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基于PCA的最小包围盒

发布时间 2023-08-24 17:36:12作者: 舒勤

参考文章：

http://t.csdn.cn/LK1RZ

http://t.csdn.cn/DEhQC

http://t.csdn.cn/2LKWV

http://t.csdn.cn/AGicg

http://t.csdn.cn/9Vqk6

下面基于PCA的最小包围盒的代码是一样的，都是参考上述博客。

引用代码：

#include <vtkAutoInit.h>         
VTK_MODULE_INIT(vtkRenderingOpenGL);
VTK_MODULE_INIT(vtkInteractionStyle);
VTK_MODULE_INIT(vtkRenderingFreeType);

#include <iostream>
#include <string>
#include <pcl/io/pcd_io.h>
#include <pcl/point_cloud.h>
#include <pcl/point_types.h>
#include <Eigen/Core>
#include <Eigen/Eigenvalues>
#include <pcl/common/transforms.h>
#include <pcl/common/common.h>
#include <pcl/visualization/pcl_visualizer.h>

using namespace std;
typedef pcl::PointXYZ PointType;

int main(int argc, char** argv)
{
    pcl::PointCloud<PointType>::Ptr cloud(new pcl::PointCloud<PointType>());

    pcl::io::loadPCDFile("C:\\Users\\80hu_mian.pcd", *cloud);
/*利用PCA主元分析法获得点云的三个主方向，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 */
    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;


    //visualization
    pcl::visualization::PCLVisualizer viewer;

    pcl::visualization::PointCloudColorHandlerCustom<PointType> tc_handler(transformedCloud, 0, 255, 0); //转换到原点的点云相关
    viewer.addPointCloud(transformedCloud, tc_handler, "transformCloud");
    viewer.addCube(bboxT1, bboxQ1, whd1(0), whd1(1), whd1(2), "bbox1");
    viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATION_WIREFRAME, "bbox1");
    viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 0.0, 1.0, 0.0, "bbox1");

    viewer.addArrow(pcaX, op, 1.0, 0.0, 0.0, false, "arrow_X");
    viewer.addArrow(pcaY, op, 0.0, 1.0, 0.0, false, "arrow_Y");
    viewer.addArrow(pcaZ, op, 0.0, 0.0, 1.0, false, "arrow_Z");

    pcl::visualization::PointCloudColorHandlerCustom<PointType> color_handler(cloud, 255, 0, 0);  //输入的初始点云相关
    viewer.addPointCloud(cloud, color_handler, "cloud");
    viewer.addCube(bboxT, bboxQ, whd(0), whd(1), whd(2), "bbox");
    viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_REPRESENTATION, pcl::visualization::PCL_VISUALIZER_REPRESENTATION_WIREFRAME, "bbox");
    viewer.setShapeRenderingProperties(pcl::visualization::PCL_VISUALIZER_COLOR, 1.0, 0.0, 0.0, "bbox");

    viewer.addArrow(pcX, cp, 1.0, 0.0, 0.0, false, "arrow_x");
    viewer.addArrow(pcY, cp, 0.0, 1.0, 0.0, false, "arrow_y");
    viewer.addArrow(pcZ, cp, 0.0, 0.0, 1.0, false, "arrow_z");

    viewer.addCoordinateSystem(0.5f * sc1);
    viewer.setBackgroundColor(1.0, 1.0, 1.0);
    while (!viewer.wasStopped())
    {
        viewer.spinOnce(100);
    }

    return 0;
}

运行时出现以下报错：

1>D:\PCL\new\pcl\Project1\pcl_test.cpp(97,7): error C2672: “pcl::transformVector”: 未找到匹配的重载函数
1>D:\PCL\new\pcl\Project1\pcl_test.cpp(97,59): error C2784: “void pcl::transformVector(const Eigen::Matrix<_Scalar,3,1,0,3,1> &,Eigen::Matrix<_Scalar,3,1,0,3,1> &,const Eigen::Transform<Scalar,3,2,0> &)”: 未能从“Eigen::Block<Derived,3,1,true>”为“const Eigen::Matrix<_Scalar,3,1,0,3,1> &”推导 模板 参数
1>        with
1>        [
1>            Derived=Eigen::Matrix<float,3,3,0,3,3>
1>        ]

代码报错的位置：

    //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);

在说明解决方法之前，需要了解pcl::transformVector的调用参数格式。

/** \brief Transform a vector using an affine matrix
  * \param[in] vector_in the vector to be transformed
  * \param[out] vector_out the transformed vector
  * \param[in] transformation the transformation matrix
  *
  * \note Can be used with \c vector_in = \c vector_out
  */
  template <typename Scalar> inline void
  transformVector (const Eigen::Matrix<Scalar, 3, 1> &vector_in,
                         Eigen::Matrix<Scalar, 3, 1> &vector_out,
                   const Eigen::Transform<Scalar, 3, Eigen::Affine> &transformation)
  {
    vector_out = transformation.linear () * vector_in;
  }

可以清晰看到transformVector中三个参数类型。在debug中运行至出现报错之前，发现px、py、pz是符合vector_out，结合报错信息发现是eigenVectorsPCA.col(1)不符合要求，但按照理解应该是符合vector_in，但是运行的时候会报错。因此，想试试通过新建的一个变量代替eigenVectorsPCA.col(i)(i=0,1,2)。

替换代码如下：

Eigen::Vector3f PCAcol2 = eigenVectorsPCA.col(0).cross(eigenVectorsPCA.col(1));
    Eigen::Vector3f PCAcol0 = eigenVectorsPCA.col(1).cross(eigenVectorsPCA.col(2));
    Eigen::Vector3f PCAcol1 = eigenVectorsPCA.col(2).cross(eigenVectorsPCA.col(0));
   // 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));

报错部分代码修改如下：

    pcl::transformVector(PCAcol0, px, tm_aff);
    pcl::transformVector(PCAcol1, py, tm_aff);
    pcl::transformVector(PCAcol2, pz, tm_aff);

点击运行，运行成功。运行结果如下所示：

 

从上述运行结果来看，是实现了点云数据的最小包围盒。

如果发现有什么错误，希望大家可以指出。