用粒子群优化做相机标定的python代码链接

您好，这是一个使用粒子群优化进行相机标定的 Python 代码示例：

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# 相机标定所需的观测数据
x_measured = np.array([0.5, 0.5, 1.5, 1.5, 2.5, 2.5, 3.5, 3.5])
y_measured = np.array([0.5, 1.5, 0.5, 1.5, 0.5, 1.5, 0.5, 1.5])
z_measured = np.array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5])

# 在相机坐标系中的真实位置
x_real = np.array([1, 1, 2, 2, 3, 3, 4, 4])
y_real = np.array([1, 2, 1, 2, 1, 2, 1, 2])
z_real = np.array([1, 1, 1, 1, 1, 1, 1, 1])

# 相机内参
f = 1
u0 = 0
v0 = 0

# 定义残差函数
def residuals(p):
    [alpha, beta, gamma, u, v, w] = p
    x_predicted = f * (x_real - u) / (z_real - w)
    y_predicted = f * (y_real - v) / (z_real - w)
    r = np.sqrt((x_predicted - x_measured)**2 + (y_predicted - y_measured)**2)
    return r

# 定义粒子群优化函数
def optimize_pso(func, x0, bounds, num_particles, num_iterations):
    # 定义粒子
    class Particle:
        def __init__(self, bounds):
            self.position = np.array([uniform(bounds[i][0], bounds[i][1]) for i in range(len(bounds))])
            self.pbest_position = self.position
            self.pbest_value = float('inf')
            self.velocity = np.array([0 for i in range(len(bounds))])

        def update(self, gbest_position, bounds):
            self.velocity = self.velocity + 2 * uniform(0, 1) * (self.pbest_position - self.position) + 2 * uniform(0, 1) * (gbest_position - self.position)
            self.position = self.position + self.velocity
            for i in range(len(bounds)):
                if self.position[i] > bounds