在C中使用FFTW的高通滤波器

Question

我对FFT有疑问。我已经设法在C中使用FFTW向前和向后进行FFT。现在，我想对边缘检测应用高通滤波器，我的一些消息来源说只是将幅度的中心归零。

这是我的输入图片 http://i62.tinypic.com/2wnxvfl.jpg

基本上我所做的是：

1. 正向FFT
2. 将输出转换为2D数组
3. 转发FFT移位
4. 当距离中心的距离为高度的25％
时，将real和imag值设为0
5. 生成幅度
6. 执行反向FFT移位
7. 转换为1D数组
8. 做向后FFT。

这是原始幅度，处理幅度和结果

http://i58.tinypic.com/aysx9s.png

有人可以帮助我，告诉我哪个部分是错的，以及如何在C中使用FFTW进行高通滤波。

谢谢。

源代码：

unsigned char **FFT2(int width,int height, unsigned char **pixel, char line1[100],char line2[100], char line3[100],char filename[100])
{
  fftw_complex* in, * dft, * idft, * dft2;

  //fftw_complex tmp1,tmp2;
  fftw_plan plan_f,plan_i;
  int i,j,k,w,h,N,w2,h2;

  w = width;
  h = height;
  N = w*h;

  unsigned char **pixel_out;
  pixel_out = malloc(h*sizeof(unsigned char*));
  for(i = 0 ; i<h;i++)
    pixel_out[i]=malloc(w*sizeof(unsigned char));



  in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *N);
  dft = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *N);
  dft2 = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *N);
  idft = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) *N);



  /*run forward FFT*/

  plan_f = fftw_plan_dft_2d(w,h,in,dft,FFTW_FORWARD,FFTW_ESTIMATE);
  for(i = 0,k = 0 ; i < h ; i++)
  {
    for(j = 0 ; j < w ; j++,k++)
    {
      in[k][0] = pixel[i][j];
      in[k][1] = 0.0;
    }
  }
  fftw_execute(plan_f);


  double maxReal = 0.0;
  for(i = 0 ; i < N ; i++)
    maxReal = dft[i][0] > maxReal ? dft[i][0] : maxReal;

  printf("MAX REAL : %f\n",maxReal);




  /*fftshift*/
  //convert to 2d
  double ***temp1;
  temp1 = malloc(h * sizeof (double**));
  for (i = 0;i < h; i++){
      temp1[i] = malloc(w*sizeof (double*));
      for (j = 0; j < w; j++){
          temp1[i][j] = malloc(2*sizeof(double));
      }
  }

  double ***temp2;
  temp2 = malloc(h * sizeof (double**));
  for (i = 0;i < h; i++){
      temp2[i] = malloc(w*sizeof (double*));
      for (j = 0; j < w; j++){
          temp2[i][j] = malloc(2*sizeof(double));
      }
  }




  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          temp1[i][j][0] = dft[i*w+j][0];
          temp1[i][j][1] = dft[i*w+j][1];
      }
  }





  int m2 = h/2;
  int n2 = w/2;



  //forward shifting
  for (i = 0; i < m2; i++)
  {
     for (k = 0; k < n2; k++)
     {
          double tmp13[2]         = {temp1[i][k][0],temp1[i][k][1]};
          temp1[i][k][0]       = temp1[i+m2][k+n2][0];
          temp1[i][k][1]    = temp1[i+m2][k+n2][1];
          temp1[i+m2][k+n2][0] = tmp13[0];
          temp1[i+m2][k+n2][1] = tmp13[1];

          double tmp24[2]       = {temp1[i+m2][k][0],temp1[i+m2][k][1]};
          temp1[i+m2][k][0]    = temp1[i][k+n2][0];
          temp1[i+m2][k][1]    = temp1[i][k+n2][1];
          temp1[i][k+n2][0]   = tmp24[0];
          temp1[i][k+n2][1]    = tmp24[1];
     }
  }



  //process

  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          if(distance_to_center(i,j,m2,n2) < 0.25*h)
          {
            temp1[i][j][0] = (double)0.0;
            temp1[i][j][1] = (double)0.0;
          }
      }
  }



  /* copy for magnitude */
  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          temp2[i][j][0] = temp1[i][j][0];
          temp2[i][j][1] = temp1[i][j][1];
      }
  }


  //backward shifting
  for (i = 0; i < m2; i++)
  {
     for (k = 0; k < n2; k++)
     {
          double tmp13[2]         = {temp1[i][k][0],temp1[i][k][1]};
          temp1[i][k][0]       = temp1[i+m2][k+n2][0];
          temp1[i][k][1]    = temp1[i+m2][k+n2][1];
          temp1[i+m2][k+n2][0] = tmp13[0];
          temp1[i+m2][k+n2][1] = tmp13[1];

          double tmp24[2]       = {temp1[i+m2][k][0],temp1[i+m2][k][1]};
          temp1[i+m2][k][0]    = temp1[i][k+n2][0];
          temp1[i+m2][k][1]    = temp1[i][k+n2][1];
          temp1[i][k+n2][0]   = tmp24[0];
          temp1[i][k+n2][1]    = tmp24[1];
     }
  }



  //convert back to 1d
  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          dft[i*w+j][0] = temp1[i][j][0];

          dft[i*w+j][1] = temp1[i][j][1];


          dft2[i*w+j][0] = temp2[i][j][0];

          dft2[i*w+j][1] = temp2[i][j][1];

      }
  }




  /* magnitude */

  double max = 0;
  double min = 0;
  double mag=0;
  for (i = 0, k = 1; i < h; i++){
      for (j = 0; j < w; j++, k++){
          mag = sqrt(pow(dft2[i*w+j][0],2) + pow(dft2[i*w+j][1],2));
          if (max < mag)
              max = mag;
      }
  }


  double **magTemp;
  magTemp = malloc(h * sizeof (double*));
  for (i = 0;i < h; i++){
      magTemp[i] = malloc(w*sizeof (double));
  }

  for(i = 0,k = 0 ; i < h ; i++)
  {
    for(j = 0 ; j < w ; j++,k++)
    {

      double mag = sqrt(pow(dft2[i*w+j][0],2) + pow(dft2[i*w+j][1],2));
      mag = 255*(mag/max);
      //magTemp[i][j] = 255-mag; //Putih
      magTemp[i][j] = mag; //Item


    }
  }



  /* brightening magnitude*/

  for(i = 0,k = 0 ; i < h ; i++)
  {
    for(j = 0 ; j < w ; j++,k++)
    {
      //double temp = magTemp[i][j];
      double temp = (double)(255/(log(1+255)))*log(1+magTemp[i][j]);
      pixel_out[i][j] = (unsigned char)temp;

    }
  }

  generateImage(width,height,pixel_out,line1,line2,line3,filename,"magnitude");


  /* backward fft */
  plan_i = fftw_plan_dft_2d(w,h,dft,idft,FFTW_BACKWARD,FFTW_ESTIMATE);
  fftw_execute(plan_i);
  for(i = 0,k = 0 ; i < h ; i++)
  {
    for(j = 0 ; j < w ; j++,k++)
    {
      double temp = idft[i*w+j][0]/N;
      pixel_out[i][j] = (unsigned char)temp; //+ pixel[i][j];

    }
  }
  generateImage(width,height,pixel_out,line1,line2,line3,filename,"backward");

  return pixel_out;
}

编辑新的源代码

我在前移之前添加了这个部分，结果也是预期的。

//proses
  //create filter
  unsigned char **pixel_filter;
  pixel_filter = malloc(h*sizeof(unsigned char*));
  for(i = 0 ; i<h;i++)
    pixel_filter[i]=malloc(w*sizeof(unsigned char));
  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          if(distance_to_center(i,j,m2,n2) < 20)
          {
            pixel_filter[i][j] = 0;
          }
          else
          {
            pixel_filter[i][j] = 255;
          }
      }
  }
  generateImage(width,height,pixel_filter,line1,line2,line3,filename,"filter1");
  for (i = 0; i < m2; i++)
  {
     for (k = 0; k < n2; k++)
     {
          unsigned char tmp13         = pixel_filter[i][k];
          pixel_filter[i][k]       = pixel_filter[i+m2][k+n2];
          pixel_filter[i+m2][k+n2] = tmp13;

          unsigned char tmp24       = pixel_filter[i+m2][k];
          pixel_filter[i+m2][k]    = pixel_filter[i][k+n2];
          pixel_filter[i][k+n2]   = tmp24;
     }
  }
  generateImage(width,height,pixel_filter,line1,line2,line3,filename,"filter2");
  for (i = 0;i < h; i++){
      for (j = 0; j < w; j++){
          temp1[i][j][0] *= pixel_filter[i][j]; 
          temp1[i][j][1] *= pixel_filter[i][j];
      }
  }

Answer 1

你的总体想法没问题。从输出中，很难判断程序中是否存在会计问题，或者这是否是预期的结果。尝试使用更多的空白区域填充源图像，并在频域中过滤掉较小的区域。

作为旁注，在C中这样做会显得非常痛苦。这是Matlab中的等效实现。不包括绘图，它大约有10行代码。您也可以尝试使用Numerical Python（NumPy）。

% Demonstrate frequency-domain image filtering in Matlab

% Define the grid
x = linspace(-1, 1, 1001);
y = x;
[X, Y] = meshgrid(x, y);

% Make a square (source image)
rect = (abs(X) < 0.1) & (abs(Y) < 0.1);

% Compute the transform
rect_hat = fft2(rect);

% Make the high-pass filter
R = sqrt(X.^2 + Y.^2);
filt = (R > 0.05);

% Apply the filter
rect_hat_filtered = rect_hat .* ifftshift(filt);

% Compute the inverse transform
rect_filtered = ifft2(rect_hat_filtered);

%% Plot everything

figure(1)
imagesc(rect);
title('source');
axis square
saveas(gcf, 'fig1.png');

figure(2)
imagesc(abs(fftshift(rect_hat)));
title('fft(source)');
axis square
saveas(gcf, 'fig2.png');

figure(3)
imagesc(filt);
title('filter (frequency domain)');
axis square
saveas(gcf, 'fig3.png');

figure(4)
imagesc(fftshift(abs(rect_hat_filtered)));
title('fft(source) .* filter');
axis square
saveas(gcf, 'fig4.png');

figure(5)
imagesc(abs(rect_filtered))
title('result');
axis square
saveas(gcf, 'fig5.png');

源图片：

源图像的傅里叶变换：

过滤器：

使用源图像的傅里叶变换应用（相乘）滤镜的结果：

采用逆变换得出最终结果：