在本教程中，我們將詳細介紹如何使用KdTree來查詢特定點或位置的K個最近鄰居，然後我們將繼續介紹如何在使用者指定的半徑範圍內找到所有鄰居（在本例中為隨機） 。

#理論引入

kd樹或k維樹是電腦科學中用於在具有k維的空間中組織若干點的資料結構。這是一個二叉搜尋樹，其他約束條件是強加給它的。Kd樹對於範圍和最近的鄰居搜尋非常有用。就我們的目的而言，我們通常只會在三維空間中處理點雲，所以我們所有的kd樹都是三維的。kd樹的每個級別都使用與相應軸垂直的超平面沿特定維度分割所有的孩子。在樹的根部，所有的孩子都將根據第一維進行分割（即，如果第一維座標小於根，它將在左子樹中，並且如果它大於根，則顯然將在正確的子樹）。樹下的每一層在下一個維度上分開，一旦所有其他維度都用盡，則返回到第一維。構建kd樹的最有效的方法是使用像Quick Sort一樣使用的分割槽方法將中間點放在根上，並將所有具有較小一維值的東西放在左邊，並且放大到右邊。然後，在左側和右側的子樹上重複此過程，直到要分割槽的最後一棵樹僅由一個元素組成。

來自Wikipedia：

一個二維kd樹的例子
這是一個二維kd樹的例子

這是最近鄰居搜尋工作的一個小時的示範。

#程式碼
用你最喜歡的編輯器建立一個名為kdtree_search.cpp的檔案，並在裡面放置以下內容：

#include <pcl/point_cloud.h>
#include <pcl/kdtree/kdtree_flann.h>

#include <iostream>
#include <vector>
#include <ctime>

int
main (int argc, char** argv)
{
  srand (time (NULL));

  pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);

  // Generate pointcloud data
  cloud->width = 1000;
  cloud->height = 1;
  cloud->points.resize (cloud->width * cloud->height);

  for (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);
  }

  pcl::KdTreeFLANN<pcl::PointXYZ> kdtree;

  kdtree.setInputCloud (cloud);

  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);

  // K nearest neighbor search

  int K = 10;

  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;

  if ( kdtree.nearestKSearch (searchPoint, K, pointIdxNKNSearch, pointNKNSquaredDistance) > 0 )
  {
    for (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

  std::vector<int> pointIdxRadiusSearch;
  std::vector<float> pointRadiusSquaredDistance;

  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 ( kdtree.radiusSearch (searchPoint, radius, pointIdxRadiusSearch, pointRadiusSquaredDistance) > 0 )
  {
    for (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;
}
 

#說明
下面的程式碼首先將rand()與系統時間聯絡起來，然後用隨機資料建立並填充PointCloud。

  srand (time (NULL));

  pcl::PointCloud<pcl::PointXYZ>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZ>);

  // Generate pointcloud data
  cloud->width = 1000;
  cloud->height = 1;
  cloud->points.resize (cloud->width * cloud->height);

  for (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);
  }
 

下一個程式碼建立我們的kdtree物件，並將我們隨機建立的雲作為輸入。然後我們建立一個分配隨機座標的“searchPoint”。

  pcl::KdTreeFLANN<pcl::PointXYZ> kdtree;

  kdtree.setInputCloud (cloud);

  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);

現在我們建立一個整數（並設定它等於10）和兩個向量來儲存我們搜尋到的最近鄰居。

  // K nearest neighbor search

  int K = 10;

  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;

假設我們的KdTree返回多於0個最接近的鄰居，它將把所有10個最近鄰居的位置列印到我們的隨機“searchPoint”中，這個“searchPoint”被儲存在我們以前建立的向量中。

  if ( kdtree.nearestKSearch (searchPoint, K, pointIdxNKNSearch, pointNKNSquaredDistance) > 0 )
  {
    for (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;
  }

現在我們的程式碼演示了在某個（隨機生成的）半徑內找到給定的“searchPoint”的所有鄰居。它再次建立2個向量來儲存關於我們的鄰居的資訊。

  // Neighbors within radius search

  std::vector<int> pointIdxRadiusSearch;
  std::vector<float> pointRadiusSquaredDistance;

  float radius = 256.0f * rand () / (RAND_MAX + 1.0f);

再次，像以前一樣，如果我們的KdTree在指定的半徑範圍內返回多於0個鄰居，它將打印出已儲存在我們向量中的這些點的座標。

  if ( kdtree.radiusSearch (searchPoint, radius, pointIdxRadiusSearch, pointRadiusSquaredDistance) > 0 )
  {
    for (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;
  }

#編譯和執行程式
將下面的行新增到您的CMakeLists.txt檔案中：

cmake_minimum_required(VERSION 2.8 FATAL_ERROR)

project(kdtree_search)

find_package(PCL 1.2 REQUIRED)

include_directories(${PCL_INCLUDE_DIRS})
link_directories(${PCL_LIBRARY_DIRS})
add_definitions(${PCL_DEFINITIONS})

add_executable (kdtree_search kdtree_search.cpp)
target_link_libraries (kdtree_search ${PCL_LIBRARIES})

製作好可執行檔案之後，就可以執行它了。簡單地做：

./kdtree_search

一旦你執行它，你應該看到類似的東西：

K nearest neighbor search at (455.807 417.256 406.502) with K=10
  494.728 371.875 351.687 (squared distance: 6578.99)
  506.066 420.079 478.278 (squared distance: 7685.67)
  368.546 427.623 416.388 (squared distance: 7819.75)
  474.832 383.041 323.293 (squared distance: 8456.34)
  470.992 334.084 468.459 (squared distance: 10986.9)
  560.884 417.637 364.518 (squared distance: 12803.8)
  466.703 475.716 306.269 (squared distance: 13582.9)
  456.907 336.035 304.529 (squared distance: 16996.7)
  452.288 387.943 279.481 (squared distance: 17005.9)
  476.642 410.422 268.057 (squared distance: 19647.9)
Neighbors within radius search at (455.807 417.256 406.502) with radius=225.932
  494.728 371.875 351.687 (squared distance: 6578.99)
  506.066 420.079 478.278 (squared distance: 7685.67)
  368.546 427.623 416.388 (squared distance: 7819.75)
  474.832 383.041 323.293 (squared distance: 8456.34)
  470.992 334.084 468.459 (squared distance: 10986.9)
  560.884 417.637 364.518 (squared distance: 12803.8)
  466.703 475.716 306.269 (squared distance: 13582.9)
  456.907 336.035 304.529 (squared distance: 16996.7)
  452.288 387.943 279.481 (squared distance: 17005.9)
  476.642 410.422 268.057 (squared distance: 19647.9)
  499.429 541.532 351.35 (squared distance: 20389)
  574.418 452.961 334.7 (squared distance: 20498.9)
  336.785 391.057 488.71 (squared distance: 21611)
  319.765 406.187 350.955 (squared distance: 21715.6)
  528.89 289.583 378.979 (squared distance: 22399.1)
  504.509 459.609 541.732 (squared distance: 22452.8)
  539.854 349.333 300.395 (squared distance: 22936.3)
  548.51 458.035 292.812 (squared distance: 23182.1)
  546.284 426.67 535.989 (squared distance: 25041.6)
  577.058 390.276 508.597 (squared distance: 25853.1)
  543.16 458.727 276.859 (squared distance: 26157.5)
  613.997 387.397 443.207 (squared distance: 27262.7)
  608.235 467.363 327.264 (squared distance: 32023.6)
  506.842 591.736 391.923 (squared distance: 33260.3)
  529.842 475.715 241.532 (squared distance: 36113.7)
  485.822 322.623 244.347 (squared distance: 36150.5)
  362.036 318.014 269.201 (squared distance: 37493.6)
  493.806 600.083 462.742 (squared distance: 38032.3)
  392.315 368.085 585.37 (squared distance: 38442.9)
  303.826 428.659 533.642 (squared distance: 39392.8)
  616.492 424.551 289.524 (squared distance: 39556.8)
  320.563 333.216 278.242 (squared distance: 41804.5)
  646.599 502.256 424.46 (squared distance: 43948.8)
  556.202 325.013 568.252 (squared distance: 44751)
  291.27 497.352 515.938 (squared distance: 45463.9)
  286.483 322.401 495.377 (squared distance: 45567.2)
  367.288 550.421 550.551 (squared distance: 46318.6)
  595.122 582.77 394.894 (squared distance: 46938.1)
  256.784 499.401 379.931 (squared distance: 47064.1)
  430.782 230.854 293.829 (squared distance: 48067.2)
  261.051 486.593 329.854 (squared distance: 48612.7)
  602.061 327.892 545.269 (squared distance: 48632.4)
  347.074 610.994 395.622 (squared distance: 49475.6)
  482.876 284.894 583.888 (squared distance: 49718.6)
  356.962 247.285 514.959 (squared distance: 50423.7)
  282.065 509.488 516.216 (squared distance: 50730.4)

How to use a KdTree to search