OpenCV Mahalanobis例子

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本文介绍如何使用OpenCV库进行矩阵操作，包括创建矩阵、填充矩阵元素、计算协方差矩阵及其逆矩阵，以及利用计算出的协方差逆矩阵计算两个点与均值之间的马氏距离。

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$\f[\texttt{r}_{mahalonobis}=\sqrt{(\vec{x}-u)^T\begin{matrix} \sum^{-1}\end{matrix}(\vec{x}-u)}\f]$

//包含OpenCV的头文件
#include <opencv2/opencv.hpp>
#include <opencv2/core/mat.hpp>
#include <iostream>
#include <time.h>
using namespace  std;
//使用OpenCV的命名空间
using namespace cv;

int main()
{
	//2行5列
	Mat Pt(2, 5, CV_64FC1);
	Pt.at<double>(0, 0) = 2;
	Pt.at<double>(1, 0) = 4;

	Pt.at<double>(0, 1) = 2;
	Pt.at<double>(1, 1) = 2;

	Pt.at<double>(0, 2) = 3;
	Pt.at<double>(1, 2) = 3;

	Pt.at<double>(0, 3) = 4;
	Pt.at<double>(1, 3) = 4;

	Pt.at<double>(0, 4) = 4;
	Pt.at<double>(1, 4) = 2;
	cout << Pt << endl;

	//计算协方差矩阵
	Mat coVar, meanVar;
	calcCovarMatrix(Pt, coVar, meanVar, COVAR_NORMAL|COVAR_COLS);
	cout << "Covar is:\n" << coVar << endl;
	cout << "Mean is:\n" << meanVar << endl;
	//计算协方差的逆
	Mat iCovar;
	invert(coVar, iCovar, DECOMP_SVD);

	Mat pt1(2, 1, CV_64FC1);
	Mat pt2(2, 1, CV_64FC1);
	pt1.at<double>(0, 0) = 1;
	pt1.at<double>(1, 0) = 1;
	pt2.at<double>(0, 0) = 5;
	pt2.at<double>(1, 0) = 5;

	double Maha1 = Mahalanobis(pt1, meanVar, iCovar);
	double Maha2 = Mahalanobis(pt2, meanVar, iCovar);
	cout << "Maha 距离1是：\t" << Maha1 << endl;
	cout << "Maha 距离2是:\t" << Maha2 << endl;
	return 0;
}