Tutorial Discrete Fourier Transform

This commit is contained in:
tribta
2017-08-20 13:45:46 +01:00
parent 13317bdfda
commit 954e2f9b9c
5 changed files with 374 additions and 85 deletions
@@ -8,45 +8,58 @@
using namespace cv;
using namespace std;
static void help(char* progName)
static void help(void)
{
cout << endl
<< "This program demonstrated the use of the discrete Fourier transform (DFT). " << endl
<< "The dft of an image is taken and it's power spectrum is displayed." << endl
<< "Usage:" << endl
<< progName << " [image_name -- default ../data/lena.jpg] " << endl << endl;
<< "./discrete_fourier_transform [image_name -- default ../data/lena.jpg]" << endl;
}
int main(int argc, char ** argv)
{
help(argv[0]);
help();
const char* filename = argc >=2 ? argv[1] : "../data/lena.jpg";
Mat I = imread(filename, IMREAD_GRAYSCALE);
if( I.empty())
if( I.empty()){
cout << "Error opening image" << endl;
return -1;
}
//! [expand]
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));
//! [expand]
//! [complex_and_real]
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
//! [complex_and_real]
//! [dft]
dft(complexI, complexI); // this way the result may fit in the source matrix
//! [dft]
// compute the magnitude and switch to logarithmic scale
// => log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
//! [magnitude]
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];
//! [magnitude]
//! [log]
magI += Scalar::all(1); // switch to logarithmic scale
log(magI, magI);
//! [log]
//! [crop_rearrange]
// crop the spectrum, if it has an odd number of rows or columns
magI = magI(Rect(0, 0, magI.cols & -2, magI.rows & -2));
@@ -67,9 +80,12 @@ int main(int argc, char ** argv)
q1.copyTo(tmp); // swap quadrant (Top-Right with Bottom-Left)
q2.copyTo(q1);
tmp.copyTo(q2);
//! [crop_rearrange]
//! [normalize]
normalize(magI, magI, 0, 1, NORM_MINMAX); // Transform the matrix with float values into a
// viewable image form (float between values 0 and 1).
//! [normalize]
imshow("Input Image" , I ); // Show the result
imshow("spectrum magnitude", magI);