6;
dpdk_p[dpdk_step+7] = fy*y*cdist*(-icdist2)*icdist2*r6;
dXdYd = dMatTilt*Vec2d(
x*cdist*(-icdist2)*icdist2*r2, y*cdist*(-icdist2)*icdist2*r2);
dpdk_p[5] = fx*dXdYd(0);
dpdk_p[dpdk_step+5] = fy*dXdYd(1);
dXdYd = dMatTilt*Vec2d(
x*cdist*(-icdist2)*icdist2*r4, y*cdist*(-icdist2)*icdist2*r4);
dpdk_p[6] = fx*dXdYd(0);
dpdk_p[dpdk_step+6] = fy*dXdYd(1);
dXdYd = dMatTilt*Vec2d(
x*cdist*(-icdist2)*icdist2*r6, y*cdist*(-icdist2)*icdist2*r6);
dpdk_p[7] = fx*dXdYd(0);
dpdk_p[dpdk_step+7] = fy*dXdYd(1);
if( _dpdk->cols > 8 )
{
dpdk_p[8] = fx*r2; //s1
dpdk_p[9] = fx*r4; //s2
dpdk_p[10] = 0;//s3
dpdk_p[11] = 0;//s4
dpdk_p[dpdk_step+8] = 0; //s1
dpdk_p[dpdk_step+9] = 0; //s2
dpdk_p[dpdk_step+10] = fy*r2; //s3
dpdk_p[dpdk_step+11] = fy*r4; //s4
dXdYd = dMatTilt*Vec2d(r2, 0);
dpdk_p[8] = fx*dXdYd(0); //s1
dpdk_p[dpdk_step+8] = fy*dXdYd(1); //s1
dXdYd = dMatTilt*Vec2d(r4, 0);
dpdk_p[9] = fx*dXdYd(0); //s2
dpdk_p[dpdk_step+9] = fy*dXdYd(1); //s2
dXdYd = dMatTilt*Vec2d(0, r2);
dpdk_p[10] = fx*dXdYd(0);//s3
dpdk_p[dpdk_step+10] = fy*dXdYd(1); //s3
dXdYd = dMatTilt*Vec2d(0, r4);
dpdk_p[11] = fx*dXdYd(0);//s4
dpdk_p[dpdk_step+11] = fy*dXdYd(1); //s4
if( _dpdk->cols > 12 )
{
dVecTilt = dMatTiltdTauX * Vec3d(xd0, yd0, 1);
dpdk_p[12] = fx * invProjSquare * (
dVecTilt(0) * vecTilt(2) - dVecTilt(2) * vecTilt(0));
dpdk_p[dpdk_step+12] = fy*invProjSquare * (
dVecTilt(1) * vecTilt(2) - dVecTilt(2) * vecTilt(1));
dVecTilt = dMatTiltdTauY * Vec3d(xd0, yd0, 1);
dpdk_p[13] = fx * invProjSquare * (
dVecTilt(0) * vecTilt(2) - dVecTilt(2) * vecTilt(0));
dpdk_p[dpdk_step+13] = fy * invProjSquare * (
dVecTilt(1) * vecTilt(2) - dVecTilt(2) * vecTilt(1));
}
}
}
}
@ -850,12 +903,13 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
double dcdist_dt = k[0]*dr2dt + 2*k[1]*r2*dr2dt + 3*k[4]*r4*dr2dt;
double dicdist2_dt = -icdist2*icdist2*(k[5]*dr2dt + 2*k[6]*r2*dr2dt + 3*k[7]*r4*dr2dt);
double da1dt = 2*(x*dydt[j] + y*dxdt[j]);
double dmxdt = fx*(dxdt[j]*cdist*icdist2 + x*dcdist_dt*icdist2 + x*cdist*dicdist2_dt +
double dmxdt = (dxdt[j]*cdist*icdist2 + x*dcdist_dt*icdist2 + x*cdist*dicdist2_dt +
k[2]*da1dt + k[3]*(dr2dt + 2*x*dxdt[j]) + k[8]*dr2dt + 2*r2*k[9]*dr2dt);
double dmydt = fy*(dydt[j]*cdist*icdist2 + y*dcdist_dt*icdist2 + y*cdist*dicdist2_dt +
double dmydt = (dydt[j]*cdist*icdist2 + y*dcdist_dt*icdist2 + y*cdist*dicdist2_dt +
k[2]*(dr2dt + 2*y*dydt[j]) + k[3]*da1dt + k[10]*dr2dt + 2*r2*k[11]*dr2dt);
dpdt_p[j] = dmxdt;
dpdt_p[dpdt_step+j] = dmydt;
dXdYd = dMatTilt*Vec2d(dmxdt, dmydt);
dpdt_p[j] = fx*dXdYd(0);
dpdt_p[dpdt_step+j] = fy*dXdYd(1);
}
dpdt_p += dpdt_step*2;
}
@ -885,15 +939,16 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
double dxdr = z*(dx0dr[j] - x*dz0dr[j]);
double dydr = z*(dy0dr[j] - y*dz0dr[j]);
double dr2dr = 2*x*dxdr + 2*y*dydr;
double dcdist_dr = k[0]*dr2dr + 2*k[1]*r2*dr2dr + 3*k[4]*r4*dr2dr;
double dicdist2_dr = -icdist2*icdist2*(k[5]*dr2dr + 2*k[6]*r2*dr2dr + 3*k[7]*r4*dr2dr);
double dcdist_dr = (k[0] + 2*k[1]*r2 + 3*k[4]*r4)*dr2dr;
double dicdist2_dr = -icdist2*icdist2*(k[5] + 2*k[6]*r2 + 3*k[7]*r4)*dr2dr;
double da1dr = 2*(x*dydr + y*dxdr);
double dmxdr = fx*(dxdr*cdist*icdist2 + x*dcdist_dr*icdist2 + x*cdist*dicdist2_dr +
k[2]*da1dr + k[3]*(dr2dr + 2*x*dxdr) + k[8]*dr2dr + 2*r2*k[9]*dr2dr);
double dmydr = fy*(dydr*cdist*icdist2 + y*dcdist_dr*icdist2 + y*cdist*dicdist2_dr +
k[2]*(dr2dr + 2*y*dydr) + k[3]*da1dr + k[10]*dr2dr + 2*r2*k[11]*dr2dr);
dpdr_p[j] = dmxdr;
dpdr_p[dpdr_step+j] = dmydr;
double dmxdr = (dxdr*cdist*icdist2 + x*dcdist_dr*icdist2 + x*cdist*dicdist2_dr +
k[2]*da1dr + k[3]*(dr2dr + 2*x*dxdr) + (k[8] + 2*r2*k[9])*dr2dr);
double dmydr = (dydr*cdist*icdist2 + y*dcdist_dr*icdist2 + y*cdist*dicdist2_dr +
k[2]*(dr2dr + 2*y*dydr) + k[3]*da1dr + (k[10] + 2*r2*k[11])*dr2dr);
dXdYd = dMatTilt*Vec2d(dmxdr, dmydr);
dpdr_p[j] = fx*dXdYd(0);
dpdr_p[dpdr_step+j] = fy*dXdYd(1);
}
dpdr_p += dpdr_step*2;
}
@ -1231,11 +1286,11 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
CvSize imageSize, CvMat* cameraMatrix, CvMat* distCoeffs,
CvMat* rvecs, CvMat* tvecs, int flags, CvTermCriteria termCrit )
{
const int NINTRINSIC = 16;
const int NINTRINSIC = 18;
double reprojErr = 0;
Matx33d A;
double k[12] = {0};
double k[14] = {0};
CvMat matA = cvMat(3, 3, CV_64F, A.val), _k;
int i, nimages, maxPoints = 0, ni = 0, pos, total = 0, nparams, npstep, cn;
double aspectRatio = 0.;
@ -1252,9 +1307,19 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
(npoints->rows != 1 && npoints->cols != 1) )
CV_Error( CV_StsUnsupportedFormat,
"the array of point counters must be 1-dimensional integer vector" );
//when the thin prism model is used the distortion coefficients matrix must have 12 parameters
if((flags & CALIB_THIN_PRISM_MODEL) && (distCoeffs->cols*distCoeffs->rows != 12))
CV_Error( CV_StsBadArg, "Thin prism model must have 12 parameters in the distortion matrix" );
if(flags & CV_CALIB_TILTED_MODEL)
{
//when the tilted sensor model is used the distortion coefficients matrix must have 14 parameters
if (distCoeffs->cols*distCoeffs->rows != 14)
CV_Error( CV_StsBadArg, "The tilted sensor model must have 14 parameters in the distortion matrix" );
}
else
{
//when the thin prism model is used the distortion coefficients matrix must have 12 parameters
if(flags & CV_CALIB_THIN_PRISM_MODEL)
if (distCoeffs->cols*distCoeffs->rows != 12)
CV_Error( CV_StsBadArg, "Thin prism model must have 12 parameters in the distortion matrix" );
}
nimages = npoints->rows*npoints->cols;
npstep = npoints->rows == 1 ? 1 : npoints->step/CV_ELEM_SIZE(npoints->type);
@ -1293,7 +1358,8 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
(distCoeffs->cols*distCoeffs->rows != 4 &&
distCoeffs->cols*distCoeffs->rows != 5 &&
distCoeffs->cols*distCoeffs->rows != 8 &&
distCoeffs->cols*distCoeffs->rows != 12) )
distCoeffs->cols*distCoeffs->rows != 12 &&
distCoeffs->cols*distCoeffs->rows != 14) )
CV_Error( CV_StsBadArg, cvDistCoeffErr );
for( i = 0; i < nimages; i++ )
@ -1398,7 +1464,7 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
uchar* mask = solver.mask->data.ptr;
param[0] = A(0, 0); param[1] = A(1, 1); param[2] = A(0, 2); param[3] = A(1, 2);
std::copy(k, k + 12, param + 4);
std::copy(k, k + 14, param + 4);
if( flags & CV_CALIB_FIX_FOCAL_LENGTH )
mask[0] = mask[1] = 0;
@ -1413,6 +1479,8 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
flags |= CALIB_FIX_K4 + CALIB_FIX_K5 + CALIB_FIX_K6;
if( !(flags & CV_CALIB_THIN_PRISM_MODEL))
flags |= CALIB_FIX_S1_S2_S3_S4;
if( !(flags & CV_CALIB_TILTED_MODEL))
flags |= CALIB_FIX_TAUX_TAUY;
mask[ 4] = !(flags & CALIB_FIX_K1);
mask[ 5] = !(flags & CALIB_FIX_K2);
@ -1428,6 +1496,11 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
mask[14] = 0;
mask[15] = 0;
}
if(flags & CALIB_FIX_TAUX_TAUY)
{
mask[16] = 0;
mask[17] = 0;
}
}
// 2. initialize extrinsic parameters
@ -1461,7 +1534,7 @@ CV_IMPL double cvCalibrateCamera2( const CvMat* objectPoints,
}
A(0, 0) = param[0]; A(1, 1) = param[1]; A(0, 2) = param[2]; A(1, 2) = param[3];
std::copy(param + 4, param + 4 + 12, k);
std::copy(param + 4, param + 4 + 14, k);
if( !proceed )
break;
@ -1636,11 +1709,11 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
int flags,
CvTermCriteria termCrit )
{
const int NINTRINSIC = 16;
const int NINTRINSIC = 18;
Ptr<CvMat> npoints, err, J_LR, Je, Ji, imagePoints[2], objectPoints, RT0;
double reprojErr = 0;
double A[2][9], dk[2][12]={{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0}}, rlr[9];
double A[2][9], dk[2][14]={{0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0}}, rlr[9];
CvMat K[2], Dist[2], om_LR, T_LR;
CvMat R_LR = cvMat(3, 3, CV_64F, rlr);
int i, k, p, ni = 0, ofs, nimages, pointsTotal, maxPoints = 0;
@ -1686,7 +1759,7 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
(_imagePoints1->rows == 1 && _imagePoints1->cols == pointsTotal && cn == 2)) );
K[k] = cvMat(3,3,CV_64F,A[k]);
Dist[k] = cvMat(1,12,CV_64F,dk[k]);
Dist[k] = cvMat(1,14,CV_64F,dk[k]);
imagePoints[k].reset(cvCreateMat( points->rows, points->cols, CV_64FC(CV_MAT_CN(points->type))));
cvConvert( points, imagePoints[k] );
@ -1752,6 +1825,8 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
flags |= CV_CALIB_FIX_K4 | CV_CALIB_FIX_K5 | CV_CALIB_FIX_K6;
if( !(flags & CV_CALIB_THIN_PRISM_MODEL) )
flags |= CV_CALIB_FIX_S1_S2_S3_S4;
if( !(flags & CV_CALIB_TILTED_MODEL) )
flags |= CV_CALIB_FIX_TAUX_TAUY;
if( flags & CV_CALIB_FIX_ASPECT_RATIO )
imask[0] = imask[NINTRINSIC] = 0;
if( flags & CV_CALIB_FIX_FOCAL_LENGTH )
@ -1779,6 +1854,11 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
imask[14] = imask[NINTRINSIC+14] = 0;
imask[15] = imask[NINTRINSIC+15] = 0;
}
if( flags & CV_CALIB_FIX_TAUX_TAUY )
{
imask[16] = imask[NINTRINSIC+16] = 0;
imask[17] = imask[NINTRINSIC+17] = 0;
}
}
/*
@ -1857,6 +1937,8 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
iparam[13] = dk[k][9];
iparam[14] = dk[k][10];
iparam[15] = dk[k][11];
iparam[16] = dk[k][12];
iparam[17] = dk[k][13];
}
om_LR = cvMat(3, 1, CV_64F, solver.param->data.db);
@ -1927,6 +2009,8 @@ double cvStereoCalibrate( const CvMat* _objectPoints, const CvMat* _imagePoints1
dk[k][9] = iparam[k*NINTRINSIC+13];
dk[k][10] = iparam[k*NINTRINSIC+14];
dk[k][11] = iparam[k*NINTRINSIC+15];
dk[k][12] = iparam[k*NINTRINSIC+16];
dk[k][13] = iparam[k*NINTRINSIC+17];
}
}
@ -3026,15 +3110,17 @@ static Mat prepareCameraMatrix(Mat& cameraMatrix0, int rtype)
static Mat prepareDistCoeffs(Mat& distCoeffs0, int rtype)
{
Mat distCoeffs = Mat::zeros(distCoeffs0.cols == 1 ? Size(1, 12) : Size(12, 1), rtype);
Mat distCoeffs = Mat::zeros(distCoeffs0.cols == 1 ? Size(1, 14) : Size(14, 1), rtype);
if( distCoeffs0.size() == Size(1, 4) ||
distCoeffs0.size() == Size(1, 5) ||
distCoeffs0.size() == Size(1, 8) ||
distCoeffs0.size() == Size(1, 12) ||
distCoeffs0.size() == Size(1, 14) ||
distCoeffs0.size() == Size(4, 1) ||
distCoeffs0.size() == Size(5, 1) ||
distCoeffs0.size() == Size(8, 1) ||
distCoeffs0.size() == Size(12, 1) )
distCoeffs0.size() == Size(12, 1) ||
distCoeffs0.size() == Size(14, 1) )
{
Mat dstCoeffs(distCoeffs, Rect(0, 0, distCoeffs0.cols, distCoeffs0.rows));
distCoeffs0.convertTo(dstCoeffs, rtype);
@ -3219,7 +3305,9 @@ double cv::calibrateCamera( InputArrayOfArrays _objectPoints,
cameraMatrix = prepareCameraMatrix(cameraMatrix, rtype);
Mat distCoeffs = _distCoeffs.getMat();
distCoeffs = prepareDistCoeffs(distCoeffs, rtype);
if( !(flags & CALIB_RATIONAL_MODEL) &&(!(flags & CALIB_THIN_PRISM_MODEL)))
if( !(flags & CALIB_RATIONAL_MODEL) &&
(!(flags & CALIB_THIN_PRISM_MODEL)) &&
(!(flags & CALIB_TILTED_MODEL)))
distCoeffs = distCoeffs.rows == 1 ? distCoeffs.colRange(0, 5) : distCoeffs.rowRange(0, 5);
int nimages = int(_objectPoints.total());
@ -3314,7 +3402,9 @@ double cv::stereoCalibrate( InputArrayOfArrays _objectPoints,
distCoeffs1 = prepareDistCoeffs(distCoeffs1, rtype);
distCoeffs2 = prepareDistCoeffs(distCoeffs2, rtype);
if( !(flags & CALIB_RATIONAL_MODEL) &&(!(flags & CALIB_THIN_PRISM_MODEL)))
if( !(flags & CALIB_RATIONAL_MODEL) &&
(!(flags & CALIB_THIN_PRISM_MODEL)) &&
(!(flags & CALIB_TILTED_MODEL)))
{
distCoeffs1 = distCoeffs1.rows == 1 ? distCoeffs1.colRange(0, 5) : distCoeffs1.rowRange(0, 5);
distCoeffs2 = distCoeffs2.rows == 1 ? distCoeffs2.colRange(0, 5) : distCoeffs2.rowRange(0, 5);

700
modules/calib3d/test/test_cameracalibration_tilt.cpp Normal file
View File

@ -0,0 +1,700 @@
/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009-2011, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
#include "test_precomp.hpp"
#include <opencv2/ts/cuda_test.hpp>
#include "opencv2/calib3d.hpp"
#define NUM_DIST_COEFF_TILT 14
/**
Some conventions:
- the first camera determines the world coordinate system
- y points down, hence top means minimal y value (negative) and
bottom means maximal y value (positive)
- the field of view plane is tilted around x such that it
intersects the xy-plane in a line with a large (positive)
y-value
- image sensor and object are both modelled in the halfspace
z > 0
**/
class cameraCalibrationTiltTest : public ::testing::Test {
protected:
cameraCalibrationTiltTest()
: m_toRadian(acos(-1.0)/180.0)
, m_toDegree(180.0/acos(-1.0))
{}
virtual void SetUp();
protected:
static const cv::Size m_imageSize;
static const double m_pixelSize;
static const double m_circleConfusionPixel;
static const double m_lensFocalLength;
static const double m_lensFNumber;
static const double m_objectDistance;
static const double m_planeTiltDegree;
static const double m_pointTargetDist;
static const int m_pointTargetNum;
/** image distance coresponding to working distance */
double m_imageDistance;
/** image tilt angle corresponding to the tilt of the object plane */
double m_imageTiltDegree;
/** center of the field of view, near and far plane */
std::vector<cv::Vec3d> m_fovCenter;
/** normal of the field of view, near and far plane */
std::vector<cv::Vec3d> m_fovNormal;
/** points on a plane calibration target */
std::vector<cv::Point3d> m_pointTarget;
/** rotations for the calibration target */
std::vector<cv::Vec3d> m_pointTargetRvec;
/** translations for the calibration target */
std::vector<cv::Vec3d> m_pointTargetTvec;
/** camera matrix */
cv::Matx33d m_cameraMatrix;
/** distortion coefficients */
cv::Vec<double, NUM_DIST_COEFF_TILT> m_distortionCoeff;
/** random generator */
cv::RNG m_rng;
/** degree to radian conversion factor */
const double m_toRadian;
/** radian to degree conversion factor */
const double m_toDegree;
/**
computes for a given distance of an image or object point
the distance of the corresponding object or image point
*/
double opticalMap(double dist) {
return m_lensFocalLength*dist/(dist - m_lensFocalLength);
}
/** magnification of the optical map */
double magnification(double dist) {
return m_lensFocalLength/(dist - m_lensFocalLength);
}
/**
Changes given distortion coefficients randomly by adding
a uniformly distributed random variable in [-max max]
\param coeff input
\param max limits for the random variables
*/
void randomDistortionCoeff(
cv::Vec<double, NUM_DIST_COEFF_TILT>& coeff,
const cv::Vec<double, NUM_DIST_COEFF_TILT>& max)
{
for (int i = 0; i < coeff.rows; ++i)
coeff(i) += m_rng.uniform(-max(i), max(i));
}
/** numerical jacobian */
void numericalDerivative(
cv::Mat& jac,
double eps,
const std::vector<cv::Point3d>& obj,
const cv::Vec3d& rvec,
const cv::Vec3d& tvec,
const cv::Matx33d& camera,
const cv::Vec<double, NUM_DIST_COEFF_TILT>& distor);
/** remove points with projection outside the sensor array */
void removeInvalidPoints(
std::vector<cv::Point2d>& imagePoints,
std::vector<cv::Point3d>& objectPoints);
/** add uniform distribute noise in [-halfWidthNoise, halfWidthNoise]
to the image points and remove out of range points */
void addNoiseRemoveInvalidPoints(
std::vector<cv::Point2f>& imagePoints,
std::vector<cv::Point3f>& objectPoints,
std::vector<cv::Point2f>& noisyImagePoints,
double halfWidthNoise);
};
/** Number of Pixel of the sensor */
const cv::Size cameraCalibrationTiltTest::m_imageSize(1600, 1200);
/** Size of a pixel in mm */
const double cameraCalibrationTiltTest::m_pixelSize(.005);
/** Diameter of the circle of confusion */
const double cameraCalibrationTiltTest::m_circleConfusionPixel(3);
/** Focal length of the lens */
const double cameraCalibrationTiltTest::m_lensFocalLength(16.4);
/** F-Number */
const double cameraCalibrationTiltTest::m_lensFNumber(8);
/** Working distance */
const double cameraCalibrationTiltTest::m_objectDistance(200);
/** Angle between optical axis and object plane normal */
const double cameraCalibrationTiltTest::m_planeTiltDegree(55);
/** the calibration target are points on a square grid with this side length */
const double cameraCalibrationTiltTest::m_pointTargetDist(5);
/** the calibration target has (2*n + 1) x (2*n + 1) points */
const int cameraCalibrationTiltTest::m_pointTargetNum(15);
void cameraCalibrationTiltTest::SetUp()
{
m_imageDistance = opticalMap(m_objectDistance);
m_imageTiltDegree = m_toDegree * atan2(
m_imageDistance * tan(m_toRadian * m_planeTiltDegree),
m_objectDistance);
// half sensor height
double tmp = .5 * (m_imageSize.height - 1) * m_pixelSize
* cos(m_toRadian * m_imageTiltDegree);
// y-Value of tilted sensor
double yImage[2] = {tmp, -tmp};
// change in z because of the tilt
tmp *= sin(m_toRadian * m_imageTiltDegree);
// z-values of the sensor lower and upper corner
double zImage[2] = {
m_imageDistance + tmp,
m_imageDistance - tmp};
// circle of confusion
double circleConfusion = m_circleConfusionPixel*m_pixelSize;
// aperture of the lense
double aperture = m_lensFocalLength/m_lensFNumber;
// near and far factor on the image side
double nearFarFactorImage[2] = {
aperture/(aperture - circleConfusion),
aperture/(aperture + circleConfusion)};
// on the object side - points that determin the field of
// view
std::vector<cv::Vec3d> fovBottomTop(6);
std::vector<cv::Vec3d>::iterator itFov = fovBottomTop.begin();
for (size_t iBottomTop = 0; iBottomTop < 2; ++iBottomTop)
{
// mapping sensor to field of view
*itFov = cv::Vec3d(0,yImage[iBottomTop],zImage[iBottomTop]);
*itFov *= magnification((*itFov)(2));
++itFov;
for (size_t iNearFar = 0; iNearFar < 2; ++iNearFar, ++itFov)
{
// scaling to the near and far distance on the
// image side
*itFov = cv::Vec3d(0,yImage[iBottomTop],zImage[iBottomTop]) *
nearFarFactorImage[iNearFar];
// scaling to the object side
*itFov *= magnification((*itFov)(2));
}
}
m_fovCenter.resize(3);
m_fovNormal.resize(3);
for (size_t i = 0; i < 3; ++i)
{
m_fovCenter[i] = .5*(fovBottomTop[i] + fovBottomTop[i+3]);
m_fovNormal[i] = fovBottomTop[i+3] - fovBottomTop[i];
m_fovNormal[i] = cv::normalize(m_fovNormal[i]);
m_fovNormal[i] = cv::Vec3d(
m_fovNormal[i](0),
-m_fovNormal[i](2),
m_fovNormal[i](1));
// one target position in each plane
m_pointTargetTvec.push_back(m_fovCenter[i]);
cv::Vec3d rvec = cv::Vec3d(0,0,1).cross(m_fovNormal[i]);
rvec = cv::normalize(rvec);
rvec *= acos(m_fovNormal[i](2));
m_pointTargetRvec.push_back(rvec);
}
// calibration target
size_t num = 2*m_pointTargetNum + 1;
m_pointTarget.resize(num*num);
std::vector<cv::Point3d>::iterator itTarget = m_pointTarget.begin();
for (int iY = -m_pointTargetNum; iY <= m_pointTargetNum; ++iY)
{
for (int iX = -m_pointTargetNum; iX <= m_pointTargetNum; ++iX, ++itTarget)
{
*itTarget = cv::Point3d(iX, iY, 0) * m_pointTargetDist;
}
}
// oblique target positions
// approximate distance to the near and far plane
double dist = std::max(
std::abs(m_fovNormal[0].dot(m_fovCenter[0] - m_fovCenter[1])),
std::abs(m_fovNormal[0].dot(m_fovCenter[0] - m_fovCenter[2])));
// maximal angle such that target border "reaches" near and far plane
double maxAngle = atan2(dist, m_pointTargetNum*m_pointTargetDist);
std::vector<double> angle;
angle.push_back(-maxAngle);
angle.push_back(maxAngle);
cv::Matx33d baseMatrix;
cv::Rodrigues(m_pointTargetRvec.front(), baseMatrix);
for (std::vector<double>::const_iterator itAngle = angle.begin(); itAngle != angle.end(); ++itAngle)
{
cv::Matx33d rmat;
for (int i = 0; i < 2; ++i)
{
cv::Vec3d rvec(0,0,0);
rvec(i) = *itAngle;
cv::Rodrigues(rvec, rmat);
rmat = baseMatrix*rmat;
cv::Rodrigues(rmat, rvec);
m_pointTargetTvec.push_back(m_fovCenter.front());
m_pointTargetRvec.push_back(rvec);
}
}
// camera matrix
double cx = .5 * (m_imageSize.width - 1);
double cy = .5 * (m_imageSize.height - 1);
double f = m_imageDistance/m_pixelSize;
m_cameraMatrix = cv::Matx33d(
f,0,cx,
0,f,cy,
0,0,1);
// distortion coefficients
m_distortionCoeff = cv::Vec<double, NUM_DIST_COEFF_TILT>::all(0);
// tauX
m_distortionCoeff(12) = -m_toRadian*m_imageTiltDegree;
}
void cameraCalibrationTiltTest::numericalDerivative(
cv::Mat& jac,
double eps,
const std::vector<cv::Point3d>& obj,
const cv::Vec3d& rvec,
const cv::Vec3d& tvec,
const cv::Matx33d& camera,
const cv::Vec<double, NUM_DIST_COEFF_TILT>& distor)
{
cv::Vec3d r(rvec);
cv::Vec3d t(tvec);
cv::Matx33d cm(camera);
cv::Vec<double, NUM_DIST_COEFF_TILT> dc(distor);
double* param[10+NUM_DIST_COEFF_TILT] = {
&r(0), &r(1), &r(2),
&t(0), &t(1), &t(2),
&cm(0,0), &cm(1,1), &cm(0,2), &cm(1,2),
&dc(0), &dc(1), &dc(2), &dc(3), &dc(4), &dc(5), &dc(6),
&dc(7), &dc(8), &dc(9), &dc(10), &dc(11), &dc(12), &dc(13)};
std::vector<cv::Point2d> pix0, pix1;
double invEps = .5/eps;
for (int col = 0; col < 10+NUM_DIST_COEFF_TILT; ++col)
{
double save = *(param[col]);
*(param[col]) = save + eps;
cv::projectPoints(obj, r, t, cm, dc, pix0);
*(param[col]) = save - eps;
cv::projectPoints(obj, r, t, cm, dc, pix1);
*(param[col]) = save;
std::vector<cv::Point2d>::const_iterator it0 = pix0.begin();
std::vector<cv::Point2d>::const_iterator it1 = pix1.begin();
int row = 0;
for (;it0 != pix0.end(); ++it0, ++it1)
{
cv::Point2d d = invEps*(*it0 - *it1);
jac.at<double>(row, col) = d.x;
++row;
jac.at<double>(row, col) = d.y;
++row;
}
}
}
void cameraCalibrationTiltTest::removeInvalidPoints(
std::vector<cv::Point2d>& imagePoints,
std::vector<cv::Point3d>& objectPoints)
{
// remove object and imgage points out of range
std::vector<cv::Point2d>::iterator itImg = imagePoints.begin();
std::vector<cv::Point3d>::iterator itObj = objectPoints.begin();
while (itImg != imagePoints.end())
{
bool ok =
itImg->x >= 0 &&
itImg->x <= m_imageSize.width - 1.0 &&
itImg->y >= 0 &&
itImg->y <= m_imageSize.height - 1.0;
if (ok)
{
++itImg;
++itObj;
}
else
{
itImg = imagePoints.erase(itImg);
itObj = objectPoints.erase(itObj);
}
}
}
void cameraCalibrationTiltTest::addNoiseRemoveInvalidPoints(
std::vector<cv::Point2f>& imagePoints,
std::vector<cv::Point3f>& objectPoints,
std::vector<cv::Point2f>& noisyImagePoints,
double halfWidthNoise)
{
std::vector<cv::Point2f>::iterator itImg = imagePoints.begin();
std::vector<cv::Point3f>::iterator itObj = objectPoints.begin();
noisyImagePoints.clear();
noisyImagePoints.reserve(imagePoints.size());
while (itImg != imagePoints.end())
{
cv::Point2f pix = *itImg + cv::Point2f(
(float)m_rng.uniform(-halfWidthNoise, halfWidthNoise),
(float)m_rng.uniform(-halfWidthNoise, halfWidthNoise));
bool ok =
pix.x >= 0 &&
pix.x <= m_imageSize.width - 1.0 &&
pix.y >= 0 &&
pix.y <= m_imageSize.height - 1.0;
if (ok)
{
noisyImagePoints.push_back(pix);
++itImg;
++itObj;
}
else
{
itImg = imagePoints.erase(itImg);
itObj = objectPoints.erase(itObj);
}
}
}
TEST_F(cameraCalibrationTiltTest, projectPoints)
{
std::vector<cv::Point2d> imagePoints;
std::vector<cv::Point3d> objectPoints = m_pointTarget;
cv::Vec3d rvec = m_pointTargetRvec.front();
cv::Vec3d tvec = m_pointTargetTvec.front();
cv::Vec<double, NUM_DIST_COEFF_TILT> coeffNoiseHalfWidth(
.1, .1, // k1 k2
.01, .01, // p1 p2
.001, .001, .001, .001, // k3 k4 k5 k6
.001, .001, .001, .001, // s1 s2 s3 s4
.01, .01); // tauX tauY
for (size_t numTest = 0; numTest < 10; ++numTest)
{
// create random distortion coefficients
cv::Vec<double, NUM_DIST_COEFF_TILT> distortionCoeff = m_distortionCoeff;
randomDistortionCoeff(distortionCoeff, coeffNoiseHalfWidth);
// projection
cv::projectPoints(
objectPoints,
rvec,
tvec,
m_cameraMatrix,
distortionCoeff,
imagePoints);
// remove object and imgage points out of range
removeInvalidPoints(imagePoints, objectPoints);
int numPoints = (int)imagePoints.size();
int numParams = 10 + distortionCoeff.rows;
cv::Mat jacobian(2*numPoints, numParams, CV_64FC1);
// projection and jacobian
cv::projectPoints(
objectPoints,
rvec,
tvec,
m_cameraMatrix,
distortionCoeff,
imagePoints,
jacobian);
// numerical derivatives
cv::Mat numericJacobian(2*numPoints, numParams, CV_64FC1);
double eps = 1e-7;
numericalDerivative(
numericJacobian,
eps,
objectPoints,
rvec,
tvec,
m_cameraMatrix,
distortionCoeff);
#if 0
for (size_t row = 0; row < 2; ++row)
{
std::cout << "------ Row = " << row << " ------\n";
for (size_t i = 0; i < 10+NUM_DIST_COEFF_TILT; ++i)
{
std::cout << i
<< " jac = " << jacobian.at<double>(row,i)
<< " num = " << numericJacobian.at<double>(row,i)
<< " rel. diff = " << abs(numericJacobian.at<double>(row,i) - jacobian.at<double>(row,i))/abs(numericJacobian.at<double>(row,i))
<< "\n";
}
}
#endif
// relative difference for large values (rvec and tvec)
cv::Mat check = abs(jacobian(cv::Range::all(), cv::Range(0,6)) - numericJacobian(cv::Range::all(), cv::Range(0,6)))/
(1 + abs(jacobian(cv::Range::all(), cv::Range(0,6))));
double minVal, maxVal;
cv::minMaxIdx(check, &minVal, &maxVal);
EXPECT_LE(maxVal, .01);
// absolute difference for distortion and camera matrix
EXPECT_MAT_NEAR(jacobian(cv::Range::all(), cv::Range(6,numParams)), numericJacobian(cv::Range::all(), cv::Range(6,numParams)), 1e-5);
}
}
TEST_F(cameraCalibrationTiltTest, undistortPoints)
{
cv::Vec<double, NUM_DIST_COEFF_TILT> coeffNoiseHalfWidth(
.2, .1, // k1 k2
.01, .01, // p1 p2
.01, .01, .01, .01, // k3 k4 k5 k6
.001, .001, .001, .001, // s1 s2 s3 s4
.001, .001); // tauX tauY
double step = 99;
double toleranceBackProjection = 1e-5;
for (size_t numTest = 0; numTest < 10; ++numTest)
{
cv::Vec<double, NUM_DIST_COEFF_TILT> distortionCoeff = m_distortionCoeff;
randomDistortionCoeff(distortionCoeff, coeffNoiseHalfWidth);
// distorted points
std::vector<cv::Point2d> distorted;
for (double x = 0; x <= m_imageSize.width-1; x += step)
for (double y = 0; y <= m_imageSize.height-1; y += step)
distorted.push_back(cv::Point2d(x,y));
std::vector<cv::Point2d> normalizedUndistorted;
// undistort
cv::undistortPoints(distorted,
normalizedUndistorted,
m_cameraMatrix,
distortionCoeff);
// copy normalized points to 3D
std::vector<cv::Point3d> objectPoints;
for (std::vector<cv::Point2d>::const_iterator itPnt = normalizedUndistorted.begin();
itPnt != normalizedUndistorted.end(); ++itPnt)
objectPoints.push_back(cv::Point3d(itPnt->x, itPnt->y, 1));
// project
std::vector<cv::Point2d> imagePoints(objectPoints.size());
cv::projectPoints(objectPoints,
cv::Vec3d(0,0,0),
cv::Vec3d(0,0,0),
m_cameraMatrix,
distortionCoeff,
imagePoints);
EXPECT_MAT_NEAR(distorted, imagePoints, toleranceBackProjection);
}
}
template <typename INPUT, typename ESTIMATE>
void show(const std::string& name, const INPUT in, const ESTIMATE est)
{
std::cout << name << " = " << est << " (init = " << in
<< ", diff = " << est-in << ")\n";
}
template <typename INPUT>
void showVec(const std::string& name, const INPUT& in, const cv::Mat& est)
{
for (size_t i = 0; i < in.channels; ++i)
{
std::stringstream ss;
ss << name << "[" << i << "]";
show(ss.str(), in(i), est.at<double>(i));
}
}
/**
For given camera matrix and distortion coefficients
- project point target in different positions onto the sensor
- add pixel noise
- estimate camera modell with noisy measurements
- compare result with initial model parameter
Parameter are differently affected by the noise
*/
TEST_F(cameraCalibrationTiltTest, calibrateCamera)
{
cv::Vec<double, NUM_DIST_COEFF_TILT> coeffNoiseHalfWidth(
.2, .1, // k1 k2
.01, .01, // p1 p2
0, 0, 0, 0, // k3 k4 k5 k6
.001, .001, .001, .001, // s1 s2 s3 s4
.001, .001); // tauX tauY
double pixelNoiseHalfWidth = .5;
std::vector<cv::Point3f> pointTarget;
pointTarget.reserve(m_pointTarget.size());
for (std::vector<cv::Point3d>::const_iterator it = m_pointTarget.begin(); it != m_pointTarget.end(); ++it)
pointTarget.push_back(cv::Point3f(
(float)(it->x),
(float)(it->y),
(float)(it->z)));
for (size_t numTest = 0; numTest < 5; ++numTest)
{
// create random distortion coefficients
cv::Vec<double, NUM_DIST_COEFF_TILT> distortionCoeff = m_distortionCoeff;
randomDistortionCoeff(distortionCoeff, coeffNoiseHalfWidth);
// container for calibration data
std::vector<std::vector<cv::Point3f> > viewsObjectPoints;
std::vector<std::vector<cv::Point2f> > viewsImagePoints;
std::vector<std::vector<cv::Point2f> > viewsNoisyImagePoints;
// simulate calibration data with projectPoints
std::vector<cv::Vec3d>::const_iterator itRvec = m_pointTargetRvec.begin();
std::vector<cv::Vec3d>::const_iterator itTvec = m_pointTargetTvec.begin();
// loop over different views
for (;itRvec != m_pointTargetRvec.end(); ++ itRvec, ++itTvec)
{
std::vector<cv::Point3f> objectPoints(pointTarget);
std::vector<cv::Point2f> imagePoints;
std::vector<cv::Point2f> noisyImagePoints;
// project calibration target to sensor
cv::projectPoints(
objectPoints,
*itRvec,
*itTvec,
m_cameraMatrix,
distortionCoeff,
imagePoints);
// remove invisible points
addNoiseRemoveInvalidPoints(
imagePoints,
objectPoints,
noisyImagePoints,
pixelNoiseHalfWidth);
// add data for view
viewsNoisyImagePoints.push_back(noisyImagePoints);
viewsImagePoints.push_back(imagePoints);
viewsObjectPoints.push_back(objectPoints);
}
// Output
std::vector<cv::Mat> outRvecs, outTvecs;
cv::Mat outCameraMatrix(3, 3, CV_64F, cv::Scalar::all(1)), outDistCoeff;
// Stopping criteria
cv::TermCriteria stop(
cv::TermCriteria::COUNT+cv::TermCriteria::EPS,
50000,
1e-14);
// modell coice
int flag =
cv::CALIB_FIX_ASPECT_RATIO |
// cv::CALIB_RATIONAL_MODEL |
cv::CALIB_FIX_K3 |
// cv::CALIB_FIX_K6 |
cv::CALIB_THIN_PRISM_MODEL |
cv::CALIB_TILTED_MODEL;
// estimate
double backProjErr = cv::calibrateCamera(
viewsObjectPoints,
viewsNoisyImagePoints,
m_imageSize,
outCameraMatrix,
outDistCoeff,
outRvecs,
outTvecs,
flag,
stop);
EXPECT_LE(backProjErr, pixelNoiseHalfWidth);
#if 0
std::cout << "------ estimate ------\n";
std::cout << "back projection error = " << backProjErr << "\n";
std::cout << "points per view = {" << viewsObjectPoints.front().size();
for (size_t i = 1; i < viewsObjectPoints.size(); ++i)
std::cout << ", " << viewsObjectPoints[i].size();
std::cout << "}\n";
show("fx", m_cameraMatrix(0,0), outCameraMatrix.at<double>(0,0));
show("fy", m_cameraMatrix(1,1), outCameraMatrix.at<double>(1,1));
show("cx", m_cameraMatrix(0,2), outCameraMatrix.at<double>(0,2));
show("cy", m_cameraMatrix(1,2), outCameraMatrix.at<double>(1,2));
showVec("distor", distortionCoeff, outDistCoeff);
#endif
if (pixelNoiseHalfWidth > 0)
{
double tolRvec = pixelNoiseHalfWidth;
double tolTvec = m_objectDistance * tolRvec;
// back projection error
for (size_t i = 0; i < viewsNoisyImagePoints.size(); ++i)
{
double dRvec = norm(
m_pointTargetRvec[i] -
cv::Vec3d(
outRvecs[i].at<double>(0),
outRvecs[i].at<double>(1),
outRvecs[i].at<double>(2)));
// std::cout << dRvec << " " << tolRvec << "\n";
EXPECT_LE(dRvec,
tolRvec);
double dTvec = norm(
m_pointTargetTvec[i] -
cv::Vec3d(
outTvecs[i].at<double>(0),
outTvecs[i].at<double>(1),
outTvecs[i].at<double>(2)));
// std::cout << dTvec << " " << tolTvec << "\n";
EXPECT_LE(dTvec,
tolTvec);
std::vector<cv::Point2f> backProjection;
cv::projectPoints(
viewsObjectPoints[i],
outRvecs[i],
outTvecs[i],
outCameraMatrix,
outDistCoeff,
backProjection);
EXPECT_MAT_NEAR(backProjection, viewsNoisyImagePoints[i], 1.5*pixelNoiseHalfWidth);
EXPECT_MAT_NEAR(backProjection, viewsImagePoints[i], 1.5*pixelNoiseHalfWidth);
}
}
pixelNoiseHalfWidth *= .25;
}
}

20
modules/core/include/opencv2/core/matx.hpp
View File

@ -114,6 +114,10 @@ public:
Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
_Tp v4, _Tp v5, _Tp v6, _Tp v7,
_Tp v8, _Tp v9, _Tp v10, _Tp v11); //!< 1x12, 2x6, 3x4, 4x3, 6x2 or 12x1 matrix
Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
_Tp v4, _Tp v5, _Tp v6, _Tp v7,
_Tp v8, _Tp v9, _Tp v10, _Tp v11,
_Tp v12, _Tp v13); //!< 1x14, 2x7, 7x2 or 14x1 matrix
Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3,
_Tp v4, _Tp v5, _Tp v6, _Tp v7,
_Tp v8, _Tp v9, _Tp v10, _Tp v11,
@ -319,6 +323,7 @@ public:
Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7); //!< 8-element vector constructor
Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8); //!< 9-element vector constructor
Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9); //!< 10-element vector constructor
Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13); //!< 14-element vector constructor
explicit Vec(const _Tp* values);
Vec(const Vec<_Tp, cn>& v);
@ -581,6 +586,17 @@ Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp
for(int i = 12; i < channels; i++) val[i] = _Tp(0);
}
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13)
{
CV_StaticAssert(channels == 14, "Matx should have at least 14 elements.");
val[0] = v0; val[1] = v1; val[2] = v2; val[3] = v3;
val[4] = v4; val[5] = v5; val[6] = v6; val[7] = v7;
val[8] = v8; val[9] = v9; val[10] = v10; val[11] = v11;
val[12] = v12; val[13] = v13;
}
template<typename _Tp, int m, int n> inline
Matx<_Tp,m,n>::Matx(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13, _Tp v14, _Tp v15)
{
@ -931,6 +947,10 @@ template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9)
: Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9) {}
template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(_Tp v0, _Tp v1, _Tp v2, _Tp v3, _Tp v4, _Tp v5, _Tp v6, _Tp v7, _Tp v8, _Tp v9, _Tp v10, _Tp v11, _Tp v12, _Tp v13)
: Matx<_Tp, cn, 1>(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13) {}
template<typename _Tp, int cn> inline
Vec<_Tp, cn>::Vec(const _Tp* values)
: Matx<_Tp, cn, 1>(values) {}

36
modules/imgproc/include/opencv2/imgproc.hpp
View File

@ -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

123
modules/imgproc/include/opencv2/imgproc/detail/distortion_model.hpp Normal file
View File

@ -0,0 +1,123 @@
/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
#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__

52
modules/imgproc/src/undistort.cpp
View File

@ -41,6 +41,7 @@
//M*/
#include "precomp.hpp"
#include "opencv2/imgproc/detail/distortion_model.hpp"
cv::Mat cv::getDefaultNewCameraMatrix( InputArray _cameraMatrix, Size imgsize,
bool centerPrincipalPoint )
@ -94,7 +95,7 @@ void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoef
distCoeffs = Mat_<double>(distCoeffs);
else
{
distCoeffs.create(12, 1, CV_64F);
distCoeffs.create(14, 1, CV_64F);
distCoeffs = 0.;
}
@ -109,7 +110,8 @@ void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoef
CV_Assert( distCoeffs.size() == Size(1, 4) || distCoeffs.size() == Size(4, 1) ||
distCoeffs.size() == Size(1, 5) || distCoeffs.size() == Size(5, 1) ||
distCoeffs.size() == Size(1, 8) || distCoeffs.size() == Size(8, 1) ||
distCoeffs.size() == Size(1, 12) || distCoeffs.size() == Size(12, 1));
distCoeffs.size() == Size(1, 12) || distCoeffs.size() == Size(12, 1) ||
distCoeffs.size() == Size(1, 14) || distCoeffs.size() == Size(14, 1));
if( distCoeffs.rows != 1 && !distCoeffs.isContinuous() )
distCoeffs = distCoeffs.t();
@ -127,6 +129,12 @@ void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoef
double s2 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[9] : 0.;
double s3 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[10] : 0.;
double s4 = distCoeffs.cols + distCoeffs.rows - 1 >= 12 ? distPtr[11] : 0.;
double tauX = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[12] : 0.;
double tauY = distCoeffs.cols + distCoeffs.rows - 1 >= 14 ? distPtr[13] : 0.;
// Matrix for trapezoidal distortion of tilted image sensor
cv::Matx33d matTilt = cv::Matx33d::eye();
cv::detail::computeTiltProjectionMatrix(tauX, tauY, &matTilt);
for( int i = 0; i < size.height; i++ )
{
@ -142,8 +150,12 @@ void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoef
double x2 = x*x, y2 = y*y;
double r2 = x2 + y2, _2xy = 2*x*y;
double kr = (1 + ((k3*r2 + k2)*r2 + k1)*r2)/(1 + ((k6*r2 + k5)*r2 + k4)*r2);
double u = fx*(x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+s2*r2*r2) + u0;
double v = fy*(y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+s4*r2*r2) + v0;
double xd = (x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+s2*r2*r2);
double yd = (y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+s4*r2*r2);
cv::Vec3d vecTilt = matTilt*cv::Vec3d(xd, yd, 1);
double invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
double u = fx*invProj*vecTilt(0) + u0;
double v = fy*invProj*vecTilt(1) + v0;
if( m1type == CV_16SC2 )
{
int iu = saturate_cast<int>(u*INTER_TAB_SIZE);
@ -266,7 +278,7 @@ void cvUndistortPoints( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatr
const CvMat* _distCoeffs,
const CvMat* matR, const CvMat* matP )
{
double A[3][3], RR[3][3], k[12]={0,0,0,0,0,0,0,0,0,0,0}, fx, fy, ifx, ify, cx, cy;
double A[3][3], RR[3][3], k[14]={0,0,0,0,0,0,0,0,0,0,0,0,0,0}, fx, fy, ifx, ify, cx, cy;
CvMat matA=cvMat(3, 3, CV_64F, A), _Dk;
CvMat _RR=cvMat(3, 3, CV_64F, RR);
const CvPoint2D32f* srcf;
@ -276,6 +288,7 @@ void cvUndistortPoints( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatr
int stype, dtype;
int sstep, dstep;
int i, j, n, iters = 1;
cv::Matx33d invMatTilt = cv::Matx33d::eye();
CV_Assert( CV_IS_MAT(_src) && CV_IS_MAT(_dst) &&
(_src->rows == 1 || _src->cols == 1) &&
@ -296,13 +309,16 @@ void cvUndistortPoints( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatr
(_distCoeffs->rows*_distCoeffs->cols == 4 ||
_distCoeffs->rows*_distCoeffs->cols == 5 ||
_distCoeffs->rows*_distCoeffs->cols == 8 ||
_distCoeffs->rows*_distCoeffs->cols == 12));
_distCoeffs->rows*_distCoeffs->cols == 12 ||
_distCoeffs->rows*_distCoeffs->cols == 14));
_Dk = cvMat( _distCoeffs->rows, _distCoeffs->cols,
CV_MAKETYPE(CV_64F,CV_MAT_CN(_distCoeffs->type)), k);
cvConvert( _distCoeffs, &_Dk );
iters = 5;
if (k[12] != 0 || k[13] != 0)
cv::detail::computeTiltProjectionMatrix<double>(k[12], k[13], NULL, NULL, NULL, &invMatTilt);
}
if( matR )
@ -354,8 +370,14 @@ void cvUndistortPoints( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatr
y = srcd[i*sstep].y;
}
x0 = x = (x - cx)*ifx;
y0 = y = (y - cy)*ify;
x = (x - cx)*ifx;
y = (y - cy)*ify;
// compensate tilt distortion
cv::Vec3d vecUntilt = invMatTilt * cv::Vec3d(x, y, 1);
double invProj = vecUntilt(2) ? 1./vecUntilt(2) : 1;
x0 = x = invProj * vecUntilt(0);
y0 = y = invProj * vecUntilt(1);
// compensate distortion iteratively
for( j = 0; j < iters; j++ )
@ -500,7 +522,7 @@ float cv::initWideAngleProjMap( InputArray _cameraMatrix0, InputArray _distCoeff
OutputArray _map1, OutputArray _map2, int projType, double _alpha )
{
Mat cameraMatrix0 = _cameraMatrix0.getMat(), distCoeffs0 = _distCoeffs0.getMat();
double k[12] = {0,0,0,0,0,0,0,0,0,0,0}, M[9]={0,0,0,0,0,0,0,0,0};
double k[14] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0}, M[9]={0,0,0,0,0,0,0,0,0};
Mat distCoeffs(distCoeffs0.rows, distCoeffs0.cols, CV_MAKETYPE(CV_64F,distCoeffs0.channels()), k);
Mat cameraMatrix(3,3,CV_64F,M);
Point2f scenter((float)cameraMatrix.at<double>(0,2), (float)cameraMatrix.at<double>(1,2));
@ -513,7 +535,7 @@ float cv::initWideAngleProjMap( InputArray _cameraMatrix0, InputArray _distCoeff
int ndcoeffs = distCoeffs0.cols*distCoeffs0.rows*distCoeffs0.channels();
CV_Assert((distCoeffs0.cols == 1 || distCoeffs0.rows == 1) &&
(ndcoeffs == 4 || ndcoeffs == 5 || ndcoeffs == 8));
(ndcoeffs == 4 || ndcoeffs == 5 || ndcoeffs == 8 || ndcoeffs == 12 || ndcoeffs == 14));
CV_Assert(cameraMatrix0.size() == Size(3,3));
distCoeffs0.convertTo(distCoeffs,CV_64F);
cameraMatrix0.convertTo(cameraMatrix,CV_64F);
@ -540,6 +562,8 @@ float cv::initWideAngleProjMap( InputArray _cameraMatrix0, InputArray _distCoeff
Mat mapxy(dsize, CV_32FC2);
double k1 = k[0], k2 = k[1], k3 = k[2], p1 = k[3], p2 = k[4], k4 = k[5], k5 = k[6], k6 = k[7], s1 = k[8], s2 = k[9], s3 = k[10], s4 = k[11];
double fx = cameraMatrix.at<double>(0,0), fy = cameraMatrix.at<double>(1,1), cx = scenter.x, cy = scenter.y;
cv::Matx33d matTilt;
cv::detail::computeTiltProjectionMatrix(k[12], k[13], &matTilt);
for( int y = 0; y < dsize.height; y++ )
{
@ -556,8 +580,12 @@ float cv::initWideAngleProjMap( InputArray _cameraMatrix0, InputArray _distCoeff
double x2 = q.x*q.x, y2 = q.y*q.y;
double r2 = x2 + y2, _2xy = 2*q.x*q.y;
double kr = 1 + ((k3*r2 + k2)*r2 + k1)*r2/(1 + ((k6*r2 + k5)*r2 + k4)*r2);
double u = fx*(q.x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+ s2*r2*r2) + cx;
double v = fy*(q.y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+ s4*r2*r2) + cy;
double xd = (q.x*kr + p1*_2xy + p2*(r2 + 2*x2) + s1*r2+ s2*r2*r2);
double yd = (q.y*kr + p1*(r2 + 2*y2) + p2*_2xy + s3*r2+ s4*r2*r2);
cv::Vec3d vecTilt = matTilt*cv::Vec3d(xd, yd, 1);
double invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
double u = fx*invProj*vecTilt(0) + cx;
double v = fy*invProj*vecTilt(1) + cy;
mxy[x] = Point2f((float)u, (float)v);
}