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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?(a) H(u, v)= -(u^2+ v^2)(b) H(u, v)= -(u^2– v^2)(c) H(u, v)= -[(u – M/2)^2+ (v – N/2)^2].(d) H(u, v)= -[(u – M/2)^2– (v – N/2)^2].This question was posed to me in an interview for internship.My doubt is from Laplacian in Frequency Domain in division Image Enhancement of Digital Image Processing

Answer»

Right CHOICE is (c) H(u, V)= -[(u – M/2)^2+ (v – N/2)^2].

Easiest 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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