Discrete Fourier Transform



#include "opencv2/core/core.hpp"#include "opencv2/imgproc/imgproc.hpp"#include "opencv2/highgui/highgui.hpp"#include <iostream>int main(int argc, char ** argv){    const char* filename = argc >=2 ? argv[1] : "lena.jpg";    Mat I = imread(filename, 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                                            // viewable image form (float between values 0 and 1).    imshow("Input Image"       , I   );    // Show the result    imshow("spectrum magnitude", magI);    waitKey();    return 0;}