标定原理介绍

• 摄像机小孔模型 Cv照相机定标和三维重建#针孔相机模型和变形

标定程序1（opencv自带的示例程序）

简介

读者可以直接使用Opencv自带的摄像机标定示例程序，该程序位于 “\OpenCV\samples\c目录下的calibration.cpp”，程序的输入支持直接从USB摄像机读取图片标定，或者读取avi文件或者已经存放于电脑上图片进行标定。

使用说明

编译运行程序，如果未设置任何命令行参数，则程序会有提示，告诉你应该在你编译出来的程序添加必要的命令行，比如你的程序是calibration.exe(以windows操作系统为例）。则你可以添加如下命令行（以下加粗的字体所示）：

calibration -w 6 -h 8 -s 2 -n 10 -o camera.yml -op -oe [<list_of_views.txt>]

调用命令行和参数介绍

Usage: calibration

    -w <board_width>         # 图片某一维方向上的交点个数    -h <board_height>        # 图片另一维上的交点个数    [-n <number_of_frames>]  # 标定用的图片帧数                             # (if not specified, it will be set to the number                             #  of board views actually available)    [-d <delay>]             # a minimum delay in ms between subsequent attempts to capture a next view                             # (used only for video capturing)    [-s <square_size>]       # square size in some user-defined units (1 by default)    [-o <out_camera_params>] # the output filename for intrinsic [and extrinsic] parameters    [-op]                    # write detected feature points    [-oe]                    # write extrinsic parameters    [-zt]                    # assume zero tangential distortion    [-a <aspect_ratio>]      # fix aspect ratio (fx/fy)    [-p]                     # fix the principal point at the center    [-v]                     # flip the captured images around the horizontal axis    [input_data]             # 输入数据，是下面三种之中的一种:                             #  - 指定的包含图片列表的txt文件                             #  - name of video file with a video of the board                             # if input_data not specified, a live view from the camera is used

标定图片示例

上图中，横向和纵向分别为9个交点和6个交点，对应上面的命令行的命令参数应该为： -w 9 -h 6。

• 经多次使用发现，不指定 -p参数时计算的结果误差较大，主要表现在对u0,v0的估计误差较大，因此建议使用时加上-p参数

list_of_views.txt

该txt文件表示的是你在电脑上面需要用以标定的图片列表。

view000.pngview001.png#view002.pngview003.pngview010.pngone_extra_view.jpg

上面的例子中，前面加“井号”的图片被忽略。

• 在windows的命令行中，有一种简便的办法来产生此txt文件。在CMD窗口中输入如下命令（假设当前目录里面的所有jpg文件都用作标定,并且生成的文件为a.txt）。

dir *.jpg /B >> a.txt

输入为摄像机或者avi文件时

        "When the live video from camera is used as input, the following hot-keys may be used:\n"            "  <ESC>, ‘q‘ - quit the program\n"            "  ‘g‘ - start capturing images\n"            "  ‘u‘ - switch undistortion on/off\n";

代码

请直接复制 calibration.cpp 中的相关代码。

标定程序2

OPENCV没有提供完整的示例，自己整理了一下，贴出来记录。

1. 首先自制一张标定图片，用A4纸打印出来，设定距离，再设定标定棋盘的格子数目，如8×6，以下是我做的图片8×8

1. 然后利用cvFindChessboardCorners找到棋盘在摄像头中的2D位置，这里cvFindChessboardCorners不太稳定，有时不能工作，也许需要图像增强处理。
2. 计算实际的距离，应该是3D的距离。我设定为21.6毫米，既在A4纸上为两厘米。
3. 再用cvCalibrateCamera2计算内参，
4. 最后用cvUndistort2纠正图像的变形。

结果如下：

代码

代码下载

具体的函数使用，请参考Cv照相机定标和三维重建#照相机定标

#include "stdafx.h"#include <stdio.h>#include <stdlib.h>#include <string.h>// OpenCV#include <cxcore.h>#include <cv.h>#include <highgui.h>#include <cvaux.h>  void InitCorners3D(CvMat *Corners3D, CvSize ChessBoardSize, int Nimages, float SquareSize);void makeChessBoard();int myFindChessboardCorners( const void* image, CvSize pattern_size,                             CvPoint2D32f* corners, int* corner_count=NULL,                             int flags=CV_CALIB_CB_ADAPTIVE_THRESH );  inline int drawCorssMark(IplImage *dst,CvPoint pt)/*************************************************  Function:        main_loop  Description:     绘制一个十字标记					  Calls:            Called By:        Input:           RGB image,  pt                 Output:           Return:           Others:          需要检查坐标是否越界 to do list*************************************************/{ 	const int cross_len = 4;	CvPoint pt1,pt2,pt3,pt4;	pt1.x = pt.x;	pt1.y = pt.y - cross_len;	pt2.x = pt.x;	pt2.y = pt.y + cross_len;	pt3.x = pt.x - cross_len;	pt3.y = pt.y;	pt4.x = pt.x + cross_len;	pt4.y = pt.y; 	cvLine(dst,pt1,pt2,CV_RGB(0,255,0),2,CV_AA, 0 );		cvLine(dst,pt3,pt4,CV_RGB(0,255,0),2,CV_AA, 0 ); 	return 0;} /* declarations for OpenCV */IplImage                 *current_frame_rgb,grid;IplImage                 *current_frame_gray;IplImage                 *chessBoard_Img; int                       Thresholdness = 120; int image_width = 320;int image_height = 240; bool verbose = false; const int ChessBoardSize_w = 7;const int ChessBoardSize_h = 7;// Calibration stuffbool			calibration_done = false;const CvSize 	ChessBoardSize = cvSize(ChessBoardSize_w,ChessBoardSize_h);//float 			SquareWidth = 21.6f; //实际距离 毫米单位 在A4纸上为两厘米float 			SquareWidth = 17; //投影实际距离 毫米单位  200 const   int NPoints = ChessBoardSize_w*ChessBoardSize_h;const   int NImages = 20; //Number of images to collect  CvPoint2D32f corners[NPoints*NImages];int corner_count[NImages] = {0};int captured_frames = 0; CvMat *intrinsics;CvMat *distortion_coeff;CvMat *rotation_vectors;CvMat *translation_vectors;CvMat *object_points;CvMat *point_counts;CvMat *image_points;int find_corners_result =0 ;  void on_mouse( int event, int x, int y, int flags, void* param ){     if( event == CV_EVENT_LBUTTONDOWN )    {		//calibration_done = true;     }}  int main(int argc, char *argv[]){    CvFont font;  cvInitFont( &font, CV_FONT_VECTOR0,5, 5, 0, 7, 8);   intrinsics 		= cvCreateMat(3,3,CV_32FC1);  distortion_coeff 	= cvCreateMat(1,4,CV_32FC1);  rotation_vectors 	= cvCreateMat(NImages,3,CV_32FC1);  translation_vectors 	= cvCreateMat(NImages,3,CV_32FC1);   point_counts 		= cvCreateMat(NImages,1,CV_32SC1);   object_points 	= cvCreateMat(NImages*NPoints,3,CV_32FC1);  image_points 		= cvCreateMat(NImages*NPoints,2,CV_32FC1);    // Function to fill in the real-world points of the checkerboard  InitCorners3D(object_points, ChessBoardSize, NImages, SquareWidth);    CvCapture* capture = 0;    if( argc == 1 || (argc == 2 && strlen(argv[1]) == 1 && isdigit(argv[1][0])))	  capture = cvCaptureFromCAM( argc == 2 ? argv[1][0] - ‘0‘ : 0 );  else if( argc == 2 )	  capture = cvCaptureFromAVI( argv[1] );   if( !capture )  {	  fprintf(stderr,"Could not initialize capturing...\n");	  return -1;  }    // Initialize all of the IplImage structures  current_frame_rgb = cvCreateImage(cvSize(image_width, image_height), IPL_DEPTH_8U, 3);   IplImage *current_frame_rgb2 = cvCreateImage(cvSize(image_width, image_height), IPL_DEPTH_8U, 3);  current_frame_gray = cvCreateImage(cvSize(image_width, image_height), IPL_DEPTH_8U, 1);   chessBoard_Img   = cvCreateImage(cvSize(image_width, image_height), IPL_DEPTH_8U, 3);    current_frame_rgb2->origin = chessBoard_Img->origin  = current_frame_gray->origin = current_frame_rgb->origin = 1;   makeChessBoard();   cvNamedWindow( "result", 0);  cvNamedWindow( "Window 0", 0);  cvNamedWindow( "grid", 0);  cvMoveWindow( "grid", 100,100);  cvSetMouseCallback( "Window 0", on_mouse, 0 );    cvCreateTrackbar("Thresholdness","Window 0",&Thresholdness, 255,0);   while (!calibration_done)  { 	while (captured_frames < NImages)    {	  current_frame_rgb = cvQueryFrame( capture );	  //current_frame_rgb = cvLoadImage( "c:\\BoardStereoL3.jpg" );	  //cvCopy(chessBoard_Img,current_frame_rgb); 	  if( !current_frame_rgb )		  break; 	  cvCopy(current_frame_rgb,current_frame_rgb2);	  cvCvtColor(current_frame_rgb, current_frame_gray, CV_BGR2GRAY);	  //cvThreshold(current_frame_gray,current_frame_gray,Thresholdness,255,CV_THRESH_BINARY);	  //cvThreshold(current_frame_gray,current_frame_gray,150,255,CV_THRESH_BINARY_INV); /*	int pos = 1;	IplConvKernel* element = 0;	const int element_shape = CV_SHAPE_ELLIPSE;	element = cvCreateStructuringElementEx( pos*2+1, pos*2+1, pos, pos, element_shape, 0 );	cvDilate(current_frame_gray,current_frame_gray,element,1);	cvErode(current_frame_gray,current_frame_gray,element,1);	cvReleaseStructuringElement(&element);*/ 	find_corners_result = cvFindChessboardCorners(current_frame_gray,                                          ChessBoardSize,                                          &corners[captured_frames*NPoints],                                          &corner_count[captured_frames],                                          0);   	cvDrawChessboardCorners(current_frame_rgb2, ChessBoardSize, &corners[captured_frames*NPoints], NPoints, find_corners_result);  	cvShowImage("Window 0",current_frame_rgb2);	cvShowImage("grid",chessBoard_Img); 	if(find_corners_result==1)	{		cvWaitKey(2000);		cvSaveImage("c:\\hardyinCV.jpg",current_frame_rgb2);		captured_frames++;	}	//cvShowImage("result",current_frame_gray); 	intrinsics->data.fl[0] = 256.8093262;   //fx			intrinsics->data.fl[2] = 160.2826538;   //cx	intrinsics->data.fl[4] = 254.7511139;   //fy	intrinsics->data.fl[5] = 127.6264572;   //cy 	intrinsics->data.fl[1] = 0;   	intrinsics->data.fl[3] = 0;   	intrinsics->data.fl[6] = 0;   	intrinsics->data.fl[7] = 0;   	intrinsics->data.fl[8] = 1;   	 	distortion_coeff->data.fl[0] = -0.193740;  //k1	distortion_coeff->data.fl[1] = -0.378588;  //k2	distortion_coeff->data.fl[2] = 0.028980;   //p1	distortion_coeff->data.fl[3] = 0.008136;   //p2 	cvWaitKey(40);	find_corners_result = 0;    }   	//if (find_corners_result !=0)	{ 		printf("\n"); 		cvSetData( image_points, corners, sizeof(CvPoint2D32f));		cvSetData( point_counts, &corner_count, sizeof(int));  		cvCalibrateCamera2( object_points,			image_points,			point_counts,			cvSize(image_width,image_height),			intrinsics,			distortion_coeff,			rotation_vectors,			translation_vectors,			0);  		// [fx 0 cx; 0 fy cy; 0 0 1].		cvUndistort2(current_frame_rgb,current_frame_rgb,intrinsics,distortion_coeff);		cvShowImage("result",current_frame_rgb);  		float intr[3][3] = {0.0};		float dist[4] = {0.0};		float tranv[3] = {0.0};		float rotv[3] = {0.0}; 		for ( int i = 0; i < 3; i++)		{			for ( int j = 0; j < 3; j++)			{				intr[i][j] = ((float*)(intrinsics->data.ptr + intrinsics->step*i))[j];			}			dist[i] = ((float*)(distortion_coeff->data.ptr))[i];			tranv[i] = ((float*)(translation_vectors->data.ptr))[i];			rotv[i] = ((float*)(rotation_vectors->data.ptr))[i];		}		dist[3] = ((float*)(distortion_coeff->data.ptr))[3]; 		printf("-----------------------------------------\n");		printf("INTRINSIC MATRIX: \n");		printf("[ %6.4f %6.4f %6.4f ] \n", intr[0][0], intr[0][1], intr[0][2]);		printf("[ %6.4f %6.4f %6.4f ] \n", intr[1][0], intr[1][1], intr[1][2]);		printf("[ %6.4f %6.4f %6.4f ] \n", intr[2][0], intr[2][1], intr[2][2]);		printf("-----------------------------------------\n");		printf("DISTORTION VECTOR: \n");		printf("[ %6.4f %6.4f %6.4f %6.4f ] \n", dist[0], dist[1], dist[2], dist[3]);		printf("-----------------------------------------\n");		printf("ROTATION VECTOR: \n");		printf("[ %6.4f %6.4f %6.4f ] \n", rotv[0], rotv[1], rotv[2]);		printf("TRANSLATION VECTOR: \n");		printf("[ %6.4f %6.4f %6.4f ] \n", tranv[0], tranv[1], tranv[2]);		printf("-----------------------------------------\n"); 		cvWaitKey(0); 		calibration_done = true;      	}   }   exit(0);  cvDestroyAllWindows();} void InitCorners3D(CvMat *Corners3D, CvSize ChessBoardSize, int NImages, float SquareSize){  int CurrentImage = 0;  int CurrentRow = 0;  int CurrentColumn = 0;  int NPoints = ChessBoardSize.height*ChessBoardSize.width;  float * temppoints = new float[NImages*NPoints*3];   // for now, assuming we‘re row-scanning  for (CurrentImage = 0 ; CurrentImage < NImages ; CurrentImage++)  {    for (CurrentRow = 0; CurrentRow < ChessBoardSize.height; CurrentRow++)    {      for (CurrentColumn = 0; CurrentColumn < ChessBoardSize.width; CurrentColumn++)      {		  temppoints[(CurrentImage*NPoints*3)+(CurrentRow*ChessBoardSize.width + CurrentColumn)*3]=(float)CurrentRow*SquareSize;		  temppoints[(CurrentImage*NPoints*3)+(CurrentRow*ChessBoardSize.width + CurrentColumn)*3+1]=(float)CurrentColumn*SquareSize;		  temppoints[(CurrentImage*NPoints*3)+(CurrentRow*ChessBoardSize.width + CurrentColumn)*3+2]=0.f;      }    }  }  (*Corners3D) = cvMat(NImages*NPoints,3,CV_32FC1, temppoints);} int myFindChessboardCorners( const void* image, CvSize pattern_size,                             CvPoint2D32f* corners, int* corner_count,                             int flags ) {  	IplImage* eig = cvCreateImage( cvGetSize(image), 32, 1 );	IplImage* temp = cvCreateImage( cvGetSize(image), 32, 1 );	double quality = 0.01;	double min_distance = 5;	int win_size =10; 	int count = pattern_size.width * pattern_size.height;	cvGoodFeaturesToTrack( image, eig, temp, corners, &count,		quality, min_distance, 0, 3, 0, 0.04 );	cvFindCornerSubPix( image, corners, count,		cvSize(win_size,win_size), cvSize(-1,-1),		cvTermCriteria(CV_TERMCRIT_ITER|CV_TERMCRIT_EPS,20,0.03)); 	cvReleaseImage( &eig );	cvReleaseImage( &temp ); 	return 1;} void makeChessBoard(){   CvScalar e;   e.val[0] =255;  e.val[1] =255;  e.val[2] =255;  cvSet(chessBoard_Img,e,0);  for(int i = 0;i<ChessBoardSize.width+1;i++)	  for(int j = 0;j<ChessBoardSize.height+1;j++)	  {		  int w =(image_width)/2/(ChessBoardSize.width);		  int h = w; //(image_height)/2/(ChessBoardSize.height); 		  int ii = i+1;		  int iii = ii+1;		  int jj =j+1;		  int jjj =jj+1;		  int s_x = image_width/6;		   		if((i+j)%2==1)		   cvRectangle( chessBoard_Img, cvPoint(w*i+s_x,h*j+s_x),cvPoint(w*ii-1+s_x,h*jj-1+s_x), CV_RGB(0,0,0),CV_FILLED, 8, 0 );	  }}