k-d tree与八叉树

1 k-d tree与八叉树

本文并不涉及具体原理的解释，文章着重在k-d树与八叉树在近邻搜索方面的API的使用

1.1 k-d tree

k-d tree算法及原理： https://www.cnblogs.com/flyinggod/p/8727584.html

实现功能

使用k-d tree找到某个具体点的k近邻
在指定半径内搜索其近邻

关键API

//k近邻搜索
int pcl::search::KdTree< PointT, Tree >::nearestKSearch (const PointT &point,                 //搜索点int k,                                 //搜索个数  std::vector<int> &k_indices,      //保存近邻的索引值std::vector<float> &k_distances     //保存近邻的平方距离
)const//半径radius内近邻搜索
int pcl::search::KdTree< PointT, Tree >::radiusSearch (const PointT &point,               //搜索点double radius,                     //搜索半径std::vector<int> &k_indices,        //保存近邻的索引值std::vector<float> &k_sqr_dists,    //保存近邻的平方距离unsigned int max_nn              //默认值0,如果给定一个数值，则将返回近邻的最大值限制在这个数值以下(包括该数值)，如果给0或者高于输入点云中的个数，则返回半径中的所有近邻
)const

完整代码

    #include <pcl/point_cloud.h>#include <pcl/kdtree/kdtree_flann.h>#include <iostream>#include <vector>#include <ctime>intmain(int argc, char** argv){srand(time(NULL));  //初始化随机数种子pcl::PointCloud<pcl::PointXYZ>::Ptr cloud(new pcl::PointCloud<pcl::PointXYZ>);// Generate pointcloud data//随机点云生成cloud->width = 1000;    //点云数量 cloud->height = 1;      //无序点云cloud->points.resize(cloud->width * cloud->height);for (std::size_t i = 0; i < cloud->points.size(); ++i)  //循环填充点云数据{cloud->points[i].x = 1024.0f * rand() / (RAND_MAX + 1.0f);cloud->points[i].y = 1024.0f * rand() / (RAND_MAX + 1.0f);cloud->points[i].z = 1024.0f * rand() / (RAND_MAX + 1.0f);}pcl::KdTreeFLANN<pcl::PointXYZ> kdtree;     //创建KdTreeFLANN对象kdtree.setInputCloud(cloud);                //设置被搜索的点云pcl::PointXYZ searchPoint;                  //定义搜索点searchPoint.x = 1024.0f * rand() / (RAND_MAX + 1.0f);searchPoint.y = 1024.0f * rand() / (RAND_MAX + 1.0f);searchPoint.z = 1024.0f * rand() / (RAND_MAX + 1.0f);// K nearest neighbor search/*--------------k近邻搜索----------------------*///近邻个数int K = 10;//这两个向量用来分别存储近邻的索引值、近邻的中心距std::vector<int> pointIdxNKNSearch(K);std::vector<float> pointNKNSquaredDistance(K);std::cout << "K nearest neighbor search at (" << searchPoint.x<< " " << searchPoint.y<< " " << searchPoint.z<< ") with K=" << K << std::endl;//核心函数nearestKSearch()，第三个参数的类型为pcl::Indices，进一步参看该类型可以发现为vector<int>，这也就是为什么前面pointIdxNKNSearch的类型声明为vector<int>if (kdtree.nearestKSearch(searchPoint, K, pointIdxNKNSearch, pointNKNSquaredDistance) > 0){for (std::size_t i = 0; i < pointIdxNKNSearch.size(); ++i)std::cout << "    " << cloud->points[pointIdxNKNSearch[i]].x<< " " << cloud->points[pointIdxNKNSearch[i]].y<< " " << cloud->points[pointIdxNKNSearch[i]].z<< " (squared distance: " << pointNKNSquaredDistance[i] << ")" << std::endl;}// Neighbors within radius search/*--------------在半径范围内搜索所有近邻点----------------------*///这两个向量用来分别存储近邻的索引值、近邻的平方距离std::vector<int> pointIdxRadiusSearch;std::vector<float> pointRadiusSquaredDistance;//指定随机半径float radius = 256.0f * rand() / (RAND_MAX + 1.0f);std::cout << "Neighbors within radius search at (" << searchPoint.x<< " " << searchPoint.y<< " " << searchPoint.z<< ") with radius=" << radius << std::endl;//radiusSearch最后一个参数，用于限制满足近邻条件后的结果的个数，默认值为0，代表全部输出if (kdtree.radiusSearch(searchPoint, radius, pointIdxRadiusSearch, pointRadiusSquaredDistance, 3) > 0){for (std::size_t i = 0; i < pointIdxRadiusSearch.size(); ++i)std::cout << "    " << cloud->points[pointIdxRadiusSearch[i]].x<< " " << cloud->points[pointIdxRadiusSearch[i]].y<< " " << cloud->points[pointIdxRadiusSearch[i]].z<< " (squared distance: " << pointRadiusSquaredDistance[i] << ")" << std::endl;}return 0;}

运行结果

//k近邻搜索结果
K nearest neighbor search at (443.625 766.75 839.094) with K=10450.813 818.625 869.688 (squared distance: 3678.65)449.688 737.063 784.75 (squared distance: 3871.34)445.344 825.344 864.063 (squared distance: 4059.62)497.906 737.563 874.625 (squared distance: 5060.83)392.219 728.281 870.125 (squared distance: 5085.39)437.094 762.938 766.313 (squared distance: 5354.3)463.188 814.344 780.063 (squared distance: 6132.54)441.531 791.875 745.313 (squared distance: 9430.57)465.75 811.781 754.781 (squared distance: 9625.93)491.125 677.094 821 (squared distance: 10621.9)//指定半径内的搜索结果
Neighbors within radius search at (443.625 766.75 839.094) with radius=130.57450.813 818.625 869.688 (squared distance: 3678.65)449.688 737.063 784.75 (squared distance: 3871.34)445.344 825.344 864.063 (squared distance: 4059.62)497.906 737.563 874.625 (squared distance: 5060.83)392.219 728.281 870.125 (squared distance: 5085.39)437.094 762.938 766.313 (squared distance: 5354.3)463.188 814.344 780.063 (squared distance: 6132.54)441.531 791.875 745.313 (squared distance: 9430.57)465.75 811.781 754.781 (squared distance: 9625.93)491.125 677.094 821 (squared distance: 10621.9)395.406 670.344 847.875 (squared distance: 11696.3)513.594 749.344 930.344 (squared distance: 13525.2)447.656 660.813 898.438 (squared distance: 14760.7)449.969 763.281 961.281 (squared distance: 14982.1)419.344 869.75 776.75 (squared distance: 15085.3)380.563 866.75 886.688 (squared distance: 16242)492.063 684.906 925.594 (squared distance: 16526.8)//结果是由小到大依次排列

对最大的距离进行验证发现

对16526开平方==128 < 130.57 可以判断所得到的结果都是在规定的搜索半径内的

1.2 八叉树

八叉树相关解释见：https://blog.csdn.net/qq_37855507/article/details/90957798

实现功能

学习使用八叉树在点云数据中进行近邻搜索

体素内近邻搜索

K近邻搜索

半径内近邻搜搜

关键API

//[in]表示输入参数， [out]表示输出参数
bool pcl::octree::OctreePointCloudSearch< PointT, LeafContainerT, BranchContainerT >::voxelSearch(const PointT& point,                //[in]搜索点std::vector<int>& point_idx_data     //[out]搜索到的近邻带你索引
) //k近邻搜索
int pcl::search::Octree< PointT, LeafTWrap, BranchTWrap, OctreeT >::nearestKSearch(const PointT& point,           //[in]搜索点int k,                         //[in]近邻点个数std::vector<int>& k_indices,   //[out]搜索到的近邻带你索引std::vector<float>& k_sqr_distances  //[out]搜索到的紧邻点的平方距离
)const //半径搜搜
int pcl::search::Octree< PointT, LeafTWrap, BranchTWrap, OctreeT >::radiusSearch(const PointT& p_q,           //[in]搜索点double radius,                 //[in]搜索半径std::vector<int>& k_indices,    //[out]搜索到的近邻带你索引std::vector<float>& k_sqr_distances,  //[out]搜索到的紧邻点的平方距离unsigned int max_nn = 0        //[in]用来限制找到的结果的最大个数，默认为0，即报错所有结果
)const

完整代码

#include <pcl/point_cloud.h>
#include <pcl/octree/octree_search.h>#include <iostream>
#include <vector>
#include <ctime>int
main(int argc, char** argv)
{srand((unsigned int)time(NULL));pcl::PointCloud<pcl::PointXYZ>::Ptr cloud(new pcl::PointCloud<pcl::PointXYZ>);// Generate pointcloud datacloud->width = 1000;cloud->height = 1;cloud->points.resize(cloud->width * cloud->height);for (std::size_t i = 0; i < cloud->points.size(); ++i){cloud->points[i].x = 1024.0f * rand() / (RAND_MAX + 1.0f);cloud->points[i].y = 1024.0f * rand() / (RAND_MAX + 1.0f);cloud->points[i].z = 1024.0f * rand() / (RAND_MAX + 1.0f);}float resolution = 256.0f;  //八叉树的分辨率参数，用来描述最低一级八叉树的最小体素的尺寸pcl::octree::OctreePointCloudSearch<pcl::PointXYZ> octree(resolution);  //初始化八叉树octree.setInputCloud(cloud);        //设置输入点云octree.addPointsFromInputCloud();   //构建八叉树pcl::PointXYZ searchPoint;searchPoint.x = 1024.0f * rand() / (RAND_MAX + 1.0f);searchPoint.y = 1024.0f * rand() / (RAND_MAX + 1.0f);searchPoint.z = 1024.0f * rand() / (RAND_MAX + 1.0f);// Neighbors within voxel search//体素内近邻搜索std::vector<int> pointIdxVec;       //用于保存体素近邻搜索的结果向量if (octree.voxelSearch(searchPoint, pointIdxVec)){std::cout << "Neighbors within voxel search at (" << searchPoint.x<< " " << searchPoint.y<< " " << searchPoint.z << ")"<< std::endl;for (std::size_t i = 0; i < pointIdxVec.size(); ++i)std::cout << "    " << cloud->points[pointIdxVec[i]].x<< " " << cloud->points[pointIdxVec[i]].y<< " " << cloud->points[pointIdxVec[i]].z << std::endl;}// K nearest neighbor search//K近邻搜索int K = 10;std::vector<int> pointIdxNKNSearch;             //存储k近邻搜索点的索引结果         std::vector<float> pointNKNSquaredDistance;     //存储k近邻搜索的平方距离std::cout << "K nearest neighbor search at (" << searchPoint.x<< " " << searchPoint.y<< " " << searchPoint.z<< ") with K=" << K << std::endl;if (octree.nearestKSearch(searchPoint, K, pointIdxNKNSearch, pointNKNSquaredDistance) > 0){for (std::size_t i = 0; i < pointIdxNKNSearch.size(); ++i)std::cout << "    " << cloud->points[pointIdxNKNSearch[i]].x<< " " << cloud->points[pointIdxNKNSearch[i]].y<< " " << cloud->points[pointIdxNKNSearch[i]].z<< " (squared distance: " << pointNKNSquaredDistance[i] << ")" << std::endl;}// Neighbors within radius search//半径内近邻搜索std::vector<int> pointIdxRadiusSearch;              //存储半径近邻搜索点的索引结果         std::vector<float> pointRadiusSquaredDistance;      //存储半径近邻搜索的平方距离    float radius = 256.0f * rand() / (RAND_MAX + 1.0f);std::cout << "Neighbors within radius search at (" << searchPoint.x<< " " << searchPoint.y<< " " << searchPoint.z<< ") with radius=" << radius << std::endl;if (octree.radiusSearch(searchPoint, radius, pointIdxRadiusSearch, pointRadiusSquaredDistance) > 0){for (std::size_t i = 0; i < pointIdxRadiusSearch.size(); ++i)std::cout << "    " << cloud->points[pointIdxRadiusSearch[i]].x<< " " << cloud->points[pointIdxRadiusSearch[i]].y<< " " << cloud->points[pointIdxRadiusSearch[i]].z<< " (squared distance: " << pointRadiusSquaredDistance[i] << ")" << std::endl;}
}

运行结果

在指定的半径内没有搜索到满足条件的点

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PCL点云库调库学习系列——k-d tree与八叉树

k-d tree与八叉树

1 k-d tree与八叉树

1.1 k-d tree

实现功能

关键API

完整代码

运行结果

1.2 八叉树

实现功能

关键API

完整代码

运行结果

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