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When does the degradation model satisfy position invariant property in image processing?

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An operator having input-output relationship g(x,y)=H[f(x,y)] is said to

position invariant if H[f(x-,y-_)]=g(x-,y-_) for any f(x,y) and and _.

This definition indicates that the response at any point in the image depends only

on the value of the input at that point not on its position.

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