vs2015 + opencv3 双目摄像头标定（C++实现）_#include #include

    参考资料：张正友标定流程_张正友3d标定步骤_学之之博未若知之之要知之之要未若行之之实的博客-CSDN博客

    以前在本科的时候，做智能小车发现一个问题，当摄像头镜头视角越大，摄像头成像的照片出现变形的现象越严重，当时我们的解决办法是：使用小视角的镜头。今天学到摄像头标定之后，我发现，我们可以不用换小视角的镜头来解决这个问题，而是通过标定来解决这个问题。标定的目的：获得获取摄像机的内参和外参矩阵，通过这两个矩阵来矫正变形的图片，而内参矩阵指代：摄像头本身的畸变参数，外参矩阵指代：描述了如何把点从世界坐标系转换到摄像机坐标系。

    对于标定的方法，网上资料很多，有通过Matlab标定，有通过c++标定，我个人比较推荐c++标定。下面我将一一介绍“张正友标定”流程：

     1. 准备标定板

      本人因为是自学双目摄像头而且又比较穷，所以没有钱买标定板，也没有钱打印标定板，所以想了一个简单粗暴的办法，直接将电脑的显示器当标定板来用，

     2.保存样本图片

     在标定过程中，我们需要拍照一些图片，其内容必须得包含整幅标定板，用来求摄像机的内参和外参矩阵。由于我们标定的摄像头是双目，所以需要保存两份图片（左摄像头和右摄像头）

   3.对每一张标定图片，提取角点信息

     使用到的函数为：findChessboardCorners，但要注意一个问题，它提取的内角点，对于上面的标定板，每行9个角点数，每列6个角点数

Size board_size = Size(9, 6);    /* 标定板上每行、列的角点数 */
Mat imageInput = imread(filename);
vector<vector<Point2f>> image_points_seq; /* 保存检测到的所有角点 */
findChessboardCorners(imageInput, board_size, image_points_buf)     

  4.对粗提取的角点进行精确化

    使用到函数为：find4QuadCornerSubpix，其中Size(5,5)是角点搜索窗口的尺寸，相对于上面的结果，有些角点值被精确化了，可以对比上下两张图片的内容。

Mat view_gray;
cvtColor(imageInput, view_gray, CV_RGB2GRAY);
/* 亚像素精确化 */
find4QuadCornerSubpix(view_gray, image_points_buf, Size(5, 5)); //对粗提取的角点进行精确化

 

5.将内角点可视化

     使用到的函数为：drawChessboardCorners

drawChessboardCorners(view_gray, board_size, image_points_buf, false); //用于在图片中标记角点  

6.相机标定

   使用到函数为：calibrateCamera

vector<vector<Point3f>> object_points; /* 保存标定板上角点的三维坐标 */
vector<vector<Point2f>> image_points_seq; /* 保存检测到的所有角点 */
Mat cameraMatrix = Mat(3, 3, CV_32FC1, Scalar::all(0)); /* 摄像机内参数矩阵 */
Mat distCoeffs = Mat(1, 5, CV_32FC1, Scalar::all(0)); /* 摄像机的5个畸变系数：k1,k2,p1,p2,k3 */
vector<Mat> tvecsMat;  /* 每幅图像的旋转向量 */
vector<Mat> rvecsMat; /* 每幅图像的平移向量 */
calibrateCamera(object_points, image_points_seq, image_size, cameraMatrix, distCoeffs, rvecsMat, tvecsMat, 0);   

  在相机标定之后，我们可以得到相机内参数矩阵与畸变系数

 

7.对标定结果进行评价

   对标定结果进行评价的方法是通过得到的摄像机内外参数，对空间的三维点进行重新投影计算，得到空间三维点在图像上新的投影点的坐标，计算投影坐标和亚像素角点坐标之间的偏差，偏差越小，标定结果越好，使用到的函数为：projectPoints

vector<Point2f> image_points2; /* 保存重新计算得到的投影点 */
/* 通过得到的摄像机内外参数，对空间的三维点进行重新投影计算，得到新的投影点 */
projectPoints(tempPointSet, rvecsMat[i], tvecsMat[i], cameraMatrix, distCoeffs, image_points2);   

亚像素角点坐标：

计算投影坐标：

经过循环计算，可以统计出所有的误差：

8.利用标定结果对棋盘图进行矫正

 左边为矫正后的图片，右边为原始图片，效果还是不错的。

以下完整的工程代码（代码重复运行两次分别得到左右摄像头的内参和外参）

#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/calib3d/calib3d.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <iostream>
#include <fstream>
 
using namespace cv;
using namespace std;
 
void main()
{
	ifstream fin("calibdata_right.txt"); /* 标定所用图像文件的路径 */
	ofstream fout("caliberation_right_result.txt");  /* 保存标定结果的文件 */
											   //读取每一幅图像，从中提取出角点，然后对角点进行亚像素精确化	
	cout << "开始提取角点………………";
	int image_count = 0;  /* 图像数量 */
	Size image_size;  /* 图像的尺寸 */
	Size board_size = Size(9, 6);    /* 标定板上每行、列的角点数 */
	vector<Point2f> image_points_buf;  /* 缓存每幅图像上检测到的角点 */
	vector<vector<Point2f>> image_points_seq; /* 保存检测到的所有角点 */
	string filename;
	int count = -1;//用于存储角点个数。
	while (getline(fin, filename))
	{
		image_count++;
		// 用于观察检验输出
		cout << "image_count = " << image_count << endl;
		/* 输出检验*/
		cout << "-->count = " << count;
		Mat imageInput = imread(filename);
		if (image_count == 1)  //读入第一张图片时获取图像宽高信息
		{
			image_size.width = imageInput.cols;
			image_size.height = imageInput.rows;
			cout << "image_size.width = " << image_size.width << endl;
			cout << "image_size.height = " << image_size.height << endl;
		}
 
		/* 提取角点 */
		if (0 == findChessboardCorners(imageInput, board_size, image_points_buf))
		{
			cout << "can not find chessboard corners!\n"; //找不到角点
			exit(1);
		}
		else
		{
			Mat view_gray;
			cvtColor(imageInput, view_gray, CV_RGB2GRAY);
			/* 亚像素精确化 */
			find4QuadCornerSubpix(view_gray, image_points_buf, Size(5, 5)); //对粗提取的角点进行精确化
																			//cornerSubPix(view_gray,image_points_buf,Size(5,5),Size(-1,-1),TermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,30,0.1));
			image_points_seq.push_back(image_points_buf);  //保存亚像素角点
														   /* 在图像上显示角点位置 */
			drawChessboardCorners(view_gray, board_size, image_points_buf, false); //用于在图片中标记角点
			imshow("Camera Calibration", view_gray);//显示图片
			waitKey(500);//暂停0.5S		
		}
	}
	int total = image_points_seq.size();
	cout << "total = " << total << endl;
	int CornerNum = board_size.width*board_size.height;  //每张图片上总的角点数
	for (int ii = 0; ii<total; ii++)
	{
		if (0 == ii%CornerNum)// 24 是每幅图片的角点个数。此判断语句是为了输出 图片号，便于控制台观看 
		{
			int i = -1;
			i = ii / CornerNum;
			int j = i + 1;
			cout << "--> 第 " << j << "图片的数据 --> : " << endl;
		}
		if (0 == ii % 3)	// 此判断语句，格式化输出，便于控制台查看
		{
			cout << endl;
		}
		else
		{
			cout.width(10);
		}
		//输出所有的角点
		cout << " -->" << image_points_seq[ii][0].x;
		cout << " -->" << image_points_seq[ii][0].y;
	}
	cout << "角点提取完成！\n";
 
	//以下是摄像机标定
	cout << "开始标定………………";
	/*棋盘三维信息*/
	Size square_size = Size(10, 10);  /* 实际测量得到的标定板上每个棋盘格的大小 */
	vector<vector<Point3f>> object_points; /* 保存标定板上角点的三维坐标 */
										   /*内外参数*/
	Mat cameraMatrix = Mat(3, 3, CV_32FC1, Scalar::all(0)); /* 摄像机内参数矩阵 */
	vector<int> point_counts;  // 每幅图像中角点的数量
	Mat distCoeffs = Mat(1, 5, CV_32FC1, Scalar::all(0)); /* 摄像机的5个畸变系数：k1,k2,p1,p2,k3 */
	vector<Mat> tvecsMat;  /* 每幅图像的旋转向量 */
	vector<Mat> rvecsMat; /* 每幅图像的平移向量 */
						  /* 初始化标定板上角点的三维坐标 */
	int i, j, t;
	for (t = 0; t<image_count; t++)
	{
		vector<Point3f> tempPointSet;
		for (i = 0; i<board_size.height; i++)
		{
			for (j = 0; j<board_size.width; j++)
			{
				Point3f realPoint;
				/* 假设标定板放在世界坐标系中z=0的平面上 */
				realPoint.x = i*square_size.width;
				realPoint.y = j*square_size.height;
				realPoint.z = 0;
				tempPointSet.push_back(realPoint);
			}
		}
		object_points.push_back(tempPointSet);
	}
	/* 初始化每幅图像中的角点数量，假定每幅图像中都可以看到完整的标定板 */
	for (i = 0; i<image_count; i++)
	{
		point_counts.push_back(board_size.width*board_size.height);
	}
	/* 开始标定 */
	calibrateCamera(object_points, image_points_seq, image_size, cameraMatrix, distCoeffs, rvecsMat, tvecsMat, 0);
	cout << "标定完成！\n";
	//对标定结果进行评价
	cout << "开始评价标定结果………………\n";
	double total_err = 0.0; /* 所有图像的平均误差的总和 */
	double err = 0.0; /* 每幅图像的平均误差 */
	vector<Point2f> image_points2; /* 保存重新计算得到的投影点 */
	cout << "\t每幅图像的标定误差：\n";
	fout << "每幅图像的标定误差：\n";
	for (i = 0; i<image_count; i++)
	{
		vector<Point3f> tempPointSet = object_points[i];
		/* 通过得到的摄像机内外参数，对空间的三维点进行重新投影计算，得到新的投影点 */
		projectPoints(tempPointSet, rvecsMat[i], tvecsMat[i], cameraMatrix, distCoeffs, image_points2);
		/* 计算新的投影点和旧的投影点之间的误差*/
		vector<Point2f> tempImagePoint = image_points_seq[i];
		Mat tempImagePointMat = Mat(1, tempImagePoint.size(), CV_32FC2);
		Mat image_points2Mat = Mat(1, image_points2.size(), CV_32FC2);
		for (int j = 0; j < tempImagePoint.size(); j++)
		{
			image_points2Mat.at<Vec2f>(0, j) = Vec2f(image_points2[j].x, image_points2[j].y);
			tempImagePointMat.at<Vec2f>(0, j) = Vec2f(tempImagePoint[j].x, tempImagePoint[j].y);
		}
		err = norm(image_points2Mat, tempImagePointMat, NORM_L2);
		total_err += err /= point_counts[i];
		std::cout << "第" << i + 1 << "幅图像的平均误差：" << err << "像素" << endl;
		fout << "第" << i + 1 << "幅图像的平均误差：" << err << "像素" << endl;
	}
	std::cout << "总体平均误差：" << total_err / image_count << "像素" << endl;
	fout << "总体平均误差：" << total_err / image_count << "像素" << endl << endl;
	std::cout << "评价完成！" << endl;
	//保存定标结果  	
	std::cout << "开始保存定标结果………………" << endl;
	Mat rotation_matrix = Mat(3, 3, CV_32FC1, Scalar::all(0)); /* 保存每幅图像的旋转矩阵 */
	fout << "相机内参数矩阵：" << endl;
	fout << cameraMatrix << endl << endl;
	fout << "畸变系数：\n";
	fout << distCoeffs << endl << endl << endl;
	for (int i = 0; i<image_count; i++)
	{
		fout << "第" << i + 1 << "幅图像的旋转向量：" << endl;
		fout << tvecsMat[i] << endl;
		/* 将旋转向量转换为相对应的旋转矩阵 */
		Rodrigues(tvecsMat[i], rotation_matrix);
		fout << "第" << i + 1 << "幅图像的旋转矩阵：" << endl;
		fout << rotation_matrix << endl;
		fout << "第" << i + 1 << "幅图像的平移向量：" << endl;
		fout << rvecsMat[i] << endl << endl;
	}
	std::cout << "完成保存" << endl;
	fout << endl;
	/************************************************************************
	显示定标结果
	*************************************************************************/
	Mat mapx = Mat(image_size, CV_32FC1);
	Mat mapy = Mat(image_size, CV_32FC1);
	Mat R = Mat::eye(3, 3, CV_32F);
	std::cout << "保存矫正图像" << endl;
	string imageFileName;
	std::stringstream StrStm;
	for (int i = 0; i != image_count; i++)
	{
		std::cout << "Frame #" << i + 1 << "..." << endl;
		initUndistortRectifyMap(cameraMatrix, distCoeffs, R, cameraMatrix, image_size, CV_32FC1, mapx, mapy);
		StrStm.clear();
		imageFileName.clear();
		string filePath = "image_right_";
		StrStm << i + 6;
		StrStm >> imageFileName;
		filePath += imageFileName;
		filePath += ".jpg";
		Mat imageSource = imread(filePath);
		Mat newimage = imageSource.clone();
		//另一种不需要转换矩阵的方式
		//undistort(imageSource,newimage,cameraMatrix,distCoeffs);
		remap(imageSource, newimage, mapx, mapy, INTER_LINEAR);
		StrStm.clear();
		filePath.clear();
		StrStm << i + 1;
		StrStm >> imageFileName;
		imageFileName += "_d.jpg";
		imwrite(imageFileName, newimage);
	}
	std::cout << "保存结束" << endl;
	return;
}

9.利用左右摄像头的内参和外参进行双目标定

  代码如下（记得将第8步得到的左右摄像头的内参和外参分别填到cameraMatrixL、distCoeffL、cameraMatrixR和distCoeffR）：

#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <opencv2/highgui/highgui.hpp>
 
#include <vector>
#include <string>
#include <algorithm>
#include <iostream>
#include <iterator>
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
 
#include <opencv2/opencv.hpp>
//#include <cv.h>
//#include <cv.hpp>
 
using namespace std;
using namespace cv;
//摄像头的分辨率
const int imageWidth = 640;
const int imageHeight = 360;
//横向的角点数目
const int boardWidth = 9;
//纵向的角点数目
const int boardHeight = 6;
//总的角点数目
const int boardCorner = boardWidth * boardHeight;
//相机标定时需要采用的图像帧数
const int frameNumber = 10;
//标定板黑白格子的大小 单位是mm
const int squareSize = 10;
//标定板的总内角点
const Size boardSize = Size(boardWidth, boardHeight);
Size imageSize = Size(imageWidth, imageHeight);
 
Mat R, T, E, F;
//R旋转矢量 T平移矢量 E本征矩阵 F基础矩阵
vector<Mat> rvecs; //R
vector<Mat> tvecs; //T
				   //左边摄像机所有照片角点的坐标集合
vector<vector<Point2f>> imagePointL;
//右边摄像机所有照片角点的坐标集合
vector<vector<Point2f>> imagePointR;
//各图像的角点的实际的物理坐标集合
vector<vector<Point3f>> objRealPoint;
//左边摄像机某一照片角点坐标集合
vector<Point2f> cornerL;
//右边摄像机某一照片角点坐标集合
vector<Point2f> cornerR;
 
Mat rgbImageL, grayImageL;
Mat rgbImageR, grayImageR;
 
Mat intrinsic;
Mat distortion_coeff;
//校正旋转矩阵R，投影矩阵P，重投影矩阵Q
Mat Rl, Rr, Pl, Pr, Q;
//映射表
Mat mapLx, mapLy, mapRx, mapRy;
Rect validROIL, validROIR;
//图像校正之后，会对图像进行裁剪，其中，validROI裁剪之后的区域
/*事先标定好的左相机的内参矩阵
fx 0 cx
0 fy cy
0  0  1
*/
Mat cameraMatrixL = (Mat_<double>(3, 3) << 940.4937685941497, 0, 227.3792711982141,
	0, 949.0373173049467, 295.8358484611537,
	0, 0, 1);
//获得的畸变参数
Mat distCoeffL = (Mat_<double>(5, 1) << -1.029423693166534, 1.058780876275055, -0.02758128682125558, 0.07367092471929151, -2.428716031795587);
/*事先标定好的右相机的内参矩阵
fx 0 cx
0 fy cy
0  0  1
*/
Mat cameraMatrixR = (Mat_<double>(3, 3) << 1196.466071813248, 0, 386.9366034567681,
	0, 1210.35406268507, 306.5246050041429,
	0, 0, 1);
Mat distCoeffR = (Mat_<double>(5, 1) << -1.58519463079371, 0.08628154897902529, -0.05737733624491874, -0.07915841018512512, 10.62054373440436);
 
/*计算标定板上模块的实际物理坐标*/
void calRealPoint(vector<vector<Point3f>>& obj, int boardWidth, int boardHeight, int imgNumber, int squareSize)
{
	vector<Point3f> imgpoint;
	for (int rowIndex = 0; rowIndex < boardHeight; rowIndex++)
	{
		for (int colIndex = 0; colIndex < boardWidth; colIndex++)
		{
			imgpoint.push_back(Point3f(rowIndex * squareSize, colIndex * squareSize, 0));
		}
	}
	for (int imgIndex = 0; imgIndex < imgNumber; imgIndex++)
	{
		obj.push_back(imgpoint);
	}
}
 
 
 
void outputCameraParam(void)
{
	/*保存数据*/
	/*输出数据*/
	FileStorage fs("intrisics.yml", FileStorage::WRITE);
	if (fs.isOpened())
	{
		fs << "cameraMatrixL" << cameraMatrixL << "cameraDistcoeffL" << distCoeffL << "cameraMatrixR" << cameraMatrixR << "cameraDistcoeffR" << distCoeffR;
		fs.release();
		cout << "cameraMatrixL=:" << cameraMatrixL << endl << "cameraDistcoeffL=:" << distCoeffL << endl << "cameraMatrixR=:" << cameraMatrixR << endl << "cameraDistcoeffR=:" << distCoeffR << endl;
	}
	else
	{
		cout << "Error: can not save the intrinsics!!!!" << endl;
	}
 
	fs.open("extrinsics.yml", FileStorage::WRITE);
	if (fs.isOpened())
	{
		fs << "R" << R << "T" << T << "Rl" << Rl << "Rr" << Rr << "Pl" << Pl << "Pr" << Pr << "Q" << Q;
		cout << "R=" << R << endl << "T=" << T << endl << "Rl=" << Rl << endl << "Rr" << Rr << endl << "Pl" << Pl << endl << "Pr" << Pr << endl << "Q" << Q << endl;
		fs.release();
	}
	else
	{
		cout << "Error: can not save the extrinsic parameters\n";
	}
 
}
 
 
int main(int argc, char* argv[])
{
	Mat img;
	int goodFrameCount = 0;
	while (goodFrameCount < frameNumber)
	{
		char filename[100];
		/*读取左边的图像*/
		sprintf_s(filename, "E:\\c_pp_project\\opencv_test\\test\\test\\image_left_%d.jpg", goodFrameCount + 5);
 
		rgbImageL = imread(filename, CV_LOAD_IMAGE_COLOR);
		imshow("chessboardL", rgbImageL);
		cvtColor(rgbImageL, grayImageL, CV_BGR2GRAY);
		/*读取右边的图像*/
		sprintf_s(filename, "E:\\c_pp_project\\opencv_test\\test\\test\\image_right_%d.jpg", goodFrameCount + 5);
		rgbImageR = imread(filename, CV_LOAD_IMAGE_COLOR);
		cvtColor(rgbImageR, grayImageR, CV_BGR2GRAY);
 
		bool isFindL, isFindR;
		isFindL = findChessboardCorners(rgbImageL, boardSize, cornerL);
		isFindR = findChessboardCorners(rgbImageR, boardSize, cornerR);
		if (isFindL == true && isFindR == true)
		{
			cornerSubPix(grayImageL, cornerL, Size(5, 5), Size(-1, 1), TermCriteria(CV_TERMCRIT_EPS | CV_TERMCRIT_ITER, 20, 0.1));
			drawChessboardCorners(rgbImageL, boardSize, cornerL, isFindL);
			imshow("chessboardL", rgbImageL);
			imagePointL.push_back(cornerL);
 
			cornerSubPix(grayImageR, cornerR, Size(5, 5), Size(-1, -1), TermCriteria(CV_TERMCRIT_EPS | CV_TERMCRIT_ITER, 20, 0.1));
			drawChessboardCorners(rgbImageR, boardSize, cornerR, isFindR);
			imshow("chessboardR", rgbImageR);
			imagePointR.push_back(cornerR);
 
			goodFrameCount++;
			cout << "the image" << goodFrameCount << " is good" << endl;
		}
		else
		{
			cout << "the image is bad please try again" << endl;
		}
		if (waitKey(10) == 'q')
		{
			break;
		}
	}
 
	//计算实际的校正点的三维坐标，根据实际标定格子的大小来设置
	calRealPoint(objRealPoint, boardWidth, boardHeight, frameNumber, squareSize);
	cout << "cal real successful" << endl;
 
	//标定摄像头
	double rms = stereoCalibrate(objRealPoint, imagePointL, imagePointR,
		cameraMatrixL, distCoeffL,
		cameraMatrixR, distCoeffR,
		Size(imageWidth, imageHeight), R, T, E, F, CALIB_USE_INTRINSIC_GUESS,
		TermCriteria(TermCriteria::COUNT + TermCriteria::EPS, 100, 1e-5));
 
	cout << "Stereo Calibration done with RMS error = " << rms << endl;
 
	stereoRectify(cameraMatrixL, distCoeffL, cameraMatrixR, distCoeffR, imageSize, R, T, Rl,
		Rr, Pl, Pr, Q, CALIB_ZERO_DISPARITY, -1, imageSize, &validROIL, &validROIR);
 
 
	//摄像机校正映射
	initUndistortRectifyMap(cameraMatrixL, distCoeffL, Rl, Pl, imageSize, CV_32FC1, mapLx, mapLy);
	initUndistortRectifyMap(cameraMatrixR, distCoeffR, Rr, Pr, imageSize, CV_32FC1, mapRx, mapRy);
 
	Mat rectifyImageL, rectifyImageR;
	cvtColor(grayImageL, rectifyImageL, CV_GRAY2BGR);
	cvtColor(grayImageR, rectifyImageR, CV_GRAY2BGR);
 
	imshow("RecitifyL Before", rectifyImageL);
	imshow("RecitifyR Before", rectifyImageR);
	cout << "按Q1退出..." << endl;
	//经过remap之后，左右相机的图像已经共面并且行对准了
	Mat rectifyImageL2, rectifyImageR2;
	remap(rectifyImageL, rectifyImageL2, mapLx, mapLy, INTER_LINEAR);
	remap(rectifyImageR, rectifyImageR2, mapRx, mapRy, INTER_LINEAR);
	cout << "按Q2退出..." << endl;
 
	imshow("rectifyImageL", rectifyImageL2);
	imshow("rectifyImageR", rectifyImageR2);
 
	outputCameraParam();
 
	//显示校正结果
	Mat canvas;
	double sf;
	int w, h;
	sf = 600. / MAX(imageSize.width, imageSize.height);
	w = cvRound(imageSize.width * sf);
	h = cvRound(imageSize.height * sf);
	canvas.create(h, w * 2, CV_8UC3);
 
	//左图像画到画布上
	Mat canvasPart = canvas(Rect(0, 0, w, h));
	resize(rectifyImageL2, canvasPart, canvasPart.size(), 0, 0, INTER_AREA);
	Rect vroiL(cvRound(validROIL.x*sf), cvRound(validROIL.y*sf),
		cvRound(validROIL.width*sf), cvRound(validROIL.height*sf));
	rectangle(canvasPart, vroiL, Scalar(0, 0, 255), 3, 8);
 
	cout << "Painted ImageL" << endl;
 
	//右图像画到画布上
	canvasPart = canvas(Rect(w, 0, w, h));
	resize(rectifyImageR2, canvasPart, canvasPart.size(), 0, 0, INTER_LINEAR);
	Rect vroiR(cvRound(validROIR.x*sf), cvRound(validROIR.y*sf),
		cvRound(validROIR.width*sf), cvRound(validROIR.height*sf));
	rectangle(canvasPart, vroiR, Scalar(0, 255, 0), 3, 8);
 
	cout << "Painted ImageR" << endl;
 
	//画上对应的线条
	for (int i = 0; i < canvas.rows; i += 16)
		line(canvas, Point(0, i), Point(canvas.cols, i), Scalar(0, 255, 0), 1, 8);
 
	imshow("rectified", canvas);
 
	cout << "wait key" << endl;
	waitKey(0);
	return 0;
}

     其效果见下图：

10.其中一些函数的说明：

1.findChessboardCorners：寻找棋盘图中棋盘角点

2.find4QuadCornerSubpix：对粗提取的角点进行精确化

3.cornerSubPix：在角点检测中精确化角点位置

4.drawChessboardCorners：将发现到的所有角点绘制到所提供的图像上

5.calibrateCamera：利用定标来计算摄像机的内参数和外参数

6.projectPoints：通过得到的摄像机内外参数，对空间的三维点进行重新投影计算，得到新的投影点

7.利用标定结果对棋盘图进行矫正

    1）initUndistortRectifyMap用来计算畸变映射，remap把求得的映射应用到图像上

    2）undistort一个函数搞定

8.stereoCalibrate:双目摄像机标定，计算了两个摄像头进行立体像对之间的转换关系，根据左右相机的参数矩阵，生成两个相机之间的关系矩阵，以及基本和本质矩阵

9.stereoRectify:作用是为每个摄像头计算立体校正的映射矩阵。所以其运行结果并不是直接将图片进行立体矫正，而是得出进行立体矫正所需要的映射矩阵