CODEWITHSUNDEEP
matlabimage-processing
Sara S.
Sara S.

Reputation: 1375

what is the difference between fspecial('laplacian') and del2 matlab?

In applying the laplacian to an image,What is the difference between 

fspecial('laplacian', alpha)

and 

L = del2(U)

 
Do they do the same operation on image?

Upvotes: 2

Views: 604

Answers (1)

NoDataDumpNoContribution
NoDataDumpNoContribution

Reputation: 10859

Except for a factor of 4 (del2 is only one fourth of the laplacian for 2D images) they are both approximating the Laplacian. They are both using a 3x3 filter, however the edges are treated differently. They use exactly the same filter for parameter alpha in fspecial set to 0. For all other values of the paramter fspecial will deliver a more smooth estimate of the Laplacian which is important in cases of noisy images.

Example:

[xi, yi] = ndgrid(1:10, 1:10);
data = xi.^2 + yi.^2 + rand(10);
a = 4 * del2(data);
alpha = 0;
b = imfilter(data, fspecial('laplacian', alpha),'replicate');
sum(sum(abs(a(2:end-1,2:end-1)-b(2:end-1,2:end-1))))

gives

ans = 7.061e-13

del2 is about 4 times faster because of lower overhead and behaves better at the borders. fspecial with parameter alpha set to 0 is not very smooth. For very noisy data alpha closer to 1 might be desired. Noisy numerical derivatives is a topic for itself.

Comment: See the sources of del2 and fspecial with ctrl.+d in the editor and you see what they are doing.

Upvotes: 4

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