c++生成一个可以用最小二乘法拟合图像圆心并显示的代码

以下是一个使用C++语言实现最小二乘法拟合图像圆心并显示的示例代码：

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

using namespace std;
using namespace cv;

// 定义最小二乘法拟合圆的函数
bool fitCircle(const vector<Point2f>& points, Point2f& center, float& radius)
{
    if (points.size() < 3) // 数据点必须大于等于3个
        return false;

    float sum_x = 0, sum_y = 0, sum_x2 = 0, sum_y2 = 0, sum_xy = 0, sum_x3 = 0, sum_y3 = 0, sum_x2y = 0, sum_xy2 = 0;

    for (int i = 0; i < points.size(); i++)
    {
        float x = points[i].x;
        float y = points[i].y;
        sum_x += x;
        sum_y += y;
        sum_x2 += x * x;
        sum_y2 += y * y;
        sum_xy += x * y;
        sum_x3 += x * x * x;
        sum_y3 += y * y * y;
        sum_x2y += x * x * y;
        sum_xy2 += x * y * y;
    }

    float N = (float)points.size();
    float C = N * sum_x2 - sum_x * sum_x;
    float D = N * sum_xy - sum_x * sum_y;
    float E = N * sum_y2 - sum_y * sum_y;
    float G = (float)0.5 * (N * (sum_x2 + sum_y2) - sum_x * sum_x - sum_y * sum_y);
    float H = 0.5*(N * sum_x3 + N * sum_xy2 - sum_x2 * sum_y - sum_x * sum_y2);
    float K = 0.5*(N * sum_y3 + N * sum_x2y - sum_x * sum_y2 - sum_y * sum_x2);

    float a = (H*E - K*D) / (C*E - D*D);
    float b = (K*C - H*D) / (C*E - D*D);
    float c = -(a*sum_x + b * sum_y + G);

    center.x = a;
    center.y = b;
    radius = sqrt(a * a + b * b - c);

    return true;
}

int main()
{
    Mat image = imread("test.jpg", 0); // 读取灰度图像
    Mat dst = image.clone();

    GaussianBlur(image, image, Size(3, 3), 0); // 高斯滤波
    threshold(image, image, 0, 255, THRESH_BINARY | THRESH_OTSU); // 二值化

    vector<vector<Point>> contours;
    findContours(image, contours, RETR_EXTERNAL, CHAIN_APPROX_NONE); // 查找轮廓

    vector<Point2f> points;
    for (int i = 0; i < contours.size(); i++) // 遍历轮廓
    {
        for (int j = 0; j < contours[i].size(); j++)
        {
            Point2f pt = contours[i][j];
            points.push_back(pt);
        }
    }

    Point2f center;
    float radius;
    bool flag = fitCircle(points, center, radius); // 拟合圆

    if (flag)
    {
        circle(dst, center, radius, Scalar(255), 2); // 绘制圆
        imshow("Result", dst);
        waitKey(0);
    }

    return 0;
}

该代码首先读取一张灰度图像，并对其进行高斯滤波和二值化处理，然后查找图像中的轮廓，并将轮廓上的所有点存储在一个vector<Point2f>类型的向量中。接着调用fitCircle函数来拟合圆心和半径，并在拟合完成后在原图像上绘制出圆。最后将处理结果显示出来。