A Visulization of 2D-DFT with 3D displaying

A simple visulization function with a beautiful 3D model of Fourier field

function Fourier3D()

try

img = im2double(imread('afile'));

catch

% Fallback to another built-in image if 'peppers' is not found.

img = im2double(imread('afile'));

end

[H, W, C] = size(img);

spectrum_log = zeros(H, W, C);

img_recon = zeros(H, W, C);

for k = 1:C

% Forward FFT

F = fft2(img(:, :, k));

F_shifted = fftshift(F);

% Log-Magnitude Spectrum: S = log(1 + |F|). Normalized for visualization.

S = log(1 + abs(F_shifted));

spectrum_log(:, :, k) = (S - min(S(:))) / (max(S(:)) - min(S(:)));

% Inverse FFT (Reconstruction)

f_inv = ifft2(ifftshift(F_shifted));

f_real = real(f_inv);

img_recon(:, :, k) = max(0, min(1, f_real));

end

%% 3. Visualization I: The 2D Mathematical Triptych (Color Recovery)

% Set global dark theme for aesthetics.

fig2d = figure('Name', '2D Fourier Analysis & Color Recovery', 'Color', [0.1 0.1 0.1], ...

'Position', [50, 300, 1200, 400]);

% A. Original Image (Spatial Domain)

ax1 = subplot(1, 3, 1);

imshow(img);

title(ax1, 'Spatial Domain f(x,y)', 'Color', 'w', 'FontWeight', 'bold');

% B. Frequency Domain (RGB Composite Spectrum) - The "Nebula" Art

ax2 = subplot(1, 3, 2);

imshow(spectrum_log);

title(ax2, 'Frequency Domain log|F(u,v)|', 'Color', 'w', 'FontWeight', 'bold');

% C. Reconstructed Image (Perfect Color Recovery)

ax3 = subplot(1, 3, 3);

imshow(img_recon);

title(ax3, 'Reconstructed f^{-1}(F)', 'Color', 'w', 'FontWeight', 'bold');

%% 4. Visualization II: 3D Spectral Topology (Mathematical Beauty)

% Convert image to grayscale (Luminance) to visualize global energy landscape.

img_gray = rgb2gray(img);

F_gray = fftshift(fft2(img_gray));

Z = log(1 + abs(F_gray)); % Z-axis represents energy magnitude (topology)

% Create 3D Surface Figure

fig3d = figure('Name', '3D Spectral Topology', 'Color', [0 0 0], ...

'Position', [50, 50, 800, 600]);

% Plot surface with aesthetic refinement

hSurf = surf(Z);

% AESTHETIC OPTIMIZATIONS (Metallic, Smooth, High-Contrast)

shading interp; % Smooth out the grid lines

colormap(jet(256)); % High contrast color map

alpha(0.9); % Slight transparency

material metal; % Metallic reflection properties

% Lighting for depth perception

camlight('headlight');

lighting gouraud;

% Axis styling

axis off; % Remove axes for pure art look

view(-45, 45); % Set an effective isometric-like view angle

title('3D Magnitude Spectrum Topology', 'Color', [0.8 0.8 0.8], ...

'FontSize', 14, 'FontWeight', 'light');

% Interactive rotation hint

text(0, 0, max(Z(:)), 'DC Component (Low Freq)', 'Color', 'w');

rotate3d on;

end