原理参考：直线拟合——最小二乘法、hough变换
#include <iostream>
#include <opencv2/opencv.hpp>
using namespace std;
using namespace cv;
void fitline(std::vector<cv::Point>& points, cv::Vec4f& line_para)
{
int N = points.size();
if (N < 2) return;
double sum_x = 0, sum_y = 0, sum_xx = 0, sum_xy = 0, sum_yy = 0;
for (int i = 0; i < N; i++)
{
sum_x += points[i].x;
sum_y += points[i].y;
sum_xx += points[i].x * points[i].x;
sum_xy += points[i].x * points[i].y;
sum_yy += points[i].y * points[i].y;
}
//least squares: y=kx+b
float k = (N*sum_xy-sum_x*sum_y) / (N*sum_xx - sum_x*sum_x);
float b = (sum_xx*sum_y - sum_x*sum_xy) / (N*sum_xx - sum_x*sum_x);
std::cout << "k = " << k << ", b = " << b << std::endl;
//total least squares: ax+by+c=0
float A, B, C;
float mean_x = sum_x / N, mean_y = sum_y / N, mean_xx = sum_xx / N, mean_xy = sum_xy / N, mean_yy = sum_yy / N;
cv::Mat m = (cv::Mat_<float>(2, 2) << mean_xx - mean_x*mean_x, mean_xy - mean_x*mean_y, mean_xy - mean_x*mean_y, mean_yy - mean_y*mean_y);
cv::Mat eigenvalue, eigenvector;
cv::eigen(m * N, eigenvalue, eigenvector);
float v0 = eigenvalue.at<float>(0, 0), v1 = eigenvalue.at<float>(0, 1);
if (abs(v0) < abs(v1))
{
A = eigenvector.at<float>(0, 0);
B = eigenvector.at<float>(0, 1);
}
else {
A = eigenvector.at<float>(1, 0);
B = eigenvector.at<float>(1, 1);
}
C = -(A*mean_x + B*mean_y);
std::cout << "k = " << -A / B << ", b = " << -C / B << std::endl;
line_para[0] = B;
line_para[1] = -A;
line_para[2] = mean_x;
line_para[3] = mean_y;
}
int main(int argc, char** argv)
{
std::vector<cv::Point> points;
points.push_back(cv::Point(48, 58));
points.push_back(cv::Point(105, 98));
points.push_back(cv::Point(155, 160));
points.push_back(cv::Point(212, 220));
points.push_back(cv::Point(248, 260));
points.push_back(cv::Point(320, 300));
points.push_back(cv::Point(350, 360));
points.push_back(cv::Point(412, 400));
cv::Vec4f line_para;
cv::fitLine(points, line_para, cv::DIST_L2, 0, 1e-2, 1e-2);
std::cout << "line_para = " << line_para << std::endl;
float k = line_para[1] / line_para[0];
float b = line_para[3] - k*line_para[2];
std::cout << "k = " << k << ", b = " << b << std::endl;
fitline(points, line_para);
std::cout << "line_para = " << line_para << std::endl;
system("pause");
return EXIT_SUCCESS;
}
