方法一 、有点云旋转前的法向量、和旋转后的法向量可以进行矩阵旋转。
此时我要将点云地面与z轴垂直,已知旋转后的法向量为(0, 0, 1),
旋转前的法向量可以通过RANSAC的平面检测法检平面,得到平面法向量:
// RANSAC分割平面,获取平面法向量
pcl::ModelCoefficients::Ptr coefficients(new pcl::ModelCoefficients); // 创建一个模型参数对象,用于记录结果
pcl::PointIndices::Ptr inliers(new pcl::PointIndices); //inliers表示误差能容忍的点 记录的是点云的序号
pcl::SACSegmentation<pcl::PointXYZ> seg; // 创建分割对象
seg.setInputCloud(cloud); //输入点云
seg.setModelType(pcl::SACMODEL_PLANE); // Mandatory-设置目标几何形状
seg.setMethodType(pcl::SAC_RANSAC); //分割方法:随机采样法
seg.setDistanceThreshold(0.05); //设置误差容忍范围,也就是我说过的阈值
seg.setOptimizeCoefficients(true); // Optional,这个设置可以选定结果平面展示的点是分割掉的点还是分割剩下的点。
seg.segment(*inliers, *coefficients); //分割点云,获得平面和法向量
/*提取子集: 平面&非平面点云*/
//提取平面点
pcl::PointCloud<pcl::PointXYZ>::Ptr c_plane (new pcl::PointCloud<pcl::PointXYZ>); //存储平面点云
pcl::ExtractIndices<pcl::PointXYZ> extract; //创建点云提取对象
extract.setInputCloud (cloud); //设置输入点云
extract.setIndices (inliers); //设置分割后的内点为需要提取的点集
extract.setNegative (false); //false提取内点,true提取外点
extract.filter (*c_plane); //提取输出存储到c_plane
根据法向量计算旋转旋转角度
Eigen::Matrix4f CreateRotateMatrix(Eigen::Vector3f before, Eigen::Vector3f after) {
before.normalize();
after.normalize();
float angle = acos(before.dot(after));
Eigen::Vector3f p_rotate = before.cross(after);
p_rotate.normalize();
Eigen::Matrix4f rotationMatrix = Eigen::Matrix4f::Identity();
rotationMatrix(0, 0) = cos(angle) + p_rotate[0] * p_rotate[0] * (1 - cos(angle));
rotationMatrix(0, 1) =
p_rotate[0] * p_rotate[1] * (1 - cos(angle) - p_rotate[2] * sin(angle));//这里跟公式比多了一个括号,但是看实验结果它是对的。
rotationMatrix(0, 2) = p_rotate[1] * sin(angle) + p_rotate[0] * p_rotate[2] * (1 - cos(angle));
rotationMatrix(1, 0) = p_rotate[2] * sin(angle) + p_rotate[0] * p_rotate[1] * (1 - cos(angle));
rotationMatrix(1, 1) = cos(angle) + p_rotate[1] * p_rotate[1] * (1 - cos(angle));
rotationMatrix(1, 2) = -p_rotate[0] * sin(angle) + p_rotate[1] * p_rotate[2] * (1 - cos(angle));
rotationMatrix(2, 0) = -p_rotate[1] * sin(angle) + p_rotate[0] * p_rotate[2] * (1 - cos(angle));
rotationMatrix(2, 1) = p_rotate[0] * sin(angle) + p_rotate[1] * p_rotate[2] * (1 - cos(angle));
rotationMatrix(2, 2) = cos(angle) + p_rotate[2] * p_rotate[2] * (1 - cos(angle));
return rotationMatrix;
}
进行旋转
// 旋转点云
Eigen::Vector3f before(coefficients->values[0], coefficients->values[1], coefficients->values[2]); //旋转之前的法向量
Eigen::Vector3f after(0.f, 0.f, 1.f); //z轴垂直的法向量
Eigen::Matrix4f rotationMatrix(CreateRotateMatrix(before, after)); //计算旋转矩阵
pcl::PointCloud<pcl::PointXYZ>::Ptr cloud_calibration(new pcl::PointCloud<pcl::PointXYZ>()); //存储校准后点云
pcl::transformPointCloud(*cloud, *cloud_calibration, rotationMatrix); //进行旋转
方法二、
1、获取质心,计算协方差,获得协方差矩阵,求取协方差矩阵的特征值和特长向量,特征向量即为主方向。
2、利用获得的主方向和质心,将输入点云转换至原点,且主方向与坐标系方向重回,建立变换到原点的点云的包围盒。
3、给输入点云设置主方向和包围盒,通过输入点云到原点点云变换的逆变换实现。
Eigen::Vector4f pcaCentroid;
pcl::compute3DCentroid(*cloud, pcaCentroid);
Eigen::Matrix3f covariance;
pcl::computeCovarianceMatrixNormalized(*cloud, pcaCentroid, covariance);
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigen_solver(covariance, Eigen::ComputeEigenvectors);
Eigen::Matrix3f eigenVectorsPCA = eigen_solver.eigenvectors();
Eigen::Vector3f eigenValuesPCA = eigen_solver.eigenvalues();
eigenVectorsPCA.col(2) = eigenVectorsPCA.col(0).cross(eigenVectorsPCA.col(1)); //校正主方向间垂直
eigenVectorsPCA.col(0) = eigenVectorsPCA.col(1).cross(eigenVectorsPCA.col(2));
eigenVectorsPCA.col(1) = eigenVectorsPCA.col(2).cross(eigenVectorsPCA.col(0));
std::cout << "特征值va(3x1):\n" << eigenValuesPCA << std::endl;
std::cout << "特征向量ve(3x3):\n" << eigenVectorsPCA << std::endl;
std::cout << "质心点(4x1):\n" << pcaCentroid << std::endl;
/*
// 另一种计算点云协方差矩阵特征值和特征向量的方式:通过pcl中的pca接口,如下,这种情况得到的特征向量相似特征向量
pcl::PointCloud<pcl::PointXYZ>::Ptr cloudPCAprojection (new pcl::PointCloud<pcl::PointXYZ>);
pcl::PCA<pcl::PointXYZ> pca;
pca.setInputCloud(cloudSegmented);
pca.project(*cloudSegmented, *cloudPCAprojection);
std::cerr << std::endl << "EigenVectors: " << pca.getEigenVectors() << std::endl;//计算特征向量
std::cerr << std::endl << "EigenValues: " << pca.getEigenValues() << std::endl;//计算特征值
*/
Eigen::Matrix4f tm = Eigen::Matrix4f::Identity();
Eigen::Matrix4f tm_inv = Eigen::Matrix4f::Identity();
tm.block<3, 3>(0, 0) = eigenVectorsPCA.transpose(); //R.
tm.block<3, 1>(0, 3) = -1.0f * (eigenVectorsPCA.transpose()) *(pcaCentroid.head<3>());// -R*t
tm_inv = tm.inverse();
std::cout << "变换矩阵tm(4x4):\n" << tm << std::endl;
std::cout << "逆变矩阵tm'(4x4):\n" << tm_inv << std::endl;
pcl::PointCloud<PointType>::Ptr transformedCloud(new pcl::PointCloud<PointType>);
pcl::transformPointCloud(*cloud, *transformedCloud, tm);
PointType min_p1, max_p1;
Eigen::Vector3f c1, c;
pcl::getMinMax3D(*transformedCloud, min_p1, max_p1);
c1 = 0.5f*(min_p1.getVector3fMap() + max_p1.getVector3fMap());
std::cout << "型心c1(3x1):\n" << c1 << std::endl;
Eigen::Affine3f tm_inv_aff(tm_inv);
pcl::transformPoint(c1, c, tm_inv_aff);
Eigen::Vector3f whd, whd1;
whd1 = max_p1.getVector3fMap() - min_p1.getVector3fMap();
whd = whd1;
float sc1 = (whd1(0) + whd1(1) + whd1(2)) / 3; //点云平均尺度,用于设置主方向箭头大小
std::cout << "width1=" << whd1(0) << endl;
std::cout << "heght1=" << whd1(1) << endl;
std::cout << "depth1=" << whd1(2) << endl;
std::cout << "scale1=" << sc1 << endl;
const Eigen::Quaternionf bboxQ1(Eigen::Quaternionf::Identity());
const Eigen::Vector3f bboxT1(c1);
const Eigen::Quaternionf bboxQ(tm_inv.block<3, 3>(0, 0));
const Eigen::Vector3f bboxT(c);
//变换到原点的点云主方向
PointType op;
op.x = 0.0;
op.y = 0.0;
op.z = 0.0;
Eigen::Vector3f px, py, pz;
Eigen::Affine3f tm_aff(tm);
pcl::transformVector(eigenVectorsPCA.col(0), px, tm_aff);
pcl::transformVector(eigenVectorsPCA.col(1), py, tm_aff);
pcl::transformVector(eigenVectorsPCA.col(2), pz, tm_aff);
PointType pcaX;
pcaX.x = sc1 * px(0);
pcaX.y = sc1 * px(1);
pcaX.z = sc1 * px(2);
PointType pcaY;
pcaY.x = sc1 * py(0);
pcaY.y = sc1 * py(1);
pcaY.z = sc1 * py(2);
PointType pcaZ;
pcaZ.x = sc1 * pz(0);
pcaZ.y = sc1 * pz(1);
pcaZ.z = sc1 * pz(2);
//初始点云的主方向
PointType cp;
cp.x = pcaCentroid(0);
cp.y = pcaCentroid(1);
cp.z = pcaCentroid(2);
PointType pcX;
pcX.x = sc1 * eigenVectorsPCA(0, 0) + cp.x;
pcX.y = sc1 * eigenVectorsPCA(1, 0) + cp.y;
pcX.z = sc1 * eigenVectorsPCA(2, 0) + cp.z;
PointType pcY;
pcY.x = sc1 * eigenVectorsPCA(0, 1) + cp.x;
pcY.y = sc1 * eigenVectorsPCA(1, 1) + cp.y;
pcY.z = sc1 * eigenVectorsPCA(2, 1) + cp.z;
PointType pcZ;
pcZ.x = sc1 * eigenVectorsPCA(0, 2) + cp.x;
pcZ.y = sc1 * eigenVectorsPCA(1, 2) + cp.y;
pcZ.z = sc1 * eigenVectorsPCA(2, 2) + cp.z;
OK.