摄像机的标定问题是机器视觉领域的入门问题,可以分为传统的摄像机定标方法和摄像机自定标方法。定标的方法有很多中常见的有:Tsai(传统)和张正友(介于传统和自定标)等,
摄像机成像模型和四个座标系(通用原理)。 摄像机模型采用经典的小孔模型,如图中Oc(光心),像面π表示的是视野平面,其到光心的距离为f(镜头焦距)。 四个座标系分别为:世界座标系(Ow),摄像机座标系(Oc),图像物理座标系(O1,单位mm),图像像素座标系(O,位于视野平面的左上角,单位pix)。 空间某点P到其像点p的座标转换过程主要是通过这四套座标系的三次转换实现的,首先将世界座标系进行平移和转换得到摄像机座标系,然后根据三角几何变换得到图像物理座标系,最后根据像素和公制单位的比率得到图像像素座标系。(实际的应用过程是这个的逆过程,即由像素长度获知实际的长度)。 ps:通过摄像头的标定,可以得到视野平面上的mm/pix分辨率,对于视野平面以外的物体还是需要通过座标转换得到视野平面上。 转化的过程和公式参见:摄像机标定原理(关键是三个座标系).ppt
2 张正友算法的原理 zhang法通过对一定标板在不同方向多次(三次以上)完整拍照,不需要知道定标板的运动方式。直接获得相机的内参(参考文献上矩阵A)和畸变系数。该标定方法精度高于自定标法,且不需要高精度的定位仪器。 ZHANG的算法包含两个模型:一.经典针孔模型,包含四个座标系,二畸变模型(这个来源未知) 公式三项依次表示,径向畸变,切线畸变,薄棱镜畸变。OPENCV中函数只能给出k1,k2,p1,p2。 还存在另外一种畸变模型,见《摄像机标定算法库的设计和试验验证》一文26 page。(也不知道出处) ps:单从公式推导的过程来看,第一组公式等号右边应该是U0。 Key:这个方程怎么求?x,y 代表理想的图像座标(mm),是未知数(不太可能是已知数,xike说的是不考虑畸变的投影值,这个就太简单了)。 ************************************************************************************* #include "cvut.h" #include <iostream> #include <fstream> #include <string> using namespace cvut; using namespace std; void main() { ifstream fin("calibdata.txt"); ofstream fout("caliberation_result.txt");
cout<<"开始提取角点………………"; int image_count=0; CvSize image_size; CvSize board_size = cvSize(5,7); CvPoint2D32f * image_points_buf = new CvPoint2D32f[board_size.width*board_size.height]; Seq<CvPoint2D32f> image_points_seq;
string filename; while (std::getline(fin,filename)) { cout<<"\n 将鼠标焦点移到标定图像所在窗口并输入回车进行下一幅图像的角点提取 \n"; image_count++; int count; Image<uchar> view(filename); if (image_count == 1) {
image_size.width = view.size().width; image_size.height = view.size().height; }
if (0 == cvFindChessboardCorners( view.cvimage, board_size, image_points_buf, &count, CV_CALIB_CB_ADAPTIVE_THRESH ))
{ cout<<"can not find chessboard corners!\n"; exit(1); }
else { Image<uchar> view_gray(view.size(),8,1);
rgb2gray(view,view_gray);
cvFindCornerSubPix( view_gray.cvimage, image_points_buf, count, cvSize(11,11), cvSize(-1,-1), cvTermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 30, 0.1 ));
image_points_seq.push_back(image_points_buf,count);
cvDrawChessboardCorners( view.cvimage, board_size, image_points_buf, count, 1); view.show("calib");
cvWaitKey(); view.close(); }
} delete []image_points_buf; cout<<"角点提取完成!\n"<<endl;
cout<<"开始定标………………"<<"\n"<<endl; CvSize square_size = cvSize(10,10);
Matrix<double> object_points(1,board_size.width*board_size.height*image_count,3);
Matrix<double> image_points(1,image_points_seq.cvseq->total,2);
Matrix<int> point_counts(1,image_count,1); Matrix<double> intrinsic_matrix(3,3,1); Matrix<double> distortion_coeffs(1,4,1); Matrix<double> rotation_vectors(1,image_count,3); Matrix<double> translation_vectors(1,image_count,3);
int i,j,t; for (t=0;t<image_count;t++) { for (i=0;i<board_size.height;i++) { for (j=0;j<board_size.width;j++) {
object_points(0,t*board_size.height*board_size.width + i*board_size.width + j,0) = i*square_size.width; object_points(0,t*board_size.height*board_size.width + i*board_size.width + j,1) = j*square_size.height; object_points(0,t*board_size.height*board_size.width + i*board_size.width + j,2) = 0; } } }
char str[10]; itoa(image_points_seq.cvseq->total,str,10); cout<<str<<"\n"<<endl;
for (i=0;i<image_points_seq.cvseq->total;i++) { image_points(0,i,0) = image_points_seq[i].x; image_points(0,i,1) = image_points_seq[i].y; }
for (i=0;i<image_count;i++) point_counts(0,i) = board_size.width*board_size.height;
cvCalibrateCamera2(object_points.cvmat, image_points.cvmat, point_counts.cvmat, image_size, intrinsic_matrix.cvmat, distortion_coeffs.cvmat, rotation_vectors.cvmat, translation_vectors.cvmat, 0); cout<<"定标完成!\n";
cout<<"标定结果显示\n"; cout<<"*************************************************\n"; cout<<"相机内参intrinsic_matrix\n"; for(int h=0;h<3;h++) { cout<<"X:"<<intrinsic_matrix(h,0,0)<<"\tY:"<<intrinsic_matrix(h,1,0)<<"\tZ:"<<intrinsic_matrix(h,2,0)<<"\n"; } cout<<"\n畸变系数:distortion_coeffs\n"; for(int ndis=0;ndis<4;ndis++) { cout<<distortion_coeffs(0,ndis,0)<<"\\"; } cout<<"\n"; cout<<"\nrotation_vectors\n"; for(int rot=0;rot<7;rot++) { cout<<"X:"<<rotation_vectors(0,rot,0)<<"\tY:"<<rotation_vectors(0,rot,1)<<"\tZ:"<<rotation_vectors(0,rot,2)<<"\n"; } cout<<"\ntranslation_vectors\n"; for(i=0;i<7;i++) { cout<<"第"<<i+1<<"张图"<<"\tX:"<<translation_vectors(0,i,0)<<"\tY:"<<translation_vectors(0,i,1)<<"\tZ:"<<translation_vectors(0,i,2)<<"\n"; } cout<<"***************************************************\n";
cout<<"开始评价定标结果………………\n"; double total_err = 0.0; double err = 0.0; Matrix<double> image_points2(1,point_counts(0,0,0),2); int temp_num = point_counts(0,0,0); cout<<"\t每幅图像的定标误差:\n";
fout<<"每幅图像的定标误差:\n"; for (i=0;i<image_count;i++) {
cvProjectPoints2(object_points.get_cols(i * point_counts(0,0,0),(i+1)*point_counts(0,0,0)-1).cvmat, rotation_vectors.get_col(i).cvmat, translation_vectors.get_col(i).cvmat, intrinsic_matrix.cvmat, distortion_coeffs.cvmat, image_points2.cvmat, 0,0,0,0);
err = cvNorm(image_points.get_cols(i*point_counts(0,0,0),(i+1)*point_counts(0,0,0)-1).cvmat, image_points2.cvmat, CV_L1); total_err += err/=point_counts(0,0,0); cout<<"******************************************************************\n"; cout<<"\t\t第"<<i+1<<"幅图像的平均误差:"<<err<<"像素"<<'\n'; fout<<"\t第"<<i+1<<"幅图像的平均误差:"<<err<<"像素"<<'\n';
cout<<"显示image_point2\n"; for(int ih=0;ih<7;ih++) { cout<<"X:"<<image_points2(0,ih,0)<<"\tY:"<<image_points2(0,ih,1)<<"\n"; } cout<<"显示object_Points\n"; for(int iw=0;iw<7;iw++) { cout<<"X:"<<image_points.get_cols(i*point_counts(0,0,0),(i+1)*point_counts(0,0,0)-1)(0,iw,0) <<"\tY:"<<image_points.get_cols(i*point_counts(0,0,0),(i+1)*point_counts(0,0,0)-1)(0,iw,1)<<"\n"; } }
cout<<"\t总体平均误差:"<<total_err/image_count<<"像素"<<'\n'; fout<<"总体平均误差:"<<total_err/image_count<<"像素"<<'\n'<<'\n'; cout<<"评价完成!\n";
cout<<"开始保存定标结果………………"; Matrix<double> rotation_vector(3,1); Matrix<double> rotation_matrix(3,3);
fout<<"相机内参数矩阵:\n"; fout<<intrinsic_matrix<<'\n'; fout<<"畸变系数:\n"; fout<<distortion_coeffs<<'\n'; for (i=0;i<image_count;i++) { fout<<"第"<<i+1<<"幅图像的旋转向量:\n"; fout<<rotation_vectors.get_col(i);
for (j=0;j<3;j++) { rotation_vector(j,0,0) = rotation_vectors(0,i,j); }
cvRodrigues2(rotation_vector.cvmat,rotation_matrix.cvmat);
fout<<"第"<<i+1<<"幅图像的旋转矩阵:\n"; fout<<rotation_matrix; fout<<"第"<<i+1<<"幅图像的平移向量:\n"; fout<<translation_vectors.get_col(i)<<'\n'; } cout<<"完成保存\n"; } 原文网址:http://hi.baidu.com/%BA%A3%C0%AB99%C7%E0%CB%C9/blog/item/677634f9a1243ad3b48f3183.html |
OPENCV版本的摄像机标定(张正友)(来源于网络以备学习之需)
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