How to do inverse DFT in OpenCV [duplicate] - c++

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Inverse fourier transformation in OpenCV
(1 answer)
Closed 6 years ago.
I'm trying to implement inverse DFT using OpenCV in C++
I downloaded complete dft example in docs.opencv.org and just adjust couple of lines to inverse.
my DFT code is like this
Mat DFT(const char* filename)
{
Mat I = imread(filename, CV_LOAD_IMAGE_GRAYSCALE);
if (I.empty())
{
Mat emty(7, 7, CV_32FC2, Scalar(1, 3));
return emty;
}
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);
normalize(magI, magI, 0, 1, CV_MINMAX); // Transform the matrix with float values into a
// viewable image form (float between values 0 and 1).
imshow("Input Image", I); // Show the result
imshow(filename, magI);
// waitKey();
return magI;
}
and did IDFT. By just fix dft to idft. But the output was just look like noise. What did I do wrong? I thought the dft and idft is just same....
Mat IDFT(Mat src)
{
Mat I = src;
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, DFT_INVERSE); // this way the result may fit in the source matrix
// compute the magnitude and switch to logarithmic scale
// => log(1 + sqrt(Re(IDFT(I))^2 + Im(IDFT(I))^2))
split(complexI, planes); // planes[0] = Re(IDFT(I), planes[1] = Im(IDFT(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);
normalize(magI, magI, 0, 1, CV_MINMAX);
imshow("forged map", magI);
return magI;
}

Answer 1

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();

Answer 2

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);