// =================
// || Worksheet 6
// || In this example, we are going be performing DFT's
// =================

// for another (less detailed example) see,
// http://docs.opencv.org/doc/tutorials/core/discrete_fourier_transform/discrete_fourier_transform.html

#include "program.h"

using namespace std;
using namespace cv;



// In this worksheet, we will be performing DFT's and Inverse DFT's
int worksheetsix(Mat& src)
{
    // can rotate the image by some angle if we want to play with this
    rotate(src, 15, src);
    
    // First, lets embed our source image in a complex image, so that we can easily take its fourier transform.
    Mat complexImage = embedInComplexImage(src);
    
    // PERFORM DISCRETE FOURIER TRANSFORM (DFT)!
    // because we have stored our image in a complex image,
    // we can perform the DFT 'inplace',
    // which means we use the same block of memory we have already created.
    dft(complexImage, complexImage);
    
    // Now, we are going to compute the magnitude of our complex image.
    // i.e. we want a new image whose values are sqrt( X^2+ Y^2) of our complex image X+iY.
    Mat magnitudeImage = computeMagnitudeImage(complexImage);
    
    // now we rearrange
    rearrange(magnitudeImage);
    
    // Show the result
    imshow("Input Image"       , src   );
    imshow("Spectrum Magnitude", magnitudeImage);
    waitKey();
    
    // PERFORM THE INVERSE DISCRETE FOURIER TRANSFORM (IDFT)
    cv::Mat invtransformedImage;
    
    // perform the inverse transform of our complex image.
    cv::dft(complexImage, invtransformedImage, cv::DFT_INVERSE | cv::DFT_REAL_OUTPUT);
    
    /// just normalize our image to be safe.
    normalize(invtransformedImage, invtransformedImage, 0, 1, CV_MINMAX);
    
    imshow("Reconstructed", invtransformedImage);
    waitKey();
    
    return 0;
}