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Computing the Fourier transform of the Laplacian result in spatial domain is equivalent to multiplying the F(u, v), Fourier transformed function of f(x, y) an input image, and H(u, v), the filter used for implementing Laplacian in frequency domain. This dual relationship is expressed as _________(a) Fourier transform pair notation(b) Laplacian(c) Gradient(d) None of the mentionedThis question was addressed to me during an interview.Asked question is from Laplacian in Frequency Domain topic in chapter Image Enhancement of Digital Image Processing

Answer»

Right answer is (a) Fourier transform pair notation

Best EXPLANATION: The Fourier transform of the Laplacian result in spatial domain is EQUIVALENT to multiplying the F(u, v) and H(u, v). This dual relationship is expressed as Fourier transform pair notation GIVEN by: ∇^2 f(x,y)-[(u – M/2)^2+ (v – N/2)^2]F(u,v), for an IMAGE of size M *N.



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