点云分割-kmeans-原理+代码

kmeans做为无监督学习的一种聚类方法，原理非常简单，本质上是根据重心（密度中心）不断进行迭代的一个分割方法。

其主要步骤为：
（1）初始化k个中心点
（2）计算所有点到中心点的欧氏距离，形成集合dist
（3）找到dist最小值所在的索引i，将点加入第i个簇
（4）重新计算簇的所有中心，重复2-3直到中心点不变或者达到最大迭代次数。

具体的数学原理可以参考知乎

show the codes

语言：C++
依赖库：PCL1.9.1

//Kmeans.h
#pragma once

#include 
#include 
#include
#include
#include 
class KMeans
{
private:
	unsigned int max_iteration_;
	const unsigned int cluster_num_;//k
	double pointsDist(const pcl::PointXYZ& p1, const pcl::PointXYZ& p2);

public:

	pcl::PointCloud<pcl::PointXYZ>::Ptr centre_points_;
	//KMeans() = default;
	KMeans(unsigned int k, unsigned int max_iteration);
	void kMeans(const pcl::PointCloud<pcl::PointXYZ>::Ptr& cloud, std::vector<pcl::PointCloud<pcl::PointXYZ>> &cluster_cloud1);
	
	~KMeans(){}
};

//Kmeans.cpp
#include "KMeans.h"

double KMeans::pointsDist(const pcl::PointXYZ& p1, const pcl::PointXYZ& p2)
{
	//std::cerr << p1.x<
	
		return std::sqrt((p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y) + (p1.z - p2.z) * (p1.z - p2.z));
	
}

KMeans::KMeans(unsigned int k, unsigned int max_iteration):cluster_num_(k),max_iteration_(max_iteration),centre_points_(new pcl::PointCloud<pcl::PointXYZ>)
{
}

void KMeans::kMeans(const pcl::PointCloud<pcl::PointXYZ>::Ptr& cloud, std::vector<pcl::PointCloud<pcl::PointXYZ>> &cluster_cloud1)
{
	
	if (!cloud->empty()&&!centre_points_->empty())
	{
		unsigned int iterations = 0;
		double sum_diff = 0.2;
		std::vector<pcl::PointCloud<pcl::PointXYZ>>cluster_cloud;
		while (!(iterations>=max_iteration_||sum_diff<=0.05))//如果大于迭代次数或者两次重心之差小于0.05就停止
		//while ((iterations<= max_iteration_ || sum_diff >= 0.1))
	
		{
			sum_diff = 0;
			std::vector<int> points_processed(cloud->points.size(), 0);
			cluster_cloud.clear();
			cluster_cloud.resize(cluster_num_);
			for (size_t i = 0; i < cloud->points.size(); ++i)

			{
				if (!points_processed[i])
				{
					std::vector<double>dists(0, 0);
					for (size_t j = 0; j < cluster_num_; ++j)
					{						
						dists.emplace_back(pointsDist(cloud->points[i], centre_points_->points[j]));					
					}
					std::vector<double>::const_iterator min_dist = std::min_element(dists.cbegin(), dists.cend());
					unsigned int it = std::distance(dists.cbegin(), min_dist);//获取最小值所在的序号或者位置（从0开始）
					//unsigned int it=std::distance(std::cbegin(dists), min_dist);
					cluster_cloud[it].points.push_back(cloud->points[i]);//放进最小距离所在的簇
					points_processed[i] = 1;
				}

				else
					continue;

			}
			//重新计算簇重心
			pcl::PointCloud<pcl::PointXYZ> new_centre;
			for (size_t k = 0; k < cluster_num_; ++k)
			{
				Eigen::Vector4f centroid;
				pcl::PointXYZ centre;
				pcl::compute3DCentroid(cluster_cloud[k], centroid);
				centre.x = centroid[0];
				centre.y = centroid[1];
				centre.z = centroid[2];
				//centre_points_->clear();
				//centre_points_->points.push_back(centre);
				new_centre.points.push_back(centre);

			}
			//计算重心变化量
			for (size_t s = 0; s < cluster_num_; ++s)
			{
				std::cerr << " centre" << centre_points_->points[s] << std::endl;

				std::cerr << "new centre" << new_centre.points[s] << std::endl;
				sum_diff += pointsDist(new_centre.points[s], centre_points_->points[s]);

			}
			std::cerr << sum_diff << std::endl;
			centre_points_->points.clear();
			*centre_points_ = new_centre;
			
			++iterations;
		}
		std::cerr << cluster_cloud[0].size() << std::endl;
		std::cerr << cluster_cloud[1].size() << std::endl;

		cluster_cloud1.assign(cluster_cloud.cbegin(),cluster_cloud.cend());//复制点云向量

	}

}

//main.cpp
#include"KMeans.h"
int main()
{
    KMeans test(2, 10);
   
   
    //test.centre_points_->points.push_back(pcl::PointXYZ(16.3,-6.35,11.4));
   // test.centre_points_->points.push_back(pcl::PointXYZ(15.6, -5.13, 7.49));
    //设置初始值
    test.centre_points_->points.push_back(pcl::PointXYZ(15.88, -5.5, 11.12));
    test.centre_points_->points.push_back(pcl::PointXYZ(15.69, -4.98, 11.05));

    pcl::PointCloud<pcl::PointXYZ>::Ptr cloud(new pcl::PointCloud<pcl::PointXYZ>);
    std::vector<pcl::PointCloud<pcl::PointXYZ>> output_cloud;
    pcl::io::loadPCDFile("2.pcd",*cloud);
    std::cerr << "raw cloud size" << cloud->points.size() << std::endl;
    test.kMeans(cloud, output_cloud);

    for (int i = 0; i < 2; ++i)
    {
        //pcl::PointCloud cloud1;
        //cloud1 = output_cloud[i];
        std::cerr <<"output_cloud[i].points.size()"<< output_cloud[i].points.size()<<std::endl;
        output_cloud[i].width = output_cloud[i].points.size();
        output_cloud[i].height = 1;
        output_cloud[i].resize(output_cloud[i].width * output_cloud[i].height);
        pcl::io::savePCDFile( "kmeans"+std::to_string(i) + ".pcd", output_cloud[i]);
        //pcl::io::savePCDFile()
    }
    std::cout << "Hello World!\n";
}

实验结果

总结

1.必须已知聚类对象个数，并有合适的初始值
2.对于杆状点云效果不好，面状可以还好
3.kmean本质上还是依赖相似性，和所有依赖欧式距离的分割方法一样（欧式聚类，DBSCAN），点云的距离分布对最终的分割至关重要，当然可以换成别的距离或者度量方式可能效果会好点。