python点云配准算法代码

以下是使用CPD算法实现点云配准的Python代码示例：

import numpy as np
from scipy.spatial import KDTree
from scipy.linalg import orthogonal_procrustes

def cpd_registration(source_points, target_points, max_iterations=50, tolerance=1e-5):
    # 初始化变量
    num_points = source_points.shape[0]
    dim = source_points.shape[1]
    R = np.eye(dim)
    t = np.zeros((dim, 1))
    sigma2 = 1

    # 构建KD树
    target_tree = KDTree(target_points)

    for iteration in range(max_iterations):
        # 计算对应点对
        correspondences = find_correspondences(source_points, target_tree)

        # 计算权重矩阵
        W = compute_weight_matrix(correspondences, sigma2)

        # 计算对齐后的源点云
        aligned_points = align_points(source_points, W, correspondences)

        # 计算旋转矩阵和平移向量
        R_new, t_new = estimate_transformation(aligned_points, target_points)

        # 更新旋转矩阵和平移向量
        source_points = np.dot(source_points, R_new.T) + t_new.T

        # 计算误差
        error = np.linalg.norm(R_new - R) + np.linalg.norm(t_new - t)

        # 更新旋转矩阵、平移向量和误差
        R = R_new
        t = t_new

        # 判断是否收敛
        if error < tolerance:
            break

    return R, t

def find_correspondences(source_points, target_tree):
    _, indices = target_tree.query(source_points)
    return indices

def compute_weight_matrix(correspondences, sigma2):
    num_points = correspondences.shape[0]
    W = np.zeros((num_points, num_points))

    for i in range(num_points):
        for j in range(num_points):
            diff = correspondences[i] - correspondences[j]
            W[i, j] = np.exp(-np.linalg.norm(diff) / (2 * sigma2))

    return W

def align_points(source_points, W, correspondences):
    num_points = source_points.shape[0]
    dim = source_points.shape[1]
    aligned_points = np.zeros((num_points, dim))

    for i in range(num_points):
        aligned_points[i] = np.dot(W[i], source_points[correspondences[i]]) / np.sum(W[i])

    return aligned_points

def estimate_transformation(source_points, target_points):
    R, _ = orthogonal_procrustes(source_points, target_points)
    t = np.mean(target_points, axis=0) - np.mean(source_points, axis=0)
    return R, t

# 示例用法
source_points = np.array([[1, 2], [3, 4], [5,6]])
target_points = np.array([[2, 3], [4, 5], [6, 7]])

R, t = cpd_registration(source_points, target_points)
print("旋转矩阵：")
print(R)
print("平移向量：")
print(t)