图像相似性度量—— 归一化互信息实现

1. 概述

归一化互信息是度量两张图片相似度的一种表达方式，它的值越大代表两张图片的相似性越高。通常用来作为图像配准中的评判准则或是目标函数。它在两幅图像的灰度级数相似的情况下有良好的配准精度，较高的可靠性；但是同时存在计算量大，实时性差的不足。注：这里的实现是基于Opencv2的。
原理是分别计算图像A,B的信息熵，再计算联合的信息熵。



然后代入公式计算归一化信息熵。这里的联合概率密度P(a,b)具体指的是A图像的灰度级a在图像的相同坐标下在图像B中灰度级为b的像素点的个数与总点数的比值。

2. 实现

//************************************************************************
// 函数名称:    	GetMutualInfo
// 访问权限:    	public
// 创建日期:		2016/12/09
// 创 建 人:
// 函数说明:		计算输入图像A和输入图像B的互信息
// 函数参数: 	cv::Mat & img_a	输入图像A
// 函数参数: 	cv::Mat & img_b	输入图像B
// 返 回 值:   	double
//************************************************************************
double CCalcMutualInfo::GetMutualInfo(cv::Mat& img_a, cv::Mat& img_b)
{
if (!img_a.data || !img_b.data)
{
cout << "no input img" << endl;
return 0.0;
}
if (img_a.rows!=img_a.rows || img_a.cols!=img_b.cols)
{
cout << "input img's row and cosl not eqaul" << endl;
return 0.0;
}

int rows(img_a.rows);
int cols(img_b.cols);
int total_pixel(rows*cols);
unsigned char* data_a = nullptr;
unsigned char* data_b = nullptr;
double value(0.0);						//计算得到的互信息的结果
double H_a(0.0), H_b(0.0), H_ab(0.0);	//图像A,B或是AB的信息熵
double* count_array_a = new double[256];
memset(count_array_a, 0, sizeof(double)*256);
double* count_array_b = new double[256];
memset(count_array_b, 0, sizeof(double)* 256);
double* count_array_ab = new double[256*256];
memset(count_array_ab, 0, sizeof(double)* 256 * 256);

//计算H_a, H_b
for (int i=0; i<rows; i++)
{
data_a = img_a.ptr<unsigned char>(i);
data_b = img_b.ptr<unsigned char>(i);
for (int j=0; j<cols; j++)
{
count_array_a[data_a[j]]++;
count_array_b[data_b[j]]++;
}
}
for (int i=0; i<255; i++)
{
if (0.0 != count_array_a[i])
{
double p(count_array_a[i] / (double)total_pixel);
H_a = H_a + (-1.0*p*(std::log(p) / std::log(2)));
}

if (0.0 != count_array_b[i])
{
double p(count_array_b[i] / (double)total_pixel);
H_b = H_b + (-1.0*p*(std::log(p) / std::log(2)));
}
}

//计算H_ab
for (int m = 0; m < 256; m++)	//8位的灰度级
{
for (int n = 0; n < 256; n++)
{
for (int i = 0; i < rows; i++)
{
data_a = img_a.ptr<unsigned char>(i);
data_b = img_b.ptr<unsigned char>(i);
for (int j = 0; j < cols; j++)
{
//if ((std::abs(m-data_a[j])<20) && (std::abs(n-data_b[j])<20))
if ((m == data_a[j]) && (n == data_b[j]))	//由联合概率密度的实际物理意义，统计点数
{
count_array_ab[m*256 + n]++;
}
}
}
}
}
for (int m = 0; m < 256; m++)
{
for (int n = 0; n < 256; n++)
{
if (0.0 != count_array_ab[m*256 + n])
{
double p(count_array_ab[m*256 + n] / (double)total_pixel);
H_ab = H_ab + (-1.0*p*(std::log(p) / std::log(2)));
}
}
}

value = (H_a + H_b) / H_ab;	//得出归一化互信息
delete[] count_array_a;
delete[] count_array_b;
delete[] count_array_ab;
count_array_ab = nullptr;
count_array_a = nullptr;
count_array_b = nullptr;
return value;
}