C++圆拟合算法：最小二乘法用于拟合图像中的圆算法代码

以下是使用最小二乘法拟合圆的C++代码：

#include <iostream>
#include <vector>
#include <cmath>

// 定义点的结构体
struct Point {
    double x;
    double y;
};

// 定义圆的结构体
struct Circle {
    double x;
    double y;
    double r;
};

// 求解圆的函数
Circle calcCircle(std::vector<Point>& points) {
    int n = points.size();

    // 计算点集的中心坐标
    double sumX = 0.0, sumY = 0.0;
    for (int i = 0; i < n; ++i) {
        sumX += points[i].x;
        sumY += points[i].y;
    }
    double centerX = sumX / n;
    double centerY = sumY / n;

    // 计算协方差矩阵
    double Sxx = 0.0, Syy = 0.0, Sxy = 0.0, Sxxx = 0.0, Sxxy = 0.0, Sxyy = 0.0, Syyy = 0.0;
    for (int i = 0; i < n; ++i) {
        double xi = points[i].x - centerX;
        double yi = points[i].y - centerY;
        Sxx += xi * xi;
        Syy += yi * yi;
        Sxy += xi * yi;
        Sxxx += xi * xi * xi;
        Sxxy += xi * xi * yi;
        Sxyy += xi * yi * yi;
        Syyy += yi * yi * yi;
    }
    double C1 = Sxx + Syy;
    double C2 = Sxx * Syy - Sxy * Sxy;
    double C3 = Sxxx + Sxxy;
    double C4 = Sxxy + Sxyy;
    double C5 = Syyy - Syy * Sxx;

    // 求解圆的参数
    double a = (C4 * C2 - C5 * Sxy) / (C3 * C3 - C2 * C4);
    double b = (C5 * C3 - C4 * C4) / (C3 * C3 - C2 * C4);
    double c = -(a * centerX + b * centerY + C1) / n;

    // 计算圆心和半径
    double circleX = -a / 2.0;
    double circleY = -b / 2.0;
    double radius = std::sqrt(circleX * circleX + circleY * circleY - c);

    return {circleX + centerX, circleY + centerY, radius};
}

int main() {
    // 创建点集
    std::vector<Point> points = {{1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}};

    // 求解圆
    Circle circle = calcCircle(points);

    // 输出圆的参数
    std::cout << "centerX: " << circle.x << "\n";
    std::cout << "centerY: " << circle.y << "\n";
    std::cout << "radius: " << circle.r << "\n";

    return 0;
}

该程序使用了最小二乘法求解圆的参数，并且输入为一个点集，输出为圆的中心坐标和半径。可以根据需要修改程序以适应不同的输入格式和输出格式。