fise_otf2d

Illustrate the 2D Fourier representation of luminance images.

The Fourier transform is complex-valued. When the image is real, the complex values obey symmetry conditions, such that

where * is complex conjugate. This implies the amplitudes at those two locations are the same.

Also, for image harmonics the mean value is positive, so there will also be a positive value at

. This mean value is usually much larger than the amplitudes of the Fourier coefficients. That is why we show the image using log10(coefficient amplitude).

ISETCam initialization

ieInit;

Create a test image

Harmonics are very simple because they are 'points' in the transform domain. So let's start with that.

params = harmonicP;    % Creates a struct of harmonic parameters
params.freq = 8;       % Cycles per image
 
params.row = 33; params.col = 33;  % Image size
scene = sceneCreate('harmonic',params);
scene = sceneSet(scene,'fov',1);   % Making it 1 deg is simple
 
% Spatial frequency support.
fx = sceneGet(scene,'f support x'); fullFx = [-1*fliplr(fx), fx];
fy = sceneGet(scene,'f support y'); fullFy = [-1*fliplr(fy), fy];
 
% Space support.
x = sceneGet(scene,'spatial support x','deg');
y = sceneGet(scene,'spatial support y','deg');
 
% sceneWindow(scene);

Operate on luminance - for simplicity

One harmonic is vertical and then we create a different harmonic at 45 deg angle.

img = sceneGet(scene,'luminance');

% The 2D Fourier transform

imgF = fft2(img);

% We build up the figure

ieFigure;

tiledlayout(2,2)

nexttile

imagesc(x,y,img); axis image

xlabel('Position (deg)'); ylabel('Position (deg)');

nexttile;

imagesc(fullFx,fullFy,abs(fftshift(imgF)));

axis equal; axis image; colormap(gray);

set(gca, 'Color', 'k'); % Set background color to black

grid on; % Turn on the grid

ax = gca; % Get current axes

ax.GridColor = [0.7 0.7 0.7]; % Set grid color to dark gray

ax.GridLineStyle = '-'; % Set grid line style

ax.LineWidth = 3; % Set grid line thickness

xlabel('Frequency (cyc/deg)');

ylabel('Frequency (cyc/deg)');

% A different harmonic

params.ang = 45;

[scene,parms] = sceneCreate('harmonic',params);

scene = sceneSet(scene,'fov',1);