离散傅立叶变换(DFT)

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Lena灰度图像的结果:

Example-lena-dft.png

代码 <source lang="c">#include <cxcore.h>

  1. include <cv.h>
  2. include <highgui.h>

// Rearrange the quadrants of Fourier image so that the origin is at // the image center // src & dst arrays of equal size & type void cvShiftDFT(CvArr * src_arr, CvArr * dst_arr ) {

   CvMat * tmp;
   CvMat q1stub, q2stub;
   CvMat q3stub, q4stub;
   CvMat d1stub, d2stub;
   CvMat d3stub, d4stub;
   CvMat * q1, * q2, * q3, * q4;
   CvMat * d1, * d2, * d3, * d4;
   CvSize size = cvGetSize(src_arr);
   CvSize dst_size = cvGetSize(dst_arr);
   int cx, cy;
   if(dst_size.width != size.width || 
      dst_size.height != size.height){
       cvError( CV_StsUnmatchedSizes, "cvShiftDFT", "Source and Destination arrays must have equal sizes", __FILE__, __LINE__ );   
   }
   if(src_arr==dst_arr){
       tmp = cvCreateMat(size.height/2, size.width/2, cvGetElemType(src_arr));
   }
   
   cx = size.width/2;
   cy = size.height/2; // image center
   q1 = cvGetSubRect( src_arr, &q1stub, cvRect(0,0,cx, cy) );
   q2 = cvGetSubRect( src_arr, &q2stub, cvRect(cx,0,cx,cy) );
   q3 = cvGetSubRect( src_arr, &q3stub, cvRect(cx,cy,cx,cy) );
   q4 = cvGetSubRect( src_arr, &q4stub, cvRect(0,cy,cx,cy) );
   d1 = cvGetSubRect( dst_arr, &d1stub, cvRect(0,0,cx,cy) );
   d2 = cvGetSubRect( dst_arr, &d2stub, cvRect(cx,0,cx,cy) );
   d3 = cvGetSubRect( dst_arr, &d3stub, cvRect(cx,cy,cx,cy) );
   d4 = cvGetSubRect( dst_arr, &d4stub, cvRect(0,cy,cx,cy) );
   if(src_arr!=dst_arr){
       if( !CV_ARE_TYPES_EQ( q1, d1 )){
           cvError( CV_StsUnmatchedFormats, "cvShiftDFT", "Source and Destination arrays must have the same format", __FILE__, __LINE__ ); 
       }
       cvCopy(q3, d1, 0);
       cvCopy(q4, d2, 0);
       cvCopy(q1, d3, 0);
       cvCopy(q2, d4, 0);
   }
   else{
       cvCopy(q3, tmp, 0);
       cvCopy(q1, q3, 0);
       cvCopy(tmp, q1, 0);
       cvCopy(q4, tmp, 0);
       cvCopy(q2, q4, 0);
       cvCopy(tmp, q2, 0);
   }

}

int main(int argc, char ** argv) {

   const char* filename = argc >=2 ? argv[1] : "lena.jpg";
   IplImage * im;
   IplImage * realInput;
   IplImage * imaginaryInput;
   IplImage * complexInput;
   int dft_M, dft_N;
   CvMat* dft_A, tmp;
   IplImage * image_Re;
   IplImage * image_Im;
   double m, M;
   im = cvLoadImage( filename, CV_LOAD_IMAGE_GRAYSCALE );
   if( !im )
       return -1;
   realInput = cvCreateImage( cvGetSize(im), IPL_DEPTH_64F, 1);
   imaginaryInput = cvCreateImage( cvGetSize(im), IPL_DEPTH_64F, 1);
   complexInput = cvCreateImage( cvGetSize(im), IPL_DEPTH_64F, 2);
   cvScale(im, realInput, 1.0, 0.0);
   cvZero(imaginaryInput);
   cvMerge(realInput, imaginaryInput, NULL, NULL, complexInput);
   dft_M = cvGetOptimalDFTSize( im->height - 1 );
   dft_N = cvGetOptimalDFTSize( im->width - 1 );
   dft_A = cvCreateMat( dft_M, dft_N, CV_64FC2 );
   image_Re = cvCreateImage( cvSize(dft_N, dft_M), IPL_DEPTH_64F, 1);
   image_Im = cvCreateImage( cvSize(dft_N, dft_M), IPL_DEPTH_64F, 1);
   // copy A to dft_A and pad dft_A with zeros
   cvGetSubRect( dft_A, &tmp, cvRect(0,0, im->width, im->height));
   cvCopy( complexInput, &tmp, NULL );
   if( dft_A->cols > im->width )
   {
       cvGetSubRect( dft_A, &tmp, cvRect(im->width,0, dft_A->cols - im->width, im->height));
       cvZero( &tmp );
   }
   // no need to pad bottom part of dft_A with zeros because of
   // use nonzero_rows parameter in cvDFT() call below
   cvDFT( dft_A, dft_A, CV_DXT_FORWARD, complexInput->height );
   cvNamedWindow("win", 0);
   cvNamedWindow("magnitude", 0);
   cvShowImage("win", im);
   // Split Fourier in real and imaginary parts
   cvSplit( dft_A, image_Re, image_Im, 0, 0 );
   // Compute the magnitude of the spectrum Mag = sqrt(Re^2 + Im^2)
   cvPow( image_Re, image_Re, 2.0);
   cvPow( image_Im, image_Im, 2.0);
   cvAdd( image_Re, image_Im, image_Re, NULL);
   cvPow( image_Re, image_Re, 0.5 );
   // Compute log(1 + Mag)
   cvAddS( image_Re, cvScalarAll(1.0), image_Re, NULL ); // 1 + Mag
   cvLog( image_Re, image_Re ); // log(1 + Mag)


   // Rearrange the quadrants of Fourier image so that the origin is at
   // the image center
   cvShiftDFT( image_Re, image_Re );
   cvMinMaxLoc(image_Re, &m, &M, NULL, NULL, NULL);
   cvScale(image_Re, image_Re, 1.0/(M-m), 1.0*(-m)/(M-m));
   cvShowImage("magnitude", image_Re);
   cvWaitKey(-1);
   return 0;

} </source>


python2.7 + opencv2.4 代码 <source lang="python">from cv2.cv import * import sys

def cvShiftDFT(src_arr, dst_arr ):

   size = GetSize(src_arr)
   dst_size = GetSize(dst_arr)
   tmp = None
   if dst_size[0] != size[0] or dst_size[1] != size[1]: 
       Error( CV_StsUnmatchedSizes, "cvShiftDFT", "Source and Destination arrays must have equal sizes", __FILE__, __LINE__ )
   

   if src_arr==dst_arr :
       tmp = CreateMat(size[1]/2, size[0]/2, GetElemType(src_arr))

   cx = size[0]/2
   cy = size[1]/2

   q1 = GetSubRect( src_arr, (0,0,cx, cy) )
   q2 = GetSubRect( src_arr, (cx,0,cx,cy) )
   q3 = GetSubRect( src_arr, (cx,cy,cx,cy) )
   q4 = GetSubRect( src_arr, (0,cy,cx,cy) )
   d1 = GetSubRect( dst_arr, (0,0,cx,cy) )
   d2 = GetSubRect( dst_arr, (cx,0,cx,cy) )
   d3 = GetSubRect( dst_arr, (cx,cy,cx,cy) )
   d4 = GetSubRect( dst_arr, (0,cy,cx,cy) )

   if src_arr!=dst_arr:
       if not CV_ARE_TYPES_EQ( q1, d1 ):
           Error( CV_StsUnmatchedFormats, "cvShiftDFT", "Source and Destination arrays must have the same format", __FILE__, __LINE__ )
       Copy(q3, d1, None)
       Copy(q4, d2, None)
       Copy(q1, d3, None)
       Copy(q2, d4, None)
   
   else:
       Copy(q3, tmp, None)
       Copy(q1, q3, None)
       Copy(tmp, q1, None)
       Copy(q4, tmp, None)
       Copy(q2, q4, None)
       Copy(tmp, q2, None)
   


if __name__ == '__main__':

   filename = "Lena.jpg"
   im = LoadImage( filename, CV_LOAD_IMAGE_GRAYSCALE )
   if not im: 
       sys.exit(-1)


   realInput = CreateImage( GetSize(im), IPL_DEPTH_64F, 1)
   imaginaryInput = CreateImage( GetSize(im), IPL_DEPTH_64F, 1)
   complexInput = CreateImage( GetSize(im), IPL_DEPTH_64F, 2)

   Scale(im, realInput, 1.0, 0.0)
   SetZero(imaginaryInput)
   Merge(realInput, imaginaryInput, None, None, complexInput)

   dft_M = GetOptimalDFTSize( im.height - 1 )
   dft_N = GetOptimalDFTSize( im.width - 1 )

   dft_A = CreateMat( dft_M, dft_N, CV_64FC2 );
   image_Re = CreateImage( (dft_N, dft_M), IPL_DEPTH_64F, 1)
   image_Im = CreateImage( (dft_N, dft_M), IPL_DEPTH_64F, 1)

   tmp = GetSubRect( dft_A,(0,0, im.width, im.height))
   Copy( complexInput, tmp, None )
   if dft_A.cols > im.width:
       tmp = GetSubRect( dft_A,(im.width,0, dft_A.cols - im.width, im.height))
       SetZero( tmp )

   DFT( dft_A, dft_A, CV_DXT_FORWARD, complexInput.height )

   NamedWindow("win", 0)
   NamedWindow("magnitude", 0)
   ShowImage("win", im)

   Split( dft_A, image_Re, image_Im, None, None )

   Pow( image_Re, image_Re, 2.0)
   Pow( image_Im, image_Im, 2.0)
   Add( image_Re, image_Im, image_Re, None)
   Pow( image_Re, image_Re, 0.5 )

   AddS( image_Re, ScalarAll(1.0), image_Re, None )
   Log( image_Re, image_Re )

   cvShiftDFT( image_Re, image_Re )
   m = MinMaxLoc(image_Re, None)
   print(m)
   Scale(image_Re, image_Re, 1.0/(m[1]-m[0]), 1.0*(-m[0])/(m[1]-m[0]))
   ShowImage("magnitude", image_Re)

   WaitKey(-1)

</source> 注:python2.7版本由oldyang改写