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Tutorial Discrete Fourier Transform

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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
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samples/cpp/tutorial_code/core/discrete_fourier_transform/discrete_fourier_transform.cpp
+20 -4
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@@ -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);
samples/java/tutorial_code/core/discrete_fourier_transform/DiscreteFourierTransform.java
+109
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@@ -0,0 +1,109 @@
import org.opencv.core.*;
import org.opencv.highgui.HighGui;
import org.opencv.imgcodecs.Imgcodecs;
import java.util.List;
import java.util.*;
class DiscreteFourierTransformRun{
private void help() {
System.out.println("" +
"This program demonstrated the use of the discrete Fourier transform (DFT). \n" +
"The dft of an image is taken and it's power spectrum is displayed.\n" +
"Usage:\n" +
"./DiscreteFourierTransform [image_name -- default ../data/lena.jpg]");
}
public void run(String[] args){
help();
String filename = ((args.length > 0) ? args[0] : "../data/lena.jpg");
Mat I = Imgcodecs.imread(filename, Imgcodecs.IMREAD_GRAYSCALE);
if( I.empty() ) {
System.out.println("Error opening image");
System.exit(-1);
}
//! [expand]
Mat padded = new Mat(); //expand input image to optimal size
int m = Core.getOptimalDFTSize( I.rows() );
int n = Core.getOptimalDFTSize( I.cols() ); // on the border add zero values
Core.copyMakeBorder(I, padded, 0, m - I.rows(), 0, n - I.cols(), Core.BORDER_CONSTANT, Scalar.all(0));
//! [expand]
//! [complex_and_real]
List<Mat> planes = new ArrayList<Mat>();
padded.convertTo(padded, CvType.CV_32F);
planes.add(padded);
planes.add(Mat.zeros(padded.size(), CvType.CV_32F));
Mat complexI = new Mat();
Core.merge(planes, complexI); // Add to the expanded another plane with zeros
//! [complex_and_real]
//! [dft]
Core.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]
Core.split(complexI, planes); // planes.get(0) = Re(DFT(I)
// planes.get(1) = Im(DFT(I))
Core.magnitude(planes.get(0), planes.get(1), planes.get(0));// planes.get(0) = magnitude
Mat magI = planes.get(0);
//! [magnitude]
//! [log]
Mat matOfOnes = Mat.ones(magI.size(), magI.type());
Core.add(matOfOnes, magI, magI); // switch to logarithmic scale
Core.log(magI, magI);
//! [log]
//! [crop_rearrange]
// crop the spectrum, if it has an odd number of rows or columns
magI = magI.submat(new 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 = new Mat(magI, new Rect(0, 0, cx, cy)); // Top-Left - Create a ROI per quadrant
Mat q1 = new Mat(magI, new Rect(cx, 0, cx, cy)); // Top-Right
Mat q2 = new Mat(magI, new Rect(0, cy, cx, cy)); // Bottom-Left
Mat q3 = new Mat(magI, new Rect(cx, cy, cx, cy)); // Bottom-Right
Mat tmp = new Mat(); // 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);
//! [crop_rearrange]
magI.convertTo(magI, CvType.CV_8UC1);
//! [normalize]
Core.normalize(magI, magI, 0, 255, Core.NORM_MINMAX, CvType.CV_8UC1); // Transform the matrix with float values
// into a viewable image form (float between
// values 0 and 255).
//! [normalize]
HighGui.imshow("Input Image" , I ); // Show the result
HighGui.imshow("Spectrum Magnitude", magI);
HighGui.waitKey();
System.exit(0);
}
}
public class DiscreteFourierTransform {
public static void main(String[] args) {
// Load the native library.
System.loadLibrary(Core.NATIVE_LIBRARY_NAME);
new DiscreteFourierTransformRun().run(args);
}
}
samples/python/tutorial_code/core/discrete_fourier_transform/discrete_fourier_transform.py
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@@ -0,0 +1,80 @@
from __future__ import print_function
import sys
import cv2
import numpy as np
def print_help():
print('''
This program demonstrated the use of the discrete Fourier transform (DFT).
The dft of an image is taken and it's power spectrum is displayed.
Usage:
discrete_fourier_transform.py [image_name -- default ../../../../data/lena.jpg]''')
def main(argv):
print_help()
filename = argv[0] if len(argv) > 0 else "../../../../data/lena.jpg"
I = cv2.imread(filename, cv2.IMREAD_GRAYSCALE)
if I is None:
print('Error opening image')
return -1
## [expand]
rows, cols = I.shape
m = cv2.getOptimalDFTSize( rows )
n = cv2.getOptimalDFTSize( cols )
padded = cv2.copyMakeBorder(I, 0, m - rows, 0, n - cols, cv2.BORDER_CONSTANT, value=[0, 0, 0])
## [expand]
## [complex_and_real]
planes = [np.float32(padded), np.zeros(padded.shape, np.float32)]
complexI = cv2.merge(planes) # Add to the expanded another plane with zeros
## [complex_and_real]
## [dft]
cv2.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]
cv2.split(complexI, planes) # planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))
cv2.magnitude(planes[0], planes[1], planes[0])# planes[0] = magnitude
magI = planes[0]
## [magnitude]
## [log]
matOfOnes = np.ones(magI.shape, dtype=magI.dtype)
cv2.add(matOfOnes, magI, magI) # switch to logarithmic scale
cv2.log(magI, magI)
## [log]
## [crop_rearrange]
magI_rows, magI_cols = magI.shape
# crop the spectrum, if it has an odd number of rows or columns
magI = magI[0:(magI_rows & -2), 0:(magI_cols & -2)]
cx = int(magI_rows/2)
cy = int(magI_cols/2)
q0 = magI[0:cx, 0:cy] # Top-Left - Create a ROI per quadrant
q1 = magI[cx:cx+cx, 0:cy] # Top-Right
q2 = magI[0:cx, cy:cy+cy] # Bottom-Left
q3 = magI[cx:cx+cx, cy:cy+cy] # Bottom-Right
tmp = np.copy(q0) # swap quadrants (Top-Left with Bottom-Right)
magI[0:cx, 0:cy] = q3
magI[cx:cx + cx, cy:cy + cy] = tmp
tmp = np.copy(q1) # swap quadrant (Top-Right with Bottom-Left)
magI[cx:cx + cx, 0:cy] = q2
magI[0:cx, cy:cy + cy] = tmp
## [crop_rearrange]
## [normalize]
cv2.normalize(magI, magI, 0, 1, cv2.NORM_MINMAX) # Transform the matrix with float values into a
## viewable image form(float between values 0 and 1).
## [normalize]
cv2.imshow("Input Image" , I ) # Show the result
cv2.imshow("spectrum magnitude", magI)
cv2.waitKey()
if __name__ == "__main__":
main(sys.argv[1:])