mirror of
https://github.com/opencv/opencv.git
synced 2025-07-23 13:09:37 +08:00
975 lines
31 KiB
C++
975 lines
31 KiB
C++
// This file is part of OpenCV project.
|
||
// It is subject to the license terms in the LICENSE file found in the top-level directory
|
||
// of this distribution and at http://opencv.org/license.html.
|
||
|
||
#include "precomp.hpp"
|
||
#include "opencv2/calib3d.hpp"
|
||
|
||
namespace cv {
|
||
|
||
static Mat homogeneousInverse(const Mat& T)
|
||
{
|
||
CV_Assert(T.rows == 4 && T.cols == 4);
|
||
|
||
Mat R = T(Rect(0, 0, 3, 3));
|
||
Mat t = T(Rect(3, 0, 1, 3));
|
||
Mat Rt = R.t();
|
||
Mat tinv = -Rt * t;
|
||
Mat Tinv = Mat::eye(4, 4, T.type());
|
||
Rt.copyTo(Tinv(Rect(0, 0, 3, 3)));
|
||
tinv.copyTo(Tinv(Rect(3, 0, 1, 3)));
|
||
|
||
return Tinv;
|
||
}
|
||
|
||
// q = rot2quatMinimal(R)
|
||
//
|
||
// R - 3x3 rotation matrix, or 4x4 homogeneous matrix
|
||
// q - 3x1 unit quaternion <qx, qy, qz>
|
||
// q = sin(theta/2) * v
|
||
// theta - rotation angle
|
||
// v - unit rotation axis, |v| = 1
|
||
// Reference: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
|
||
static Mat rot2quatMinimal(const Mat& R)
|
||
{
|
||
CV_Assert(R.type() == CV_64FC1 && R.rows >= 3 && R.cols >= 3);
|
||
|
||
double m00 = R.at<double>(0,0), m01 = R.at<double>(0,1), m02 = R.at<double>(0,2);
|
||
double m10 = R.at<double>(1,0), m11 = R.at<double>(1,1), m12 = R.at<double>(1,2);
|
||
double m20 = R.at<double>(2,0), m21 = R.at<double>(2,1), m22 = R.at<double>(2,2);
|
||
double trace = m00 + m11 + m22;
|
||
|
||
double qx, qy, qz;
|
||
if (trace > 0) {
|
||
double S = sqrt(trace + 1.0) * 2; // S=4*qw
|
||
qx = (m21 - m12) / S;
|
||
qy = (m02 - m20) / S;
|
||
qz = (m10 - m01) / S;
|
||
} else if (m00 > m11 && m00 > m22) {
|
||
double S = sqrt(1.0 + m00 - m11 - m22) * 2; // S=4*qx
|
||
qx = 0.25 * S;
|
||
qy = (m01 + m10) / S;
|
||
qz = (m02 + m20) / S;
|
||
} else if (m11 > m22) {
|
||
double S = sqrt(1.0 + m11 - m00 - m22) * 2; // S=4*qy
|
||
qx = (m01 + m10) / S;
|
||
qy = 0.25 * S;
|
||
qz = (m12 + m21) / S;
|
||
} else {
|
||
double S = sqrt(1.0 + m22 - m00 - m11) * 2; // S=4*qz
|
||
qx = (m02 + m20) / S;
|
||
qy = (m12 + m21) / S;
|
||
qz = 0.25 * S;
|
||
}
|
||
|
||
return (Mat_<double>(3,1) << qx, qy, qz);
|
||
}
|
||
|
||
static Mat skew(const Mat& v)
|
||
{
|
||
CV_Assert(v.type() == CV_64FC1 && v.rows == 3 && v.cols == 1);
|
||
|
||
double vx = v.at<double>(0,0);
|
||
double vy = v.at<double>(1,0);
|
||
double vz = v.at<double>(2,0);
|
||
return (Mat_<double>(3,3) << 0, -vz, vy,
|
||
vz, 0, -vx,
|
||
-vy, vx, 0);
|
||
}
|
||
|
||
// R = quatMinimal2rot(q)
|
||
//
|
||
// q - 3x1 unit quaternion <qx, qy, qz>
|
||
// R - 3x3 rotation matrix
|
||
// q = sin(theta/2) * v
|
||
// theta - rotation angle
|
||
// v - unit rotation axis, |v| = 1
|
||
static Mat quatMinimal2rot(const Mat& q)
|
||
{
|
||
CV_Assert(q.type() == CV_64FC1 && q.rows == 3 && q.cols == 1);
|
||
|
||
Mat p = q.t()*q;
|
||
double w = sqrt(1 - p.at<double>(0,0));
|
||
|
||
Mat diag_p = Mat::eye(3,3,CV_64FC1)*p.at<double>(0,0);
|
||
return 2*q*q.t() + 2*w*skew(q) + Mat::eye(3,3,CV_64FC1) - 2*diag_p;
|
||
}
|
||
|
||
// q = rot2quat(R)
|
||
//
|
||
// q - 4x1 unit quaternion <qw, qx, qy, qz>
|
||
// R - 3x3 rotation matrix
|
||
// Reference: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
|
||
static Mat rot2quat(const Mat& R)
|
||
{
|
||
CV_Assert(R.type() == CV_64FC1 && R.rows >= 3 && R.cols >= 3);
|
||
|
||
double m00 = R.at<double>(0,0), m01 = R.at<double>(0,1), m02 = R.at<double>(0,2);
|
||
double m10 = R.at<double>(1,0), m11 = R.at<double>(1,1), m12 = R.at<double>(1,2);
|
||
double m20 = R.at<double>(2,0), m21 = R.at<double>(2,1), m22 = R.at<double>(2,2);
|
||
double trace = m00 + m11 + m22;
|
||
|
||
double qw, qx, qy, qz;
|
||
if (trace > 0) {
|
||
double S = sqrt(trace + 1.0) * 2; // S=4*qw
|
||
qw = 0.25 * S;
|
||
qx = (m21 - m12) / S;
|
||
qy = (m02 - m20) / S;
|
||
qz = (m10 - m01) / S;
|
||
} else if (m00 > m11 && m00 > m22) {
|
||
double S = sqrt(1.0 + m00 - m11 - m22) * 2; // S=4*qx
|
||
qw = (m21 - m12) / S;
|
||
qx = 0.25 * S;
|
||
qy = (m01 + m10) / S;
|
||
qz = (m02 + m20) / S;
|
||
} else if (m11 > m22) {
|
||
double S = sqrt(1.0 + m11 - m00 - m22) * 2; // S=4*qy
|
||
qw = (m02 - m20) / S;
|
||
qx = (m01 + m10) / S;
|
||
qy = 0.25 * S;
|
||
qz = (m12 + m21) / S;
|
||
} else {
|
||
double S = sqrt(1.0 + m22 - m00 - m11) * 2; // S=4*qz
|
||
qw = (m10 - m01) / S;
|
||
qx = (m02 + m20) / S;
|
||
qy = (m12 + m21) / S;
|
||
qz = 0.25 * S;
|
||
}
|
||
|
||
return (Mat_<double>(4,1) << qw, qx, qy, qz);
|
||
}
|
||
|
||
// R = quat2rot(q)
|
||
//
|
||
// q - 4x1 unit quaternion <qw, qx, qy, qz>
|
||
// R - 3x3 rotation matrix
|
||
static Mat quat2rot(const Mat& q)
|
||
{
|
||
CV_Assert(q.type() == CV_64FC1 && q.rows == 4 && q.cols == 1);
|
||
|
||
double qw = q.at<double>(0,0);
|
||
double qx = q.at<double>(1,0);
|
||
double qy = q.at<double>(2,0);
|
||
double qz = q.at<double>(3,0);
|
||
|
||
Mat R(3, 3, CV_64FC1);
|
||
R.at<double>(0, 0) = 1 - 2*qy*qy - 2*qz*qz;
|
||
R.at<double>(0, 1) = 2*qx*qy - 2*qz*qw;
|
||
R.at<double>(0, 2) = 2*qx*qz + 2*qy*qw;
|
||
|
||
R.at<double>(1, 0) = 2*qx*qy + 2*qz*qw;
|
||
R.at<double>(1, 1) = 1 - 2*qx*qx - 2*qz*qz;
|
||
R.at<double>(1, 2) = 2*qy*qz - 2*qx*qw;
|
||
|
||
R.at<double>(2, 0) = 2*qx*qz - 2*qy*qw;
|
||
R.at<double>(2, 1) = 2*qy*qz + 2*qx*qw;
|
||
R.at<double>(2, 2) = 1 - 2*qx*qx - 2*qy*qy;
|
||
|
||
return R;
|
||
}
|
||
|
||
// Kronecker product or tensor product
|
||
// https://stackoverflow.com/a/36552682
|
||
static Mat kron(const Mat& A, const Mat& B)
|
||
{
|
||
CV_Assert(A.channels() == 1 && B.channels() == 1);
|
||
|
||
Mat1d Ad, Bd;
|
||
A.convertTo(Ad, CV_64F);
|
||
B.convertTo(Bd, CV_64F);
|
||
|
||
Mat1d Kd(Ad.rows * Bd.rows, Ad.cols * Bd.cols, 0.0);
|
||
for (int ra = 0; ra < Ad.rows; ra++)
|
||
{
|
||
for (int ca = 0; ca < Ad.cols; ca++)
|
||
{
|
||
Kd(Range(ra*Bd.rows, (ra + 1)*Bd.rows), Range(ca*Bd.cols, (ca + 1)*Bd.cols)) = Bd.mul(Ad(ra, ca));
|
||
}
|
||
}
|
||
|
||
Mat K;
|
||
Kd.convertTo(K, A.type());
|
||
return K;
|
||
}
|
||
|
||
// quaternion multiplication
|
||
static Mat qmult(const Mat& s, const Mat& t)
|
||
{
|
||
CV_Assert(s.type() == CV_64FC1 && t.type() == CV_64FC1);
|
||
CV_Assert(s.rows == 4 && s.cols == 1);
|
||
CV_Assert(t.rows == 4 && t.cols == 1);
|
||
|
||
double s0 = s.at<double>(0,0);
|
||
double s1 = s.at<double>(1,0);
|
||
double s2 = s.at<double>(2,0);
|
||
double s3 = s.at<double>(3,0);
|
||
|
||
double t0 = t.at<double>(0,0);
|
||
double t1 = t.at<double>(1,0);
|
||
double t2 = t.at<double>(2,0);
|
||
double t3 = t.at<double>(3,0);
|
||
|
||
Mat q(4, 1, CV_64FC1);
|
||
q.at<double>(0,0) = s0*t0 - s1*t1 - s2*t2 - s3*t3;
|
||
q.at<double>(1,0) = s0*t1 + s1*t0 + s2*t3 - s3*t2;
|
||
q.at<double>(2,0) = s0*t2 - s1*t3 + s2*t0 + s3*t1;
|
||
q.at<double>(3,0) = s0*t3 + s1*t2 - s2*t1 + s3*t0;
|
||
|
||
return q;
|
||
}
|
||
|
||
// dq = homogeneous2dualQuaternion(H)
|
||
//
|
||
// H - 4x4 homogeneous transformation: [R | t; 0 0 0 | 1]
|
||
// dq - 8x1 dual quaternion: <q (rotation part), qprime (translation part)>
|
||
static Mat homogeneous2dualQuaternion(const Mat& H)
|
||
{
|
||
CV_Assert(H.type() == CV_64FC1 && H.rows == 4 && H.cols == 4);
|
||
|
||
Mat dualq(8, 1, CV_64FC1);
|
||
Mat R = H(Rect(0, 0, 3, 3));
|
||
Mat t = H(Rect(3, 0, 1, 3));
|
||
|
||
Mat q = rot2quat(R);
|
||
Mat qt = Mat::zeros(4, 1, CV_64FC1);
|
||
t.copyTo(qt(Rect(0, 1, 1, 3)));
|
||
Mat qprime = 0.5 * qmult(qt, q);
|
||
|
||
q.copyTo(dualq(Rect(0, 0, 1, 4)));
|
||
qprime.copyTo(dualq(Rect(0, 4, 1, 4)));
|
||
|
||
return dualq;
|
||
}
|
||
|
||
// H = dualQuaternion2homogeneous(dq)
|
||
//
|
||
// H - 4x4 homogeneous transformation: [R | t; 0 0 0 | 1]
|
||
// dq - 8x1 dual quaternion: <q (rotation part), qprime (translation part)>
|
||
static Mat dualQuaternion2homogeneous(const Mat& dualq)
|
||
{
|
||
CV_Assert(dualq.type() == CV_64FC1 && dualq.rows == 8 && dualq.cols == 1);
|
||
|
||
Mat q = dualq(Rect(0, 0, 1, 4));
|
||
Mat qprime = dualq(Rect(0, 4, 1, 4));
|
||
|
||
Mat R = quat2rot(q);
|
||
q.at<double>(1,0) = -q.at<double>(1,0);
|
||
q.at<double>(2,0) = -q.at<double>(2,0);
|
||
q.at<double>(3,0) = -q.at<double>(3,0);
|
||
|
||
Mat qt = 2*qmult(qprime, q);
|
||
Mat t = qt(Rect(0, 1, 1, 3));
|
||
|
||
Mat H = Mat::eye(4, 4, CV_64FC1);
|
||
R.copyTo(H(Rect(0, 0, 3, 3)));
|
||
t.copyTo(H(Rect(3, 0, 1, 3)));
|
||
|
||
return H;
|
||
}
|
||
|
||
//Reference:
|
||
//R. Y. Tsai and R. K. Lenz, "A new technique for fully autonomous and efficient 3D robotics hand/eye calibration."
|
||
//In IEEE Transactions on Robotics and Automation, vol. 5, no. 3, pp. 345-358, June 1989.
|
||
//C++ code converted from Zoran Lazarevic's Matlab code:
|
||
//http://lazax.com/www.cs.columbia.edu/~laza/html/Stewart/matlab/handEye.m
|
||
static void calibrateHandEyeTsai(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc,
|
||
Mat& R_cam2gripper, Mat& t_cam2gripper)
|
||
{
|
||
//Number of unique camera position pairs
|
||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0);
|
||
//Will store: skew(Pgij+Pcij)
|
||
Mat A(3*K, 3, CV_64FC1);
|
||
//Will store: Pcij - Pgij
|
||
Mat B(3*K, 1, CV_64FC1);
|
||
|
||
std::vector<Mat> vec_Hgij, vec_Hcij;
|
||
vec_Hgij.reserve(static_cast<size_t>(K));
|
||
vec_Hcij.reserve(static_cast<size_t>(K));
|
||
|
||
int idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
//Defines coordinate transformation from Gi to Gj
|
||
//Hgi is from Gi (gripper) to RW (robot base)
|
||
//Hgj is from Gj (gripper) to RW (robot base)
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i]; //eq 6
|
||
vec_Hgij.push_back(Hgij);
|
||
//Rotation axis for Rgij which is the 3D rotation from gripper coordinate frame Gi to Gj
|
||
Mat Pgij = 2*rot2quatMinimal(Hgij);
|
||
|
||
//Defines coordinate transformation from Ci to Cj
|
||
//Hci is from CW (calibration target) to Ci (camera)
|
||
//Hcj is from CW (calibration target) to Cj (camera)
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]); //eq 7
|
||
vec_Hcij.push_back(Hcij);
|
||
//Rotation axis for Rcij
|
||
Mat Pcij = 2*rot2quatMinimal(Hcij);
|
||
|
||
//Left-hand side: skew(Pgij+Pcij)
|
||
skew(Pgij+Pcij).copyTo(A(Rect(0, idx*3, 3, 3)));
|
||
//Right-hand side: Pcij - Pgij
|
||
Mat diff = Pcij - Pgij;
|
||
diff.copyTo(B(Rect(0, idx*3, 1, 3)));
|
||
}
|
||
}
|
||
|
||
Mat Pcg_;
|
||
//Rotation from camera to gripper is obtained from the set of equations:
|
||
// skew(Pgij+Pcij) * Pcg_ = Pcij - Pgij (eq 12)
|
||
solve(A, B, Pcg_, DECOMP_SVD);
|
||
|
||
Mat Pcg_norm = Pcg_.t() * Pcg_;
|
||
//Obtained non-unit quaternion is scaled back to unit value that
|
||
//designates camera-gripper rotation
|
||
Mat Pcg = 2 * Pcg_ / sqrt(1 + Pcg_norm.at<double>(0,0)); //eq 14
|
||
|
||
Mat Rcg = quatMinimal2rot(Pcg/2.0);
|
||
|
||
idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
//Defines coordinate transformation from Gi to Gj
|
||
//Hgi is from Gi (gripper) to RW (robot base)
|
||
//Hgj is from Gj (gripper) to RW (robot base)
|
||
Mat Hgij = vec_Hgij[static_cast<size_t>(idx)];
|
||
//Defines coordinate transformation from Ci to Cj
|
||
//Hci is from CW (calibration target) to Ci (camera)
|
||
//Hcj is from CW (calibration target) to Cj (camera)
|
||
Mat Hcij = vec_Hcij[static_cast<size_t>(idx)];
|
||
|
||
//Left-hand side: (Rgij - I)
|
||
Mat diff = Hgij(Rect(0,0,3,3)) - Mat::eye(3,3,CV_64FC1);
|
||
diff.copyTo(A(Rect(0, idx*3, 3, 3)));
|
||
|
||
//Right-hand side: Rcg*Tcij - Tgij
|
||
diff = Rcg*Hcij(Rect(3, 0, 1, 3)) - Hgij(Rect(3, 0, 1, 3));
|
||
diff.copyTo(B(Rect(0, idx*3, 1, 3)));
|
||
}
|
||
}
|
||
|
||
Mat Tcg;
|
||
//Translation from camera to gripper is obtained from the set of equations:
|
||
// (Rgij - I) * Tcg = Rcg*Tcij - Tgij (eq 15)
|
||
solve(A, B, Tcg, DECOMP_SVD);
|
||
|
||
R_cam2gripper = Rcg;
|
||
t_cam2gripper = Tcg;
|
||
}
|
||
|
||
//Reference:
|
||
//F. Park, B. Martin, "Robot Sensor Calibration: Solving AX = XB on the Euclidean Group."
|
||
//In IEEE Transactions on Robotics and Automation, 10(5): 717-721, 1994.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateHandEyePark(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc,
|
||
Mat& R_cam2gripper, Mat& t_cam2gripper)
|
||
{
|
||
Mat M = Mat::zeros(3, 3, CV_64FC1);
|
||
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat Rgij = Hgij(Rect(0, 0, 3, 3));
|
||
Mat Rcij = Hcij(Rect(0, 0, 3, 3));
|
||
|
||
Mat a, b;
|
||
Rodrigues(Rgij, a);
|
||
Rodrigues(Rcij, b);
|
||
|
||
M += b * a.t();
|
||
}
|
||
}
|
||
|
||
Mat eigenvalues, eigenvectors;
|
||
eigen(M.t()*M, eigenvalues, eigenvectors);
|
||
|
||
Mat v = Mat::zeros(3, 3, CV_64FC1);
|
||
for (int i = 0; i < 3; i++) {
|
||
v.at<double>(i,i) = 1.0 / sqrt(eigenvalues.at<double>(i,0));
|
||
}
|
||
|
||
Mat R = eigenvectors.t() * v * eigenvectors * M.t();
|
||
R_cam2gripper = R;
|
||
|
||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0);
|
||
Mat C(3*K, 3, CV_64FC1);
|
||
Mat d(3*K, 1, CV_64FC1);
|
||
Mat I3 = Mat::eye(3, 3, CV_64FC1);
|
||
|
||
int idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat Rgij = Hgij(Rect(0, 0, 3, 3));
|
||
|
||
Mat tgij = Hgij(Rect(3, 0, 1, 3));
|
||
Mat tcij = Hcij(Rect(3, 0, 1, 3));
|
||
|
||
Mat I_tgij = I3 - Rgij;
|
||
I_tgij.copyTo(C(Rect(0, 3*idx, 3, 3)));
|
||
|
||
Mat A_RB = tgij - R*tcij;
|
||
A_RB.copyTo(d(Rect(0, 3*idx, 1, 3)));
|
||
}
|
||
}
|
||
|
||
Mat t;
|
||
solve(C, d, t, DECOMP_SVD);
|
||
t_cam2gripper = t;
|
||
}
|
||
|
||
//Reference:
|
||
//R. Horaud, F. Dornaika, "Hand-Eye Calibration"
|
||
//In International Journal of Robotics Research, 14(3): 195-210, 1995.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateHandEyeHoraud(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc,
|
||
Mat& R_cam2gripper, Mat& t_cam2gripper)
|
||
{
|
||
Mat A = Mat::zeros(4, 4, CV_64FC1);
|
||
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat Rgij = Hgij(Rect(0, 0, 3, 3));
|
||
Mat Rcij = Hcij(Rect(0, 0, 3, 3));
|
||
|
||
Mat qgij = rot2quat(Rgij);
|
||
double r0 = qgij.at<double>(0,0);
|
||
double rx = qgij.at<double>(1,0);
|
||
double ry = qgij.at<double>(2,0);
|
||
double rz = qgij.at<double>(3,0);
|
||
|
||
// Q(r) Appendix A
|
||
Matx44d Qvi(r0, -rx, -ry, -rz,
|
||
rx, r0, -rz, ry,
|
||
ry, rz, r0, -rx,
|
||
rz, -ry, rx, r0);
|
||
|
||
Mat qcij = rot2quat(Rcij);
|
||
r0 = qcij.at<double>(0,0);
|
||
rx = qcij.at<double>(1,0);
|
||
ry = qcij.at<double>(2,0);
|
||
rz = qcij.at<double>(3,0);
|
||
|
||
// W(r) Appendix A
|
||
Matx44d Wvi(r0, -rx, -ry, -rz,
|
||
rx, r0, rz, -ry,
|
||
ry, -rz, r0, rx,
|
||
rz, ry, -rx, r0);
|
||
|
||
// Ai = (Q(vi') - W(vi))^T (Q(vi') - W(vi))
|
||
A += (Qvi - Wvi).t() * (Qvi - Wvi);
|
||
}
|
||
}
|
||
|
||
Mat eigenvalues, eigenvectors;
|
||
eigen(A, eigenvalues, eigenvectors);
|
||
|
||
Mat R = quat2rot(eigenvectors.row(3).t());
|
||
R_cam2gripper = R;
|
||
|
||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0);
|
||
Mat C(3*K, 3, CV_64FC1);
|
||
Mat d(3*K, 1, CV_64FC1);
|
||
Mat I3 = Mat::eye(3, 3, CV_64FC1);
|
||
|
||
int idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat Rgij = Hgij(Rect(0, 0, 3, 3));
|
||
|
||
Mat tgij = Hgij(Rect(3, 0, 1, 3));
|
||
Mat tcij = Hcij(Rect(3, 0, 1, 3));
|
||
|
||
Mat I_tgij = I3 - Rgij;
|
||
I_tgij.copyTo(C(Rect(0, 3*idx, 3, 3)));
|
||
|
||
Mat A_RB = tgij - R*tcij;
|
||
A_RB.copyTo(d(Rect(0, 3*idx, 1, 3)));
|
||
}
|
||
}
|
||
|
||
Mat t;
|
||
solve(C, d, t, DECOMP_SVD);
|
||
t_cam2gripper = t;
|
||
}
|
||
|
||
static Mat_<double> normalizeRotation(const Mat_<double>& R_)
|
||
{
|
||
// Make R unit determinant
|
||
Mat_<double> R = R_.clone();
|
||
double det = determinant(R);
|
||
if (std::fabs(det) < FLT_EPSILON)
|
||
{
|
||
CV_Error(Error::StsNoConv, "Rotation normalization issue: determinant(R) is null");
|
||
}
|
||
R = std::cbrt(std::copysign(1, det) / std::fabs(det)) * R;
|
||
|
||
// Make R orthogonal
|
||
Mat w, u, vt;
|
||
SVDecomp(R, w, u, vt);
|
||
R = u*vt;
|
||
|
||
// Handle reflection case
|
||
if (determinant(R) < 0)
|
||
{
|
||
Matx33d diag(1.0, 0.0, 0.0,
|
||
0.0, 1.0, 0.0,
|
||
0.0, 0.0, -1.0);
|
||
R = u*diag*vt;
|
||
}
|
||
|
||
return R;
|
||
}
|
||
|
||
//Reference:
|
||
//N. Andreff, R. Horaud, B. Espiau, "On-line Hand-Eye Calibration."
|
||
//In Second International Conference on 3-D Digital Imaging and Modeling (3DIM'99), pages 430-436, 1999.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateHandEyeAndreff(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc,
|
||
Mat& R_cam2gripper, Mat& t_cam2gripper)
|
||
{
|
||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0);
|
||
Mat A(12*K, 12, CV_64FC1);
|
||
Mat B(12*K, 1, CV_64FC1);
|
||
|
||
Mat I9 = Mat::eye(9, 9, CV_64FC1);
|
||
Mat I3 = Mat::eye(3, 3, CV_64FC1);
|
||
Mat O9x3 = Mat::zeros(9, 3, CV_64FC1);
|
||
Mat O9x1 = Mat::zeros(9, 1, CV_64FC1);
|
||
|
||
int idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat Rgij = Hgij(Rect(0, 0, 3, 3));
|
||
Mat Rcij = Hcij(Rect(0, 0, 3, 3));
|
||
|
||
Mat tgij = Hgij(Rect(3, 0, 1, 3));
|
||
Mat tcij = Hcij(Rect(3, 0, 1, 3));
|
||
|
||
//Eq 10
|
||
Mat a00 = I9 - kron(Rgij, Rcij);
|
||
Mat a01 = O9x3;
|
||
Mat a10 = kron(I3, tcij.t());
|
||
Mat a11 = I3 - Rgij;
|
||
|
||
a00.copyTo(A(Rect(0, idx*12, 9, 9)));
|
||
a01.copyTo(A(Rect(9, idx*12, 3, 9)));
|
||
a10.copyTo(A(Rect(0, idx*12 + 9, 9, 3)));
|
||
a11.copyTo(A(Rect(9, idx*12 + 9, 3, 3)));
|
||
|
||
O9x1.copyTo(B(Rect(0, idx*12, 1, 9)));
|
||
tgij.copyTo(B(Rect(0, idx*12 + 9, 1, 3)));
|
||
}
|
||
}
|
||
|
||
Mat X;
|
||
solve(A, B, X, DECOMP_SVD);
|
||
|
||
Mat R = X(Rect(0, 0, 1, 9));
|
||
int newSize[] = {3, 3};
|
||
R = R.reshape(1, 2, newSize);
|
||
//Eq 15
|
||
R_cam2gripper = normalizeRotation(R);
|
||
t_cam2gripper = X(Rect(0, 9, 1, 3));
|
||
}
|
||
|
||
//Reference:
|
||
//K. Daniilidis, "Hand-Eye Calibration Using Dual Quaternions."
|
||
//In The International Journal of Robotics Research,18(3): 286-298, 1998.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateHandEyeDaniilidis(const std::vector<Mat>& Hg, const std::vector<Mat>& Hc,
|
||
Mat& R_cam2gripper, Mat& t_cam2gripper)
|
||
{
|
||
int K = static_cast<int>((Hg.size()*Hg.size() - Hg.size()) / 2.0);
|
||
Mat T = Mat::zeros(6*K, 8, CV_64FC1);
|
||
|
||
int idx = 0;
|
||
for (size_t i = 0; i < Hg.size(); i++)
|
||
{
|
||
for (size_t j = i+1; j < Hg.size(); j++, idx++)
|
||
{
|
||
Mat Hgij = homogeneousInverse(Hg[j]) * Hg[i];
|
||
Mat Hcij = Hc[j] * homogeneousInverse(Hc[i]);
|
||
|
||
Mat dualqa = homogeneous2dualQuaternion(Hgij);
|
||
Mat dualqb = homogeneous2dualQuaternion(Hcij);
|
||
|
||
Mat a = dualqa(Rect(0, 1, 1, 3));
|
||
Mat b = dualqb(Rect(0, 1, 1, 3));
|
||
|
||
Mat aprime = dualqa(Rect(0, 5, 1, 3));
|
||
Mat bprime = dualqb(Rect(0, 5, 1, 3));
|
||
|
||
//Eq 31
|
||
Mat s00 = a - b;
|
||
Mat s01 = skew(a + b);
|
||
Mat s10 = aprime - bprime;
|
||
Mat s11 = skew(aprime + bprime);
|
||
Mat s12 = a - b;
|
||
Mat s13 = skew(a + b);
|
||
|
||
s00.copyTo(T(Rect(0, idx*6, 1, 3)));
|
||
s01.copyTo(T(Rect(1, idx*6, 3, 3)));
|
||
s10.copyTo(T(Rect(0, idx*6 + 3, 1, 3)));
|
||
s11.copyTo(T(Rect(1, idx*6 + 3, 3, 3)));
|
||
s12.copyTo(T(Rect(4, idx*6 + 3, 1, 3)));
|
||
s13.copyTo(T(Rect(5, idx*6 + 3, 3, 3)));
|
||
}
|
||
}
|
||
|
||
Mat w, u, vt;
|
||
SVDecomp(T, w, u, vt);
|
||
Mat v = vt.t();
|
||
|
||
Mat u1 = v(Rect(6, 0, 1, 4));
|
||
Mat v1 = v(Rect(6, 4, 1, 4));
|
||
Mat u2 = v(Rect(7, 0, 1, 4));
|
||
Mat v2 = v(Rect(7, 4, 1, 4));
|
||
|
||
//Solves Eq 34, Eq 35
|
||
Mat ma = u1.t()*v1;
|
||
Mat mb = u1.t()*v2 + u2.t()*v1;
|
||
Mat mc = u2.t()*v2;
|
||
|
||
double a = ma.at<double>(0,0);
|
||
double b = mb.at<double>(0,0);
|
||
double c = mc.at<double>(0,0);
|
||
|
||
double s1 = (-b + sqrt(b*b - 4*a*c)) / (2*a);
|
||
double s2 = (-b - sqrt(b*b - 4*a*c)) / (2*a);
|
||
|
||
Mat sol1 = s1*s1*u1.t()*u1 + 2*s1*u1.t()*u2 + u2.t()*u2;
|
||
Mat sol2 = s2*s2*u1.t()*u1 + 2*s2*u1.t()*u2 + u2.t()*u2;
|
||
double s, val;
|
||
if (sol1.at<double>(0,0) > sol2.at<double>(0,0))
|
||
{
|
||
s = s1;
|
||
val = sol1.at<double>(0,0);
|
||
}
|
||
else
|
||
{
|
||
s = s2;
|
||
val = sol2.at<double>(0,0);
|
||
}
|
||
|
||
double lambda2 = sqrt(1.0 / val);
|
||
double lambda1 = s * lambda2;
|
||
|
||
Mat dualq = lambda1 * v(Rect(6, 0, 1, 8)) + lambda2*v(Rect(7, 0, 1, 8));
|
||
Mat X = dualQuaternion2homogeneous(dualq);
|
||
|
||
Mat R = X(Rect(0, 0, 3, 3));
|
||
Mat t = X(Rect(3, 0, 1, 3));
|
||
R_cam2gripper = R;
|
||
t_cam2gripper = t;
|
||
}
|
||
|
||
void calibrateHandEye(InputArrayOfArrays R_gripper2base, InputArrayOfArrays t_gripper2base,
|
||
InputArrayOfArrays R_target2cam, InputArrayOfArrays t_target2cam,
|
||
OutputArray R_cam2gripper, OutputArray t_cam2gripper,
|
||
HandEyeCalibrationMethod method)
|
||
{
|
||
CV_Assert(R_gripper2base.isMatVector() && t_gripper2base.isMatVector() &&
|
||
R_target2cam.isMatVector() && t_target2cam.isMatVector());
|
||
|
||
std::vector<Mat> R_gripper2base_, t_gripper2base_;
|
||
R_gripper2base.getMatVector(R_gripper2base_);
|
||
t_gripper2base.getMatVector(t_gripper2base_);
|
||
|
||
std::vector<Mat> R_target2cam_, t_target2cam_;
|
||
R_target2cam.getMatVector(R_target2cam_);
|
||
t_target2cam.getMatVector(t_target2cam_);
|
||
|
||
CV_Assert(R_gripper2base_.size() == t_gripper2base_.size() &&
|
||
R_target2cam_.size() == t_target2cam_.size() &&
|
||
R_gripper2base_.size() == R_target2cam_.size());
|
||
CV_Check(R_gripper2base_.size(), R_gripper2base_.size() >= 3, "At least 3 measurements are needed");
|
||
|
||
//Notation used in Tsai paper
|
||
//Defines coordinate transformation from G (gripper) to RW (robot base)
|
||
std::vector<Mat> Hg;
|
||
Hg.reserve(R_gripper2base_.size());
|
||
for (size_t i = 0; i < R_gripper2base_.size(); i++)
|
||
{
|
||
Mat m = Mat::eye(4, 4, CV_64FC1);
|
||
Mat R = m(Rect(0, 0, 3, 3));
|
||
if(R_gripper2base_[i].size() == Size(3, 3))
|
||
R_gripper2base_[i].convertTo(R, CV_64F);
|
||
else
|
||
Rodrigues(R_gripper2base_[i], R);
|
||
|
||
Mat t = m(Rect(3, 0, 1, 3));
|
||
t_gripper2base_[i].convertTo(t, CV_64F);
|
||
|
||
Hg.push_back(m);
|
||
}
|
||
|
||
//Defines coordinate transformation from CW (calibration target) to C (camera)
|
||
std::vector<Mat> Hc;
|
||
Hc.reserve(R_target2cam_.size());
|
||
for (size_t i = 0; i < R_target2cam_.size(); i++)
|
||
{
|
||
Mat m = Mat::eye(4, 4, CV_64FC1);
|
||
Mat R = m(Rect(0, 0, 3, 3));
|
||
if(R_target2cam_[i].size() == Size(3, 3))
|
||
R_target2cam_[i].convertTo(R, CV_64F);
|
||
else
|
||
Rodrigues(R_target2cam_[i], R);
|
||
|
||
Mat t = m(Rect(3, 0, 1, 3));
|
||
t_target2cam_[i].convertTo(t, CV_64F);
|
||
|
||
Hc.push_back(m);
|
||
}
|
||
|
||
Mat Rcg = Mat::eye(3, 3, CV_64FC1);
|
||
Mat Tcg = Mat::zeros(3, 1, CV_64FC1);
|
||
|
||
switch (method)
|
||
{
|
||
case CALIB_HAND_EYE_TSAI:
|
||
calibrateHandEyeTsai(Hg, Hc, Rcg, Tcg);
|
||
break;
|
||
|
||
case CALIB_HAND_EYE_PARK:
|
||
calibrateHandEyePark(Hg, Hc, Rcg, Tcg);
|
||
break;
|
||
|
||
case CALIB_HAND_EYE_HORAUD:
|
||
calibrateHandEyeHoraud(Hg, Hc, Rcg, Tcg);
|
||
break;
|
||
|
||
case CALIB_HAND_EYE_ANDREFF:
|
||
calibrateHandEyeAndreff(Hg, Hc, Rcg, Tcg);
|
||
break;
|
||
|
||
case CALIB_HAND_EYE_DANIILIDIS:
|
||
calibrateHandEyeDaniilidis(Hg, Hc, Rcg, Tcg);
|
||
break;
|
||
|
||
default:
|
||
break;
|
||
}
|
||
|
||
Rcg.copyTo(R_cam2gripper);
|
||
Tcg.copyTo(t_cam2gripper);
|
||
}
|
||
|
||
//Reference:
|
||
//M. Shah, "Solving the robot-world/hand-eye calibration problem using the kronecker product"
|
||
//Journal of Mechanisms and Robotics, vol. 5, p. 031007, 2013.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateRobotWorldHandEyeShah(const std::vector<Mat_<double>>& cRw, const std::vector<Mat_<double>>& ctw,
|
||
const std::vector<Mat_<double>>& gRb, const std::vector<Mat_<double>>& gtb,
|
||
Matx33d& wRb, Matx31d& wtb, Matx33d& cRg, Matx31d& ctg)
|
||
{
|
||
Mat_<double> T = Mat_<double>::zeros(9, 9);
|
||
for (size_t i = 0; i < cRw.size(); i++)
|
||
{
|
||
T += kron(gRb[i], cRw[i]);
|
||
}
|
||
|
||
Mat_<double> w, u, vt;
|
||
SVDecomp(T, w, u, vt);
|
||
|
||
Mat_<double> RX(3,3), RZ(3,3);
|
||
for (int i = 0; i < 3; i++)
|
||
{
|
||
for (int j = 0; j < 3; j++)
|
||
{
|
||
RX(j,i) = vt(0, i*3+j);
|
||
RZ(j,i) = u(i*3+j, 0);
|
||
}
|
||
}
|
||
|
||
wRb = normalizeRotation(RX);
|
||
cRg = normalizeRotation(RZ);
|
||
Mat_<double> Z = Mat(cRg.t()).reshape(1, 9);
|
||
|
||
const int n = static_cast<int>(cRw.size());
|
||
Mat_<double> A = Mat_<double>::zeros(3*n, 6);
|
||
Mat_<double> b = Mat_<double>::zeros(3*n, 1);
|
||
Mat_<double> I3 = Mat_<double>::eye(3,3);
|
||
|
||
for (int i = 0; i < n; i++)
|
||
{
|
||
Mat cRw_ = -cRw[i];
|
||
cRw_.copyTo(A(Range(i*3, (i+1)*3), Range(0,3)));
|
||
I3.copyTo(A(Range(i*3, (i+1)*3), Range(3,6)));
|
||
|
||
Mat ctw_ = ctw[i] - kron(gtb[i].t(), I3) * Z;
|
||
ctw_.copyTo(b(Range(i*3, (i+1)*3), Range::all()));
|
||
}
|
||
|
||
Mat_<double> t;
|
||
solve(A, b, t, DECOMP_SVD);
|
||
|
||
for (int i = 0; i < 3; i++)
|
||
{
|
||
wtb(i) = t(i);
|
||
ctg(i) = t(i+3);
|
||
}
|
||
}
|
||
|
||
//Reference:
|
||
//A. Li, L. Wang, and D. Wu, "Simultaneous robot-world and hand-eye calibration using dual-quaternions and kronecker product"
|
||
//International Journal of Physical Sciences, vol. 5, pp. 1530–1536, 2010.
|
||
//Matlab code: http://math.loyola.edu/~mili/Calibration/
|
||
static void calibrateRobotWorldHandEyeLi(const std::vector<Mat_<double>>& cRw, const std::vector<Mat_<double>>& ctw,
|
||
const std::vector<Mat_<double>>& gRb, const std::vector<Mat_<double>>& gtb,
|
||
Matx33d& wRb, Matx31d& wtb, Matx33d& cRg, Matx31d& ctg)
|
||
{
|
||
const int n = static_cast<int>(cRw.size());
|
||
Mat_<double> A = Mat_<double>::zeros(12*n, 24);
|
||
Mat_<double> b = Mat_<double>::zeros(12*n, 1);
|
||
Mat_<double> I3 = Mat_<double>::eye(3,3);
|
||
|
||
for (int i = 0; i < n; i++)
|
||
{
|
||
//Eq 19
|
||
kron(cRw[i], I3).copyTo(A(Range(i*12, i*12 + 9), Range(0, 9)));
|
||
kron(-I3, gRb[i].t()).copyTo(A(Range(i*12, i*12 + 9), Range(9, 18)));
|
||
|
||
kron(I3, gtb[i].t()).copyTo(A(Range(i*12 + 9, (i+1)*12), Range(9, 18)));
|
||
Mat cRw_ = -cRw[i];
|
||
cRw_.copyTo(A(Range(i*12 + 9, (i+1)*12), Range(18, 21)));
|
||
I3.copyTo(A(Range(i*12 + 9, (i+1)*12), Range(21, 24)));
|
||
|
||
ctw[i].copyTo(b(Range(i*12 + 9, i*12+12), Range::all()));
|
||
}
|
||
|
||
Mat_<double> x;
|
||
solve(A, b, x, DECOMP_SVD);
|
||
|
||
Mat_<double> RX = x(Range(0,9), Range::all()).reshape(3, 3);
|
||
wRb = normalizeRotation(RX);
|
||
x(Range(18,21), Range::all()).copyTo(wtb);
|
||
|
||
Mat_<double> RZ = x(Range(9,18), Range::all()).reshape(3, 3);
|
||
cRg = normalizeRotation(RZ);
|
||
x(Range(21,24), Range::all()).copyTo(ctg);
|
||
}
|
||
|
||
void calibrateRobotWorldHandEye(InputArrayOfArrays R_world2cam, InputArrayOfArrays t_world2cam,
|
||
InputArrayOfArrays R_base2gripper, InputArrayOfArrays t_base2gripper,
|
||
OutputArray R_base2world, OutputArray t_base2world,
|
||
OutputArray R_gripper2cam, OutputArray t_gripper2cam,
|
||
RobotWorldHandEyeCalibrationMethod method)
|
||
{
|
||
CV_Assert(R_base2gripper.isMatVector() && t_base2gripper.isMatVector() &&
|
||
R_world2cam.isMatVector() && t_world2cam.isMatVector());
|
||
|
||
std::vector<Mat> R_base2gripper_tmp, t_base2gripper_tmp;
|
||
R_base2gripper.getMatVector(R_base2gripper_tmp);
|
||
t_base2gripper.getMatVector(t_base2gripper_tmp);
|
||
|
||
std::vector<Mat> R_world2cam_tmp, t_world2cam_tmp;
|
||
R_world2cam.getMatVector(R_world2cam_tmp);
|
||
t_world2cam.getMatVector(t_world2cam_tmp);
|
||
|
||
CV_Assert(R_base2gripper_tmp.size() == t_base2gripper_tmp.size() &&
|
||
R_world2cam_tmp.size() == t_world2cam_tmp.size() &&
|
||
R_base2gripper_tmp.size() == R_world2cam_tmp.size());
|
||
CV_Check(R_base2gripper_tmp.size(), R_base2gripper_tmp.size() >= 3, "At least 3 measurements are needed");
|
||
|
||
// Convert to double
|
||
std::vector<Mat_<double>> R_base2gripper_, t_base2gripper_;
|
||
std::vector<Mat_<double>> R_world2cam_, t_world2cam_;
|
||
|
||
R_base2gripper_.reserve(R_base2gripper_tmp.size());
|
||
t_base2gripper_.reserve(R_base2gripper_tmp.size());
|
||
R_world2cam_.reserve(R_world2cam_tmp.size());
|
||
t_world2cam_.reserve(R_base2gripper_tmp.size());
|
||
|
||
// Convert to rotation matrix if needed
|
||
for (size_t i = 0; i < R_base2gripper_tmp.size(); i++)
|
||
{
|
||
{
|
||
Mat rot = R_base2gripper_tmp[i];
|
||
Mat R(3, 3, CV_64FC1);
|
||
if (rot.size() == Size(3,3))
|
||
{
|
||
rot.convertTo(R, CV_64F);
|
||
R_base2gripper_.push_back(R);
|
||
}
|
||
else
|
||
{
|
||
Rodrigues(rot, R);
|
||
R_base2gripper_.push_back(R);
|
||
}
|
||
Mat tvec = t_base2gripper_tmp[i];
|
||
Mat t;
|
||
tvec.convertTo(t, CV_64F);
|
||
t_base2gripper_.push_back(t);
|
||
}
|
||
{
|
||
Mat rot = R_world2cam_tmp[i];
|
||
Mat R(3, 3, CV_64FC1);
|
||
if (rot.size() == Size(3,3))
|
||
{
|
||
rot.convertTo(R, CV_64F);
|
||
R_world2cam_.push_back(R);
|
||
}
|
||
else
|
||
{
|
||
Rodrigues(rot, R);
|
||
R_world2cam_.push_back(R);
|
||
}
|
||
Mat tvec = t_world2cam_tmp[i];
|
||
Mat t;
|
||
tvec.convertTo(t, CV_64F);
|
||
t_world2cam_.push_back(t);
|
||
}
|
||
}
|
||
|
||
CV_Assert(R_world2cam_.size() == t_world2cam_.size() &&
|
||
R_base2gripper_.size() == t_base2gripper_.size() &&
|
||
R_world2cam_.size() == R_base2gripper_.size());
|
||
|
||
Matx33d wRb, cRg;
|
||
Matx31d wtb, ctg;
|
||
switch (method)
|
||
{
|
||
case CALIB_ROBOT_WORLD_HAND_EYE_SHAH:
|
||
calibrateRobotWorldHandEyeShah(R_world2cam_, t_world2cam_, R_base2gripper_, t_base2gripper_, wRb, wtb, cRg, ctg);
|
||
break;
|
||
|
||
case CALIB_ROBOT_WORLD_HAND_EYE_LI:
|
||
calibrateRobotWorldHandEyeLi(R_world2cam_, t_world2cam_, R_base2gripper_, t_base2gripper_, wRb, wtb, cRg, ctg);
|
||
break;
|
||
}
|
||
|
||
Mat(wRb).copyTo(R_base2world);
|
||
Mat(wtb).copyTo(t_base2world);
|
||
|
||
Mat(cRg).copyTo(R_gripper2cam);
|
||
Mat(ctg).copyTo(t_gripper2cam);
|
||
}
|
||
}
|