java - 如何使用离散傅里叶变换在频域中的图像上实现低通滤波器？

Question

我正在尝试在图像上实现二维傅里叶变换。我有了它，所以我的 DFT 和逆 DFT 可以在图像上工作。但是当我应用滤波器时，通过将复数相乘，并对结果求逆，我只会得到图像噪声。

这是我的 2d DFT

public void dft(double[][] inreal, double[][] inimag) {
int n = inreal.length;

double[][] tempreal = new double[n][n];
double[][] tempimag = new double[n][n];
realArray = new double[n][n];
imagArray = new double[n][n];

  for(int row = 0; row < n; row++) {  
    for (int col = 0; col < n; col++) {  
        double sumreal = 0;
        double sumimag = 0;
        for (int t = 0; t < n; t++) {  
            double angle = 2 * Math.PI * t * col / n;
            sumreal +=  inreal[row][t] * Math.cos(angle) + inimag[row][t] * Math.sin(angle);
            sumimag += -inreal[row][t] * Math.sin(angle) + inimag[row][t] * Math.cos(angle);
            
        }
        //System.out.println("r" + row + " " + "c" + col + " " + sumreal + " " + sumimag);
        tempreal[row][col] = sumreal;
        tempimag[row][col] = sumimag;
    }
}
    
    //now do it over the columns
 for (int col = 0; col < n; col++) {
    for (int row = 0; row < n; row++) {  // For each output element
        double sumreal = 0;
        double sumimag = 0;
        for (int t = 0; t < n; t++) {  // For each input element
            double angle = 2 * Math.PI * t * row / n;
            sumreal +=  tempreal[t][col] * Math.cos(angle) + tempimag[t][col] * Math.sin(angle);
            sumimag += -tempreal[t][col] * Math.sin(angle) + tempimag[t][col] * Math.cos(angle);
        }
        realArray[row][col] = sumreal;
        imagArray[row][col] = sumimag;
        //System.out.println(realArray[row][col] + " " + imagArray[row][col] + "i");
    }
 }
 
 

}

这是我的逆 DFT

public void inverseDFT(double[][] inRealArray, double[][] inImagArray) {
 int n = realArray.length;
    outRealArray = new double[n][n];
    outImagArray = new double[n][n];
    outputarray = new int[n][n];
    
    double[][] tempreal = new double[n][n];
    double[][] tempimag = new double[n][n];
 
    for (int col = 0; col < n; col++) {
        for (int row = 0; row < n; row++) {   // For each output element
           double sumreal = 0;
           double sumimag = 0;
           for (int t = 0; t < n; t++) {  // For each input element
               double angle = 2 * Math.PI * t * row / n;
               sumreal +=  inRealArray[t][col] * Math.cos(angle) - inImagArray[t][col] * Math.sin(angle);
               sumimag +=  inRealArray[t][col] * Math.sin(angle) + inImagArray[t][col] * Math.cos(angle);
        
           }
           //System.out.println("r" + row + " " + "c" + col + " " + sumreal + " " + sumimag);
           tempreal[row][col] = sumreal;
           tempimag[row][col] = sumimag;
       }
   }

    //now do it over the columns
    for(int row = 0; row < n; row++) {  
        for (int col = 0; col < n; col++) {  // For each output element
           double sumreal = 0;
           double sumimag = 0;
           for (int t = 0; t < n; t++) {  // For each input element
               double angle = 2 * Math.PI * t * col / n;
               sumreal +=  tempreal[row][t] * Math.cos(angle) - tempimag[row][t] * Math.sin(angle);
               sumimag +=  tempreal[row][t] * Math.sin(angle) + tempimag[row][t] * Math.cos(angle);
           }
           outRealArray[row][col] = sumreal / (n * n);
           outImagArray[row][col] = sumimag / (n * n);
           outputarray[row][col] = (int)Math.abs(outRealArray[row][col]);
           //System.out.println(outRealArray[row][col] + " " + outImagArray[row][col] + "i");
       }
  }
    
}

图像经过并返回相同。 我将图像移动到中心并获取光谱图像来测试它是否有效。

这是复数的大小并移至中心

低通滤波器

过滤器通过 DFT。

这是我将两者相乘的代码。

    public void applyLowPassFilter(String filename, double[][] realArray, double[][] imagArray) throws IOException {
    ReadPGMFile readPGM = new ReadPGMFile(filename);
    double[][] filterArrayR = readPGM.loadArray();
    double[][] filterArrayI = new double[filterArrayR.length][filterArrayR.length];
    
    FourierTransform ft = new FourierTransform();
    ft.dft(filterArrayR, filterArrayI);
    filterReal = ft.getRealArray();
    filterImag = ft.getImagArray();
    
    int n = realArray.length;
    resultRealArray = new double[n][n];
    resultImagArray = new double[n][n];
    
    for(int i = 0; i < n; i++){
        int colValue = 0;
        int rowValue = 0;
        for(int j = 0; j < n; j++) {
         if(j < n / 2 ){
             colValue = (n / 2) - j;
         } else {
             colValue = (n - 1) - (j - ((n - 1) / 2));
         }
         if (i < n / 2) {
             rowValue = (n / 2) - i;
         } else {
             rowValue = (n - 1) - (i - ((n - 1) / 2));
         }
            
            
            resultRealArray[i][j] = realArray[rowValue][colValue] * filterReal[i][j] - imagArray[rowValue][colValue] * filterImag[i][j];
            resultImagArray[i][j] = realArray[rowValue][colValue] * filterImag[i][j] + imagArray[rowValue][colValue] * filterReal[i][j];
        }
    }
}

这就是我得到的结果。抱歉发了这么长的帖子。如果有人有任何见解，我将不胜感激。我已经为此苦苦挣扎了几个星期。

Answer 1

这是我用来测试它的代码:

      int[] pix=bim.getRGB(0, 0, wc, hc, null, 0, wc);
      double[][] ri=new double[hc][hc], ii=new double[hc][hc], ro=new double[hc][hc], io=new double[hc][hc];
      for(i=0; i<hc; i++)
      for(j=0; j<hc; j++) {
        int rr=(pix[i+j*wc]&0x00ff0000)>>16, rg=(pix[i+j*wc]&0x0000ff00)>>8, rb=pix[i+j*wc]&0x000000ff;
        ri[i][j]=0.2126*rr+0.7152*rg+0.0722*rb;
      }
      double[][] ff=new double[hc][hc];
      ff[hc/2][hc/2]=ff[hc/2][hc/2+1]=ff[hc/2][hc/2-1]=ff[hc/2+1][hc/2]=ff[hc/2-1][hc/2]=1;
      // ff[hc/2][hc/2]=ff[hc/2][hc/2+1]=ff[hc/2][hc/2-1]=ff[hc/2+1][hc/2]=ff[hc/2-1][hc/2]=ff[hc/2-1][hc/2-1]=ff[hc/2-1][hc/2+1]=ff[hc/2+1][hc/2-1]=ff[hc/2+1][hc/2+1]=0.125;
      filterDFT(ff, ri, ro, io);
      int[] pix2=new int[hc*hc];
      for(i=0; i<hc; i++)
      for(j=0; j<hc; j++) pix2[i+j*hc]=0xff000000|(int)Math.abs(ro[i][j]);
      BufferedImage b2=new BufferedImage(hc, hc, BufferedImage.TYPE_INT_RGB);
      b2.setRGB(0, 0, hc, hc, pix2, 0, hc);

现在 b2 就是你的图像；它显示得很好 - 你必须重新洗牌象限。

因此，我建议您再次查看您的过滤器读取的下载内容。