基于Kruskal算法的点云最小生成树提取（附代码）

{"title": "#include \n#include <pcl/point_types.h>\n#include <pcl/io/ply_io.h>\n#include <pcl/visualization/pcl_visualizer.h>\n#include <pcl/common/centroid.h>\n#include <pcl/features/normal_3d.h>\n#include <pcl/visualization/cloud_viewer.h>\n#include <pcl/segmentation/extract_clusters.h>\n#include \n#include <unordered_map>\n"vtkAutoInit.h"

VTK_MODULE_INIT(vtkRenderingOpenGL); // VTK was built with vtkRenderingOpenGL2

using namespace pcl; typedef pcl::PointXYZ PointT; typedef pcl::PointCloud PointCloudT;

// Structure to represent an edge struct Edge { int src, tgt; float weight; };

// Structure to represent a subset for union-find struct Subset { int parent, rank; };

// Class to represent a connected, undirected and weighted graph class Graph { public: int V, E; std::vector edges;

Graph(int v, int e)
{
	V = v;
	E = e;
}

// Add an edge to the graph
void addEdge(int src, int tgt, float weight)
{
	Edge edge;
	edge.src = src;
	edge.tgt = tgt;
	edge.weight = weight;
	edges.push_back(edge);
}

// Find set of an element i
int find(Subset subsets[], int i)
{
	if (subsets[i].parent != i)
		subsets[i].parent = find(subsets, subsets[i].parent);
	return subsets[i].parent;
}

// Union of two sets x and y
void Union(Subset subsets[], int x, int y)
{
	int xroot = find(subsets, x);
	int yroot = find(subsets, y);
	if (subsets[xroot].rank < subsets[yroot].rank)
		subsets[xroot].parent = yroot;
	else if (subsets[xroot].rank > subsets[yroot].rank)
		subsets[yroot].parent = xroot;
	else {
		subsets[yroot].parent = xroot;
		subsets[xroot].rank++;
	}
}

// Kruskal's algorithm to find MST
void KruskalMST(PointCloudT::Ptr cloud, std::vector<Edge>& result)
{
	// Sort all the edges in non-decreasing order of their weight
	std::sort(edges.begin(), edges.end(), [](const Edge& a, const Edge& b)
	{
		return a.weight < b.weight;
	});

	// Allocate memory for creating V subsets
	Subset* subsets = new Subset[V];
	for (int v = 0; v < V; ++v)
	{
		subsets[v].parent = v;
		subsets[v].rank = 0;
	}

	int i = 0;  // Index used to pick the next smallest edge
	int e = 0;  // Index used to pick the next edge to include in MST

	// Number of edges to be taken is equal to V-1
	while (e < V - 1 && i < E)
	{
		Edge next_edge = edges[i++];

		int x = find(subsets, next_edge.src);
		int y = find(subsets, next_edge.tgt);

		// If including this edge doesn't cause a cycle, include it in result and increment the index of result for next edge
		if (x != y && next_edge.weight < 0.045 && next_edge.weight > 0.044)
		{
			result.push_back(next_edge);
			Union(subsets, x, y);
			++e;
		}
	}

	// Visualize the resulting minimum spanning tree
	pcl::visualization::PCLVisualizer viewer("Minimum Spanning Tree");
	viewer.setBackgroundColor(0, 0, 0);

	// Add the original point cloud to the viewer
	pcl::visualization::PointCloudColorHandlerCustom<pcl::PointXYZ> single_color(cloud, 255, 255, 255);
	viewer.addPointCloud<pcl::PointXYZ>(cloud, single_color, "original_cloud");
	// 将最小生成树的边添加到视图器中
	for (const auto& edge : result)
	{
		const auto& src_point = cloud->points[edge.src];
		const auto& tgt_point = cloud->points[edge.tgt];
		std::stringstream ss;
		ss << "edge_" << edge.src << "_" << edge.tgt;
		viewer.addLine<pcl::PointXYZ>(src_point, tgt_point, ss.str());
	}

	// Connect two disconnected edges
	pcl::PointXYZ point1 = cloud->points[14];
	pcl::PointXYZ point2 = cloud->points[34];
	pcl::PointXYZ point3 = cloud->points[68];
	pcl::PointXYZ point4 = cloud->points[62];
	 viewer.addLine<pcl::PointXYZ, pcl::PointXYZ>(point1, point2, 0, 255, 0, "line1");
	viewer.addLine<pcl::PointXYZ, pcl::PointXYZ>(point3, point4, 0, 255, 0, "line2");

	// Count the number of points in the minimum spanning tree
	int numPoints = 0;
	for (const auto& edge : result)
	{
		const auto& src_point = cloud->points[edge.src];
		const auto& tgt_point = cloud->points[edge.tgt];
		numPoints += 2;
	}

	std::cout << "Number of points in the minimum spanning tree: " << numPoints << std::endl;

	while (!viewer.wasStopped())
	{
		viewer.spinOnce();
	}

}

};

double euclideanDistance(PointXYZ p1, PointXYZ p2) { double dx = p2.x - p1.x; double dy = p2.y - p1.y; double dz = p2.z - p1.z; return std::sqrt(dx * dx + dy * dy + dz * dz); }

int main() { // Load the input point cloud from PLY file pcl::PointCloudpcl::PointXYZ::Ptr cloud(new pcl::PointCloudpcl::PointXYZ); pcl::io::loadPLYFilepcl::PointXYZ("D:\DIANYUNWENJIANJIA\newOUSHIJULEI_ply.ply", *cloud);

// Compute the centroid of the point cloud
Eigen::Vector4f centroid;
pcl::compute3DCentroid(*cloud, centroid);

// Compute the normals of the point cloud
pcl::NormalEstimation<pcl::PointXYZ, pcl::Normal> ne;
pcl::PointCloud<pcl::Normal>::Ptr cloud_normals(new pcl::PointCloud<pcl::Normal>);
pcl::search::KdTree<pcl::PointXYZ>::Ptr tree(new pcl::search::KdTree<pcl::PointXYZ>);
ne.setInputCloud(cloud);
ne.setSearchMethod(tree);
ne.setKSearch(40);
ne.compute(*cloud_normals);

// Create a graph with V vertices and E edges
int V = cloud->size();
int E = V * (V - 1) / 2;
Graph graph(V, E);

// Calculate the edge weights based on Euclidean distance between points
for (int i = 0; i < V - 1; ++i)
{
	const auto& src_point = cloud->points[i];
	for (int j = i + 1; j < V; ++j)
	{
		const auto& tgt_point = cloud->points[j];
		float distance = euclideanDistance(src_point, tgt_point);
		graph.addEdge(i, j, distance);
	}
}

// Perform Kruskal's algorithm to find the minimum spanning tree
std::vector<Edge> result;
graph.KruskalMST(cloud, result);

// Create a new point cloud object to save the result of the minimum spanning tree
pcl::PointCloud<pcl::PointXYZ>::Ptr new_cloud(new pcl::PointCloud<pcl::PointXYZ>);
new_cloud->width = cloud->width;
new_cloud->height = cloud->height;
new_cloud->points.resize(cloud->points.size());

// Add the vertices of the minimum spanning tree to the new point cloud object
for (const auto& edge : result)
{
	const auto& src_point = cloud->points[edge.src];
	const auto& tgt_point = cloud->points[edge.tgt];
	new_cloud->points[edge.src] = src_point;
	new_cloud->points[edge.tgt] = tgt_point;
}

// Save the new point cloud as a PLY file
pcl::io::savePLYFile("D:\\DIANYUNWENJIANJIA\\newKRUSKAL_ply.ply", *new_cloud, true);
return 0;