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 [ outputImage ] = spatial_filter( I,M )

%SPATIAL_FILTER Summary of this function goes here

% Detailed explanation goes here

corr = M;

pad1 = size(corr,1) - 1;

pad2 = size(corr,2) - 1;

output = uint8(zeros(size(I)));

if size(corr,1) == 1

B = zeros(size(I,1),size(A,2)+pad2);

m = 0;

n = floor(size(corr,2)/2);

sz1 = size(B,1);

sz2 = size(B,2) - pad2;

elseif size(corr,2) == 1

B = zeros(size(A,1) + pad1, size(A,2));

m = floor(size(corr,1)/2);

n = 0;

sz1 = size(B,1) - pad1;

sz2 = size(B,2);

else

B = zeros(size(I,1) + pad1, size(I,2) + pad2);

m = floor(size(corr,1)/2);

n = floor(size(corr,2)/2);

sz1 = size(B,1) - pad1;

sz2 = size(B,2) - pad2;

end

for i = 1:size(I,1)

for j = 1:size(I,2)

B(i+m,j+n) = I(i,j);

end

end

szcorr1 = size(corr,1);

szcorr2 = size(corr,2);

for i = 1:sz1

for j = 1:sz2

sum = 0;

m = i;

n = j;

for x = 1:szcorr1

for y = 1:szcorr2

sum = sum + (B(m,n)*corr(x,y));

n = n + 1;

end

n = j;

m = m + 1;

end

output(i,j) = sum;

end

end

outputImage = double(output);

end