. Discrete Fourier Transform

#include “opencv2/core.hpp”
#include “opencv2/imgproc.hpp”
#include “opencv2/imgcodecs.hpp”
#include “opencv2/highgui.hpp”
#include

using namespace cv;
using namespace std;

int main(void)
{
const char* filename = “/home/chang/projects/opencv_GPU_example/1.jpg”;
Mat I = imread( samples::findFile( filename ), IMREAD_GRAYSCALE);
if( I.empty()){
cout << “Error opening image” << endl;
return EXIT_FAILURE;
}

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

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

imshow("Input Image", I);
imshow("spectrum magnitude", magI);
waitKey();

return 0;

}