粒子群优化做相机标定的python代码

粒子群优化(Particle Swarm Optimization, PSO)是一种基于群体智能的优化方法，它可以用来解决各种优化问题。在相机标定中，粒子群优化可以用来优化相机的内参数和畸变系数，使得重投影误差最小。

以下是一个使用粒子群优化进行相机标定的简单python代码示例：

import numpy as np
from scipy.optimize import minimize

# 相机标定函数，用于计算重投影误差
def calibrate(params, points_2d, points_3d):
    fx, fy, cx, cy, k1, k2, p1, p2 = params
    K = np.array([[fx, 0, cx], [0, fy, cy], [0, 0, 1]])
    points_3d = points_3d.T
    points_2d = points_2d.T
    num_points = points_3d.shape[1]
    error = 0
    for i in range(num_points):
        X, Y, Z = points_3d[:, i]
        x, y = points_2d[:, i]
        x_, y_, w = np.dot(K, np.array([X, Y, Z]))
        x_ /= w
        y_ /= w
        r2 = x_**2 + y_**2
        dx = 2*p1*x_*y_ + p2*(r2 + 2*x_**2)
        dy = p1*(r2 + 2*y_**2) + 2*p2*x_*y_
        x_ = x_ + dx
        y_ = y_ + dy
        error += (x - x_)**2 + (y - y_)**2
    return error

# 粒子群优化函数
def pso(calibrate, params_bounds, points_2d, points_3d, num_particles=50, num_iterations=100):
    params_bounds = np.array(params_bounds)
    params_min = params_bounds[:, 0]
    params_max = params_bounds[:, 1]
    particles = np.random.uniform(params_min, params_max, (num_particles, len(params_min)))
    velocities = np.zeros((num_particles, len(params_min)))
    pbest = particles.copy()
    gbest = particles[0