OpenCV 直线拟合及应用

直线拟合顾名思义就是根据多个有限个数的点确定一条直线。依据为：

其中为第i个点到直线的距离，p(d)则为确定最小值的函数。而不同的p(d)对应着不同的直线拟合方法：

OpenCV提供了7种（-1为用户定义）直线拟合方法，如下：

CV_DIST_USER    =-1,  /* User defined distance */CV_DIST_L1      =1,   /* distance = |x1-x2| + |y1-y2| */CV_DIST_L2      =2,   /* the simple euclidean distance */CV_DIST_C       =3,   /* distance = max(|x1-x2|,|y1-y2|) */CV_DIST_L12     =4,   /* L1-L2 metric: distance = 2(sqrt(1+x*x/2) - 1)) */CV_DIST_FAIR    =5,   /* distance = c^2(|x|/c-log(1+|x|/c)), c = 1.3998 */CV_DIST_WELSCH  =6,   /* distance = c^2/2(1-exp(-(x/c)^2)), c = 2.9846 */CV_DIST_HUBER   =7    /* distance = |x|<c ? x^2/2 : c(|x|-c/2), c=1.345 */

OpenCV直线拟合函数：

CV_EXPORTS_W void fitLine( InputArray points, OutputArray line, int distType,double param, double reps, double aeps );

points为2D的点：
distType即为上面提到的算法；
param 是 上述公式中的常数C。如果取 0，则程序自动选取合适的值；
reps 表示直线到原点距离的精度，建议取 0.01；
aeps 表示直线角度的精度，建议取 0.01；
拟合结果即为函数的输出 line，为Vec4f类型，line[0]、line[1] 存放的是直线的方向向量。line[2]、line[3] 存放的是直线上一个点的坐标。
所以 ，直线的斜率即为：line[1]/line[0]。

直线拟合的应用：

#include <iostream>  #include <opencv2/core/core.hpp>  #include <opencv2/highgui/highgui.hpp>  #include <opencv2/opencv.hpp>  #define  PI 3.141592653using namespace cv;  using namespace std;  int main(){       Mat SrcImage, thresholdImage,grayImage;    SrcImage = imread("2.jpg");    cvtColor(SrcImage,grayImage,CV_BGR2GRAY);    threshold(grayImage,thresholdImage, 0, 255, CV_THRESH_OTSU+CV_THRESH_BINARY);    imshow("threshold",thresholdImage);    vector<Point2f> onefitlinepoints,twofitlinepoints;   //从上自下选择点    for (int i =SrcImage.cols/2-SrcImage.cols/5;i<SrcImage.cols/2+SrcImage.cols/5;i++)     { for (int j=0;j<SrcImage.rows-1;j++)        {if ((int)thresholdImage.at<uchar>(j,i)==255)            {  circle(thresholdImage,Point(i,j),2,Scalar(0,255,0));                onefitlinepoints.push_back(Point(i,j));                break;              }}}             //从下自上选择点     for (int k =SrcImage.cols/2-SrcImage.cols/5;k<SrcImage.cols/2+SrcImage.cols/5;k++)      {  for (int l=SrcImage.rows-1;l>0;l--)         {if ((int)thresholdImage.at<uchar>(l,k)==255)            { circle(thresholdImage,Point(k,l),2,Scalar(0,255,0));               twofitlinepoints.push_back(Point(k,l));               break;              }}}         //计算第一次拟合角度     Vec4f oneline;     fitLine(onefitlinepoints, oneline, CV_DIST_L1, 0, 0.01, 0.01);     cout<<oneline[0]<<endl;     cout<<oneline[1]<<endl;    //求角度     double  onefitlineradian =  atan(oneline[1]/oneline[0]);     double  onefitlineangle = (onefitlineradian*180)/CV_PI;     cout<<"直线拟合角度="<<onefitlineangle<<endl;    //计算第二次拟合角度    Vec4f twoline;    fitLine(twofitlinepoints, twoline, CV_DIST_L1, 0, 0.01, 0.01);    cout<<twoline[0]<<endl;    cout<<twoline[1]<<endl;    //求角度    double  twofitlineradian =  atan(twoline[1]/twoline[0]);    double  twofitlineangle = (twofitlineradian*180)/CV_PI;    cout<<"直线拟合角度="<<twofitlineangle<<endl;    double averagefitlineangle = (onefitlineangle+twofitlineangle)/2;    cout<<"直线拟合平均角度="<<averagefitlineangle<<endl;    //画出直线    Point2f point1,point2,point3;    point2.x = oneline[2];    point2.y = oneline[3];    point1.x = 0;    point1.y = oneline[1]*(point1.x-oneline[2])/oneline[0]+oneline[3];    point3.x = SrcImage.cols;    point3.y = oneline[1]*(point3.x-oneline[2])/oneline[0]+oneline[3];    line(SrcImage,point1,point3,Scalar(0,0,255));    imshow("直线拟合",SrcImage);    waitKey(0);    getchar();    return 0;}