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?

Question

TuteeHUB · Accepted Answer

H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)²‚Äö√Ñ√∂‚àö√ë‚àö¬® (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)²].

TuteeHUB · Answer

H(u, v)= -(u2+ v2)

TuteeHUB · Answer

H(u, v)= -(u2‚Äö√Ñ√∂‚àö√ë‚àö¬® v2)

TuteeHUB · Answer

H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)2+ (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)2].

TuteeHUB · Answer

H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)2‚Äö√Ñ√∂‚àö√ë‚àö¬® (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)2].

1.	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<sup>2</sup>+ v<sup>2</sup>)
B.	H(u, v)= -(u<sup>2</sup>‚Äö√Ñ√∂‚àö√ë‚àö¬® v<sup>2</sup>)
C.	H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)<sup>2</sup>+ (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)<sup>2</sup>].
D.	H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)<sup>2</sup>‚Äö√Ñ√∂‚àö√ë‚àö¬® (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)<sup>2</sup>].
Answer» D. H(u, v)= -[(u ‚Äö√Ñ√∂‚àö√ë‚àö¬® M/2)<sup>2</sup>‚Äö√Ñ√∂‚àö√ë‚àö¬® (v ‚Äö√Ñ√∂‚àö√ë‚àö¬® N/2)<sup>2</sup>].

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