C++ 相关系数的计算以及在图像配准领域应用演示

相关系数（皮尔逊相关系数）公式如下

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

using namespace std;

// 计算平均值
double mean(vector<double> v) {
    double sum = 0;
    for (int i = 0; i < v.size(); i++) {
        sum += v[i];
    }
    return sum / v.size();
}

// 计算协方差
double covariance(vector<double> x, vector<double> y) {
    double x_mean = mean(x);
    double y_mean = mean(y);
    double sum = 0;
    for (int i = 0; i < x.size(); i++) {
        sum += (x[i] - x_mean) * (y[i] - y_mean);
    }
    return sum / x.size();
}

// 计算相关系数
double correlation(vector<double> x, vector<double> y) {
    double cov = covariance(x, y);
    double x_std = sqrt(covariance(x, x));
    double y_std = sqrt(covariance(y, y));
    return cov / (x_std * y_std);
}


int main() {
    vector<double> x = { 2, 3, 4, 5, 6};
    vector<double> y = { 20, 30, 40, 50, 61};
    cout << "Correlation: " << correlation(x, y) << endl;
    return 0;
}

运行结果