Question about computing the sum of pixels and subtracting the Laplacian

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suk

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Question 1:
Let’s deal with operators whose function is to compute the sum of pixel
values in a small sub-image area, S. Show that these are linear operators.

Question 2:
Show that subtracting the Laplacian from an image is proportional to unsharp
masking. Using the definition for the Laplacian r2f = [f(x+1; y)+
f(x ¡ 1; y) + f(x; y + 1) + f(x; y ¡ 1)] ¡ 4f(x; y)

how know how to answer that question ?

Really thx you
 

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