Table of contents
1. Intrinsic Participation Distortion
For the theoretical part, you can refer to other blogs or Lecture 14 of Visual Slam.
Camera calibration is mainly to obtain the camera’s internal reference matrix K and distortion parameters.
Internal reference matrix K
Distortion coefficient: radial distortion (k1, k2, k3), tangential distortion (p1, p2) radial distortion
formula
tangential distortion formula
Zhang Zhengyou's calibration method can provide a better initial solution for subsequent optimization.
Here, checkerboard is used for calibration. If the eccentric error of the circle can be dealt with, it may be better to use a circular pattern to calibrate the board.
At least three pictures, generally 10-20 pictures are the best, and it is necessary to ensure that there are images from all angles, positions, and directions within the camera's field of view. As many angles and positions as possible.
It is best to use the purchased calibration board, which has good effect and is flat. It is best to use a backlight board, which can ensure sufficient brightness and uniformity.
2. Use OpenCV to calibrate the camera program
1. Extract corner points
2. Sub-pixel corner points
3. Visually extract corner points (not required)
4. Calibration
5. Error calculation (reprojection error)
#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. Draw a checkerboard calibration board
//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 to take pictures
#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;
}