In Matlab, write the function gradient_magnitude that takes one input: a grayscale image (a matrix, not a filename). This function should return an image (a matrix, not a file) of type double with the same dimensions as the input. This output contains the magnitude of the gradient. You should compute the gradient using the Sobel masks using your spatial_filter function(code below).

function [ output ] = spatial_filter( I,w )

%SPATIAL_FILTER Summary of this function goes here

% Detailed explanation goes here

%I = double(I);

[M,N] = size(I);

g = zeros(M+2,N+2);

for i = 1:M

for j = 1:N

g(i+1,j+1) = I(i,j);

end

end

for i = 1:M

for j = 1:N

output(i,j) = g(i,j)*w(1,1) + g(i+1,j)*w(2,1) + g(i+2,j)*w(3,1)...

+ g(i,j+1)*w(1,2) + g(i+1,j+1)*w(2,2) + g(i+2,j+1)*w(3,2)...

+ g(i,j+2)*w(1,3) + g(i+1,j+2)*w(2,3) + g(i+2,j+2)*w(3,3);

end

end

output = double(output)/255;

end