get hessian of gaussian of images in matlab

To get the Hessian of Gaussian (HOG) of an image in Matlab, you can use the hessian function from the Image Processing Toolbox. Here's a code snippet that demonstrates how to do this:

main.m
% Load an image
img = imread('myimage.jpg');

% Convert the image to grayscale
img = rgb2gray(img);

% Define the standard deviation of the Gaussian kernel
sigma = 2;

% Compute the Hessian of Gaussian
[U,V] = hessian(img,sigma);

% Compute the eigenvalues of the Hessian matrix
lambda1 = U + V + sqrt((U-V).^2 + 4*sigma^2.*U.*V);
lambda2 = U + V - sqrt((U-V).^2 + 4*sigma^2.*U.*V);

% Compute the Hessian determinant and trace
detH = lambda1 .* lambda2;
traceH = lambda1 + lambda2;

% Compute the HOG response
hog = (detH - 0.5*(traceH.^2)) .* (sigma.^-5);
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In this code, we first load an image and convert it to grayscale. Next, we define the standard deviation of the Gaussian kernel used to compute the Hessian. We then use the hessian function to compute the Hessian matrix of the image. We compute the eigenvalues of the Hessian matrix and use them to compute the Hessian determinant and trace. Finally, we compute the HOG response using the determinant and trace, and the standard deviation of the Gaussian kernel.