c++ - Inverse fourier transformation in OpenCV

Question

I am new in OpenCV and image processing algorithms. I need to do inverse discrete fourier transformation in OpenCV in C++, but I don't know how. I searched over internet and I didn't find answer. I am doing fourier transformation in my program with this code from this page: http://opencv.itseez.com/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html. I have tried to do inverse to that code, but I don't know where I am doing wrong. My code is here (I think that whole code is wrong):

void doFourierInverse(const Mat &src, Mat &dst) {
  normalize(src, dst, 0, -1, CV_MINMAX); 

  int cx = dst.cols/2;
  int cy = dst.rows/2;

  Mat q0(dst, Rect(0, 0, cx, cy));   
  Mat q1(dst, Rect(cx, 0, cx, cy));  
  Mat q2(dst, Rect(0, cy, cx, cy));  
  Mat q3(dst, Rect(cx, cy, cx, cy)); 

  Mat tmp;         
  q0.copyTo(tmp);
  q3.copyTo(q0);
  tmp.copyTo(q3);

  q1.copyTo(tmp);      
  q2.copyTo(q1);
  tmp.copyTo(q2);

  dst = dst(Rect(0, 0, dst.cols & -2, dst.rows & -2));

  exp(dst, dst);
  dst -= Scalar::all(1);  

  Mat planes[2];

  polarToCart(dst, Mat::zeros(dst.rows, dst.cols, dst.type()), planes[0], planes[1]);

  merge(planes, 2, dst);    

  idft(dst, dst, DFT_INVERSE | DFT_SCALE); 

  split(dst, planes);   

  dst = planes[0];
}

Answer 1

Actually, you don't have to swap the different quadrants, it's needed only if you're a human and want a more natural looking visualization of the FFT result (i.e. with the 0 frequency in the middle, negative frequencies left/bottom and positive frequencies up/right).

To invert the FFT, you need to pass the result of the forward transform "as is" (or after the frequency filtering you wanted) to the same dft() function, only adding the flag DFT_INVERSE. If you remember your math about FFT, the forward and backward transforms have very tight kinks in the formulation...

--- EDIT ---

What exactly doesn't work ? The following code does perform forward-then-backward FFT, and everything works just fine as expected.

// Load an image
cv::Mat inputImage = cv::imread(argv[argc-1], 0);

// Go float
cv::Mat fImage;
inputImage.convertTo(fImage, CV_32F);

// FFT
std::cout << "Direct transform...
";
cv::Mat fourierTransform;
cv::dft(fImage, fourierTransform, cv::DFT_SCALE|cv::DFT_COMPLEX_OUTPUT);

// Some processing
doSomethingWithTheSpectrum();

// IFFT
std::cout << "Inverse transform...
";
cv::Mat inverseTransform;
cv::dft(fourierTransform, inverseTransform, cv::DFT_INVERSE|cv::DFT_REAL_OUTPUT);

// Back to 8-bits
cv::Mat finalImage;
inverseTransform.convertTo(finalImage, CV_8U);