2d gaussian surface fitting in matlab

main.m
% Generate some example data
[x, y] = meshgrid(1:100, 1:100);
A = 10; % amplitude
x0 = 50; % x-coordinate of the center
y0 = 50; % y-coordinate of the center
sigma_x = 20; % standard deviation in the x-direction
sigma_y = 10; % standard deviation in the y-direction
z = A * exp(-(x - x0).^2 / (2 * sigma_x^2) - (y - y0).^2 / (2 * sigma_y^2));

% Add some noise to the data
rng(0); % for reproducibility
z_noisy = z + randn(size(z));

% Define the Gaussian function for fitting
gaussian = @(x, p) p(1) * exp(-(x(:, 1) - p(2)).^2 / (2 * p(3)^2) - (x(:, 2) - p(4)).^2 / (2 * p(5)^2));

% Initial parameter guess
p0 = [max(z_noisy(:)), x0, sigma_x, y0, sigma_y];

% Perform the fitting
p_fit = lsqcurvefit(gaussian, p0, [x(:), y(:)], z_noisy(:));

% Extract the fitted parameters
A_fit = p_fit(1);
x0_fit = p_fit(2);
sigma_x_fit = p_fit(3);
y0_fit = p_fit(4);
sigma_y_fit = p_fit(5);

% Generate the fitted surface
z_fit = gaussian([x(:), y(:)], p_fit);
z_fit = reshape(z_fit, size(x));

% Plotting the results
figure;
subplot(1, 2, 1);
surf(x, y, z_noisy);
title('Noisy Data');
subplot(1, 2, 2);
surf(x, y, z_fit);
title('Fitted Surface');
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