直線擬合顧名思義就是根據多個有限個數的點確定一條直線。依據為：

其中為第i個點到直線的距離，p(d)則為確定最小值的函式。而不同的p(d)對應著不同的直線擬合方法：

OpenCV提供了7種（-1為使用者定義）直線擬合方法，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直線擬合函式：

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

points為2D的點：
distType即為上面提到的演算法；
param 是 上述公式中的常數C。如果取 0，則程式自動選取合適的值；
reps 表示直線到原點距離的精度，建議取 0.01；
aeps 表示直線角度的精度，建議取 0.01；
擬合結果即為函式的輸出 line，為Vec4f型別，line[0]、line[1] 存放的是直線的方向向量。line[2]、line[3] 存放的是直線上一個點的座標。
所以 ，直線的斜率即為：line[1]/line[0]。

直線擬合的應用：

#include <iostream>  
#include <opencv2/core/core.hpp>  
#include <opencv2/highgui/highgui.hpp>  
#include <opencv2/opencv.hpp>  

#define  PI 3.141592653

using 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;
   //從上自下選擇點
    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; 
             }}}
             //從下自上選擇點
     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; 
             }}}
         //計算第一次擬合角度
     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<<"直線擬合角度="<<onefitlineangle<<endl;

    //計算第二次擬合角度
    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<<"直線擬合角度="<<twofitlineangle<<endl;

    double averagefitlineangle = (onefitlineangle+twofitlineangle)/2;
    cout<<"直線擬合平均角度="<<averagefitlineangle<<endl;

    //畫出直線
    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("直線擬合",SrcImage);
    waitKey(0);
    getchar();
    return 0;
}