Q:
Assuming that the origin of F(u, v), Fourier transformed function of f(x, y) an input image, has been correlated by performing the operation f(x, y)(-1)x+y prior to taking the transform of the image. If F and f are of same size M*N, then which of the following is an expression for H(u, v), the filter used for implementing Laplacian in frequency domain?
Answer & Explanation
Answer: C) H(u, v)= -[(u – M/2)²+ (v – N/2)²].
Explanation: The given operation f(x, y)(-1)x+y shifts the center transform so that (u, v)=(0, 0) is at point (M/2, N/2) and hence the filter is: H(u, v)= -[(u – M/2)²+ (v – N/2)²].
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