二维高斯分布随机数

第一种方式：

#include
#include
using namespace cv;
using namespace std;

#define PI 3.1415926

double AverageRandom(double min, double max)//生成一个平均分布的随机数
{
	int minInteger = (int)(min * 10000);
	int maxInteger = (int)(max * 10000);
	int randInteger = rand()*rand();
	int diffInteger = maxInteger - minInteger;
	int resultInteger = randInteger % diffInteger + minInteger;
	return resultInteger / 10000.0;
}
double Normal2(double x, double y, double miu1, double miu2, Mat matrix, float detCov) //二维正态分布密度函数
{
	float a = matrix.at(0, 0);
	float b = matrix.at(0, 1);
	float c = matrix.at(1, 0);
	float d = matrix.at(1, 1);

	double A = 2 * PI*detCov;
	double B = a*(x - miu1)*(x - miu1) + (b + c)*(x - miu1)*(y - miu2) + d*(y - miu2)*(y - miu2);

	//cout << "==" << 1.0 / A*exp(-0.5*B)<= z);
	return p;
}//产生二维正态分布随机数

void covMatrix(float a, float b, float c, float d, Mat& inverse_matrix, float& detCov)  //协方差矩阵
{
	Mat cov_matrix(2, 2, CV_32FC1);    //协方差矩阵
	cov_matrix.at(0, 0) = a;
	cov_matrix.at(0, 1) = b;
	cov_matrix.at(1, 0) = c;
	cov_matrix.at(1, 1) = d;
	detCov = abs(a*d - b*c);

	//Mat inverse_matrix(2, 2, CV_32FC1);   //协方差逆矩阵
	inverse_matrix.at(0, 0) = cov_matrix.at(1, 1) / detCov;
	inverse_matrix.at(0, 1) = -cov_matrix.at(0, 1) / detCov;
	inverse_matrix.at(1, 0) = -cov_matrix.at(1, 0) / detCov;
	inverse_matrix.at(1, 1) = cov_matrix.at(0, 0) / detCov;

	cout << "【默认风格】" << endl << cov_matrix << endl << endl;
	cout << "【默认风格】" << endl << inverse_matrix / detCov << endl << endl;
	cout << "detCov= " << detCov << endl;
}
int main()
{
	Mat src(200, 200, CV_8UC1);
	for (int i = 0; i < src.rows; i++)
	{
		for (int j = 0; j < src.cols; j++)
		{
			src.at(i, j) = 0;
		}
	}
	float detCov = 0;   //协方差矩阵det
	Mat inverse_matrix(2, 2, CV_32FC1);   //协方差逆矩阵
	covMatrix(1, 0, 0, 6, inverse_matrix, detCov);

	int min = 0;
	int max = 200;
	Point2i p;
	for (int i = 0; i < 12000; i++)
		{
		p = NormalRandom2(100, 100, inverse_matrix,detCov,min,max);
			cout << p.x << "  " << p.y << endl;
			src.at((int)p.x, (int)p.y) = 255;
		}
	imshow("src", src);
	imwrite("1006.jpg", src);
	waitKey(0);
	return 0;
}

第二种方式：效果好像不是很好，思路很好，第一种就是参考这个的

#include
#include
using namespace cv;
using namespace std;
#define PI 3.1415926

/*http://blog.csdn.net/fdybit/article/details/8018687*/
struct vector1
{ 
	double x;
	double y; };//二维向量

double AverageRandom(double min, double max)//生成一个平均分布的随机数
{
	int minInteger = (int)(min * 10000);
	int maxInteger = (int)(max * 10000);
	int randInteger = rand()*rand();
	int diffInteger = maxInteger - minInteger;
	int resultInteger = randInteger % diffInteger + minInteger;
	return resultInteger / 10000.0;
}


double Normal2(double x, double y, double miu1, double miu2, double sigma1, double sigma2, double r) //二维正态分布密度函数
{
	double m = 1.0 / (sqrt(1 - r*r)*(2 * PI*sigma1*sigma2)) * exp((-1 / (2 * (1 - r*r)))*((x - miu1)*(x - miu1) / (sigma1*sigma1) 
		- 2 * r*(x - miu1)*(y - miu2) / (sigma1*sigma2) + (y - miu2)*(y - miu2) / (sigma2*sigma2)));
	//cout << "====" << m << "=====" << endl;
	return m;
}

vector1 NormalRandom2(double miu1, double miu2, double sigma1, double sigma2, double r, double min, double max)//产生二维正态分布随机数
{
	vector1 vec;
	double z;
	double dScope;

	do
	{
		vec.x = AverageRandom(min, max);
		vec.y = AverageRandom(min, max);
		z = Normal2(vec.x, vec.y, miu1, miu2, sigma1, sigma2, r);
		dScope = AverageRandom(0, Normal2(miu1, miu2, miu1, miu2, sigma1, sigma2, r));
	} while (dScope > z);
	return vec;
}

int main()
{
	struct vector1 P;
	Mat src(200, 200, CV_8UC1);
	for (int i = 0; i < src.rows; i++)
	{
		for (int j = 0; j < src.cols; j++)
		{
			src.at(i, j) = 0;
		}

	}
	for (int i = 0; i < 11300; i++)
	{
		P = NormalRandom2(100, 100, 20, 4, 0, 0, 200);
		//cout << P.x << "  " << P.y << endl;
		src.at((int)P.x, (int)P.y) = 255;
	}
	imshow("src", src);
	waitKey(0);
	
	return 0;
}