MATLAB Answers

Fourrier transform on image

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Chantal Hajjar
Chantal Hajjar on 12 Jan 2020
Commented: Meg Noah on 17 Jan 2020
How can we compute numerically the features orientation and spacing from a FFT2 applied on image with oriented grid of objects?

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Answers (1)

Meg Noah
Meg Noah on 12 Jan 2020
Edited: Meg Noah on 12 Jan 2020
Here's an example - the grid of features is space every 20 meters, the frequency found at 0.05/m corresponds to the frequency of dots.
% Online references for FFT's
% https://www.gaussianwaves.com/2015/11/interpreting-fft-results-complex-dft-frequency-bins-and-fftshift/
% https://blogs.uoregon.edu/seis/wiki/unpacking-the-matlab-fft/
clc
close all
clear all
% generate spatial frame data and coordinates
dx_m = 1; % [m]
dy_m = 1; % [m]
nx = 101;
ny = nx;
% a grid of values
imgData = zeros(1,nx);
imgData(10:20:nx-9) = 1;
imgData = imgData.*imgData';
if (mod(nx,2) == 0)
X1D = dx_m.*[-nx/2:1:nx/2-1];
else
X1D = dx_m.*[-(nx-1)/2:1:(nx-1)/2];
end
if (mod(ny,2) == 0)
Y1D = dy_m.*[-ny/2:1:ny/2-1];
else
Y1D = dy_m.*[-(ny-1)/2:1:(ny-1)/2];
end
% visualize spatial data
figure('Color','white');
subplot(2,1,1)
imagesc(X1D,Y1D,imgData);
title({'Image Data'},'fontsize',12);
axis equal
axis tight
colorbar
set(gca,'fontweight','bold');
xlabel('X [m]'); ylabel('Y [m]');
% now to show the power spectrum
% with frequency space grid
dfy = 1/(ny*dy_m);
dfx = 1/(nx*dx_m);
if (mod(nx,2) == 0)
FX = dfy.*[-nx/2:1:nx/2-1];
else
FX = dfy.*[-(nx-1)/2:1:(nx-1)/2];
end
if (mod(ny,2) == 0)
FY = dfy.*[-ny/2:1:ny/2-1];
else
FY = dfy.*[-(ny-1)/2:1:(ny-1)/2];
end
subplot(2,1,2)
% imagesc(FX,FY,20*log10(abs(fftshift(fft2(imgData)))));
imagesc(FX,FY,(abs(fftshift(fft2(imgData)))));
axis equal; axis tight; colorbar
set(gca,'fontweight','bold');
xlabel('Frequency [1/m]'); ylabel('Frequency [1/m]');
title('FFT2D Output','fontsize',12);
Adding the ability to rotate the image
clc
close all
clear all
% generate spatial frame data and coordinates
dx_m = 1; % [m]
dy_m = 1; % [m]
nx = 101;
ny = nx;
rotation = 30;
% a grid of values
imgData = zeros(1,nx);
imgData(10:20:nx-9) = 1;
imgData = imgData.*imgData';
imgData = imrotate(imgData,rotation,'crop');
if (mod(nx,2) == 0)
X1D = dx_m.*[-nx/2:1:nx/2-1];
else
X1D = dx_m.*[-(nx-1)/2:1:(nx-1)/2];
end
if (mod(ny,2) == 0)
Y1D = dy_m.*[-ny/2:1:ny/2-1];
else
Y1D = dy_m.*[-(ny-1)/2:1:(ny-1)/2];
end
% visualize spatial data
figure('Color','white');
subplot(2,1,1)
imagesc(X1D,Y1D,imgData);
title({'Image Data'},'fontsize',12);
axis equal
axis tight
colorbar
set(gca,'fontweight','bold');
xlabel('X [m]'); ylabel('Y [m]');
% now to show the power spectrum
% with frequency space grid
dfy = 1/(ny*dy_m);
dfx = 1/(nx*dx_m);
if (mod(nx,2) == 0)
FX = dfy.*[-nx/2:1:nx/2-1];
else
FX = dfy.*[-(nx-1)/2:1:(nx-1)/2];
end
if (mod(ny,2) == 0)
FY = dfy.*[-ny/2:1:ny/2-1];
else
FY = dfy.*[-(ny-1)/2:1:(ny-1)/2];
end
subplot(2,1,2)
% imagesc(FX,FY,20*log10(abs(fftshift(fft2(imgData)))));
imagesc(FX,FY,(abs(fftshift(fft2(imgData)))));
axis equal; axis tight; colorbar
set(gca,'fontweight','bold');
xlabel('Frequency [1/m]'); ylabel('Frequency [1/m]');
title('FFT2D Output','fontsize',12);
FFTGridExampleWithRotation.png

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Meg Noah
Meg Noah on 13 Jan 2020
It should be possible. Do you have an example image?
Chantal Hajjar
Chantal Hajjar on 17 Jan 2020
Please find attached the image that I wish to analyze. In fact, I would like to know numerically both orientations of the grid using Fourrier Transform or using another method.
Thank you in advance
Meg Noah
Meg Noah on 17 Jan 2020
What is the spatial dimension of the x-axis and y-axis - in other words, how many meters is this image from pixel center to pixel center along a row and along a column?

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R2019b