本系列文章由 @YhL_Leo 出品，转载请注明出处。
文章链接： http://blog.csdn.net/yhl_leo/article/details/49427383
Opencv中Camera Calibration and 3D Reconstruction中使用的是Z. Zhang(PAMI, 2000). A Flexible New Technique for Camera Calibration的方法。原理见原理简介（五）本文将对其进行介绍。
1 标定步骤
简单来说，Opencv中基于二维标定平面的标定方法主要步骤有：
- 1 读取相关设置信息，包括采用的pattern 信息（类型，尺寸），输入标定数据的信息（图像列表文件，视频采样方法），输出文件设置等，这些信息可以存为XML或YAML文件的形式或者在代码里直接显示设置。这里给出Opencv中提供的configuration file：
<?xml version="1.0"?>
<opencv_storage>
<Settings>
<!--
Number of inner corners per a item row and column. (square, circle)
-->
<BoardSize_Width>9</BoardSize_Width>
<BoardSize_Height>6</BoardSize_Height>
<!--
The size of a square in some user defined metric system (pixel, millimeter)
-->
<Square_Size>50</Square_Size>
<!--
The type of input used for camera calibration. One of: CHESSBOARD CIRCLES_GRID ASYMMETRIC_CIRCLES_GRID
-->
<Calibrate_Pattern>"CHESSBOARD"</Calibrate_Pattern>
<!--
The input to use for calibration.
To use an input camera -> give the ID of the camera, like "1"
To use an input video -> give the path of the input video, like "/tmp/x.avi"
To use an image list -> give the path to the XML or YAML file containing the list of the images, like "/tmp/circles_list.xml"
-->
<Input>"images/CameraCalibraation/VID5/VID5.xml"</Input>
<!--
If true (non-zero) we flip the input images around the horizontal axis.
-->
<Input_FlipAroundHorizontalAxis>0</Input_FlipAroundHorizontalAxis>
<!-- Time delay between frames in case of camera. -->
<Input_Delay>100</Input_Delay>
<!-- How many frames to use, for calibration. -->
<Calibrate_NrOfFrameToUse>25</Calibrate_NrOfFrameToUse>
<!--
Consider only fy as a free parameter, the ratio fx/fy stays the same as in the input cameraMatrix.
Use or not setting. 0 - False Non-Zero - True
-->
<Calibrate_FixAspectRatio>1</Calibrate_FixAspectRatio>
<!--
If true (non-zero) tangential distortion coefficients are set to zeros and stay zero.
-->
<Calibrate_AssumeZeroTangentialDistortion>1</Calibrate_AssumeZeroTangentialDistortion>
<!--
If true (non-zero) the principal point is not changed during the global optimization.
-->
<Calibrate_FixPrincipalPointAtTheCenter>1</Calibrate_FixPrincipalPointAtTheCenter>
<!-- The name of the output log file. -->
<Write_outputFileName>"out_camera_data.xml"</Write_outputFileName>
<!--
If true (non-zero) we write to the output file the feature points.
-->
<Write_DetectedFeaturePoints>1</Write_DetectedFeaturePoints>
<!--
If true (non-zero) we write to the output file the extrinsic camera parameters.
-->
<Write_extrinsicParameters>1</Write_extrinsicParameters>
<!--
If true (non-zero) we show after calibration the undistorted images.
-->
<Show_UndistortedImage>1</Show_UndistortedImage>
</Settings>
</opencv_storage>其中，图像文件列表images/CameraCalibraation/VID5/VID5.xmlOpencv中采用列举法：
<?xml version="1.0"?>
<opencv_storage>
<images>
images/CameraCalibraation/VID5/xx1.jpg
images/CameraCalibraation/VID5/xx2.jpg
images/CameraCalibraation/VID5/xx3.jpg
images/CameraCalibraation/VID5/xx4.jpg
images/CameraCalibraation/VID5/xx5.jpg
images/CameraCalibraation/VID5/xx6.jpg
images/CameraCalibraation/VID5/xx7.jpg
images/CameraCalibraation/VID5/xx8.jpg
</images>
</opencv_storage>文件中参数的含义比较清晰明了，此处就不累述。
- 2 依次从图像中检测pattern信息，如果检测成功，角点信息将会存储记录，用于标定解算。
cv::Mat viewGray;
if ( view.channels() == 3 )
cv::cvtColor( view, viewGray, CV_BGR2GRAY );
else
view.copyTo( viewGray );
std::vector<cv::Point2f> imagePoints;
bool success = cv::findChessboardCorners( viewGray , boardSize, imagePoints);- 3 优化角点检测精度，将上述检测成功的角点，通过精确角点定位方法，提高精度，下图为Opencv提供的检测结果。
cv::cornerSubPix( viewGray,
imagePoints,
cv::Size(11,11),
cv::TermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 30, 0.1 ));- 4 标定解算，每幅图像都进行上述的角点检测后，一般给像点对应的物方角点虚拟坐标的方式赋予对应的坐标，即可进行相机标定解算，包括相机内参，相机畸变系数，以及相机在虚拟坐标所在坐标系中相对于每幅图像的相对位置姿态（旋转向量和平移向量）。
double reprojectionError= cv::calibrateCamera(
objectPoints, // calibration pattern points in the calibration pattern coordinate space
imagePoints, // projections of calibration pattern points
imageSize, // Size of the image used only to initialize the intrinsic camera matrix
cameraMatrix, // camera matrix A
distCoeffs, // distortion coefficients (k1,k2,p1,p2[,k3[,k4,k5,k6]])
rvecs, // rotation vectors
tvecs, // translation vectors
flag, // different calibration model
criteria); // Termination criteria for iterative optimization algorithm5 标定精度评估，为了评价标定后的结果，可以按照标定得到的相机成像模型，由像点反算出物方空间坐标，进而得到一系列点云，通过对比解算点云与虚拟点云之间的差异性，就可以知道获得模型的好坏（严格来讲，如果误差较小，两者基本应该是一致的）。
6 图像畸变校正，在opencv示例中，作为标定的最后一个步骤，但是个人认为，这个应该可以作为一个相机标定后的副产品，对于处理的图像产品精度要求较高时，可以先进行畸变校正，再投入生产。下图为Opencv提供的畸变校正结果。
2 代码及结果
下面是个人的代码程序，有些部分并没完全按照Opencv的做法：
/*
Calibrate camera with chess board pattern.
- Editor: Menghan Xia, Yahui Liu.
- Data: 2015-07-28
- Email: [email protected]
- Address: Computer Vision and Remote Sensing(CVRS) Lab, Wuhan University.
**/
#include<iostream>
#include <vector>
#include <string>
#include "cv.h"
#include "highgui.h"
#include "toolFunction.h"
#define DEBUG_OUTPUT_INFO
using namespace std;
using namespace cv;
void main()
{
char* folderPath = "E:/Images/New"; // image folder
std::vector<std::string> graphPaths;
std::vector<std::string> graphSuccess;
CalibrationAssist calAssist;
graphPaths = calAssist.get_filelist(folderPath); // collect image list
#ifdef DEBUG_OUTPUT_INFO
std::cout << "loaded " << graphPaths.size() << " images"<< std::endl;
#endif
if ( !graphPaths.empty() )
{
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Start corner detection ..." << std::endl;
#endif
cv::Mat curGraph; // current image
cv::Mat gray; // gray image of current image
int imageCount = graphPaths.size();
int imageCountSuccess = 0;
cv::Size image_size;
cv::Size boardSize = cv::Size(19, 19); // chess board pattern size
cv::Size squareSize = cv::Size(15, 15); // grid physical size, as a scale factor
std::vector<cv::Point2f> corners; // one image corner list
std::vector<std::vector<cv::Point2f> > seqCorners; // n images corner list
if ( graphPaths.size() < 3 )
{
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Calibrate failed, with less than three images!" << std::endl;
#endif
return ;
}
for ( int i=0; i<graphPaths.size(); i++ )
{
string graphpath = folderPath;
graphpath += "/" + graphPaths[i];
curGraph = cv::imread(graphpath);
if ( curGraph.channels() == 3 )
cv::cvtColor( curGraph, gray, CV_BGR2GRAY );
else
curGraph.copyTo( gray );
// for every image, empty the corner list
std::vector<cv::Point2f>().swap( corners );
// corners detection
bool success = cv::findChessboardCorners( curGraph, boardSize, corners );
if ( success ) // succeed
{
#ifdef DEBUG_OUTPUT_INFO
std::cout << i << " " << graphPaths[i] << " succeed"<< std::endl;
#endif
int row = curGraph.rows;
int col = curGraph.cols;
graphSuccess.push_back( graphpath );
imageCountSuccess ++;
image_size = cv::Size( col, row );
// find sub-pixels
cv::cornerSubPix(
gray,
corners,
cv::Size( 11, 11 ),
cv::Size( -1, -1 ),
cv::TermCriteria( CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1 ) );
seqCorners.push_back( corners );
#if 1
// draw corners and show them in current image
cv::Mat imageDrawCorners;
if ( curGraph.channels() == 3 )
curGraph.copyTo( imageDrawCorners );
else
cv::cvtColor( curGraph, imageDrawCorners, CV_GRAY2RGB );
for ( int j = 0; j < corners.size(); j ++)
{
cv::Point2f dotPoint = corners[j];
cv::circle( imageDrawCorners, dotPoint, 3.0, cv::Scalar( 0, 255, 0 ), -1 );
cv::Point2f pt_m = dotPoint + cv::Point2f(4,4);
char text[100];
sprintf( text, "%d", j+1 ); // corner indexes which start from 1
cv::putText( imageDrawCorners, text, pt_m, 1, 0.5, cv::Scalar( 255, 0, 255 ) );
}
std::string pathTemp;
pathTemp = folderPath;
pathTemp += "/#" + graphPaths[i];
// save image drawn with corners and labeled with indexes
cv::imwrite( pathTemp, imageDrawCorners );
#endif
}
#ifdef DEBUG_OUTPUT_INFO
else // failed
{
std::cout << graphPaths[i] << " corner detect failed!" << std::endl;
}
#endif
}
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Corner detect done!" << std::endl
<< imageCountSuccess << " succeed! " << std::endl;
#endif
if ( imageCountSuccess < 3 )
{
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Calibrated success " << imageCountSuccess
<< " images, less than 3 images." << std::endl;
#endif
return ;
}
else
{
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Start calibration ..." << std::endl;
#endif
cv::Point3f point3D;
std::vector<cv::Point3f> objectPoints;
std::vector<double> distCoeffs;
std::vector<double> rotation;
std::vector<double> translation;
std::vector<std::vector<cv::Point3f>> seqObjectPoints;
std::vector<std::vector<double>> seqRotation;
std::vector<std::vector<double>> seqTranslation;
cv::Mat_<double> cameraMatrix;
// calibration pattern points in the calibration pattern coordinate space
for ( int t=0; t<imageCountSuccess; t++ )
{
objectPoints.clear();
for ( int i=0; i<boardSize.height; i++ )
{
for ( int j=0; j<boardSize.width; j++ )
{
point3D.x = i * squareSize.width;
point3D.y = j * squareSize.height;
point3D.z = 0;
objectPoints.push_back(point3D);
}
}
seqObjectPoints.push_back(objectPoints);
}
double reprojectionError = calibrateCamera(
seqObjectPoints,
seqCorners,
image_size,
cameraMatrix,
distCoeffs,
seqRotation,
seqTranslation,
CV_CALIB_FIX_ASPECT_RATIO|CV_CALIB_FIX_PRINCIPAL_POINT );
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Calibration done!" << std::endl;
#endif
// calculate the calibration pattern points with the camera model
std::vector<cv::Mat_<double>> projectMats;
for ( int i=0; i<imageCountSuccess; i++ )
{
cv::Mat_<double> R, T;
// translate rotation vector to rotation matrix via Rodrigues transformation
cv::Rodrigues( seqRotation[i], R );
T = cv::Mat( cv::Matx31d(
seqTranslation[i][0],
seqTranslation[i][1],
seqTranslation[i][2]) );
cv::Mat_<double> P = cameraMatrix * cv::Mat( cv::Matx34d(
R(0,0), R(0,1), R(0,2), T(0),
R(1,0), R(1,1), R(1,2), T(1),
R(2,0), R(2,1), R(2,2), T(2) ) );
projectMats.push_back(P);
}
std::vector<cv::Point2d> PointSet;
int pointNum = boardSize.width*boardSize.height;
std::vector<cv::Point3d> objectClouds;
for ( int i=0; i<pointNum; i++ )
{
PointSet.clear();
for ( int j=0; j<imageCountSuccess; j++ )
{
cv::Point2d tempPoint = seqCorners[j][i];
PointSet.push_back(tempPoint);
}
// calculate calibration pattern points
cv::Point3d objectPoint = calAssist.triangulate(projectMats,PointSet);
objectClouds.push_back(objectPoint);
}
std::string pathTemp_point;
pathTemp_point = folderPath;
pathTemp_point += "/point.txt";
calAssist.save3dPoint(pathTemp_point,objectClouds);
std::string pathTemp_calib;
pathTemp_calib = folderPath;
pathTemp_calib += "/calibration.txt";
FILE* fp = fopen( pathTemp_calib.c_str(), "w" );
fprintf( fp, "The average of re-projection error : %lf\n", reprojectionError );
for ( int i=0; i<imageCountSuccess; i++ )
{
std::vector<cv::Point2f> errorList;
cv::projectPoints(
seqObjectPoints[i],
seqRotation[i],
seqTranslation[i],
cameraMatrix,
distCoeffs,
errorList );
corners.clear();
corners = seqCorners[i];
double meanError(0.0);
for ( int j=0; j<corners.size(); j++ )
{
meanError += std::sqrt((errorList[j].x - corners[j].x)*(errorList[j].x - corners[j].x) +
(errorList[j].y - corners[j].y)*(errorList[j].y - corners[j].y));
}
rotation.clear();
translation.clear();
rotation = seqRotation[i];
translation = seqTranslation[i];
fprintf( fp, "Re-projection of image %d：%lf\n", i+1, meanError/corners.size() );
fprintf( fp, "Rotation vector :\n" );
fprintf( fp, "%lf %lf %lf\n", rotation[0], rotation[1], rotation[2] );
fprintf( fp, "Translation vector :\n" );
fprintf( fp, "%lf %lf %lf\n\n", translation[0], translation[1], translation[2] );
}
fprintf( fp, "Camera internal matrix :\n" );
fprintf( fp, "%lf %lf %lf\n%lf %lf %lf\n%lf %lf %lf\n",
cameraMatrix(0,0), cameraMatrix(0,1), cameraMatrix(0,2),
cameraMatrix(1,0), cameraMatrix(1,1), cameraMatrix(1,2),
cameraMatrix(2,0), cameraMatrix(2,1), cameraMatrix(2,2));
fprintf( fp,"Distortion coefficient :\n" );
for ( int k=0; k<distCoeffs.size(); k++)
fprintf( fp, "%lf ", distCoeffs[k] );
#ifdef DEBUG_OUTPUT_INFO
std::cout << "Results are saved!" << std::endl;
#endif
}
}
}// toolFunction.h
#ifndef TOOL_FUNCTION_H
#pragma once
#define TOOL_FUNCTION_H
#include<iostream>
#include <Windows.h>
#include <math.h>
#include <fstream>
#include <vector>
#include <string>
#include "cv.h"
#include "highgui.h"
using namespace cv;
using namespace std;
class CalibrationAssist
{
public:
CalibrationAssist() {}
~CalibrationAssist() {}
public:
std::vector<std::string>get_filelist( std::string foldname );
cv::Point3d triangulate( std::vector<cv::Mat_<double>> &ProjectMats,
std::vector<cv::Point2d> &imagePoints );
void save3dPoint( std::string path_, std::vector<cv::Point3d> &Point3dLists );
};
#endif // TOOL_FUNCTION_H// toolFunction.cpp
#include "toolFunction.h"
std::vector<std::string> CalibrationAssist::get_filelist( std::string foldname )
{
foldname += "/*.*";
const char * mystr=foldname.c_str();
std::vector<std::string> flist;
std::string lineStr;
std::vector<std::string> extendName;
extendName.push_back("jpg");
extendName.push_back("JPG");
extendName.push_back("bmp");
extendName.push_back("png");
extendName.push_back("gif");
HANDLE file;
WIN32_FIND_DATA fileData;
char line[1024];
wchar_t fn[1000];
mbstowcs( fn, mystr, 999 );
file = FindFirstFile( fn, &fileData );
FindNextFile( file, &fileData );
while(FindNextFile( file, &fileData ))
{
wcstombs( line, (const wchar_t*)fileData.cFileName, 259);
lineStr = line;
// remove the files which are not images
for (int i = 0; i < 4; i ++)
{
if (lineStr.find(extendName[i]) < 999)
{
flist.push_back(lineStr);
break;
}
}
}
return flist;
}
cv::Point3d CalibrationAssist::triangulate(
std::vector<cv::Mat_<double>> &ProjectMats,
std::vector<cv::Point2d> &imagePoints)
{
int i,j;
std::vector<cv::Point2d> pointSet;
int frameSum = ProjectMats.size();
cv::Mat A(2*frameSum,3,CV_32FC1);
cv::Mat B(2*frameSum,1,CV_32FC1);
cv::Point2d u,u1;
cv::Mat_<double> P;
cv::Mat_<double> rowA1,rowA2,rowB1,rowB2;
int k = 0;
for ( i = 0; i < frameSum; i++ ) //get the coefficient matrix A and B
{
u = imagePoints[i];
P = ProjectMats[i];
cv::Mat( cv::Matx13d(
u.x*P(2,0)-P(0,0),
u.x*P(2,1)-P(0,1),
u.x*P(2,2)-P(0,2) ) ).copyTo( A.row(k) );
cv::Mat( cv::Matx13d(
u.y*P(2,0)-P(1,0),
u.y*P(2,1)-P(1,1),
u.y*P(2,2)-P(1,2) ) ).copyTo( A.row(k+1) );
cv::Mat rowB1( 1, 1, CV_32FC1, cv::Scalar( -(u.x*P(2,3)-P(0,3)) ) );
cv::Mat rowB2( 1, 1, CV_32FC1, cv::Scalar(-(u.y*P(2,3)-P(1,3)) ) );
rowB1.copyTo( B.row(k) );
rowB2.copyTo( B.row(k+1) );
k += 2;
}
cv::Mat X;
cv::solve( A, B, X, DECOMP_SVD );
return Point3d(X);
}
void CalibrationAssist::save3dPoint( std::string path_, std::vector<cv::Point3d> &Point3dLists)
{
const char * path = path_.c_str();
FILE* fp = fopen( path, "w" );
for ( int i = 0; i < Point3dLists.size(); i ++)
{
// fprintf(fp,"%d ",i);
fprintf( fp, "%lf %lf %lf\n",
Point3dLists[i].x, Point3dLists[i].y, Point3dLists[i].z);
}
fclose(fp);
#if 1
std::cout << "clouds of points are saved!" << std::endl;
#endif
}使用数据为9张1200×800的图像：
程序运行结果：
1 运行控制台输出结果
2 角点检测图
- 3 反投影点云（CloudCompare显示）
对于上述结果的生成文件，此处用了C语言写成txt的方式，读者完全可以考虑使用XML或YAML格式文件保存，至于畸变纠正的问题，也很简单，直接利用标定得到的相机内参和畸变系数，查询remap函数的使用方法即可。此外，处理较大图像时，Opencv提供的方法速度可能会较慢，遇到这种情况，可以考虑把图像缩小或重写角点检测算法。