读入RGB文件得到各分量的概率分布及熵

在编写之前需要进行一些准备工作：

• 需要有支持RGB文件读入的头文件
• Xcode本身不支持对数运算，所以在求熵时需要添加cmath头文件

#include <iostream>
#include<cmath>
#include <fstream>

准备工作做好后，可以开始编写代码了：

#include <iostream>
#include<cmath>
#include <fstream>
#define Size 65536
using namespace std;
int main()
{
    //导入rgb文件并对txt存储文件命名
    ifstream iofile("/Users/yaohaoyuan/Downloads/The Third Work/down.rgb", ios::binary);
    ofstream outfileR("/Users/yaohaoyuan/Downloads/The Third Work/R.txt", ios::trunc);
    ofstream outfileG("/Users/yaohaoyuan/Downloads/The Third Work/G.txt", ios::trunc);
    ofstream outfileB("/Users/yaohaoyuan/Downloads/The Third Work/B.txt", ios::trunc);
    
    //输出txt文件抬头
    outfileR << "Symbol \t Frequency" << endl;
    outfileG << "Symbol \t Frequency" << endl;
    outfileB << "Symbol \t Frequency" << endl;
 
    if (!iofile)
    {
         cout << "File import failed!" << endl;
         exit(1);
    }
    
    //创建三个数组用于存储
    unsigned char R_i[Size];
    unsigned char G_i[Size];
    unsigned char B_i[Size];
    int R[256] = { 0 }, G[256] = { 0 }, B[256] = { 0 };
    
    
    //文件读取&复制
    for (int i = 0; i < Size; i++)
    {
         iofile.read((char*)&B_i[i], sizeof(unsigned char));
         B[int(B_i[i])]++;
         iofile.read((char*)&G_i[i], sizeof(unsigned char));
         G[int(G_i[i])]++;
         iofile.read((char*)&R_i[i], sizeof(unsigned char));
         R[int(R_i[i])]++;
     }

    
    //计算各分量的信源熵，信源熵计算公式：H(x)=E[I(xi)]=E[log2 1/p(xi)]=-ξp(xi)log2 p(xi)(i=1,2,..n)
    double  Entropy_G = 0,   Entropy_B = 0,   Entropy_R = 0;
    for (int i = 0; i < 256; i++)
    {
         double Probability_G = G[i] / Size;
         if (Probability_G != 0)
         {
             Entropy_G += Probability_G * log(1 / Probability_G) / log(2);
         }
         double Probability_B = B[i] / Size;
         if (Probability_B != 0)
         {
             Entropy_B += Probability_B * log(1 / Probability_B) / log(2);
         }
         double Probability_R = R[i] / Size;
         if (Probability_R != 0)
         {
             Entropy_R += Probability_R * log(1 / Probability_R) / log(2);
         }
    }
    
    
    //输出各分量的熵值
    cout << "Entropy_Red=" << Entropy_R << endl;
    cout << "Entropy_Green=" << Entropy_G << endl;
    cout << "Entropy_Blue=" << Entropy_B << endl;

    //利用outfile对象把希望输出到文件中的数据输出到txt中 
    for (int i = 0; i < 256; i++)
    {
         outfileR << i << "\t" << R[i] / Size << endl;
         outfileG << i << "\t" << G[i] / Size << endl;
         outfileB << i << "\t" << B[i] / Size << endl;
    }
    
    //输出完成后要关闭对象与文件之间的联接
    iofile.close();
    outfileR.close();
    outfileG.close();
    outfileB.close();
    cout << "Files created successfully!" << endl;
    return 0;
}

R,G,B的熵值如下：

将数据导入Excel，作表可得：

各熵值比较：