opencv 最小二乘法擬合輪廓點

bool polynomial_curve_fit(std::vector<cv::Point>& key_point, int n, cv::Mat& A)
{
	//Number of key points
	int N = key_point.size();
 
	//構造矩陣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);
			}
		}
	}
 
	//構造矩陣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);
	//求解矩陣A
	cv::solve(X, Y, A, cv::DECOMP_LU); //X*A = Y
	return true;
}

int main()
{
	//創建用於繪制的深藍色背景圖像
	cv::Mat image = cv::Mat::zeros(480, 640, CV_8UC3);
	image.setTo(cv::Scalar(100, 0, 0));
 
	//輸入擬合點  
	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.));
 
	//將擬合點繪制到空白圖上  
	for (int i = 0; i < points.size(); i++)
	{
		cv::circle(image, points[i], 5, cv::Scalar(0, 0, 255), 2, 8, 0);
	}
 
	//繪制折線
	cv::polylines(image, points, false, cv::Scalar(0, 255, 0), 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(0, 255, 255), 1, 8, 0);
 
	cv::imshow("image", image);
 
	cv::waitKey(0);
	return 0;
}