PCL-基于PCA计算点云的最小包围盒、顶点坐标和主轴方向

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目录

最小包围盒

包围盒计算步骤

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。
2.利用计算得到的主方向和质心，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。

最小包围盒顶点坐标计算步骤

1.输入点云转换至原点后,计算变换后点云的最大最小x,y,z轴的坐标,此时(max.x,max.y,max.z),(max.x,min.y,max.z),(max.x,max.y,min.z),(min.x,max.y,max.z),(min.x,max.y,min.z),(min.x,min.y,max.z),(min.x,min.y,max.z),(min.x,min.y,min.z)
即为变换后点云的包围盒,也是原始输入点云包围盒顶点坐标经过变化后的坐标.
2.将上述求得的6个包围盒坐标逆变换回输入点云的坐标系,即得到原始输入点云的包围盒顶点坐标

代码实现


#include <iostream>
#include <pcl/ModelCoefficients.h>
#include <pcl/io/pcd_io.h>
#include <pcl/filters/project_inliers.h>
#include <pcl/filters/extract_indices.h>
#include <pcl/sample_consensus/method_types.h>
#include <pcl/sample_consensus/model_types.h>
#include <pcl/segmentation/sac_segmentation.h>
#include <pcl/visualization/cloud_viewer.h>
#include <pcl/point_types.h>
#include <pcl/filters/voxel_grid.h>
#include <pcl/filters/passthrough.h>
#include <pcl/features/normal_3d.h>
#include <pcl/filters/radius_outlier_removal.h>
#include <pcl/kdtree/kdtree_flann.h>
#include <pcl/segmentation/extract_clusters.h>
#include <Eigen/Core>
#include <pcl/common/transforms.h>
#include <pcl/common/common.h>
#include <pcl/common/time.h>
#include <pcl/common/angles.h>
#include <pcl/registration/transformation_estimation_svd.h>


using namespace std;
typedef pcl::PointXYZ PointType;
typedef struct myPointType
{
	double x;  //mm world coordinate x  
	double y;  //mm world coordinate y  
	double z;  //mm world coordinate z  
	int num;   //point num
};

// Get N bits of the string from back to front.
char* Substrend(char* str, int n)
{
	char* substr = (char*)malloc(n + 1);
	int length = strlen(str);
	if (n >= length)
	{
		strcpy(substr, str);
		return substr;
	}
	int k = 0;
	for (int i = length - n; i < length; i++)
	{
		substr[k] = str[i];
		k++;
	}
	substr[k] = '\0';
	return substr;
}

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


	pcl::io::loadPCDFile("E:\\***\\cloud_cluster_1.pcd", *cloud);

	// start calculating time
	pcl::StopWatch time;


	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;

	//Rectangular vertex 
	pcl::PointCloud<PointType>::Ptr transVertexCloud(new pcl::PointCloud<PointType>);//存放变换后点云包围盒的6个顶点
	pcl::PointCloud<PointType>::Ptr VertexCloud(new pcl::PointCloud<PointType>);//存放原来点云中包围盒的6个顶点
	transVertexCloud->width = 6;
	transVertexCloud->height = 1;
	transVertexCloud->is_dense = false;
	transVertexCloud->points.resize(transVertexCloud->width * transVertexCloud->height);
	transVertexCloud->points[0].x = max_p1.x;
	transVertexCloud->points[0].y = max_p1.y;
	transVertexCloud->points[0].z = max_p1.z;
	transVertexCloud->points[1].x = max_p1.x;
	transVertexCloud->points[1].y = max_p1.y;
	transVertexCloud->points[1].z = min_p1.z;
	transVertexCloud->points[2].x = max_p1.x;
	transVertexCloud->points[2].y = min_p1.y;
	transVertexCloud->points[2].z = min_p1.z;
	transVertexCloud->points[3].x = min_p1.x;
	transVertexCloud->points[3].y = max_p1.y;
	transVertexCloud->points[3].z = max_p1.z;
	transVertexCloud->points[4].x = min_p1.x;
	transVertexCloud->points[4].y = min_p1.y;
	transVertexCloud->points[4].z = max_p1.z;
	transVertexCloud->points[5].x = min_p1.x;
	transVertexCloud->points[5].y = min_p1.y;
	transVertexCloud->points[5].z = min_p1.z;
	pcl::transformPointCloud(*transVertexCloud, *VertexCloud, tm_inv);

	// 逆变换回来的角度
	cout << whd1(0) << " " << whd1(1) << " " << whd1(2) << endl;
	auto euler = bboxQ1.toRotationMatrix().eulerAngles(0, 1, 2);
	std::cout << "Euler from quaternion in roll, pitch, yaw" << std::endl << euler / 3.14 * 180 << std::endl << std::endl;

	//Output time consumption 
	std::cout << "运行时间" << time.getTime() << "ms" << std::endl;

	//visualization
	pcl::visualization::PCLVisualizer viewer;
	pcl::visualization::PointCloudColorHandlerCustom<PointType> tc_handler(transformedCloud, 0, 255, 0); //设置点云颜色
	//Visual transformed point cloud
	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);
	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(0.0, 0.0, 0.0);

	viewer.addPointCloud(VertexCloud, "temp_cloud");
	viewer.setPointCloudRenderingProperties(pcl::visualization::PCL_VISUALIZER_POINT_SIZE, 10, "temp_cloud");
	while (!viewer.wasStopped())
	{
		viewer.spinOnce();
	}

	return 0;
}

实验结果

在这里插入图片描述
在这里插入图片描述

总结

  1. 实验环境：pcl1.11.0+vs2019+win10
  2. 点云包围盒在碰撞检测时，可以使用包围盒来提前排除大部分不在关注区域内的点云。
  3. 顶点坐标精确描述了点云的位置。
  4. 点云主轴方向可做帮助识别点云的旋转状态，此外，在点云处理中，通常需要将不同视角或不同时间采集的点云数据进行配准和对齐，主轴方向是一种常用的参考依据。

参考

PCL 主成分分析(PCA)在三维点云中的应用
PCA主成分分析方法
特征方向说说主成分分析(PCA)的源头

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