主成分特征向量彼此不垂直

Question

我使用下面的代码获得了簇点云的特征向量。

   for (size_t j = 0; j < cluster_indices.size (); j++){
     static int line=0;
     Eigen::Vector4f centroid;
     Eigen::Matrix3f covariance_matrix;

    // Extract the eigenvalues and eigenvectors
    Eigen::Vector3f eigen_values;
    Eigen::Matrix3f eigen_vectors;

    pcl::compute3DCentroid(*cloud_filtered,cluster_indices[j],centroid);

    // Compute the 3x3 covariance matrix 
    pcl::computeCovarianceMatrix (*cloud_filtered, centroid, covariance_matrix);
    pcl::eigen33 (covariance_matrix, eigen_vectors, eigen_values);
    //~ _viewer->addLine<pcl::PointXYZRGB> (centroid, eigen_vectors, "line");


    std::cout << "centroid:"<<centroid<<std::endl;

    cloud_cluster->points.push_back(centroidToPoints(centroid));  
    for(int i=0; i<3;i++){   

        std::cout << "eigenvector "<<i<<":"<<eigen_vectors.col(i)<<std::endl;
     cloud_cluster->points.push_back(matrixToPoints(eigen_vectors.col(i)));
     _viewer->addLine<pcl::PointXYZRGB> (centroidToPoints(centroid), matrixToPoints(eigen_vectors.col(i)), "line"+line);
     line++;
     }
    }

然后我将质心和特征向量分别转换为点。在下面的代码的帮助下。

pcl::PointXYZRGB centroidToPoints(Eigen::Vector4f& c){
     pcl::PointCloud<pcl::PointXYZRGB>::Ptr cloud_eigen (new pcl::PointCloud<pcl::PointXYZRGB>);
     cloud_eigen->width  = 15;
     cloud_eigen->height = 1;
     cloud_eigen->points.resize (cloud_eigen->width * cloud_eigen->height);
     cloud_eigen->points[0].x=c[0];
     cloud_eigen->points[0].y=c[1];
     cloud_eigen->points[0].z=c[2];
     //~ pcl::visualization::PointCloudColorHandlerGenericField<pcl::PointXYZRGB> cloud_handler2 (cloud_eigen, "z");
    //~ _viewer->addPointCloud<pcl::PointXYZRGB> (cloud_eigen, cloud_handler2, "second cloud");
    //~ _viewer->setPointCloudRenderingProperties (pcl::visualization::PCL_VISUALIZER_POINT_SIZE, 2, "second cloud");
 return cloud_eigen->points[0]; 

}

pcl::PointXYZRGB EigenToPoints(Eigen::DenseBase<Eigen::Matrix<float, 3, 3> >::ColXpr ev){

  pcl::PointCloud<pcl::PointXYZRGB>::Ptr cloud_eigen (new pcl::PointCloud<pcl::PointXYZRGB>);
     cloud_eigen->width  = 15;
     cloud_eigen->height = 1;
     cloud_eigen->points.resize (cloud_eigen->width * cloud_eigen->height);
     cloud_eigen->points[0].x=ev[0];
     cloud_eigen->points[0].y=ev[1];
     cloud_eigen->points[0].z=ev[2];

 return cloud_eigen->points[0]; 

}

但是特征向量不是垂直的。如下所示（绿色和红色点是特征向量）。

谁能告诉我什么是错的？。