1. 巴特沃斯低通滤波

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#include<iostream>
#include<opencv2/opencv.hpp>
#include"mydft.h"
#include"Salt.h"
#include<math.h>


using namespace std;
using namespace cv;

int main(){
    Mat img,img_gray,img_out,img_transform;

    img = imread("/home/v/home.png");
    if (img.empty()){
        cout<<"can not open the image"<<endl;
        return -1;
    }

    imshow("img",img);
    cvtColor(img,img_gray,COLOR_BGR2GRAY);
    imshow("img_gray",img_gray);

    Salt(img_gray,1000);
    imshow("img_gray_salt",img_gray);

    //1. 傅里叶变换，img_out为可显示频谱图，img_transform为傅里叶变换的复数结果
    mydft(img_gray,img_out,img_transform);
    imshow("img_out",img_out);

    //2. 巴特沃斯低通滤波
    Mat planes[] = {Mat_<float>(img_out),Mat::zeros(img_out.size(),CV_32F)};
    split(img_transform,planes); // 分离通道获取实部和虚部
    Mat img_transform_real = planes[0];
    Mat img_transform_imag = planes[1];

    int core_x = img_transform_real.rows/2;
    int core_y = img_transform_real.cols/2;
    int r = 60;
    float h;
    float n = 2; // 巴特沃斯系数
    float D; // 距离中心距离

    for(int i=0;i<img_transform_real.rows;i++){
        for (int j=0;j<img_transform_real.cols;j++){
            D = (i-core_x)*(i-core_x)+(j-core_y)*(j-core_y);
            h = 1/(1+pow((D/(r*r)),n));
            img_transform_real.at<float>(i,j) *= h;
            img_transform_imag.at<float>(i,j) *= h;
        }
    }

    planes[0] = img_transform_real;
    planes[1] = img_transform_imag;
    Mat img_transform_ilpf; // 定义巴特沃斯低通滤波结果
    merge(planes,2,img_transform_ilpf);

    //3. 傅里叶逆变换
    Mat iDft[] = {Mat_<float>(img_out),Mat::zeros(img_out.size(),CV_32F)};
    idft(img_transform_ilpf,img_transform_ilpf); // 傅里叶逆变换
    split(img_transform_ilpf,iDft); // 分离通道，主要获取0通道
    magnitude(iDft[0],iDft[1],iDft[0]); // 计算复数的幅值，保存在iDft[0]
    normalize(iDft[0],iDft[0],0,1,NORM_MINMAX);
    imshow("idft",iDft[0]); // 显示逆变换结果

    waitKey(0);
    return 0;
}