三维点云学习（2）上

二叉树实现K-NN Radius-NN Search

个人心得

二叉树的搜寻方法

正如老师课堂所说，实现二叉树的搜寻有两种方法，一种是递归，一种是循环判断，本质区别并不大

#递归搜寻
def searchrecursively(root,key):               #1NN 搜索 ，递归法if root is None or root.key == key:return rootif key < root.key:return searchrecursively(root.left,key)elif key > root.key:return searchrecursively(root.right,key)#循环判断搜寻
def searchiterative(root, key):                #1NN 搜索 ，循环判断currentnode = root while currentnode is not None: if currentnode.key == key: return currentnode elif key < currentnode.key: currentnode = currentnode.left elif key > currentnode.key: currentnode = currentnode.right return currentnode

二叉树的优势，减少搜寻的复杂度

实际运行结果

Search in 100 points, takes 7 comparison only #使用二叉树仅仅比较7次
Complexity is around O(log2(n)), n is number of
database points, if tree is balanced #假设二叉树是平衡的，复杂度为log2(n)，n为二叉树的深度
Worst O(N) #最坏结果，比较100次

kNN Search:
index - distance
24 - 0.00
85 - 1.00
42 - 1.00
12 - 2.00
86 - 2.00
In total 8 comparison operations.
Radius NN Search:
index - distance
24 - 0.00
85 - 1.00
42 - 1.00
12 - 2.00
86 - 2.00
In total 5 neighbors within 2.000000.
There are 8 comparison operations.

二叉树的三种应用

#二叉树的三种应用
def inorder(root):# Inorder (Left, Root, Right)if root is not None:inorder(root.left)print(root)inorder(root.right)def preorder(root):# Preorder (Root, Left, Right)if root is not None:print(root)preorder(root.left)preorder(root.right)def postorder(root):# Postorder (Left, Right, Root)if root is not None:postorder(root.left)postorder(root.right)print(root)

1NN搜寻过程

KNN search

worst Distance for KNN

具体思路：
1.先创建一个能容纳需要的临近点结果的list
2.将暂时的KNN result 进行sorted
3.最大worstdist 的点在KNN result list的最后(随时被替代)
4.根据worstlist的不断更新，动态修改KNN result里的结果

Radius NN search

方法思路和KNN算法差不多，区别在于
Worst distance is fixed.(Radius NN search预先设定检测radius，在radius里进行点的筛选)

KNN search VS Radius NN search

完整代码

lidar_KnnRnnMain_2.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Feb 20 10:23:37 2021@author: renzhanqi
"""import random
import math
import  numpy as npfrom lidar_KnnRnnClass_2 import  KNNResultSet,RadiusNNResultSetclass Node:                          #节点，每一个数都是一个分支节点def __init__(self,key,value=-1):self.left = Noneself.right = Noneself.key =keyself.value = value      #value可以用作储存其他数值，譬如点原来的序号def __str__(self):return "key: %s, value: %s" % (str(self.key), str(self.value))def insert(root,key,value=-1):    #构建二叉树if root is None:root = Node(key,value)      #赋初值else:if key < root.key:root.left = insert(root.left,key,value)   #小数放左边elif key > root.key:root.right = insert(root.right,key,value)  #大数放右边else:   # don't insert if key already exist in the treepassreturn  root#二叉树的三种应用
def inorder(root):# Inorder (Left, Root, Right)if root is not None:inorder(root.left)print(root)inorder(root.right)def preorder(root):# Preorder (Root, Left, Right)if root is not None:print(root)preorder(root.left)preorder(root.right)def postorder(root):# Postorder (Left, Right, Root)if root is not None:postorder(root.left)postorder(root.right)print(root)def knn_search(root:Node,result_set:KNNResultSet,key):if root is None:return False# compare the root itselfresult_set.add_point(math.fabs(root.key - key),root.value)       #计算worst_dist ,并把当前root.value(index二叉树)里的值加入到resut_set 中if result_set.worstDist() == 0:return Trueif root.key >= key:# iterate left branch firstif knn_search(root.left, result_set, key):return Trueelif math.fabs(root.key-key) < result_set.worstDist():return knn_search(root.right, result_set, key)return Falseelse:# iterate right branch firstif knn_search(root.right, result_set, key):return Trueelif math.fabs(root.key-key) < result_set.worstDist():return knn_search(root.left, result_set, key)return Falsedef radius_search(root: Node, result_set: RadiusNNResultSet, key):if root is None:return False# compare the root itselfresult_set.add_point(math.fabs(root.key - key), root.value)if root.key >= key:# iterate left branch firstif radius_search(root.left, result_set, key):return Trueelif math.fabs(root.key-key) < result_set.worstDist():return radius_search(root.right, result_set, key)return Falseelse:# iterate right branch firstif radius_search(root.right, result_set, key):return Trueelif math.fabs(root.key-key) < result_set.worstDist():return radius_search(root.left, result_set, key)return Falsedef search_recursively(root,key):               #1NN 搜索 ，递归法if root is None or root.key == key:return rootif key < root.key:return search_recursively(root.left,key)elif key > root.key:return search_recursively(root.right,key)def search_iterative(root, key):                #1NN 搜索 ，循环判断current_node = rootwhile current_node is not None:if current_node.key == key:return current_nodeelif key < current_node.key:current_node = current_node.leftelif key > current_node.key:current_node = current_node.rightreturn current_nodedef main():# Data generationdb_size = 100k = 5    #搜寻5个点radius = 2.0data = np.random.permutation(db_size).tolist()   #random.permutation 随机排列一个数组root =Nonefor i,point in enumerate(data):root = insert(root,point,i)query_key = 6result_set = KNNResultSet(capacity=k)knn_search(root, result_set, query_key)print('kNN Search:')print('index - distance')print(result_set)result_set = RadiusNNResultSet(radius=radius)radius_search(root, result_set, query_key)print('Radius NN Search:')print('index - distance')print(result_set)# print("inorder")# inorder(root)# print("preorder")# preorder(root)# print("postorder")# postorder(root)# node = search_recursive(root, 2)# print(node)## node = search_iterative(root, 2)# print(node)if __name__ == '__main__':main()

lidar_KnnRnnClass_2.py(KNN Radius NN search config fcn)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Feb 20 10:22:24 2021@author: renzhanqi
"""import copyclass DistIndex:def __init__(self, distance, index):self.distance = distanceself.index = indexdef __lt__(self, other):return self.distance < other.distanceclass KNNResultSet:def __init__(self, capacity):self.capacity = capacityself.count = 0self.worst_dist = 1e10self.dist_index_list = []for i in range(capacity):self.dist_index_list.append(DistIndex(self.worst_dist, 0))self.comparison_counter = 0def size(self):return self.countdef full(self):return self.count == self.capacitydef worstDist(self):return self.worst_distdef add_point(self, dist, index):self.comparison_counter += 1if dist > self.worst_dist:returnif self.count < self.capacity:self.count += 1i = self.count - 1while i > 0:if self.dist_index_list[i - 1].distance > dist:self.dist_index_list[i] = copy.deepcopy(self.dist_index_list[i - 1])i -= 1else:breakself.dist_index_list[i].distance = distself.dist_index_list[i].index = indexself.worst_dist = self.dist_index_list[self.capacity - 1].distancedef __str__(self):output = ''for i, dist_index in enumerate(self.dist_index_list):output += '%d - %.2f\n' % (dist_index.index, dist_index.distance)output += 'In total %d comparison operations.' % self.comparison_counterreturn outputclass RadiusNNResultSet:def __init__(self, radius):self.radius = radiusself.count = 0self.worst_dist = radiusself.dist_index_list = []self.comparison_counter = 0def size(self):return self.countdef worstDist(self):return self.radiusdef add_point(self, dist, index):self.comparison_counter += 1if dist > self.radius:returnself.count += 1self.dist_index_list.append(DistIndex(dist, index))def __str__(self):self.dist_index_list.sort()output = ''for i, dist_index in enumerate(self.dist_index_list):output += '%d - %.2f\n' % (dist_index.index, dist_index.distance)output += 'In total %d neighbors within %f.\nThere are %d comparison operations.' \% (self.count, self.radius, self.comparison_counter)return output

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三维点云学习（2）上- 二叉树实现K-NN Radius-NN Search