PCL中点云BoundingBox包围盒绘制（基于PCA）

！！！实现环境：pcl1.8.0+vs2015+win10

大致过程：

1、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_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));

2、利用1中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。

4、完整代码：

#include          
VTK_MODULE_INIT(vtkRenderingOpenGL);
VTK_MODULE_INIT(vtkInteractionStyle);
VTK_MODULE_INIT(vtkRenderingFreeType);

#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;
typedef pcl::PointXYZ PointType;

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

	std::cout << "请输入需要显示的点云文件名：";
	std::string fileName("rabbit");
	getline(cin, fileName);
	fileName += ".pcd";
	//std::string fileName(argv[1]);
	pcl::io::loadPCDFile(fileName, *cloud);

	Eigen::Vector4f pcaCentroid;
	pcl::compute3DCentroid(*cloud, pcaCentroid);
	Eigen::Matrix3f covariance;
	pcl::computeCovarianceMatrixNormalized(*cloud, pcaCentroid, covariance);
	Eigen::SelfAdjointEigenSolver 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::Ptr cloudPCAprojection (new pcl::PointCloud);
	pcl::PCA 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::Ptr transformedCloud(new pcl::PointCloud);
	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 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 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;
}

注：如有问题请批评指正。

参考资料：

[1] Finding oriented bounding box of a cloud

[2] 计算点云的最小BBOX