opencv 最小二乘法拟合曲线

//-----------------------------------【头文件包含部分】---------------------------------------
//       描述：包含程序所依赖的头文件
//----------------------------------------------------------------------------------------------
#include"opencv2/highgui/highgui.hpp"
#include"opencv2/imgproc/imgproc.hpp"
#include <iostream>

//-----------------------------------【命名空间声明部分】--------------------------------------
//    描述：包含程序所使用的命名空间
//-----------------------------------------------------------------------------------------------
using namespace cv;


bool polynomial_curve_fit(std::vector<cv::Point>& key_point, int n, cv::Mat& A)
{
    //Number of key points
    int N = key_point.size();

    //构造矩阵X
    cv::Mat X = cv::Mat::zeros(n + 1, n + 1, CV_64FC1);
    for (int i = 0; i < n + 1; i++)
    {
        for (int j = 0; j < n + 1; j++)
        {
            for (int k = 0; k < N; k++)
            {
                X.at<double>(i, j) = X.at<double>(i, j) +
                    std::pow(key_point[k].x, i + j);
            }
        }
    }

    //构造矩阵Y
    cv::Mat Y = cv::Mat::zeros(n + 1, 1, CV_64FC1);
    for (int i = 0; i < n + 1; i++)
    {
        for (int k = 0; k < N; k++)
        {
            Y.at<double>(i, 0) = Y.at<double>(i, 0) +
                std::pow(key_point[k].x, i) * key_point[k].y;
        }
    }

    A = cv::Mat::zeros(n + 1, 1, CV_64FC1);
    //求解矩阵A
    cv::solve(X, Y, A, cv::DECOMP_LU);
    return true;
}

int main()
{
    //创建用于绘制的深蓝色背景图像
    cv::Mat image = cv::Mat::zeros(480, 640, CV_8UC3);
    image.setTo(cv::Scalar(0, 0, 100));

    //输入拟合点
    std::vector<cv::Point> points;
    points.push_back(cv::Point(100., 58.));
    points.push_back(cv::Point(150., 70.));
    points.push_back(cv::Point(200., 90.));
    points.push_back(cv::Point(252., 140.));
    points.push_back(cv::Point(300., 220.));
    points.push_back(cv::Point(350., 400.));

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

    //绘制折线
    cv::polylines(image, points, false, cv::Scalar(0, 255, 255), 1, 8, 0);

    cv::Mat A;

    polynomial_curve_fit(points, 3, A);
    std::cout << "A = " << A << std::endl;

    std::vector<cv::Point> points_fitted;

    for (int x = 0; x < 400; x++)
    {
        double y = A.at<double>(0, 0) + A.at<double>(1, 0) * x +
            A.at<double>(2, 0)*std::pow(x, 2) + A.at<double>(3, 0)*std::pow(x, 3);

        points_fitted.push_back(cv::Point(x, y));
    }
    cv::polylines(image, points_fitted, false, cv::Scalar(255, 255, 255), 1, 8, 0);

    cv::imshow("image", image);

    cv::waitKey(0);
    return 0;
}