opencv-fitLine

§ fitLine()

#include <opencv2/imgproc.hpp>

Fits a line to a 2D or 3D point set.

The function fitLine fits a line to a 2D or 3D point set by minimizing ∑iρ(ri) where ri is a distance between the ith point, the line and ρ(r) is a distance function, one of the following:

• DIST_L2

  ρ(r)=r2/2(the simplest and the fastest least-squares method)

• DIST_L1

  ρ(r)=r

• DIST_L12

  ρ(r)=2⋅(1+r22−−−−−−√−1)

• DIST_FAIR

  ρ(r)=C2⋅(rC−log(1+rC))whereC=1.3998

• DIST_WELSCH

  ρ(r)=C22⋅(1−exp(−(rC)2))whereC=2.9846

• DIST_HUBER

  ρ(r)={r2/2C⋅(r−C/2)if r<CotherwisewhereC=1.345

The algorithm is based on the M-estimator ( http://en.wikipedia.org/wiki/M-estimator ) technique that iteratively fits the line using the weighted least-squares algorithm. After each iteration the weights wi are adjusted to be inversely proportional to ρ(ri) .

Parameters

The example below:  

	Mat img = Mat::zeros(1000,1000,CV_8UC3);
	vector<Point> point_set;
	Point P1(100, 100), P2(100, 400), P3(150, 300), P4(200, 200), \
		P5(300, 300), P6(300, 800), P7(700, 100),P8(750,750);
	point_set.push_back(P1);
	point_set.push_back(P2);
	point_set.push_back(P3);
	point_set.push_back(P4);
	point_set.push_back(P5);
	point_set.push_back(P6);
	point_set.push_back(P7);
	point_set.push_back(P8);



	//将拟合点绘制到空白图上
	for (int i = 0; i < point_set.size(); i++)
	{
		cv::circle(img, point_set[i], 5, cv::Scalar(0, 255, 0), 2, 8, 0);
	}

	Vec4f fitline;
	fitLine(point_set, fitline, DIST_L2, 0, 0.01, 0.01);

	// 求出直线上的两个点
	double k_line = fitline[1] / fitline[0];

	//计算直线的端点: y = k(x - x0） + y0 
	//其中 fitline[2],fitline[3]为点斜式的点
	Point p1(0, k_line*(0 - fitline[2]) + fitline[3]);
	Point p2(img.rows - 1, k_line*(img.rows - 1 - fitline[2]) + fitline[3]);

	//显示拟合出的直线方程
	char text_equation[1024];
	sprintf(text_equation, "y-%.2f=%.2f(x-%.2f)", fitline[3], k_line, fitline[2]);

	putText(img, text_equation, Point(img.rows/2, img.cols/2),\
		FONT_HERSHEY_COMPLEX, 1, Scalar(0, 0, 255), 2, 8);
	//显示拟合出的直线
	line(img, p1, p2, Scalar(0, 0, 255), 2);
	imshow("原图+拟合结果", img);

	waitKey();

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