三维点云学习（2）上

二叉树实现K-NN Radius-NN Search

代码来自 黎老师github

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

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worst_dist 的点在KNN result list的最后(随时被替代)
4.根据worst_list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

bst.py

import random
import math
import  numpy as np

from result_set import  KNNResultSet,RadiusNNResultSet

class Node:                          #节点，每一个数都是一个分支节点
    def __init__(self,key,value=-1):
        self.left = None
        self.right = None
        self.key =key
        self.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 tree
            pass
    return  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 itself
    result_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 True

    if root.key >= key:
        # iterate left branch first
        if knn_search(root.left, result_set, key):
            return True
        elif math.fabs(root.key-key) < result_set.worstDist():
            return knn_search(root.right, result_set, key)
        return False
    else:
        # iterate right branch first
        if knn_search(root.right, result_set, key):
            return True
        elif math.fabs(root.key-key) < result_set.worstDist():
            return knn_search(root.left, result_set, key)
        return False

def radius_search(root: Node, result_set: RadiusNNResultSet, key):
    if root is None:
        return False

    # compare the root itself
    result_set.add_point(math.fabs(root.key - key), root.value)

    if root.key >= key:
        # iterate left branch first
        if radius_search(root.left, result_set, key):
            return True
        elif math.fabs(root.key-key) < result_set.worstDist():
            return radius_search(root.right, result_set, key)
        return False
    else:
        # iterate right branch first
        if radius_search(root.right, result_set, key):
            return True
        elif math.fabs(root.key-key) < result_set.worstDist():
            return radius_search(root.left, result_set, key)
        return False





def search_recursively(root,key):               #1NN 搜索 ，递归法
    if root is None or root.key == key:
        return root
    if 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 = root
    while current_node is not None:
        if current_node.key == key:
            return current_node
        elif key < current_node.key:
            current_node = current_node.left
        elif key > current_node.key:
            current_node = current_node.right
    return current_node



def main():
    # Data generation
    db_size = 100
    k = 5    #搜寻5个点
    radius = 2.0
    data = np.random.permutation(db_size).tolist()   #random.permutation 随机排列一个数组

    root =None
    for i,point in enumerate(data):
        root = insert(root,point,i)

    query_key = 6
    result_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()

result_set.py (KNN Radius NN search config fcn)

import copy


class DistIndex:
    def __init__(self, distance, index):
        self.distance = distance
        self.index = index

    def __lt__(self, other):
        return self.distance < other.distance


class KNNResultSet:
    def __init__(self, capacity):
        self.capacity = capacity
        self.count = 0
        self.worst_dist = 1e10
        self.dist_index_list = []
        for i in range(capacity):
            self.dist_index_list.append(DistIndex(self.worst_dist, 0))

        self.comparison_counter = 0

    def size(self):
        return self.count

    def full(self):
        return self.count == self.capacity

    def worstDist(self):
        return self.worst_dist

    def add_point(self, dist, index):
        self.comparison_counter += 1
        if dist > self.worst_dist:
            return

        if self.count < self.capacity:
            self.count += 1

        i = self.count - 1
        while 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 -= 1
            else:
                break

        self.dist_index_list[i].distance = dist
        self.dist_index_list[i].index = index
        self.worst_dist = self.dist_index_list[self.capacity - 1].distance

    def __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_counter
        return output


class RadiusNNResultSet:
    def __init__(self, radius):
        self.radius = radius
        self.count = 0
        self.worst_dist = radius
        self.dist_index_list = []

        self.comparison_counter = 0

    def size(self):
        return self.count

    def worstDist(self):
        return self.radius

    def add_point(self, dist, index):
        self.comparison_counter += 1
        if dist > self.radius:
            return

        self.count += 1
        self.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

本文地址：https://blog.csdn.net/weixin_41281151/article/details/107190715

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