利用opencv ,通过几个点拟合曲线_拟合曲线opencv

#include <iostream>
#include <vector>
#include <opencv2/opencv.hpp>

using namespace std;
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) +pow(key_point[k].x, i + j);
				
			}
		}
	}

	//构造矩阵Y
	cv::Mat Y = cv::Mat::zeros(n + 1, 1, CV_64FC1);
	cout << Y << endl;
	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) +pow(key_point[k].x, i) * key_point[k].y;
		}
	}
	cout << Y << endl;

	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
	Mat image = Mat::zeros(480, 640, CV_8UC3);
	image.setTo(Scalar(100, 0, 0));


	//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, 0), 1, 8, 0);

	cv::Mat A;
	int m=4;//为多项式的最高次幂
	polynomial_curve_fit(points, m, A);
	std::cout << "A = " << A << std::endl;
	
	std::vector<cv::Point> points_fitted;
	double y=0;
	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);*/

		for (int k = 0; k < m+1; k++)
		{
			double tmp = A.at<double>(k, 0) * pow(x, k);
			y = y + tmp;
		}


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

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

	cv::waitKey(0);
	return 0;
}
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98