下面是一个完整的 使用 OpenCV 进行相机内参标定（Camera Calibration） 的示例，包括 C++ 和 Python 两个版本，基于棋盘格图案标定。

一、目标：相机标定

通过拍摄多张带有棋盘格图案的图像，估计相机的内参：

相机矩阵（内参） K
畸变系数 distCoeffs
可选外参（R, T）
标定精度指标（如重投影误差）

二、棋盘格参数设置（根据自己的棋盘格设置）：

棋盘格角点数：9 x 6（内角点，9列×6行）；
每个格子实际尺寸为：25.0 mm（自定义）；
图像列表已存为多张 JPG /或者其他格式图片。

三、Python 示例（

import cv2
import numpy as np
import glob# 设置棋盘格参数
chessboard_size = (9, 6)
square_size = 25.0  # mm# 生成世界坐标系下的 3D 点
objp = np.zeros((np.prod(chessboard_size), 3), np.float32)
objp[:, :2] = np.indices(chessboard_size).T.reshape(-1, 2)
objp *= square_size# 储存所有图像的角点
objpoints = []  # 3D points
imgpoints = []  # 2D points# 读取图片
images = glob.glob("calib_images/*.jpg")for fname in images:img = cv2.imread(fname)gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)# 检测角点ret, corners = cv2.findChessboardCorners(gray, chessboard_size, None)if ret:objpoints.append(objp)corners2 = cv2.cornerSubPix(gray, corners, (11,11), (-1,-1),criteria=(cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001))imgpoints.append(corners2)# 可视化角点cv2.drawChessboardCorners(img, chessboard_size, corners2, ret)cv2.imshow('img', img)cv2.waitKey(100)cv2.destroyAllWindows()# 标定相机
ret, K, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)print("相机内参矩阵 K：\n", K)
print("畸变系数 dist:\n", dist)
print("重投影误差：", ret)

四、C++ 示例

#include <opencv2/opencv.hpp>
#include <vector>
#include <iostream>
#include <filesystem>using namespace cv;
using namespace std;int main() {Size boardSize(9, 6);float squareSize = 25.0f;vector<vector<Point3f>> objectPoints;vector<vector<Point2f>> imagePoints;vector<Point3f> objp;for (int i = 0; i < boardSize.height; ++i)for (int j = 0; j < boardSize.width; ++j)objp.emplace_back(j * squareSize, i * squareSize, 0);vector<String> imageFiles;glob("calib_images/*.jpg", imageFiles);for (const auto& fname : imageFiles) {Mat img = imread(fname);Mat gray;cvtColor(img, gray, COLOR_BGR2GRAY);vector<Point2f> corners;bool found = findChessboardCorners(gray, boardSize, corners);if (found) {cornerSubPix(gray, corners, Size(11,11), Size(-1,-1),TermCriteria(TermCriteria::EPS + TermCriteria::MAX_ITER, 30, 0.001));imagePoints.push_back(corners);objectPoints.push_back(objp);drawChessboardCorners(img, boardSize, corners, found);imshow("Corners", img);waitKey(100);}}destroyAllWindows();Mat K, distCoeffs;vector<Mat> rvecs, tvecs;calibrateCamera(objectPoints, imagePoints, Size(640, 480),K, distCoeffs, rvecs, tvecs);cout << "Camera Matrix K:\n" << K << endl;cout << "Distortion Coefficients:\n" << distCoeffs << endl;
}

五、输出参数解释

参数	含义
`K` / `cameraMatrix`	相机内参矩阵 (fx, fy, cx, cy)
`distCoeffs`	畸变参数 [k1, k2, p1, p2, k3]
`rvecs`	每张图像的旋转向量
`tvecs`	每张图像的平移向量
`ret`	平均重投影误差（数值越小越好）