# Fourier Spectrum

Hello, I'm new to OpenCV, I've done the Fourier Transform of an image and got it's Spectrum.

I would like to remove frequency components (from the Spectrum) that are greater than a circle that's diameter is 100, I don't think my code is the right thing for what I want, thank you in advance for helping me Here's my code :

#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <iostream>
#include "stdafx.h"
#include <opencv2\opencv.hpp>
using namespace cv;
using namespace std;
int main(int argc, char ** argv)
{
const char* filename = argc >= 2 ? argv[1] : "lena.bmp";

if (I.empty())
return -1;

Mat padded;                            //expand input image to optimal size
int m = getOptimalDFTSize(I.rows);
int n = getOptimalDFTSize(I.cols);
copyMakeBorder(I, padded, 0, m - I.rows, 0, n - I.cols, BORDER_CONSTANT, Scalar::all(0));

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

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);

// Recadrer le spectre, si il y a un nombre impair de lignes ou de colonnes
magI = magI(Rect(0, 0, magI.cols & -2, magI.rows & -2));

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;
q0.copyTo(tmp);
q3.copyTo(q0);
tmp.copyTo(q3);

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

normalize(magI, magI, 0, 1, CV_MINMAX);
imshow("Input Image", I);   imshow("spectrum magnitude", magI);
/*________________________________________________________________________________________________*/

Mat src, dst;

Mat kernel;
Point anchor;
double delta;
int ddepth;
int kernel_size;
char* window_name = "filter2D Demo";

int c;

/// Create window
namedWindow(window_name, CV_WINDOW_AUTOSIZE);

/// Initialize arguments for the filter
anchor = Point(-1, -1);
delta = 0;
ddepth = -1;

/// Loop - Will filter the image with different kernel sizes each 0.5 seconds
int ind = 0;
while (true)
{
c = waitKey(500);
/// Press 'ESC' to exit the program
if ((char)c == 27)
{
break;
}

/// Update kernel size for a normalized box filter

kernel_size = 10 + 10 * (ind % 10);
ind++;
if (kernel_size == 100) { break; }
kernel = Mat::ones(kernel_size, kernel_size, CV_32F) / (float)(kernel_size*kernel_size);

/// Apply filter
filter2D(magI, dst, ddepth, kernel, anchor, delta, BORDER_DEFAULT);
imshow(window_name, dst);
ind++;

/*_______________________________________________________________________________________*/

//calculating the idft
Mat inverseTransform;
dft(complexI, inverseTransform, DFT_INVERSE | DFT_REAL_OUTPUT);
normalize(inverseTransform, inverseTransform, 0, 1, CV_MINMAX);
imshow("Reconstructed", inverseTransform);

waitKey();

return 0;
}
}

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( 2017-03-09 13:38:57 -0500 )edit

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Filter2d is definitely the wrong function.

Simply create an image the size of your spectrum of the same data type (CV_32F) and use the circle function to draw a binary circle.

Mat mask = Mat(rows, cols, CV_32F);
circle(mask, Point(rows/2, cols/2), 50, 1.0, -1);  //50 is the radius, 1.0 is the color, -1 means filled.


Then multiply your amplitude by the mask. Remember to undo the fft quadrant shift before doing the inverse DFT.

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