How to do inverse DFT in OpenCV [duplicate]

Answer 1

for some reason using the normalize function in the given idft block doesn't give exactly the desired original image (contrast wise). Instead use convertTo. To be precise, replace the normalize function with the following line.

inverseTransform.convertTo(inverseTransform, CV_8U);

Answer 2

you have to rewrite your code like this to get the inverse DFT which is the original image read :

#include "stdafx.h"
#include <opencv2/core/core.hpp>
#include <opencv2\highgui\highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <iostream>
using namespace std;
using namespace cv;

int main()
{
    Mat I = imread("test.tif", CV_LOAD_IMAGE_GRAYSCALE);
    if( I.empty())
        return -1;

    Mat padded;                            //expand input image to optimal size
    int m = getOptimalDFTSize( I.rows );
    int n = getOptimalDFTSize( I.cols ); // on the border add zero values
    copyMakeBorder(I, padded, 0, m - I.rows, 0, n - I.cols, BORDER_CONSTANT, Scalar::all(0));

    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
    Mat complexI;
    merge(planes, 2, complexI);         // Add to the expanded another plane with zeros

    dft(complexI, complexI);            // this way the result may fit in the source matrix

    // compute the magnitude and switch to logarithmic scale
    // => log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
    split(complexI, planes);                   // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))

    magnitude(planes[0], planes[1], planes[0]);// planes[0] = magnitude
    Mat magI = planes[0];

    magI += Scalar::all(1);                    // switch to logarithmic scale
    log(magI, magI);

    // crop the spectrum, if it has an odd number of rows or columns
    magI = magI(Rect(0, 0, magI.cols & -2, magI.rows & -2));

    // rearrange the quadrants of Fourier image  so that the origin is at the image center
    int cx = magI.cols/2;
    int cy = magI.rows/2;

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

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

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


    normalize(magI, magI, 0, 1, CV_MINMAX); // Transform the matrix with float values into a
    normalize(phaseVals, phaseVals, 0, 1, CV_MINMAX);
                                            // viewable image form (float between values 0 and 1).

    imshow("Input Image"       , I   );    // Show the result
    imshow("Spectrum Magnitude", magI);
    waitKey();

    //calculating the idft
    cv::Mat inverseTransform;
    cv::dft(complexI, inverseTransform, cv::DFT_INVERSE|cv::DFT_REAL_OUTPUT);
    normalize(inverseTransform, inverseTransform, 0, 1, CV_MINMAX);
    imshow("Reconstructed", inverseTransform);
    waitKey();

    return 0;
}

I just added this part to your code :

//calculating the idft
        cv::Mat inverseTransform;
        cv::dft(complexI, inverseTransform, cv::DFT_INVERSE|cv::DFT_REAL_OUTPUT);
        normalize(inverseTransform, inverseTransform, 0, 1, CV_MINMAX);
        imshow("Reconstructed", inverseTransform);
        waitKey();