1. 内参与畸变

理论部分可以参考其他博客或者视觉slam十四讲
相机标定主要是为了获得相机的内参矩阵K和畸变参数

内参矩阵K

畸变系数:径向畸变(k1,k2,k3), 切向畸变(p1,p2)
径向畸变公式
切向畸变公式
张正友标定方法能够提供一个比较好的初始解,用于后序的最优化.

这里用棋盘格进行标定,如果能够处理圆的偏心误差问题,用圆形图案标定板可能效果更好.

至少三张图片,一般用10-20张图片为最佳,要保证相机视野内各个角度,各个位置,各个方向都有图像.尽量多角度多位置.

最好用买的标定板,效果好,平.最好是背光板,能够保证足够的亮度和均匀度.

2. 用OpenCV标定相机程序

1,提取角点
2,亚像素角点
3,可视化提取角点(非必须)
4,标定
5,误差计算(重投影误差)

#include <iostream>
#include <fstream>
#include <string>
#include <opencv2/opencv.hpp>
using namespace std;
int main(int argc, char **argv)
{
    string dir = "/home/wfq/MyProjects/cal_images/";  //标定图片所在文件夹
    ifstream fin(dir + "file_images.txt"); //读取标定图片的路径，与cpp程序在同一路径下
    if (!fin)                              //检测是否读取到文件
    {
        cerr << "没有找到文件" << endl;
        return -1;
    }
    ofstream fout(dir + "calibration_result.txt"); //输出结果保存在此文本文件下
    //依次读取每一幅图片，从中提取角点
    cout << "开始提取角点……" << endl;
    int image_nums = 0;  //图片数量
    cv::Size image_size; //图片尺寸
    int points_per_row = 10;  //每行的内点数
    int points_per_col = 7;   //每列的内点数
    cv::Size corner_size = cv::Size(points_per_row, points_per_col); //标定板每行每列角点个数，共10*7个角点
    vector<cv::Point2f> points_per_image;                            //缓存每幅图检测到的角点
    vector<vector<cv::Point2f>> points_all_images;                   //用一个二维数组保存检测到的所有角点
    string image_file_name;                                          //声明一个文件名的字符串

    while (getline(fin, image_file_name)) //逐行读取，将行读入字符串
    {
        image_nums++;
        //读入图片
        cv::Mat image_raw = cv::imread(dir + image_file_name);
        if (image_nums == 1)
        {
            // cout<<"channels = "<<image_raw.channels()<<endl;
            // cout<<image_raw.type()<<endl;  //CV_8UC3
            image_size.width = image_raw.cols;  //图像的宽对应着列数
            image_size.height = image_raw.rows; //图像的高对应着行数
            cout << "image_size.width = " << image_size.width << endl;
            cout << "image_size.height = " << image_size.height << endl;
        }
        //角点检测
        cv::Mat image_gray;                               //存储灰度图的矩阵
        cv::cvtColor(image_raw, image_gray, CV_BGR2GRAY); //将BGR图转化为灰度图
        // cout<<"image_gray.type() = "<<image_gray.type()<<endl;  //CV_8UC1
        //step1 提取角点
        bool success = cv::findChessboardCorners(image_gray, corner_size, points_per_image);
        if (!success)
        {
            cout << "can not find the corners " << endl;
            exit(1);
        }
        else
        {
            //亚像素精确化（两种方法）
            //step2 亚像素角点
            cv::find4QuadCornerSubpix(image_gray, points_per_image, cv::Size(5, 5));
            // cornerSubPix(image_gray,points_per_image,Size(5,5));
            points_all_images.push_back(points_per_image); //保存亚像素角点
            //在图中画出角点位置
            //step3 角点可视化
            cv::drawChessboardCorners(image_raw, corner_size, points_per_image, success); //将角点连线
            cv::imshow("Camera calibration", image_raw);
            cv::waitKey(0); //等待按键输入
        }
    }
    cv::destroyAllWindows();
    //输出图像数目
    int image_sum_nums = points_all_images.size();
    cout << "image_sum_nums = " << image_sum_nums << endl;

    //开始相机标定
    cv::Size block_size(21, 21);                            //每个小方格实际大小, 只会影响最后求解的平移向量t
    cv::Mat camera_K(3, 3, CV_32FC1, cv::Scalar::all(0));   //内参矩阵3*3
    cv::Mat distCoeffs(1, 5, CV_32FC1, cv::Scalar::all(0)); //畸变矩阵1*5
    vector<cv::Mat> rotationMat;                            //旋转矩阵
    vector<cv::Mat> translationMat;                         //平移矩阵
    //初始化角点三维坐标,从左到右,从上到下!!!
    vector<cv::Point3f> points3D_per_image;
    for (int i = 0; i < corner_size.height; i++)
    {
        for (int j = 0; j < corner_size.width; j++)
        {
            points3D_per_image.push_back(cv::Point3f(block_size.width * j, block_size.height * i, 0));
        }
    }
    vector<vector<cv::Point3f>> points3D_all_images(image_nums,points3D_per_image);        //保存所有图像角点的三维坐标, z=0

    int point_counts = corner_size.area(); //每张图片上角点个数
    //!标定
    /**
     * points3D_all_images: 真实三维坐标
     * points_all_images: 提取的角点
     * image_size: 图像尺寸
     * camera_K : 内参矩阵K
     * distCoeffs: 畸变参数
     * rotationMat: 每个图片的旋转向量
     * translationMat: 每个图片的平移向量
     * */
    //step4 标定
    cv::calibrateCamera(points3D_all_images, points_all_images, image_size, camera_K, distCoeffs, rotationMat, translationMat, 0);

    //step5 对标定结果进行评价
    double total_err = 0.0;               //所有图像平均误差总和
    double err = 0.0;                     //每幅图像的平均误差
    vector<cv::Point2f> points_reproject; //重投影点
    cout << "\n\t每幅图像的标定误差:\n";
    fout << "每幅图像的标定误差：\n";
    for (int i = 0; i < image_nums; i++)
    {
        vector<cv::Point3f> points3D_per_image = points3D_all_images[i];
        //通过之前标定得到的相机内外参，对三维点进行重投影
        cv::projectPoints(points3D_per_image, rotationMat[i], translationMat[i], camera_K, distCoeffs, points_reproject);
        //计算两者之间的误差
        vector<cv::Point2f> detect_points = points_all_images[i];  //提取到的图像角点
        cv::Mat detect_points_Mat = cv::Mat(1, detect_points.size(), CV_32FC2); //变为1*70的矩阵,2通道保存提取角点的像素坐标
        cv::Mat points_reproject_Mat = cv::Mat(1, points_reproject.size(), CV_32FC2);  //2通道保存投影角点的像素坐标
        for (int j = 0; j < detect_points.size(); j++)
        {
            detect_points_Mat.at<cv::Vec2f>(0, j) = cv::Vec2f(detect_points[j].x, detect_points[j].y);
            points_reproject_Mat.at<cv::Vec2f>(0, j) = cv::Vec2f(points_reproject[j].x, points_reproject[j].y);
        }
        err = cv::norm(points_reproject_Mat, detect_points_Mat, cv::NormTypes::NORM_L2);
        total_err += err /= point_counts;
        cout << "第" << i + 1 << "幅图像的平均误差为： " << err << "像素" << endl;
        fout << "第" << i + 1 << "幅图像的平均误差为： " << err << "像素" << endl;
    }
    cout << "总体平均误差为： " << total_err / image_nums << "像素" << endl;
    fout << "总体平均误差为： " << total_err / image_nums << "像素" << endl;
    cout << "评价完成！" << endl;

    //将标定结果写入txt文件
    cv::Mat rotate_Mat = cv::Mat(3, 3, CV_32FC1, cv::Scalar::all(0)); //保存旋转矩阵
    cout << "\n相机内参数矩阵:" << endl;
    cout << camera_K << endl<< endl;
    fout << "\n相机内参数矩阵:" << endl;
    fout << camera_K << endl<< endl;
    cout << "畸变系数：\n";
    cout << distCoeffs << endl<< endl<< endl;
    fout << "畸变系数：\n";
    fout << distCoeffs << endl<< endl<< endl;
    for (int i = 0; i < image_nums; i++)
    {
        cv::Rodrigues(rotationMat[i], rotate_Mat); //将旋转向量通过罗德里格斯公式转换为旋转矩阵
        fout << "第" << i + 1 << "幅图像的旋转矩阵为：" << endl;
        fout << rotate_Mat << endl;
        fout << "第" << i + 1 << "幅图像的平移向量为：" << endl;
        fout << translationMat[i] << endl
             << endl;
    }
    fout << endl;
    fout.close();

    return 0;
}

3.画棋盘标定板

//函数声明,默认每行11个block, 没列8个block, block大小为75个像素. 也就是10*7个内点
void drawChessBoard(int blocks_per_row=11, int blocks_per_col=8, int block_size = 75);

// 11  8  75
void drawChessBoard(int blocks_per_row, int blocks_per_col, int block_size)
{
    //blocks_per_row=11 //每行11个格子,也就是10个点
    //blocks_per_col=8  //每列8个格子,也就是7个点
    //block_size=75     //每个格子的像素大小
    cv::Size board_size = cv::Size(block_size * blocks_per_row, block_size * blocks_per_col);
    cv::Mat chessboard = cv::Mat(board_size, CV_8UC1);
    unsigned char color = 0;
    for (int i = 0; i < blocks_per_row; i++)
    {
        color = ~color;
        for (int j = 0; j < blocks_per_col; j++)
        {
            chessboard(cv::Rect(i * block_size, j * block_size, block_size, block_size)).setTo(color);
            color = ~color;
        }
    }
    cv::Mat chess_board = cv::Mat(board_size.height + 100, board_size.width + 100, CV_8UC1, cv::Scalar::all(256)); //上下左右留出50个像素空白
    chessboard.copyTo(chess_board.rowRange(50, 50 + board_size.height).colRange(50, 50 + board_size.width));
    cv::imshow("chess_board", chess_board);
    cv::imwrite("chess_board.png", chess_board);
    cv::waitKey(-1);
    cv::destroyAllWindows();
}

4.OpenCV拍照

#include <iostream>
#include <opencv2/opencv.hpp>
using namespace std;
int main(int argc, char **argv)
{
    cv::namedWindow("Camera",cv::WINDOW_AUTOSIZE);

    cv::VideoCapture cap;
    cap.open(0);

    if(!cap.isOpened())
    {
        cout<<"camera open failed!\n";
        return -1;
    }

    cv::Mat image;
    int id=1;
    char symbol;
    while(id<=6)
    {
        cap>>image;
        if(image.empty())
            break;
        cout<<"y or n"<<endl;
        cin>>symbol;
        if(symbol=='y')
        {
            cv::imwrite(to_string(id)+".png",image);
            cout<<"第"<<id<<"张图片"<<endl;
            id++;
        }
    }
    return 0;
}