我在 OpenCV 中没有找到所需的功能,所以我编写了自己的实现。基于以下想法OpenSFM.
cv::Vec3d
CalculateMean(const cv::Mat_<cv::Vec3d> &points)
{
cv::Mat_<cv::Vec3d> result;
cv::reduce(points, result, 0, CV_REDUCE_AVG);
return result(0, 0);
}
cv::Mat_<double>
FindRigidTransform(const cv::Mat_<cv::Vec3d> &points1, const cv::Mat_<cv::Vec3d> points2)
{
/* Calculate centroids. */
cv::Vec3d t1 = -CalculateMean(points1);
cv::Vec3d t2 = -CalculateMean(points2);
cv::Mat_<double> T1 = cv::Mat_<double>::eye(4, 4);
T1(0, 3) = t1[0];
T1(1, 3) = t1[1];
T1(2, 3) = t1[2];
cv::Mat_<double> T2 = cv::Mat_<double>::eye(4, 4);
T2(0, 3) = -t2[0];
T2(1, 3) = -t2[1];
T2(2, 3) = -t2[2];
/* Calculate covariance matrix for input points. Also calculate RMS deviation from centroid
* which is used for scale calculation.
*/
cv::Mat_<double> C(3, 3, 0.0);
double p1Rms = 0, p2Rms = 0;
for (int ptIdx = 0; ptIdx < points1.rows; ptIdx++) {
cv::Vec3d p1 = points1(ptIdx, 0) + t1;
cv::Vec3d p2 = points2(ptIdx, 0) + t2;
p1Rms += p1.dot(p1);
p2Rms += p2.dot(p2);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
C(i, j) += p2[i] * p1[j];
}
}
}
cv::Mat_<double> u, s, vh;
cv::SVD::compute(C, s, u, vh);
cv::Mat_<double> R = u * vh;
if (cv::determinant(R) < 0) {
R -= u.col(2) * (vh.row(2) * 2.0);
}
double scale = sqrt(p2Rms / p1Rms);
R *= scale;
cv::Mat_<double> M = cv::Mat_<double>::eye(4, 4);
R.copyTo(M.colRange(0, 3).rowRange(0, 3));
cv::Mat_<double> result = T2 * M * T1;
result /= result(3, 3);
return result.rowRange(0, 3);
}