用粒子群优化做相机标定的python代码

下面是使用粒子群优化来进行相机标定的 Python 代码示例：

import numpy as np
from scipy.optimize import minimize

def cost_function(params, points_2d, points_3d):
    fx, fy, cx, cy, k1, k2, p1, p2, k3 = params

    # 将参数转换为内参矩阵
    K = np.array([[fx, 0, cx],
                  [0, fy, cy],
                  [0, 0, 1]])

    # 将参数转换为畸变系数
    distortion = np.array([k1, k2, p1, p2, k3])

    # 计算重投影误差
    total_error = 0
    for i in range(points_2d.shape[0]):
        x, y = points_2d[i, :]
        X, Y, Z = points_3d[i, :]

        # 计算重投影误差
        x_reprojected, y_reprojected, _ = project(X, Y, Z, K, distortion)
        error = np.sqrt((x - x_reprojected)**2 + (y - y_reprojected)**2)
        total_error += error
    
    return total_error

# 初始化参数
fx = ...  # 焦距
fy = ...  # 焦距
cx = ...  # 光心坐标
cy = ...  # 光心坐标
k1 = ...  # 畸变系数
k2 = ...  # 畸变系数
p1 = ...  # 畸变系数
p2 = ...  # 畸变系数
k3 = ...  # 畸变系数

# 估计参数
params_init = np.array([fx, fy, cx, cy, k1, k2, p1, p2, k3])
result = minimize(cost_function, params_init, args=(points_2d, points_3d))
params_optimized = result.x

# 将优化后的参数转换为内参矩阵
fx, fy, cx, cy, k1, k2, p1, p2, k3 = params_optimized
K = np.array([[fx, 0, cx],
              [0, fy, cy],
              [0, 0, 1]])

# 将优化后的参数转换为畸变系