DFT

Mat img = Cv2.ImRead("foo.png", LoadMode.GrayScale);

// expand input image to optimal size
Mat padded = new Mat(); 
int m = Cv2.GetOptimalDFTSize(img.Rows);
int n = Cv2.GetOptimalDFTSize(img.Cols); // on the border add zero values
Cv2.CopyMakeBorder(img, padded, 0, m - img.Rows, 0, n - img.Cols, BorderType.Constant, Scalar.All(0));

// Add to the expanded another plane with zeros
Mat paddedF32 = new Mat();
padded.ConvertTo(paddedF32, MatType.CV_32F);
Mat[] planes = { paddedF32, Mat.Zeros(padded.Size(), MatType.CV_32F) };
Mat complex = new Mat();
Cv2.Merge(planes, complex);         

// this way the result may fit in the source matrix
Mat dft = new Mat();
Cv2.Dft(complex, dft);            

// compute the magnitude and switch to logarithmic scale
// => log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
Mat[] dftPlanes;
Cv2.Split(dft, out dftPlanes);  // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))

// planes[0] = magnitude
Mat magnitude = new Mat();
Cv2.Magnitude(dftPlanes[0], dftPlanes[1], magnitude);

magnitude += Scalar.All(1);  // switch to logarithmic scale
Cv2.Log(magnitude, magnitude);

// crop the spectrum, if it has an odd number of rows or columns
Mat spectrum = magnitude[
    new Rect(0, 0, magnitude.Cols & -2, magnitude.Rows & -2)];

// rearrange the quadrants of Fourier image  so that the origin is at the image center
int cx = spectrum.Cols / 2;
int cy = spectrum.Rows / 2;

Mat q0 = new Mat(spectrum, new Rect(0, 0, cx, cy));   // Top-Left - Create a ROI per quadrant
Mat q1 = new Mat(spectrum, new Rect(cx, 0, cx, cy));  // Top-Right
Mat q2 = new Mat(spectrum, new Rect(0, cy, cx, cy));  // Bottom-Left
Mat q3 = new Mat(spectrum, new Rect(cx, cy, cx, cy)); // Bottom-Right

// swap quadrants (Top-Left with Bottom-Right)
Mat tmp = new Mat();                           
q0.CopyTo(tmp);
q3.CopyTo(q0);
tmp.CopyTo(q3);

// swap quadrant (Top-Right with Bottom-Left)
q1.CopyTo(tmp);                    
q2.CopyTo(q1);
tmp.CopyTo(q2);

// Transform the matrix with float values into a
Cv2.Normalize(spectrum, spectrum, 0, 1, NormType.MinMax); 

// Show the result
Cv2.ImShow("Input Image"       , img);
Cv2.ImShow("Spectrum Magnitude", spectrum);

// calculating the idft
Mat inverseTransform = new Mat();
Cv2.Dft(dft, inverseTransform, DftFlag2.Inverse | DftFlag2.RealOutput);
Cv2.Normalize(inverseTransform, inverseTransform, 0, 1, NormType.MinMax);
Cv2.ImShow("Reconstructed by Inverse DFT", inverseTransform);
Cv2.WaitKey();